U.S. patent application number 14/500901 was filed with the patent office on 2015-01-22 for uses of systems with degrees of freedom poised between fully quantum and fully classical states.
The applicant listed for this patent is Tampere University of Technology, The University of Vermont. Invention is credited to Stuart Kauffman, Samuli Niiranen, Gabor Vattay.
Application Number | 20150024964 14/500901 |
Document ID | / |
Family ID | 45818256 |
Filed Date | 2015-01-22 |
United States Patent
Application |
20150024964 |
Kind Code |
A1 |
Kauffman; Stuart ; et
al. |
January 22, 2015 |
USES OF SYSTEMS WITH DEGREES OF FREEDOM POISED BETWEEN FULLY
QUANTUM AND FULLY CLASSICAL STATES
Abstract
Disclosed herein are systems and uses of systems operating
between fully quantum coherent and fully classical states. Such
systems operate in what is termed the "Poised realm" and exhibit
unique behaviors that can be applied to a number of useful
applications. Non-limiting examples include drug discovery,
computers, and artificial intelligence
Inventors: |
Kauffman; Stuart; (Santa Fe,
NM) ; Niiranen; Samuli; (Tampere, FI) ;
Vattay; Gabor; (Budapest, HU) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
The University of Vermont
Tampere University of Technology |
Burlington
Tampere |
VT |
US
FI |
|
|
Family ID: |
45818256 |
Appl. No.: |
14/500901 |
Filed: |
September 29, 2014 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
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13187257 |
Jul 20, 2011 |
8849580 |
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14500901 |
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61367781 |
Jul 26, 2010 |
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61367779 |
Jul 26, 2010 |
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61416723 |
Nov 23, 2010 |
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61420720 |
Dec 7, 2010 |
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61431420 |
Jan 10, 2011 |
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Current U.S.
Class: |
506/9 |
Current CPC
Class: |
B82Y 10/00 20130101;
G01N 33/54366 20130101; G01N 2500/20 20130101; G01N 2500/04
20130101; G16C 20/60 20190201; G16C 20/50 20190201; G16B 35/00
20190201; G06N 10/00 20190101 |
Class at
Publication: |
506/9 |
International
Class: |
G01N 33/543 20060101
G01N033/543 |
Claims
1. A method of drug discovery, comprising: selecting a biological
target; screening a library of candidate molecules to identify a
first subset of candidate molecules that bind to the biological
target; determining the energy level spacing distribution of a
quantum degree of freedom in each of the candidate molecules in the
first subset; comparing the energy level spacing distribution to at
least one pre-determined reference function; and selecting a second
subset of molecules from the first subset as drug candidates based
on the comparison.
2. The method of claim 1, wherein the biological target is an
enzyme.
3. The method of claim 1, wherein the biological target is a
receptor.
4. The method of claim 3, wherein the receptor is a cell-surface
receptor.
5. The method of claim 1, wherein screening the library of
candidate molecules comprises conducting an in vitro binding
assay.
6. The method of claim 1, wherein screening the library of
candidate molecules comprises molecular modeling.
7. The method of claim 1, wherein determining the energy level
spacing distribution comprises spectroscopically determining the
energy level spacings of each candidate molecule in the first
subset.
8. The method of claim 7, wherein the energy level spacings are
determined using ultraviolet/visible spectroscopy.
9. The method of claim 7, wherein the energy level spacings are
determined using infrared spectroscopy.
10. The method of claim 7, wherein the energy level spacings are
determined using X-ray spectroscopy.
11. The method of claim 7, wherein the energy level spacings are
determined using nuclear magnetic resonance spectroscopy.
12. The method of claim 7, wherein the energy level spacings are
determined using electron paramagnetic resonance spectroscopy.
13. The method of claim 1, wherein determining the energy level
spacing distribution comprises computationally modeling the energy
levels.
14. The method of claim 1, wherein the one or more reference
functions include a function having the form: p(s)=4sexp(-2s) where
s is the energy level spacing and p(s) is the energy level spacing
distribution.
15. The method of claim 1, wherein the one or more reference
functions include a function having the form: p ( s ) = .pi. s 2
exp ( - .pi. s 2 / 4 ) ##EQU00020## where s is the energy level
spacing and p(s) is the energy level spacing distribution.
16. The method of claim 1, wherein the one or more reference
functions include a function having the form: p(s)=exp(-s) where s
is the energy level spacing and p(s) is the energy level spacing
distribution.
17. The method of claim 1, wherein comparing the energy level
spacing distribution to at least one pre-determined reference
function comprises determining the quantity: x = A - A p A w - A p
##EQU00021## wherein A p = .intg. 2 .infin. p p ( s ) , A w =
.intg. 2 .infin. p w ( s ) , and A = .intg. 2 .infin. p ( s ) ,
where : ##EQU00021.2## p p ( s ) = exp ( - s ) and ##EQU00021.3## p
w ( s ) = .pi. s 2 exp ( - .pi. s 2 / 4 ) , ##EQU00021.4## wherein
s is energy level spacing and p(s) is the determined energy level
spacing distribution.
18. The method of claim 17, wherein selecting a second subset of
molecules from the first subset as drug candidates comprises
selecting those molecules having an x value within a predetermined
distance from a predetermined value.
19. The method of claim 1, wherein comparing the energy level
spacing distribution to at least one pre-determined reference
function comprises fitting the determined energy level spacing
distributions to a pre-determined function.
20. The method of claim 19, wherein selecting a second subset of
molecules from the first subset as drug candidates comprises
selecting those molecules whose energy level spacing distribution
fits the pre-determined function.
21. The method of claim 1, further comprising conducting an in
vitro or in vivo assay on each drug candidate to test for
biological activity.
22. A method of drug discovery, comprising: selecting a biological
target; screening a library of candidate molecules to identify a
first subset of candidate molecules that bind to the biological
target; determining the energy level spacing distribution of a
quantum degree of freedom in each of the candidate molecules in the
first subset; conducting an in vitro or in vivo assay for
biological activity on each of the candidate molecules in the first
subset; correlating the energy level spacing distribution with
activity determined from the in vitro or in vivo assay; determining
the energy level spacing distributions of a quantum degree of
freedom in a new set of candidate molecules; comparing the energy
level spacing distributions of the new set of candidate molecules
with energy level spacing distributions that correlate with
biological activity; and select as drug candidates from the new set
of candidate molecules those molecules whose energy level spacing
distributions exhibit a pre-determined level of similarity to the
energy level spacing distributions that correlate with biological
activity.
23. The method of claim 22, wherein comparing the energy level
spacing distributions of the new set of candidate molecules with
energy level spacing distributions that correlate with biological
activity comprises using a computational fitting algorithm.
24. The method of claim 23, where the fitting algorithm comprises
least squares analysis.
25. A method of drug discovery, comprising: selecting a biological
target; screening a library of candidate molecules to identify a
first subset of candidate molecules that bind to the biological
target; measuring decoherence decay of a quantum degree of freedom
in each of the candidate molecules in the first subset; comparing
the decoherence decay to at least one pre-determined reference
function; and selecting a second subset of molecules from the first
subset as drug candidates based on the comparison.
26. The method of claim 25, wherein the reference function has the
form: S(T.sub.H).about.exp(-T.sub.H/T.sub.D)/T.sub.H.sup..alpha.
wherein S(T.sub.H) is a coherence signal as a function of time
T.sub.H and T.sub.D and .alpha. are fitting parameters.
27. The method of claim 26, wherein selecting the second subset of
molecules comprises selecting those molecules having the lowest
T.sub.D value.
28. The method of claim 25, wherein measuring decoherence decay
comprises performing a spin echo experiment.
29. The method of claim 25, wherein measuring decoherence decay
comprises performing a photon echo experiment.
30. A method of drug discovery, comprising: selecting a biological
target; screening a library of candidate molecules to identify a
first subset of candidate molecules that bind to the biological
target; measuring decoherence decay of a quantum degree of freedom
in each of the candidate molecules in the first subset; conducting
an in vitro or in vivo assay for biological activity on each of the
candidate molecules in the first subset; correlating the
decoherence decay with activity determined from the in vitro or in
vivo assay; measuring decoherence decay of a quantum degree of
freedom in a new set of candidate molecules; comparing the
decoherence decay of the new set of candidate molecules with the
decoherence decay that correlate with biological activity; and
select as drug candidates from the new set of candidate molecules
those molecules whose decoherence decay exhibit a pre-determined
level of similarity to the decoherence decay that correlate with
biological activity.
Description
CROSS-REFERENCE TO RELATED APPLICATIONS
[0001] This application is a divisional of U.S. application Ser.
No. 13/187,257, filed Jul. 20, 2011, which claims the benefit of
U.S. Provisional Application Nos. 61/367,781, filed Jul. 26, 2010;
61/367,779, filed Jul. 26, 2010; 61/416,723, filed Nov. 23, 2010;
61/420,720, filed Dec. 7, 2010; and 61/431,420, filed Jan. 10,
2011, all of which are incorporated herein by reference in their
entirety.
BACKGROUND
[0002] 1. Field of the Invention
[0003] The present invention relates to systems and uses of systems
operating between fully quantum coherent and fully classical
states. Non-limiting applications include drug discovery,
computers, and artificial intelligence.
[0004] 2. Background Description
[0005] Many physical systems having quantum degrees of freedom
quickly decohere to classicity for all practical purposes. Thus,
many designed systems consider only classical behaviors. One
example is in the field of drug discovery where traditional
approaches to drug design considers the lock-and-key fitting of a
molecule into an enzyme or receptor. Other designed systems are
carefully setup to maintain full quantum coherence, for example,
the qubits in a quantum computer. However, recent discoveries have
indicated several systems in nature that have relatively slow
decoherence. Birds are able to see magnetic field lines due to a
quantum coherent chemical reaction in their retina. Light
harvesting molecules are able to maintain quantum coherent electron
transport for times much longer than the expected coherence time at
room temperatures. The existence of such cases demonstrates that
quantum coherence can exist at room temperature and at the presence
of water bath and evolution can `design` quantum coherent
structures to play certain biological roles. Thus, there is a need
for new systems that utilize the unique properties that exist
between full quantum coherence and classicity.
SUMMARY OF THE INVENTION
[0006] Disclosed herein are various methods of classifying the
state of a system, such as a molecule interacting with its
environment, in terms of its degree of order, its degree of
coherence, and/or its rate of coherence decay. Some embodiments
include classifying only a single one of these variables whereas
other embodiments include classifying two or all three of the
variables. These methods include classifying the system in the
course of creating systems that exist and/or operate at a specific
point or region of a classification space described the variables
discussed above and all practical outcomes of such creation.
[0007] Disclosed herein is a quantum reservoir computer that
includes a plurality of nodes, each node comprising at least one
quantum degree of freedom that is coupled to at least one quantum
degree of freedom in each other node; at least one input signal
generator configured to produce at least one time-varying input
signal that couples to the quantum degree of freedom; and a
detector configured to receive a plurality of time-varying output
signals that couple to the quantum degree of freedom.
[0008] Also disclosed herein is a method of drug discovery that
includes selecting a biological target; screening a library of
candidate molecules to identify a first subset of candidate
molecules that bind to the biological target; determining the
energy level spacing distribution of a quantum degree of freedom in
each of the candidate molecules in the first subset; comparing the
energy level spacing distribution to at least one pre-determined
reference function; and selecting a second subset of molecules from
the first subset as drug candidates based on the comparison.
[0009] Further disclosed herein is a method of drug discovery that
includes selecting a biological target; screening a library of
candidate molecules to identify a first subset of candidate
molecules that bind to the biological target; determining the
energy level spacing distribution of a quantum degree of freedom in
each of the candidate molecules in the first subset; conducting an
in vitro or in vivo assay for biological activity on each of the
candidate molecules in the first subset; correlating the energy
level spacing distribution with activity determined from the in
vitro or in vivo assay; determining the energy level spacing
distributions of a quantum degree of freedom in a new set of
candidate molecules; comparing the energy level spacing
distributions of the new set of candidate molecules with energy
level spacing distributions that correlate with biological
activity; and select as drug candidates from the new set of
candidate molecules those molecules whose energy level spacing
distributions exhibit a pre-determined level of similarity to the
energy level spacing distributions that correlate with biological
activity.
[0010] Further disclosed herein is a method of drug discovery that
includes selecting a biological target; screening a library of
candidate molecules to identify a first subset of candidate
molecules that bind to the biological target; measuring decoherence
decay of a quantum degree of freedom in each of the candidate
molecules in the first subset; comparing the decoherence decay to
at least one pre-determined reference function; and selecting a
second subset of molecules from the first subset as drug candidates
based on the comparison.
[0011] Further disclosed herein is a method of drug discovery that
includes selecting a biological target; screening a library of
candidate molecules to identify a first subset of candidate
molecules that bind to the biological target; measuring decoherence
decay of a quantum degree of freedom in each of the candidate
molecules in the first subset; conducting an in vitro or in vivo
assay for biological activity on each of the candidate molecules in
the first subset; correlating the decoherence decay with activity
determined from the in vitro or in vivo assay; measuring
decoherence decay of a quantum degree of freedom in a new set of
candidate molecules; comparing the decoherence decay of the new set
of candidate molecules with the decoherence decay that correlate
with biological activity; and select as drug candidates from the
new set of candidate molecules those molecules whose decoherence
decay exhibit a pre-determined level of similarity to the
decoherence decay that correlate with biological activity.
[0012] Further disclosed herein is a Trans-Turing machine that
includes a plurality of nodes, each node comprising at least one
quantum degree of freedom that is coupled to at least one quantum
degree of freedom in another node and at least one classical degree
of freedom that is coupled to at least one classical degree of
freedom in another node, wherein the nodes are configured such that
the quantum degrees of freedom decohere to classicity and thereby
alter the classical degrees of freedom, which then alter the
decoherence rate of remaining quantum degrees of freedom; at least
one input signal generator configured to produce an input signal
that recoheres classical degrees of freedom to quantum degrees of
freedom; and a detector configured to receive quantum or classical
output signals from the nodes.
[0013] Further disclosed herein a method of measuring the state of
a physical system that includes determining the degree of quantum
coherence of at least one degree of freedom in the system;
determining the degree of order of the system; and classifying the
system based on the determined degree of quantum coherence and the
determined degree of order.
[0014] In one embodiment, determining the degree of order comprises
measuring decoherence decay of a quantum degree of freedom in the
system. In one embodiment, determining the degree of order
comprises determining the energy level spacing distribution of a
quantum degree of freedom in the system. In one embodiment, the
system is a molecule.
BRIEF DESCRIPTION OF THE DRAWINGS
[0015] FIG. 1 is graph depicting the boundaries of the Poised
Realm.
[0016] FIG. 2 is a graph depicting an Erdos-Renyi Random Graph with
Giant Component.
[0017] FIG. 3 is a graph depicting the energy level spacing for
Erdos-Renyi random graphs.
[0018] FIG. 4 is a flowchart illustrating a drug discovery
method.
[0019] FIG. 5 is a flowchart illustrating another drug discovery
method.
[0020] FIG. 6 is a graph depicting the Giant Component of a 100
node Erdos-Renyi Critical Random Graph.
[0021] FIG. 7 is a graph depicting the Giant Component of a 50 node
Erdos-Renyi Critical Random Graph.
[0022] FIG. 8 is a block diagram of a computer utilizing quantum
nodes and time-varying inputs and outputs.
[0023] FIG. 9 is flowchart illustrating a training method for the
computer described in FIG. 8.
[0024] FIG. 10 is diagram of a liposome containing
chromophores.
DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT
[0025] Described herein are several new systems and uses of systems
operating in what is termed herein as the "Poised Realm." By
"Poised Realm," it is meant a physical system that does not exhibit
fully quantum behavior nor exhibits fully classical behavior. In
this sense, the system is "poised", or even can "hover" between the
quantum and classical worlds. By Poised Realm, we mean any physical
means or procedure to achieve such a system poised between quantum
and classical behavior, including as bounding limits, fully quantum
coherent behavior and fully classical behavior.
[0026] In one characterization of the Poised Realm, we use two
independent features of, without loss of generality, open quantum
systems. The degree of decoherence and/or recoherence is one
feature. In addition to their quantum, decohering, recohering, or
classical behavior, physical systems may also be classified
according to the degree of order or chaotic behavior that they
exhibit along an order-criticality-chaos spectrum. Systems within
the Poised Realm may be characterized by any degree of order along
this spectrum. In some embodiments, the physical systems described
herein do not exhibit full order or chaos and are thus also
"poised" between order and chaos. Below we describe new theorems
which establish that WITHIN the poised realm itself, i.e. not
classical, critical poised realm systems in the presence of
decoherence lose coherence most slowly, that is in a power law
fashion, while ordered or chaotic Poised Realm systems lose
coherence exponentially, hence decohere much faster in the absence
of recoherence.
[0027] As used herein, "recoherence" refers to a system entering
again into a superposition state after it once lost its coherence.
The term "recoherence" commonly refers to the re-emergence of some
initial quantum state during coherent quantum evolution, which is
different from the meaning used herein.
[0028] Thus in at least one characterization of the Poised Realm,
the Poised Realm may be illustrated by a two-dimensional coordinate
system having as its y-axis (the vertical) the degree of quantum
behavior, stretching from fully quantum behavior at the "origin" to
fully classical behavior "up" the y axis, typically by decoherence
and movement down the Y axis toward quantum behavior via
recoherence, and on the x-axis (the horizontal) the degree of
order, stretching from full order to full chaos (see FIG. 1). The
area on the graph between fully quantum and fully classical
behavior is at least one definition of the "Poised Realm." The y
axis in FIG. 1 can be infinite in that classical behavior in some
circumstances, in particular via increasing quantum decoherence,
can be approached as closely as wished, i.e., achieved "For All
Practical Purposes" (FAPP).
[0029] Thus, as used herein, a "fully classical" system or a system
that is "classical for all practical purposes" is a probabilistic
mixture of single amplitudes. A "fully quantum" system is one in
which all or at least one of quantum degrees of freedom comprise a
superposition of possibility waves. Other possibilities or
amplitudes may have lost superposition and be comprised by one
"pure state" amplitude or a set of pure state amplitudes called a
"mixed state". These terms may be understood by the classical
double slit experiment, where photons in coherent fully quantum
states exhibit an interference pattern. If a detector is used at
one or more of the slits, interaction with the detector causes the
photons' wave functions to collapse such that they are no longer
quantum coherent (i.e., they exhibit classical behavior), resulting
in loss of the interference pattern.
[0030] Degree of Order
[0031] The system in general can be described by its Hamiltonian H.
Classical trajectories of the system can be calculated from the
Hamiltonian via solving its Hamiltonian equations. Quantization of
the Hamiltonian results in the Hamiltonian operator H, which fully
describes the system's quantum dynamics via the Schrodinger
equation. The Hamiltonian may depend on several parameters of the
system. By changing the parameters of the system we can change the
form of its Hamiltonian. Later we refer to this as "changing the
Hamiltonian".
[0032] By changing the Hamiltonian we can change the degree of
chaos in the system. Degree of chaos of trajectories can be
characterized by their Lyapunov exponents. One can assign a
Lyapunov exponent to each point in the phase space by calculating
the Lyapunov exponent of the trajectory initiated in the point. In
the phase space one can find connected areas where the Lyapunov
exponent is positive and characterized by the same value within the
patch. These chaotic patches are separated by regular areas, where
the Lyapunov exponent is zero. The degree of chaos in the system
can be characterized by the relative proportion of the volume of
the chaotic areas in the phase space. If no chaos is present, the
proportion is zero. If the system is chaotic for almost all initial
conditions the proportion is 1. The position of the system on the
x-axis (the horizontal) is this ratio. Usually changing a parameter
of the Hamiltonian such a way that its Hamiltonian equations become
more nonlinear increases the degree of chaos and moves the system
to the right on the x-axis.
[0033] In the process of moving the system to the right on the
x-axis new chaotic areas emerge, the size of the existing areas
increase and separation of some of the existing chaotic areas
disappear. There is a critical point on the x-axis, x.sub.c, below
which the chaotic areas form separated patches in the phase space.
Above the critical point the chaotic areas coalesce and form a
giant connected component. Below the critical point chaotic
trajectories are confined within their chaotic area in the phase
space. Above the critical point chaotic trajectories can diffuse
globally in the phase space.
[0034] In the critical point the Lyapunov exponent for the globally
connected chaotic area is zero and it goes through a second order
phase transition in the neighborhood of the critical point. It is
zero .lamda..sub.0 (x.sub.c)=0 below the critical point
x<x.sub.c and shows power law scaling .lamda..sub.0
(x).about.(x-x.sub.c).sup..beta. above x>x.sub.c with some
positive exponent .beta..
[0035] Some quantum systems, such as spin systems are defined only
with their Hamilton operator and their classical Hamiltonian cannot
be defined. In such systems the x-axis and its critical point can
be defined purely quantum mechanically. In the pure ordered regime
the phase space motion happens on a torus. Quantum mechanically it
is a separable system and its eigenenergies correspond to the
quantization of its tori. The energy eigenvalues of the system
follow Poissonian distribution. The nearest neighbor level spacing
distribution is exponential:
p.sub.p(s)=exp(-s)
where s.sub.n=(E.sub.n+1-E.sub.n)/.DELTA.(E.sub.n) is the level
spacing measured in the units of local mean level spacing
.DELTA.(E) at energy E. In the purely chaotic system the energy
level statistics of the system can be described by Random Matrix
Theory (RMT) and the level spacing follows approximately the Wigner
surmise:
p w ( s ) = .pi. s 2 exp ( - .pi. s 2 / 4 ) ##EQU00001##
These limiting cases correspond to the values 0 and 1 on the x-axis
respectively. In an intermediate situation, where the system is
neither fully ordered or fully chaotic, the quantity
x = A - A p A w - A p ##EQU00002##
can serve as the x-coordinate where
A p = .intg. 2 .infin. p p ( s ) , A w = .intg. 2 .infin. p w ( s )
, ##EQU00003##
and the quantity A is calculated from the actual level spacing of
the system
A = .intg. 2 .infin. p ( s ) . ##EQU00004##
[0036] In the above mentioned quantum systems the criticality can
be defined in a purely quantum mechanical way. In the ordered
region the eigenfunctions of the Hamilton operator are localized in
configuration space. In the chaotic region the eigenfunctions are
delocalized and extended over the configuration space of the entire
system. The critical value x.sub.c separates these two behaviors.
The level spacing statistics in the critical point can be well
approximated by the semi-Poissonian distribution
p(s)=4sexp(-2s).
[0037] Systems in nature don't exist in full separation. They are
coupled to their environment. Coupling a low dimensional quantum
system to an infinite degree environment exert random forces on the
system. The system loses its quantum coherence as a result. The
environment-system coupling can be described by the Hamilton
operator H=H.sub.s+H.sub.e-s+H.sub.e, where the Hamiltonian
operators correspond to the system H.sub.s, to the
environment-system coupling H.sub.e-s and to the environment
H.sub.e. The strength of the external forces causing decoherence is
measured by the variance of system-environment coupling averaged
over the states of the environment .GAMMA..sup.2=H.sub.e-s.sup.2.
The position of the system on the y-axis (the vertical) is the
ratio of .GAMMA. and the average level spacing .DELTA.(E) of the
system H.sub.s.
[0038] Some embodiments include modulating or controlling the
degree of order of a physical system (i.e., moving along the x-axis
of FIG. 1). Some such embodiments include engineering a system to
have a desired degree of order. In various embodiments, the
following describes, without limitation, three methods for
controlling the degree of order in a system.
[0039] 1) Position on the x-Axis Due to the Hamiltonian of a
System.
[0040] In general, altering the Hamiltonian of the system by any
means may alter its position on the x axis. More specifically, due
to the dynamics of the Poised Realm system ITSELF, the classical
Hamiltonian of the system can change, changing its position on the
x-axis statically or, as we will see, dynamically, as one
non-limiting example, from order to criticality to chaos and
back.
[0041] Classical dynamical systems are often describable as flows
on a Hamiltonian. Such flows can, for example, and without
limitation, describe most classical physical dynamical systems. A
periodic pendulum is a simple example of a system in the ordered
classical regime describable by a Hamiltonian. Analogous quantum
oscillators are also in the ordered regime. Other Hamiltonians can
be critical or chaotic classically.
[0042] The dynamical behaviors of such classical systems can be
ordered on the x-axis from ordered to critical to chaotic, by means
of diverse measures of their dynamical behavior. Several such
methods are known in the art. Without limitation, a preferred
method to array classical Hamiltonian dynamical systems on the
x-axis is by measuring their average Lyapunov exponent, as is known
in the art, averaged over the time behavior for short times and
from multiple initial states of the system in question. The
Lyapunov exponent measures whether nearby trajectories diverge,
(chaos), converge, (order), or flow parallel to one another,
(criticality), in state space. Account can be taken of the
attractor basin sizes, should the classical system have both at
least one attractor and may have more than one attractor, each
"draining a basin of attraction." Then, typically one measures the
Lyapunov exponent on each attractor and weights these by the basin
sizes of that attractor, averaged over all attractors, to get a
global measure of position on the x-axis. Alternatively, the
Hamiltonian system may have no attractor, as in classical
statistical mechanics and exhibit ergodic behavior, and satisfy the
Louiville equation, as is known in the art.
[0043] Thus, classical systems can be moved on the x-axis by
"tuning" their Hamiltonians. As we will see, in the Poised Realm
quantum degrees of freedom can become classical or classical for
all practical purposes, FAPP, and thereby alter the classical
Hamiltonian of the system, so the very dynamics of Poised Realm
systems can move the classical degrees of freedom from order to
criticality to chaos and back.
[0044] 2) Suppression of Decoherence.
[0045] Systems in the poised realm can be characterized by their
position on the x and y axes in terms of chaos-order and the
strength of the coupling to the environment. Depending on their
position they are exposed to the decoherence caused by the
environment. Quantum systems can be described by their density
matrices (.rho..sub.nm) as it is known to the art. Theoretically,
the decay of coherence can be characterized by the speed the off
diagonal elements (n.noteq.m) of the density matrix die out
.rho..sub.nm.about.e.sup.-t/.tau..sup.c; where .tau..sub.c is the
coherence time. An overall measure of the speed of the loss of the
coherence is the entropy production in the system. In practice the
production of the standard Shannon (S.sub.1=-Tr[.rho. log .rho.])
entropy and the more easily computable Renyi entropy (S.sub.2=log
Tr[.rho..sup.2]) are used.
[0046] The exponential time dependence of the off-diagonal elements
of the density matrix and the entropy production rate are closely
related:
S 1 or 2 t .about. 1 .tau. c ##EQU00005##
Entropy production due to decoherence is related to the dynamical
properties of the system. It has been shown via semiclassical
arguments and direct simulations that after an initial transient
the entropy production rate is related to the Kolmogorov-Sinai
entropy (h.sub.KS) of the dynamical system:
S 1 t .about. h KS = .SIGMA. i .lamda. i + ##EQU00006##
which is in turn the sum of the positive Lyapunov exponents
.lamda..sub.i.sup.+ characterizing the exponential divergence of
chaotic trajectories. Entropy production becomes slow when the
largest Lyapunov exponent and the Kolmogorov-Sinai entropy of a
system vanishes (h.sub.KS.apprxeq..lamda..sub.o.fwdarw.0). In this
case the coherence time becomes formally infinite
T.sub.c.fwdarw..infin. indicating a slower than exponential decay
of coherence in the system, where the off diagonal elements of the
density matrix stay finite or die out only in an algebraic way
.rho. nm ( t ) .about. 1 t .alpha. ##EQU00007##
where .alpha. is the exponent of the power law decay.
[0047] The zero entropy production state emerges in mechanical
systems at the border of the onset of global chaos x.sub.c of the
classical counterpart of the system. In quantum systems without
classical counterpart the transition happens also at x.sub.c, where
x.sub.c is now defined in terms of the critical level spacing
p(s)=4sexp(-2s).
[0048] Suppose, we have a parameter .epsilon. of a mechanical
system which characterizes its transition from integrability to
chaos:
H=H.sub.0+.epsilon.H.sub.1.
Here H.sub.0 is the Hamiltonian of an integrable system.
Classically and quantum mechanically it is a solvable system.
Classically it can be described by action-angle variables and it
does only simple oscillations in the angle variables. The phase
space motion happens on a torus. Quantum mechanically it is a
separable system and its eigenenergies correspond to the
quantization of its tori. The energy eigenvalues of the system are
random and follow a Poissonian distribution. The nearest neighbor
level spacing distribution is exponential
p(s)=exp(-s);
where s.sub.n=(E.sub.n+1-E.sub.n)/.DELTA.(E.sub.n) is the level
spacing measured in the units of local mean level spacing
.DELTA.(E) at energy E. The Hamiltonian H.sub.1 is a perturbation.
When .epsilon..noteq.0 the system is no longer integrable
classically and no longer separable quantum mechanically. At a
given small .epsilon., the Kolmogorov-Arnold-Moser (KAM) theory
describes the system. The perturbation breaks up some of the tori
in the phase space and chaotic diffusion emerges localized between
unbroken, so called KAM tori. Chaotic regions are localized in
small patches in the phase space surrounded by regular parts
represented by the KAM tori. At a given critical .epsilon. KAM tori
separating the system gets broken and the chaotic patches merge
into a single large chaotic sea. Above the transition
.epsilon.>.epsilon..sub.c, the system is fully chaotic
characterized by a positive largest Lyapunov exponent
.lamda..sub.o>0. The energy level statistics of the system can
be described by Random Matrix Theory (RMT) and the level spacing
follows the Wigner surmise:
p ( s ) = .pi. s 2 exp ( - .pi. s 2 / 4 ) . ##EQU00008##
[0049] For our purposes the most important region is
.epsilon.=.epsilon..sub.c. In the transition point the Lyapunov
exponent is zero and it goes through a second order phase
transition in the neighborhood of the critical point. It is zero
.lamda..sub.o(.epsilon.)=0 below the critical points
.epsilon.<.epsilon..sub.c and shows power law scaling
.lamda..sub.o(.epsilon.).about.(.epsilon.-.epsilon..sub.c).sup..beta.
above .epsilon.>.epsilon..sub.c with some positive exponent. At
the transition point the level statistics is a special universal
statistics called semi-Poissonian:
p(s)=4sexp(-2s).
[0050] In this transition point where entropy production is zero,
the system is the most robust against decoherence and a system can
stay coherent for an anomalously long time in this point. Below the
transition point the system is localized and no global transport is
possible. Although entropy production is low in this region the
system is not suitable for complex transport and also decoherence
is strong as each separate localized patch in the phase-space
supports a localized wave function quantum mechanically. Each patch
is affected by decoherence in a direct way and coherence is lost
exponentially rapidly. Far above the transition point strong chaos
induces mixing and entropy production which causes rapid
decoherence. Near the transition point from above, however
metastable states are formed and the wave functions show critical
fractal structure. The complex geometry and spatial structure of
these transitional states is able to avoid the effects of
decoherence most effectively.
[0051] The transition described above is much more general than
just the integrable-chaotic transition. An example is the
metal-insulator transition point. Such localization-global
transport (conductance) transition is present when we add static
random potential to a clean and perfectly conducting lattice. At a
critical level of the added random potential the system stops
conducting and the system becomes insulating due to Anderson
localization of its wave-function. In this system the control
parameter .epsilon. is the variance of the random potential. The
energy level statistics of the metallic system is described by RMT
and the localized states produce Poissonian statistics. In the
transition point semi-Poissonian statistics emerges. The same
transition can occur also in the conducting properties of random
networks (graphs). There the localization-global conductance
transition occurs at the percolation threshold, where the giant
component of the network emerges. Finally, the same transition can
be seen in finite quantum graphs by changing its geometry in
specific ways.
[0052] In all these systems the metal-insulator critical point is
characterized by a fractal structure of the wave function similar
to those in the chaos-integrability transition. Moreover, the
equivalence of the metal-insulator and chaos-integrability
transitions has also been proven analytically. Therefore it seems
reasonable to claim that the suppression of the decoherence is also
a universal feature of the critical point of the metal-insulator
transition. We can suppress decoherence and keep our system
coherent for an anomalously long time if we deliberately keep it in
the transition point. We call this state the Poised Realm
Critical.
[0053] Experimentally, the Poised Realm Critical state can be
identified by measuring the decay of coherence in the system. In a
non-critical system the coherence decay is exponential in time. The
Poised Realm state is signaled by a slow, typically power law decay
of coherence. State of the art coherence decay measurements are
based on various echo measurements depending on the system studied.
This includes spin echo, neutron spin echo, and photon echo.
[0054] 3) Position on the x-Axis is Tunable by the Detailed and/or
Statistical Structure of Quantum Networks and Graphs.
[0055] As known in the art, quantum graphs and quantum networks may
be used to model real systems such nano-structures. During
dynamical behavior of a Poised Realm system, the structure of a
quantum network corresponding to a real system can change, altering
position on the x-axis.
[0056] It is convenient to start with the famous Erdos Renyi (ER)
Random Graphs as the simplest possible examples of quantum
networks. An ER graph is "grown" by starting with a set of N
disconnected nodes. Random pairs of nodes are chosen, and joined by
a "line" or "link". This process is iterated, so that at any point,
some ratio of links/nodes exists. ER graphs are extraordinary and
have driven much research. Most importantly, they exhibit a first
order phase transition from essentially disconnected tree
"subgraphs" to a single "Giant Component." Define a "cluster" as a
set of interconnected nodes. When the ratio of links/nodes is less
than 0.5, the graph consists of isolated pieces. As 0.5 is
approached, initially small tree-like structures become larger and
larger. At link/node ratio 0.5, when the number of ends of links
equals the number of nodes, the phase transition to a Giant
Component occurs. Intuitively once there are a few very large
tree-like graphs for an arc/node ratio a bit below 0.5, a few
randomly connected nodes will tie all or most of the large
tree-like nodes into the Giant Component (see FIG. 2).
[0057] Amazing things happen at this phase transition. Not only
does the giant component come to exist, but for the first time
loops of all lengths emerge in the giant component.
[0058] At the critical ratio of links/nodes, 0.5, the ER graph is
said to be "critical". But many nodes are still not connected.
[0059] As the ratio of links/nodes increases past 0.5 two major
things happen. Isolated nodes and small trees are tied into an
enlarging Giant Component. Second, the Giant Component becomes
increasingly richly cross connected, so average <k>
rises.
[0060] Such graphs can be considered static quantum networks. Their
structure is given by an Adjacency N.times.N matrix, with a 1 in
matrix element i,j if there is a connection between nodes i and j.
By symmetry, the j,i matrix element is also 1. Otherwise, for all
pairs that are not joined by a line, the matrix element in the
Adjacency matrix is 0.
[0061] The eigen values of the Adjacency matrix give the energy
levels of the quantum network. From this one can compute the
"energy jumps" between all pairs of energy levels, and from this
the distribution of energy jumps, or quanta sizes, in the ER
subcritical, critical, or supracritical="chaotic" quantum
networks
[0062] FIG. 3 shows the spectrum of critical, and 2 successively
more supracritical networks, mean ratio lines/nodes=<k>=0.5,
1.0 and 1.5. All have giant components which, since they contain
most of the nodes, dominate the eigen value spectrum.
[0063] These results show that in ER critical and supracritical
graphs, position on the x-axis, critical or chaotic, can be
attained by modification of the quantum network structure.
[0064] The quantum networks above are structures, realizable, for
example, by networks of carbon nanotubes capable of quantum
behavior. Molecular systems can also be regarded as quantum
networks. Below we discuss two generic models of quantum degrees of
freedom: quantum rotors and quantum oscillators. It will be clear
to those of ordinary skill in the art that arbitrary graphs can be
endowed with quantum oscillators and/or rotors at, without
limitation, some or all nodes, and their quantum and
order-critical-chaos behaviors studied. Without limitation, quantum
oscillators can be coupled in arbitrary topologies to one another
by interactions (for example spring-like harmonic interactions). To
date, most work has focused, as we will describe, on single
"kicked" quantum rotors, or two coupled quantum oscillators coupled
by a spring and/or coupled to a quantum oscillator "heat bath," as
is known in the art. These models are fully extendable to arbitrary
networks, as above, as the quantum system in an arbitrary quantum
environment. As discussed below, these models, in particular,
networks, are suited to model chemical molecules, will be applied
to the evaluation of candidate drugs and the behaviors of nanotube
structures.
[0065] As noted above, one method of controlling position on the
x-axis is to change the network structure. For example in our
application of these ideas to drug design and nano-technology
design, a given network can model a molecule. By adducting to it
another molecule, say by hydrogen bonds or other non-covalent
interactions, the graph structure of the new network can be made
less than critical, critical, or more supracritical.
[0066] We note that networks of more arbitrary structures can be
made with carbon nanotubes or other materials, than can be made
with atoms such as carbon, hydrogen, nitrogen, oxygen, phosphorus,
and sulfur, due to the bonding properties of these specific
atoms.
Controlling the Topology of the Quantum Networks Via Proximity of
the Nodes
[0067] Consider as a non-limiting example a set of chromophores,
parts of molecules or independent molecules. Electron exchange is
one means of linking the chromophores, as a non-limiting
example.
[0068] The details of this interaction depend upon the detailed
positions of the chromophores. However, in general, if they are
sufficiently close, so each chromophore can communicate with many
neighbors, many closed quantum loops will exist and the quantum
network will be supracritical, hence "chaotic". If further apart,
the quantum network will be less connected, and critical or
subcritical, moving thereby on the x-axis. As we see below,
chromophores bound to the membrane of a liposome can be made more
or less chaotic on the x-axis by subjecting the liposome to
hypertonic or hypotonic media that shrink or swell the
liposome.
[0069] As used herein, a generalized "chromophore" refers to any
quantum network of interacting elements.
[0070] In general, these quantum networks may be on rigid
structures such as nanotech devices (e.g., carbon nanotube
structures). Or they might be inside or outside or both of a
liposome, made as is known in the art, as a bilipid double membrane
hollow vesicle, with the chromophores anchored to the bilipid
double membrane via covalent bonding to beta barrel proteins
spanning such bilipid layers. The density per liposome of
generalized or specific chromophores in the general sense used here
can be tuned through a wide range. As described later in the
section on embodied algorithmic or NON-ALGORITHMIC trans-Turing
Machine quantum-Poised Realm-classical information processing
systems, which might be nanostructures or liposomes or other
vehicles, liposomes can be constructed from lipids in water
containing the beta barrel proteins with attached chromophores. One
expects a random distribution of chromophores inside and outside
the liposome membrane, allowing such a structure to receive quantum
information via the external chromophores and internal chromophores
where light, or other quantum degrees of freedom without
limitation, reaches to and across the membrane. The set of all the
chromophores form a quantum graph that, together with the liposome
and aqueous interior with chosen concentrations of ions and other
small and larger molecules, will behave in open quantum, Poised
Realm, and classical ways, as described below, for example without
limitation via repeated decoherence and recoherence of quantum
degrees of freedom to classicity, which degrees of freedom when
classical, or classical (for all practical purposes, FAPP), will
alter both the classical Hamiltonian of the system, and thereby
also alter the Hamiltonian of the quantum degrees of freedom.
Similarly the recoherence of a classical degree of freedom, as
discussed below, will alter both the classical and quantum
Hamiltonians of the system, hence the total behavior of the coupled
classical and quantum system over time. These facts are useful in
Trans-Turing systems, below.
[0071] We also note here that quantum measurement can occur in the
Poised Realm, in the presence of decoherence and recoherence.
Measurement may be achieved, without limitation, by any means. As a
central non-limiting example, the classical degrees of freedom of a
system above, as in our Trans-Turing systems below, themselves
constitute part or all of the quantum measuring system which can
measure, in some basis, one or more of the quantum degrees of
freedom of the system.
[0072] 4) Position on the x Axis May be Controlled by Pulsed
Stimulation.
[0073] A third method to control position on the x-axis (i.e.,
degree of order), is by pulsed stimulation. This method may be
modeled by a kicked quantum rotor. Basically a quantum rotor is a
quantization of a classical rotor on a frictionless stand that is
spinning with some frequency. If the classical rotor is tapped with
"Dirac delta" inputs of momentum gently, it remains in the ordered
regime, hence left on the x-axis. As it is kicked harder and
harder, it moves out on the x-axis, becomes critical, then chaotic.
The same holds for quantum rotors as we describe below in detail.
In the quantum case, the quantum rotor degree of freedom is kicked
with Dirac delta laser light momentum kicks where the intensity,
"K," of the kick can be increased, driving the rotor from order to
chaos. This characteristic is expected to extend to systems having
arbitrary Hamiltonians. Thus, one embodiment includes modifying the
state of order or chaos of a system by stimulating the system
pulsed light.
[0074] It is expected that quantum rotors or other Hamiltonians
kicked to ordered, critical or chaotic states will exhibit
different quantum energy level distributions. Thus, measurement of
such distributions (e.g., through spectral analysis) demonstrates
the degree of order of such a system. Thus we can readily test for
position on the x-axis.
[0075] For real quantum systems, an issue is at what light
frequency to kick the quantum system. In one embodiment, the center
of one or many of the absorption/emission band(s) of that quantum
degree of freedom or a set of quantum degrees of freedom is used
for the stimulation.
[0076] Degree of Quantum Behavior
[0077] For actual physical systems, which can be modeled with
quantum network structures, the molecular topology of the system
can tune the decoherence rates, and thus movement on the y-axis, in
the processes engendered by the system. The electronic energy
transfer in chlorophyll is the best example of such a system with
both theoretical and experimental results showing long-lived
quantum coherence in an intrinsically noisy cellular environment.
Hence the structure of chlorophyll may play a major role in
resistance to decoherence.
[0078] Movement from Quantum to Classical Via Decoherence.
[0079] Decoherence is a well established phenomenon and the current
favored explanation of the transition from the quantum to the
classical worlds. In quantum mechanics, the signature interference
pattern due to constructive and destructive interference can only
occur if all the phase information is present in the quantum
system. But in an open quantum system, phase information can be
lost from the quantum system to the environment in an irretrievable
way. As this happens, the capacity for interference patterns in the
quantum system decays.
[0080] There are at least two `as if` models of decoherence. The
best established is the "Lindblad operator", which allows the off
diagonal elements of the density matrix of the system containing
the phase information to decay.
[0081] A second model of decoherence makes use of a random walk
process called either a Weiner process, .sigma.Wdt. In a Weiner
random walk process, the Weiner noise term is a random Gaussian
variable with mean 0 and a variance, .sigma.. The larger .sigma.
is, the larger is the average random phase step on the orbit in the
complex plane of the quantum degree of freedom, such as the quantum
rotor.
[0082] We have focused in our simulations of the kicked quantum
rotor on the Weiner process, but have also used the Lindblad
operator. In the Weiner process, a variance of 0, .sigma.=0, is "no
coherence," hence quantum on the y-axis. As .sigma. increases, the
noise increases, and the rate of decoherence increases.
[0083] In the Quantum Zeno effect, demonstrated experimentally, a
quantum degree of freedom is measured very frequently. Each time it
is measured, by von Neumann, it falls to a single amplitude, or
eigen state. It then slowly, quadratically in time, leaves that
quantum eigen state and "flowers" to populate nearby and then more
distant amplitudes of that quantum degree of freedom. However, if
it is frequently measured, it is almost certainly "trapped" in its
initial quantum eigen state, and the time evolution of the
Schrodinger equation is stopped. As it flowers to nearby amplitudes
it becomes a superposition state again, moving up the y-axis. So
frequent measurements, tunable, can keep a quantum system near
classical or somewhat quantum because only a small number of
amplitudes have "flowered," hence control position on the
y-axis.
[0084] Passing from Classical or Classical FAPP to More Coherent or
Fully Coherent, i.e., Down the y Axis.
[0085] One embodiment includes driving a system to be more coherent
including driving a classical system back to quantum. One
embodiment includes driving a classical system into the Poised
Realm.
[0086] We consider a time independent (autonomous) quantum system
described by the Hamiltonian H under the action of a time dependent
external potential U(x; t). We can separate the coherent and
temporally random parts U(x; t)=V.sub.r(x; t)+V.sub.c(x; t). The
random part causes decoherence while the coherent part causes
re-coherence in the system. Assuming that the random part is
uncorrelated in time and using Ito's rule we can get the time
evolution of the averaged density matrix
.differential. t .zeta. ( x , x ' , t ) = - i [ H ^ + V ^ c ,
.zeta. ( x , x ' , t ) ] - 1 2 .GAMMA. ( x , x ' ) .zeta. ( x , x '
, t ) , ( 1 ) ##EQU00009##
where .tau.(x,x')=C (x; x)+C(x', x')-2C(x, x') and
<V.sub.r(x,t)V.sub.r(x,t')>=C(x,x').delta.(t-t') is the
temporal autocorrelation of the random potential at different
spatial sites x and x'. In most relevant situations a simple
discrete Hamiltonian can describe the system with matrix elements
H.sub.nm and the simplest delta correlated noise can be assumed
C.sub.nm=C.delta..sub.nm and
.GAMMA..sub.nm=.GAMMA.(1-.delta..sub.nm). The coherent external
potential, which can come from laser pulses or any other coherent
electromagnetic source, can be reasonably modeled with a sequence
of sharp kicks {circumflex over (V)}.sub.c(x; t)=.SIGMA..sub.nV
(x)T.delta.(t-nT) at times nT.
[0087] In absence of the coherent part the evolution of the density
matrix is described by
.differential. t .rho. nm = - 1 h .SIGMA. k ( H ^ nk .rho. kn -
.rho. nk H km ) - .GAMMA. h 2 ( 1 - .delta. nm ) .rho. nm .
##EQU00010##
[0088] Decoherence kills quantum superposition states represented
by the off-diagonal elements of the density matrix. The density
matrix settles to the diagonal form
.rho..sub.nm=.delta..sub.nmP.sub.n, where P.sub.n is the classical
probability of finding the system in state n. The characteristic
decay time is h.sup.2/.GAMMA..about.10-100 femtoseconds. The
coherent part is able to re-create superposition states. The
density matrix before and after the coherent kick is
.rho. nm + = .SIGMA. n ' m ' U nn ' U m ' m , * .rho. n ' m ' -
##EQU00011##
where the unitary matrix U=exp(i{circumflex over (V)}.sub.cT/h)
describes the action of the kick on the wave function.
[0089] Even if the density matrix is diagonal before the kick
Q.sub.nm.sup.-=.delta..sub.nmP.sub.n it becomes non-diagonal after
the kick
.rho. nm + = .SIGMA. k U nk U km * P k , ##EQU00012##
indicating the presence of superposition states. Kicking the system
repeatedly can repair the coherence lost during time evolution and
keep the system levitating at the border of the `realms` of quantum
and classic. The interplay of the coherent kicks and decoherence
determines the speed of the loss of coherence in the system.
[0090] Evidence of that systems can be driven to more quantum
behavior include the following:
[0091] 1) In the Zeno Effect, the system is trapped in one eigen
state, hence classical during the interval before remeasurement. If
not remeasured, the system again flowers multiple quantum
amplitudes quadratically in time. One means by which such
reemergence of quantum amplitudes happens is in a system which is a
quantization of a classical chaotic dynamical system. One of the
quantum amplitudes of the localized quantum behaviors of the
quantum system is measured, causing the system to collapse to a
single possibility via the Born Rule and is briefly Quantum Zeno
Effect "trapped" in the eigen-state. This amplitude emerges
quadratically in time to repopulate other quantum amplitudes with
finite moduli.
[0092] 2) A second means known in the art to regain quantum
coherent behavior concerns quantum entangled degrees of freedom in
a quantum squeezed state. For specific systems, quantum
entanglement can undergo "Sudden Death", can undergo No Death, and
can undergo Sudden Death and Revival. Such Revival is a revival of
coherent entangled quantum behavior from far in the classical
region (FAPP or entirely classical). We incorporate by reference,
"Entanglement dynamics during decoherence", J. P. Paz, A. J.
Roncaglia, Quantum Inf Process (2009) 8 535-548 in it's entirety.
We also incorporate by reference in their entirety "Entanglement
and intra-molecular cooling in biological system?--A quantum
thermodynamic perspective." H. J. Briegel and S. Popescu Phys
arXhiv 0806,4552V2 [QUANT-PH] 5 Oct. 2009 and "Dynamic entanglement
is oscillating molecules", J. Cai, S. Popescu and H. J. Briegel
arXhiv:0809.4906v1 [quant ph] 29 Sep. 2008. The last two articles
computationally demonstrate and suggest recurrent passage from
coherent entanglement to classical behavior and back. The last
paper posits conformational changes of a biomolecule induced by
interaction of some other chemical at an allosteric site.
[0093] 3) A third means known in the art to regain coherence is
given by the Shor Theorem, which states that in a quantum computer
with entangled quantum degrees of freedom, the quantum system can
be quantum measured using quantum degrees of freedom not part of
the qubit calculation. Information can be injected from outside the
quantum computer that restores quantum coherent behavior to the
decohering quantum degrees of freedom, i.e., qubits.
[0094] 4) A fourth means that induces increased coherence in a
quantum or partially quantum, partially decoherent, and perhaps
partially fully decoherent system almost certainly occurs in
chlorophyll wrapped by its evolved "antenna protein." At 77 degrees
K, the expected time scale for decoherence is on the order of a
femtosecond. The chlorophyll molecule, having been excited by
absorption of a photon by an electron, remains in the quantum
coherent (or largely coherent) state for at least 700
femtoseconds.
[0095] It is believed that this astonishingly long lived coherent
state is due to the antenna protein. This can be experimentally
verified by use of mutant antenna proteins, and this has been done
with the antenna protein and its mutants for a bacterial rhodopsin
molecule, where loss of coherence occurs with mutant antenna
proteins. Long lived quantum coherence may also be partially due to
the quantum graph structure of chlorophyll.
[0096] It may be that the antenna protein entirely blocks any
decoherence to the full environment of the chlorophyll molecule. It
is more likely that the antenna protein, filled with chromophores,
acts on the chlorophyll molecule by driving it with photons in a
physically realized version of some type of Shor theorem, to inject
information into the chlorophyll and sustain or restore coherence
to the chlorophyll molecule. But restoring coherence means that in
physical reality, the antenna protein can increase coherence in
quantum degrees of freedom of the chlorophyll molecule. The
topology of the chlorophyll molecule may play a role either in its
resistance to decoherence, or ease of recoherence via input from
the antenna protein.
[0097] Chlorophyll and its antenna protein is a probable example of
a fourth general means to drive a system from classical due to
decoherence and phase randomization as above, by kicking the
quantum degree of freedom at exactly the natural frequency of any
one or a plurality or all of its quantum amplitudes. Think of a
classical rotor whose phase is being randomized by modest sized
hammer kicks at frequencies that are irrational with respect to its
natural frequency. Now hit it with a hammer of tunable size at its
natural rotation frequency. You will tend to or will overcome the
modest sized hammer irrational "noise" taps and resynchronize the
classical rotor. In the same way, consider a quantum degree of
freedom with a sharp band spectrum. Each band is the exact
frequency of light that must hit that quantum degree of freedom
with high intensity to resynchronize its phase and drive the
classical, decoherent degree of freedom down the y-axis through the
Poised Realm toward fully quantum behavior. Almost certainly, the
antenna protein chromophores are doing this, a hypothesis which is
testable by mutating the chromophores and showing that sustained
coherence of chlorophyll decreases then correlating the decreased
coherence with a change in the emission spectra of the chromophores
on the antenna protein with respect to the absorption/emission
spectrum of chlorophyll. This experiment as been done with a
bacterial rhodopsin and its antenna protein with exactly the above
result, although matching to the emission frequencies of the
antenna protein and absorption bands of chlorophyll have not, to
our knowledge, been examined.
[0098] Additional data has shown that, in a spin bath environment,
a quantum system can exhibit partial decoherence that levels off
with medium coherence, in the Poised Realm, where coherent behavior
propagating a finite number of coherent amplitudes persists
indefinitely. If the system is started with less coherence, i.e.
"more classical" in the Poised Realm, it recoheres to the same
intermediate level, propagating a finite number of quantum
amplitudes coherently. Such stable propagating amplitudes that
persist despite decoherence are useful in quantum computation.
[0099] As discussed above regarding the degree of order,
decoherence can be suppressed and the system kept coherent for an
anomalously long time if it is deliberately kept at the Poised
Realm critical transition point. Within the poised realm, ordered
and chaotic behavior is associated with rapid exponential
decoherence. In sharp contrast, along a critical locus in the
poised realm roughly paralleling the y axis and terminating at
criticality on the x axis, poised realm systems decohere much more
slowly, in a power law, not exponential decay of coherence. Thus,
within the poised realm, criticality preserves coherence better
than other positions within the poised realm.
[0100] Measuring Decoherence and Recoherence Experimentally in Real
Quantum Systems.
[0101] There is a very convenient measure of decoherence. A dilute
gas of a single atomic species, e.g., hydrogen, has very sharp
absorption and emission bands, forming its spectrum. In general, as
decoherence sets in, these bands become wider. Thus, the width of a
band is a convenient measure of the decoherence status of that
amplitude of the quantum system, which is easy to measure with
standard spectrography.
[0102] Recoherence can be seen, for example due to driving with
light whose wavelength is at the center of a broadened band, by
progressive narrowing of that band. Conversely decoherence and its
rate can be measured by narrowing and sharpening of the band. And
position on the y-axis can be measured at any time for any pair of
amplitudes whose energy gap corresponds to that band, by how narrow
or broad it is. We can follow position on the y-axis for all pairs
of amplitudes of a one or a system of coupled quantum degrees of
freedom on a quantum graph, by the breadth of such bands. In
addition, coherence can be measured using spin echo
experiments.
[0103] Our first results modeled decoherence with a Wiener process,
.sigma.Wdt, whose variance sigma could be altered from 0, hence
persistently quantum coherent in the absence of any decoherence, to
infinite, which randomizes all phases. Thus, in general, as we move
by increasing sigma in the Weiner process, we move from quantum to
decoherence to classical behavior. For a kicked quantum rotor,
position on the x-axis (degree of order) is determined by the
intensity of momentum kicks, of intensity K, to the quantum rotor.
These kicks are Dirac delta functions--that is "instantaneous"
inputs of momentum energy supplied, without loss of generality, by
laser light of any diversity of frequencies, and at any rate of
photon kicks, i.e., intensity K, to the quantum rotor per unit
time.
[0104] It will be clear to those of ordinary skill in the art, that
the photon kicks can be any quantum degree of freedom and delivered
with any time constant or varying modulated intensity, hence the
kicks to each quantum degree of freedom are a quantum time
modulated input signal to the quantum degree of freedom. Therefore,
in general, this quantum input constitutes quantum information
received by the rotor. When we generalize to a quantum network with
rotors coupled to one another, or more general systems with quantum
and classical degrees of freedom, this will become the quantum
information via one or a plurality of quantum inputs to a system of
quantum and classical degrees of freedom that responds to the
incoming quantum information, emits quantum information to its
environment, alters its Poised Realm and classical behaviors and
also the quantum and classical Hamiltonians, and constitutes a new
class of embodied quantum information processing systems that we
call Trans-Turing Systems. Due to the superpositions noted above or
pure states and the Born rule, coupled with decoherence to
classicality or quantum measurement, the Trans-Turing system is not
definite, so not algorithmic, but due to the classical degrees of
freedom and Poised Realm degrees of freedom, the behavior is also
NOT RANDOM IN THE STANDARD SENSE OF QUANTUM RANDOM given by the
Schrodinger equation and von Neumann axiomatization of closed
system quantum mechanics. We emphasize that our Poised Realm
systems in general and Trans-Turing systems are OPEN QUANTUM
SYSTEMS, WITH A DISTINCTION BETWEEN THE QUANTUM SYSTEM AND ITS
ENVIRONMENT INTO WHICH IT CAN LOSE PHASE INFORMATION.
[0105] Decoherence happens in open quantum systems because phase,
and also amplitude, information is lost from a quantum system, here
our single quantum degree of freedom, to a quantum "environment".
For example a photon emitted by an excited electron may, on one of
its many possible paths in Feynman sum over histories formulation
of quantum mechanics and quantum electro-dynamics, interact with
any quantum degree of freedom in the environment and thereby induce
decoherence.
[0106] In our studies of the driven quantum rotor, we model two
processes. We model the kicks, K, which hit the rotor once per
arbitrary period. As noted above, we model the decoherence process
as a random walk called a Weiner process, described by .sigma.W dt.
W is a Gaussian distributed 0 mean, 1 variance distribution of
"step sizes" which describes the phase change of the point on the
circle in the complex plane at each application of the Weiner
random walk, during dt. At sigma=0, there is no alteration of
phase, hence no decoherence, and the system is fully quantum. Thus,
.sigma.W dt=0 is the quantum coherent origin of the y-axis. As
.sigma. increases to ever larger values, the phase becomes ever
"noisier" driven by the white noise Weiner process. Thus as sigma
increases the rate of decoherence increases.
[0107] A second way we implement quantum measurement of an
amplitude in our algorithmic simulations of a Poised Realm system
is by taking the square of its modulus, (i.e., the Born Rule),
doing so for all amplitudes of the rotor with finite modulus, then
choosing one of these amplitudes with a probability corresponding,
via the Born Rule, to its squared modulus, and placing the rotor in
that single eigen state corresponding to the measured
amplitude.
[0108] Once the quantum degree of freedom is measured, and in its
eigen state, it can leave that eigen state quadratically in time
with the "flowering" to finite moduli, of nearby and more distant
amplitudes in the absence of decoherence. In short, at .sigma.=0,
no decoherence, full quantum behavior reemerges with all possible
amplitudes for the system. At finite sigma, a finite number of
amplitudes with finite moduli will flower as noted below.
[0109] Quantum Localization of Chaotic Dynamics.
[0110] If the classical limit of the quantum system has a
Hamiltonian corresponding a position on the x-axis to the right of
the critical point second order phase transition, the classical
system exhibits chaos. If decoherence is 0 or low enough, because
sigma is low enough, quantum behavior occurs, even in the
persistent presence of some decoherence, but the quantum behavior
is localized. In the Poised Realm, only a finite number of
amplitudes have finite moduli.
[0111] In short, in the Poised Realm FAPP only a finite and tunable
number of amplitudes are present in the quantum behavior of a
single quantum kicked rotor degree of freedom, or for any number of
independent kicked quantum rotors. The same limited number of
amplitudes obtains for kicked quantum oscillators whether single
or, if independent, any number.
[0112] Energy Scaling of Decoherence.
[0113] In our specific, non-limiting example of the use of the
Weiner process to model decoherence of any amplitude, we have found
that HIGH ENERGY AMPLITUDES ARE ONES MOST LIKELY TO DECOHERE to
classical behavior, that is they become classical degrees of
freedom, even for small values of sigma. By contrast, low energy,
small modulus amplitudes do not decohere to classical behavior as
readily.
[0114] The preferential decoherence of high energy and high
amplitude modes is reminiscent of Fermi's Golden Rule for quantum
measurement for coherent systems, where quantum systems tend to
take the largest energy drop, e.g. to the ground state, available.
But in turn, as exemplified by the famous photoelectric effect
where absorption of a photon, according to Einstein 1905, kicks out
an electron from the material, the TRANSFER OF ENERGY FROM THE
QUANTUM AMPLITUDE TO THE NOW CLASSICAL DEGREE OF FREEDOM WILL BE
LARGEST IF HIGH AMPLITUDE HIGH ENERGY AMPLITUDES PREFERENTIALLY
DECOHERE TO CLASSICALITY FAPP, OR ARE PREFERENTIALLY MEASURED IN
THE POISED REALM FOLLOWING FERMI'S GOLDEN RULE. This bears on
essential three topics: i, the efficiency of energy transfer in the
Poised Realm and Trans-Turing systems; ii. The use we make below of
this preferential decoherence of HIGH ENERGY AMPLITUDES to solve
the famous FRAME problem in algorithmic computers in our
non-algorithmic, non-deterministic, but non-random Trans-Turing
systems--see below. iii. We will use the preferential decoherence
to classicality FAPP or via measurement, below in Trans-Turing
systems such that there is an ongoing decoherence of high amplitude
modes to classical behavior, thereby altering the classical
hamiltonian, e.g. as a non-limiting example by altering the
couplings among classical degrees of freedom. In turn this will
alter the hamiltonian of the quantum degrees of freedom, in turn
altering via constructive and destructive interference of
superpositions, or of pure states, which amplitudes are of high
energy and decohere next in time, again altering the classical and
quantum hamiltonians of the trans-turing system. In turn, by
recoherence, classical degrees of freedom can recohere, again
altering the classical and quantum hamiltonians. This ongoing
behavior is the centerpiece of trans-turing non-determinate,
non-algorithmic, yet non-random behavior.
[0115] With respect to preferential deocherence of high energy
amplitudes, we reason that high energy amplitudes have high angular
momentum hence are less affected by random decoherence noise, so we
have scaled, as a non limiting computational study example,
decoherence via the Weiner process to decrease either exponentially
or as a power law, with increasing energy of the amplitude. In
particular, we use .sigma.=.sigma..sub.0 exp (E/Eo) where
.sigma..sub.0 is the sigma for a 0 energy amplitude, a constant, E
is the energy of an amplitude, and Eo is a scaling factor governing
the exponential fall off of Weiner modeled phase decoherence with
the energy, E, of an amplitude.
[0116] Behavior of a Single Kicked Quantum Rotor in the Poised
Realm.
[0117] With the above introduction, we find the following: 1) For
low enough sigma and all K, i.e., values of the x-axis, the system
is quantum and has a finite number of modes or amplitudes. 2) As
sigma increases, so decoherence increases and we move up the y-axis
in the Poised Realm, there are fewer amplitudes propagating then a
transition to classical behavior occurs. Thus classical degrees of
freedom emerge as decoherence increases. 3) The slope of this
transition from quantum to classical as sigma increases, itself
increases as X value, i.e., increasing chaos, increases. That is,
more chaotic systems undergo the transition to decoherence more for
smaller changes in sigma W than more ordered systems. 4) There is
some indication that the midpoint of the slope of this transition
to decoherence is "flat" and parallel to the x-axis in the ordered
regime, where decoherence requires similar high sigma W as X
increases toward criticality, then bends downward in sigma W
required for decoherence at criticality, and that decoherence
occurs at ever lower sigma, i.e., decoherence inducing phase noise,
as chaos increases on the x-axis. This sloping behavior of the
midpoint of the transition curve means that motion on the x-axis by
any means at a constant sigma W, can move the system from
decoherent to more quantum coherent behavior. For example,
decreasing or increasing the intensity of the momentum kicks to the
quantum rotor can move that rotor from quantum to classical
behavior and back as the kicks decrease then increase in intensity.
Similarly, altering the graph structure corresponding to a real
system from critical to supracritical and back on the x-axis can
move the system from coherent to decoherent behavior in the Poised
Realm. We make use of this in the section on drug discovery and
action below. This is also true as the Hamiltonian of the system is
changed on the x-axis, which can occur dynamically as a system of
coupled quantum and classical degrees of freedom behaves. This
constitutes a new way to move from quantum to classical behavior
and back. Thus a single degree of freedom can be quantum or can be
classical, either by tuning the position on the x-axis by tuning
the kick strength K, or by tuning position on the y-axis by tuning
decoherence. So too can a system of coupled quantum degrees of
freedom, for example in a quantum graph, or quantum and classical
degrees of freedom. For example, a critical chemical quantum
network will decohere very slowly, via a power law, not an
exponential decay. We have already noted that adducts to a quantum
network, or deletions from that network, or alteration in the
proximity of generalized chromophores, can alter the effective
quantum network topology on the x-axis moving it to or from the
critical locus of power law behavior in the poised realm.
[0118] It will also be clear to those of ordinary skill in the art
that tuning position on the x-axis for a single quantum degree of
freedom is at our liberty as it is we who determine kick intensity,
K.
[0119] Summary of the single kicked quantum rotor in the Poised
Realm: 1) only a finite number of quantum amplitudes grow and have
finite moduli. The number of modes decreases as kicking intensity
increases. 2) In the chaotic region with high intensity kicking,
quantum localization of chaotic behavior occurs. 3) A transition
from quantum to classical behavior occurs as sigma W dt is
increased, i.e., as decoherence is increased, but quantum behavior
persists for small finite .sigma.Wdt. 4 A slope in the transition
from quantum to classical behavior along the x-axis is present at
some fixed values of .sigma.Wdt, so any single independent kicked
quantum rotor can be moved from quantum to classical by tuning
momentum kicking, K, intensity, or decoherence intensity. Or a
quantum network can be moved from quantum to more classical
behavior by motion out the x-axis toward chaos, and we believe
beyond criticality on the X axis. Or motion on the x-axis by change
of the Hamiltonian of the system as quantum degrees of freedom
become classical and may, as a non-limiting example, couple in new
ways to other current classical degrees of freedom, can move the
system on the X axis, from more to less quantum behavior in the
Poised Realm. 5) A final feature is that behavior in the poised
realm is not random, and not Markovian. This behavior partakes of
the Anti-Zeno effect, is non-Markovian, hence not first order
random, as is normal quantum randomness, and is a Floquet process.
The same conclusions generalize to coupled quantum degrees of
freedom or quantum and classical degrees of freedom.
[0120] Simulations Using the Lindblad Operator.
[0121] As described above, the Lindblad operator is a mean field
Markovian model of loss of off diagonal terms in the density matrix
of a quantum system including a single kicked quantum rotor. It is
widely accepted as physically accurate, but is not a detailed "law
of decoherence." As noted above, in a Special Relativity setting
where the quantum degrees of freedom move with respect to one
another there can be no such law. Again, given events A and B,
where B is in the future light cone of A, and the past light cone
of B includes the past light cone of A, but has regions space-like
separated from A, no observer at A can know what events are
occurring outside her past light cone. Therefore, there is no way
in the Special Relativity setting to write down a law for
decoherence in the space time interval from event A until
immediately before event B. In general, there is no "law of
detailed decoherence."
[0122] Yet the Lindblad operator, a meanfield approach to the
statistics of this process, serves well, particularly for tiny
relative velocities of degrees of freedom.
[0123] We have implemented the kicked quantum rotor and increased
the frequency and intensity of kicks, such that they vary from ten
times the rotation frequency of the rotor to its rotational speed,
"continuously". In the ordered regime on the x-axis, the finite
number of amplitudes is high, and decreases as the critical phase
transition is approached. Thus, the behavior of the system is far
from the closed quantum system and unitary propagation of many
amplitudes of the Schrodinger time dependent equation. Only a
finite number of amplitudes with finite modulus are present.
[0124] When the system crosses into the chaotic regime, it becomes
fully classical. Thus, as in the case of modeling decoherence with
a Weiner process, sigma W dt, the response of the kicked rotor
depends on position on the x-axis, so the rotor can be moved from
quantum to classical and back by motion on the x-axis.
[0125] In this model, the movement on the x-axis is due to the
intensity and frequency of Dirac delta momentum kicks. More
generally, the results support the claim that motion on the x-axis
back and forth, either by momentum kicks, quantum network topology
alterations by altering network structure directly with adducts,
deletions, or altering the size, and density of generalized
chromophores, will alter position in the Poised Realm.
[0126] Evolved organic molecules, like all organic molecules, can
exist in the Poised Realm. It will be clear to one of ordinary
skill in the art, that position in the Poised Realm is likely to
affect the behaviors of one or a plurality of molecules, as a
non-limiting example, in cells. Thus, position in the poised realm
will affect the behavior of drug molecules as well. It becomes of
deep interest if EVOLVED organic molecules occupy a specific
supspace of the Poised Realm. In particular, we believe that
evolved organic molecules are likely to be at or near the critical
locus in the Poised Realm. This critical location allows such
evolved biomolecules and small organic molecules and drugs to
participate in the slow power law decoherence of criticality rather
than more rapid exponential deocherence as the system moves further
towards order or chaos. Quite interestingly, we will see below that
biological small molecules appear close to the statistics of the
critical giant components in quantum graphs, in our two examples,
while cyclic hydrocarbons, Buckmeisterfullerenes, graphite and
diamond are much more richly connected and supracritical. This may
mean that biological molecules are not purely classical, but may
well remain partially poised in the Poised Realm. The quantum
coherent behavior of chlorophyll and bacterial photoreceptor
systems is opening the field of quantum biology. Much of cell life
may hover in the Poised Realm, with new implications for medicine
and drug discovery we return to below.
[0127] A means to test whether biological molecules are in the
poised realm is afforded by the experiments of Anton Zeilinger,
University of Vienna, who has shown that C60 Buckmeisterfullerenes,
used as a "beam" in a two slit experiment, show partial reduction
in interference uniformly across all interference bands, hence are
partially decoherent. This procedure is a new means by which to
test the coherence of a particular molecule. In the two slit
experiment, molecules will show more or less signatures of partial
decoherence by greater or less reduction of interference patterns
in the two slit experiment. Thus if there is less than normal
interference, the molecules are in the Poised Realm in a "stable
way".
[0128] Drugs in the Poised Realm
[0129] It is generally thought that quantum phenomena have no
bearing on biological processes because, at body temperature (about
300K), no quantum phenomena would be present. This view is purely
one that envisions either a quantum world or a classical world, and
the von Neumann R process of "collapse" of the wave function via
the Born rule to place all the probability on one amplitude with a
probability the square of the modulus of that amplitude. Quantum
chemists have typically ignored decoherence, treated most of a
molecule with classical physical models with a classical
Hamiltonian potential, then at most focused quantum time
independent Schrodinger equation analysis of a small "active" part
of a molecule, then mathematically "glued" the quantum and
classical aspects of the modeled molecule together.
[0130] An interesting failure in this regard, where one of us,
Kauffman, has the founding patent, is combinatorial chemistry (See
Kauffman Ballivet patents 1986 France to 1992 US). The US
pharmaceutical companies have spent billions making libraries of
more or less random organic molecules then screened these for
ligand binding to shape complements of desired drugs. For example,
a random organic molecule binding to the estrogen receptor, like a
random key fitting the receptor thought of as a classical physics
"lock", is a candidate to shape mimic estrogen itself and hence be
a drug candidate. This entire approach, which Kauffman and Ballivet
invented, treats ligand binding pairs as fully classical physical
entities, locks and keys, the then prevailing theory. The approach
has failed. The drug companies in the US are said to have nearly
empty drug pipelines. By contrast, the Japanese pharmaceutical
companies continued over the past decades, we are told, to rely on
traditional medicinal chemistry and they have many drugs in their
developmental pipelines. This sharp contrast suggests that the
medicinal chemists were unwittingly probing the Poised Realm
behavior of drug candidates and combinatorial chemistry with its
screening or computational designs based largely on classical
physics models of all or most of the candidate molecule's structure
and dynamics, missed any Poised Realm behaviors relevant to drug
action. This bears on our use of the Poised Realm for drug
discovery, as well as for understanding basic cell biology.
[0131] In the standard view, the world is either fully quantum or
fully classical. There is no notion of a Poised Realm between
quantum and classical. As described above, data demonstrates that
there is in fact a Poised Realm between fully quantum and fully
classical. As an example, the long term quantum coherence of
chlorophyll is galvanizing quantum physicists and a new field of
quantum biology. The antenna protein and its chromophores almost
certainly cannot block decoherence from chlorophyll. There is
further evidence in the prior art that molecular topology within
chlorophyll can serve to slow down the rate of decoherence either
by making chlorophyll more readily subject to recoherence via the
antenna protein or chlorophyll itself, or in itself. It seems
probable that both the structure of chlorophyll makes it more
easily subject to recoherence and the antenna protein mediates this
"recoherence," perhaps by photons absorbed in the center of
chlorophyll's absorption band(s).
[0132] Beyond chlorophyll, quantum events in biology are evidenced
by quantum coherent electron transfer demonstrated in quantum
chemistry calculations, and it appears to play a role in cells in
that, as the distance between two proteins increases, electrical
conductivity falls off, but shows a plateau in electrical
conductivity at a distance of about 12 angstroms to 15 angstroms.
Conductivity falls off as distance increases. 12-15 angstroms is
just the distance that allows a water molecule to hydrogen bond
between two proteins and afford two pathways of electron transfer,
hence in analogy with the two slit experiment, allows quantum
interference patterns. The work on electron transfer by D. Salahub
and colleagues at the University of Calgary, has shown such a bound
water molecule and coherent electron transfer between two proteins.
The cell is a densely crowded matrix of proteins at about the 10-15
angstrom distance, with an abundance of coordinated water between
them. This invites the hypothesis that percolating connected
pathways of electron transfer within and between the proteins in
the cell cytoplasmic matrix occurs. This may allow extensive
quantum coherent behavior in cells. Similar evidence in bird
navigation by quantum behavior in molecules of their eyes picking
up earth's magnetic field. More generally quantum biology is
exploding, BUT IT REMAINS FOCUSED ON QUANTUM COHERENT BEHAVIORS. We
believe quantum coherent behaviors are the literal tip of the
iceberg in quantum biology, with many or most quantum effects in
the Poised Realm of open quantum systems in an environment to which
they can lose phase information, where quantum coherence is a
limiting boundary of the Poised Realm. This bears on drug discovery
and action, and molecular behaviors in cells and tissues and organs
and the whole organism.
[0133] The electrons in such electron transfer within and between
proteins with, or without such a percolating web, exchange
electrons all the time. This implies that such electrons may induce
recoherence, the Quantum Zeno Effect, and Quantum anti-Zeno effect
on otherwise decohering quantum degrees of freedom in cells. Thus,
cells may, to a substantial extent, live in the Poised Realm. In
addition, drugs near or at the critical locus in the Poised Realm
will participate in the slow, power law decoherence at criticality,
rather than the ever faster exponential deocherence further from
criticality toward order or chaos. All this concerning position on
the X axis at least, will affect drug behavior in general and in
vivo in particular. We believe this is of extraordinary
importance.
[0134] But criticality in the poised realm has universal behavior
associated with power law decoherence, not exponential decoherence.
If slow decoherence is useful biologically, then critical location
in the poised realm is useful. As noted above, a comparison of
random organic molecules and evolved organic molecules tests
whether evolved organic molecules are in a special, perhaps
critical, location in the Poised Realm. Whatever the answer may be,
it is a huge clue to effective drug design and action.
[0135] Molecules can behave in various reactions differently
depending on where they are on the chaos-order (x) and
quantum-classical (y) axes. Their position is an important
characteristic which can be used in chemical and drug design. The
position of a molecule on the x axis can be determined from the
energy level spacing distribution as it was described for general
systems before. Experimentally, the levels can be reconstructed
from the excitation spectrum as it is known to the art, their mean
level spacing .DELTA.(E) as a function of energy can be fitted and
then the distribution of spacings
s.sub.n=(E.sub.n+1-E.sub.n)/.DELTA.(E.sub.n) can be analyzed.
x = A - A p A w - A p ##EQU00013##
can serve as the x-coordinate where the quantity A is calculated
from the actual level spacing of the system
A = .intg. 2 .infin. p ( s ) . ##EQU00014##
[0136] The position on the y axis can be calculated from the
Hamiltonian operator of the molecular system and its interaction
matrix elements with the environment as we described earlier. In
reality, from the point of view of molecular design the most
important property is not the y coordinate position directly, but
the distance of the molecular system from the critical poised realm
state. This distance can be determined from the results of the
decoherence measurements, e.g. form the output of the relevant echo
type measurement. In molecular systems this is usually photon echo
or neutron spin echo measurement. The result of the echo
measurement is a signal S(T.sub.E) where T.sub.E is the echo time
(time between the first and the second pulse as known to the art).
For non-critical systems the long time behavior of the signal is
exponential S(T.sub.E).about.exp(-T.sub.E/T.sub.D) where T.sub.D is
the dephasing time, which serves as our coherence time FAPP. For
critical PR molecular systems the decay of the signal is a power
law S(T.sub.E).about.T.sub.E.sup.-.alpha. with some exponent
.alpha., which can be determined from fitting the experimental
curve. Systems in general are usually not exactly in their critical
state, therefore the ultimate decay of the signal is exponential.
However, depending on their closeness to the critical state a
transitional form
S(T.sub.E).about.exp(-T.sub.E/T.sub.D)/T.sub.D.sup..alpha. can be
fitted to the curve and the parameters T.sub.D and a can be
determined. In case of changing the parameters of the molecular
system via changing the macroscopic parameters, applying external
forces (for example laser light) transition towards the critical
poised realm state can happen. Change towards the critical state is
reached in a diminishing of the dephasing time T.sub.D.fwdarw.0
determined via fitting the transitional form to the experimental
echo signal. The value of a can change during the parameter change
but it remains finite during the process. The measured value of
T.sub.D is a good measure of the distance from the critical state.
The smaller the T.sub.D the closer the system to criticality
is.
[0137] Beyond simple parameter change the position of the molecular
system can be changed by making changes is its configuration.
Adding or removing some parts of a macromolecule or changing its
structure by any manipulation can change its position within the
poised realm.
[0138] As discussed above, degree of order (i.e., position on the
x-axis of the poised realm model) can affect the decoherence rate
of a quantum degree of freedom. For example, at the critical
transition point of the degree of order (discussed above), the
decoherence rate is suppressed. While not being bound by any
particular theory, it is proposed that biological systems, and
hence biological activity, operate optimally at particular rates of
decoherence. In some embodiments, certain biological systems
operate optimally where the decoherence rate is slow. In other
embodiments, certain biological systems operate optimally at faster
decoherence rates. Accordingly, for a particular biological system
(e.g., a particular enzyme or receptor), the best drug molecules
will be those having a particular degree of order (i.e., position
on the x-axis).
[0139] Some embodiments provide a method of drug discovery that
seeks to identify drug molecules that particular targets based on
the molecules' position on the axis. One such embodiment is
described with reference to the flowchart of FIG. 4. This method
seeks to identify the most promising drug leads for a particular
target from a library of compounds. Identification of drug leads
from libraries of compounds is a common approach to drug discovery;
however, such approaches rely on either molecular modeling methods
(e.g., ligand docking) or in vitro assays. Most compounds
identified as promising by such methods often prove to be
ineffective and/or toxic and are ultimately never developed into a
drug. The present method provides an alternative approach.
[0140] Libraries of compounds to be used with the present method
may be obtained using known means, for example, generated using
combinatorial chemistry approaches or commercially available. At
block 500 of FIG. 4, a particular biological target (e.g., an
enzyme or receptor) is selected. At block 510, a molecule from the
library is tested for binding to the target. Traditional methods of
binding detection may be used, including in vitro binding assays
and in silico modeling methods. If the test molecule binds to the
target, it proceeds to the next step. If not, a new molecule from
the library is selected at block 520 and is tested for binding.
[0141] At block 530, the energy level spacing distribution of a
quantum degree of freedom in the molecule is determined. This
distribution may be determined using known methods including
experimentally (e.g., using spectroscopic techniques) or
theoretically using known modeling algorithms. In some embodiments,
the determination of energy level spacing is determined as it would
be in the biological environment (e.g., while the molecule is bound
to the target). Once the energy level spacing distribution is
known, it may be compared to reference functions at block 540 to
determine the degree of order (i.e., position on the x-axis) of the
molecule. For example, as described above, in a pure ordered
regime, the energy level spacing distribution has the form:
p(s)=exp(-s)
where s is the energy level spacing and p(s) is the energy level
spacing distribution. In a purely chaotic system, the distribution
has the form:
p ( s ) = .pi. s 2 exp ( - .pi. s 2 / 4 ) ##EQU00015##
The actual distribution of the test molecule may be compared with
these functions to determine its position on the x-axis, for
example, using
x = A - A p A w - A p ##EQU00016##
where
A p = .intg. 2 .infin. p p ( s ) , A w = .intg. 2 .infin. p w ( s )
, and A = .intg. 2 .infin. p ( s ) , ##EQU00017##
where p.sub.p(s)=exp(-s) and
p w ( s ) = .pi. s 2 exp ( - .pi. s 2 / 4 ) . ##EQU00018##
p(s) is the actual distribution for the test molecule.
[0142] At block 550, it is determined if the energy level spacing
distribution of the test molecule has the desired relationship to
the reference function. This relationship may be a pre-determined
value for x found to correlate with high activity or in some
embodiments, is the relationship that indicates that the molecule
exists at the critical transition point along the x-axis. As
discussed above, this critical point may be determined by the
energy level spacing distribution having the form:
p(s)=4sexp(-2s).
Thus, in some embodiments, molecules are selected at block 550 that
are close the critical transition point as determined based on
their energy level spacing distribution.
[0143] If a candidate molecule has the desired relationship as
determined at block 550, it is selected as a drug candidate at
block 560. If it does not, the procedure returns to block 520 for
the selection of a new candidate from the library. Drug candidates
selected at 560 may themselves be suitable for drug development or,
alternatively, may serve as lead compounds for further optimization
using known quantitative structure active relationship (QSAR)
medicinal chemistry. In some embodiments, new candidates based on
the selected lead compound are also screened following the method
in FIG. 4 to determine if they have the desired degree of order and
are thus suitable drug candidates.
[0144] A variation of this method is described in the flow chart of
FIG. 5. Again, a library of compounds is provided and biological
target is selected at block 600. The candidate molecules are
checked for binding to the target at block 610. If binding is not
observed or predicted, a new candidate is selected at block 620. If
binding is observed or predicted, the energy level spacing
distribution is determined at block 630. Next, an in vitro and in
vivo biological assay is performed to determine the activity level
of the compound at block 640. This procedure may be repeated for a
number of molecules in the library such that a correlation may be
made at block 650 between the energy level spacing distribution and
biological activity for the particular biological target. The
correlation may be between a determination of a particular degree
of order (e.g., position on the x-axis) or may be a particular
energy level distribution obtained, for example, by averaging the
distributions of the most active compounds.
[0145] Once a suitable correlation is constructed, a new candidate
molecule may be tested without having to perform an experimental
assay for biological activity. In this case, the energy level
spacing distribution of the new candidate may be determined at
block 660 using known methods. This distribution is compared at
block 670 to the correlation determined at block 650. The
comparison may include directly fitting the distribution to average
distribution for previously determined active compounds or may
include determining the degree of order (e.g., position on the
x-axis) as described above and comparing that determination to the
known active compounds. If a close match is made, that molecule may
be advanced as a drug candidate at block 680. If not, a new
candidate molecule may be selected at block 690 and evaluated in a
similar fashion.
[0146] In some embodiments, the rate of decoherence of candidate
molecules may be directly measured using known methods including
spin echo techniques such as nuclear magnetic resonance spin echo,
neutron spin echo, or photon echo. These techniques can be
particularly useful to evaluate molecules within a biological
environment (e.g., bound to a target in part a biological mixture,
for example, a cellular extract mixture). In these embodiments, the
above methods may be modified such that rather than determining and
comparing energy level spacing distributions, candidate molecules
may be tested for a desired rate of decoherence rate. For example,
in one embodiment, candidate molecules that bind to specified
target may be evaluated to identify the molecule having the slowest
rate of decoherence. In one embodiment, the experimentally measured
decoherence rate is fitted to the functional form
S(T.sub.H).about.exp(-T.sub.H/T.sub.D)/T.sub.H.sup..alpha. and the
value of T.sub.D determined. In one embodiment, selection of a drug
candidate includes selecting molecules having low T.sub.D
values.
[0147] Another embodiment considers the modeling of molecules using
quantum networks. We use as a NON LIMITING example of quantum
networks, taken as models representing real organic molecules, and
as crude examples, the Erdos Renyi random graphs described above.
FIG. 6 depicts an example of a 100 node exactly critical
Erdos-Renyi graph, and typical Giant Component containing 83 of the
100 nodes. A critical ER Giant Component of 47 of 50 total nodes is
shown in FIG. 7. The 83 node Giant component has 28 nodes with
<k>=1 connections, 11 nodes with <k>=2 connections to
their two neighbors, 14 nodes with <k>=3 connections to three
neighboring nodes and five <k>=4 nodes connected to four
neighbors. The ratio of bonds, or lines to nodes, i.e.,
bonds/nodes=1.349. The 50 node ER graph with a critical 47 node
Giant Component has eleven <k>=1 nodes, eleven <k>=2
nodes, six <k>=3 nodes, six 6<k>=4 nodes, and seven
<k>=5 nodes. Its mean <k> is 2.34. The mean of these
two is <k>=1.8445. We do not know the mean and variance of
connectivities for critical Giant Components of Erdos-Renyi graphs,
but presume that these two are roughly typical, probably on the low
and high side of the mean <k> for such critical Giant
Components.
[0148] Preliminary analysis suggests that biological small
molecules, and perhaps proteins and nucleic acids and lipids, are
very similar in their mean <k> values to the Giant Component
of critical Erdos Renyi graphs. In contrast, many organic molecules
not found in life seem to have a higher <k>, characteristic
of the supracritical, or chaotic quantum graph regime. This
analysis treats single, double and triple covalent bonds the same
and counts only connections among pairs of atoms.
[0149] A small sample of non-biological organic molecules include
the following: Napthalene <k>=2.2; Anthracene
<k>=2.214; Methylpropane <k>=4.0; DiMethylpropane
<k>=4.0; Cyclohexane <k>=4.0; Annulene <k>=2.0;
Buckminsterfullerene <k>=3.0; and Diamond, <k>=4.0.
[0150] Over a random sample of 20 biological small to medium sized
organic molecules, the mean value of <k>=1.928. While the
sample of ER giant components is only two and we do not know the
true mean of all possible ER giant components, their average,
1.8445, is close to that for the biological organic molecule sample
(<k>=1.928). The spread in <k> values among the 20
biological organic molecules is very narrow. The 20 molecules and
their <k> values are: acetate 1.66, caffeine 1.96, abscisic
acid 1.88, acetic acid 2.0, acetylcholine 1.555, adrenaline 2.0,
alanine 1.875, arginine 1.925, asparagine 1.72, bacteriopheophytin
A 1.983, B carotine 1.987, catechol 2.0, estrone 2.09,
fructose-6-phosphate 2.0, glucose 1.965, histadine 2.04, isoleucine
1.92, lactose 2.0, phenylalanine 2.0, retinoid acid 2.0.
[0151] As noted, we do not yet know the mean and variance for the
connectivity of the giant component among all critical Erdos-Renyi
graphs. Presumably the true mean is near the mean of our two
critical Erdos Renyi Giant components, <k>=1.8445. The narrow
spread of biological organic molecules is striking, as is the close
agreement between the two means, Erdos Renyi critical Giant
components, and these biological small molecules.
[0152] Proteins and nucleic acids and lipids and polysaccarides
seem likely to be close to critical in their covalent bond
structure, again ignoring the distinction between single, double
and triple bonds in favor of "connections between atoms." They are
comprised of smaller components that are near critical.
[0153] These observations suggest that natural selection has tuned
the position of biological molecules on the x-axis to be very close
to criticality, with a very narrow range of <k> values, and
we suggest below why this may be deeply useful in drug design and
discovery. In turn, these observations suggest that cells live, due
to natural selection, partially poised in the Poised Realm between
fully quantum and fully classical and, like chlorophyll, natural
selection has made good use of the Poised Realm.
[0154] We note that in a preferred embodiment of this invention, we
can experimentally test whether random and evolved organic
molecules are located, respectively through larger regions of the
Poised Realm for random organic molecules, and whether evolved
organic molecules are CRITICAL IN THE POISED REALM, by their rates
of decoherence. Critical molecules will decohere in a power law
distribution, as described above. Thus, using line band broadening
as a measure of decoherence, spetroscopic means known in the art,
or any other means now or in the future known to measure
decoherence, we can measure an organic molecule to look for power
law decoherence as a signature of the critical location and
behavior of said organic molecule. Thus we can test, without
limitation, any organic molecule for exponential decoherence if
ordered or chaotic in the Poised Realm, or power law decoherence if
critical in the Poised Realm. Without limitation, we can test if
chlorophyll and its antenna protein are critical in the Poised
Realm by testing for power law decoherence. Thus, in general, we
can test whether evolved biological molecules are critical or near
critical, while random organic molecules or other molecules are not
critical in the Poised Realm. This is of general relevance to drug
action and thus to drug design. Testing for power law decoherence
or exponential deocherence may, without limitation, be made in vivo
or in vitro.
[0155] A striking feature of our studies of the kicked quantum
rotor using the LindBlad operator is that as kicking intensity and
frequency increase, the rotor passes from the ordered regime with a
large but finite number of quantum amplitudes with finite moduli,
to fewer amplitudes with finite moduli as criticality is
approached, to a sudden jump to classical behavior when the
critical line in the Poised Realm is passed and chaos is entered on
the x-axis. But when the system passes from quantum to classical
behavior: i. energy is transferred from the quantum to the
classical world. ii. The now classical degree of freedom can have
CLASSICAL PHYSICS effects on the classical world! The poised realm
system can then ACT on the classical world. iii. Position near the
critical line maximizes passage back and forth from quantum to
classical, thus the diversity of classical actions the system can
take, based on Poised Realm "calculations" in the quantum aspect of
the poised realm, which is non-determinate, non-algorithmic and not
random! We use this in Trans-Turing systems below as well.
[0156] The quantum network models discussed above are not yet
endowed with quantum degrees of freedom such as quantum rotors or
oscillators at their nodes, with coupling between, e.g., quantum
oscillators via springs along the arcs of the network. Ease of
decoherence for quantum systems described by classical
Hamiltonians, depends upon the average Lyapunov exponent, which is
0 in the ordered regime and bifurcates at criticality to a positive
value, where decoherence occurs more readily. This invites the
hypothesis, supported by our theorems above about power law
decoherence for critical quantum systems, which we can test
computationally, that critical quantum networks with, for example
quantum oscillators at the nodes and coupled by springs, decohere
less easily than do supracritical or ordered quantum networks with
such coupled quantum oscillators. If the hypothesis is proved, we
suspect that small evolved biological molecules, and hence also
bioactive drugs, may live poised partially in the Poised Realm and
be able to behave classically by increasing <k> via, e.g.,
hydrogen bonds where they become both subject to rapid decoherence,
and behave classically by crossing the critical line on the X axis
into chaos and decohere rapidly. We recall the evidence that
decoherence can alter the rate of a chemical reaction.
[0157] Based on the foregoing, there are two implications for drug
discovery and drug action:
[0158] 1) A drug, when quantum coherent cannot ACT classical. Thus,
we can "turn off" a drug by inducing quantum behavior either by
recoherence on the y-axis of the Poised Realm, or lowering
<k> values than about 1.8445 (i.e., moving on the x-axis of
the Poised Realm toward criticality and power law slow decoherence
rather than rapid exponential decoherence). And conversely, we can
turn the drug "on" again by inducing decoherence as in the Quantum
Anti-Zeno effect, or transition to chaos and classicity by
increasing <k> and moving <k> to be greater than
1.8445, to supracritical quantum network molecular structures and
dynamics in the chaotic regime on the x-axis of the Poised Realm.
Here the molecule remains connected, i.e. <k> equal or
greater than 1.0, and at a position further out the X axis than
criticality, decoheres exponentially rapidly to classicality FAPP
or by measurement, hence becomes classical and can have classical
effects on the classical world of the cell or organ.
[0159] 2) We can design drugs which are critical on the x-axis.
Indeed, drug molecules are open to a statistical study to see the
mean and variance of their <k> values. Improved drugs may be
obtained by tuning <k> to criticality for at least two
reasons. First, if small molecules in cells are near the quantum
classical boundary, due to natural selection, it is because their
classical physics action requires crossing that boundary back and
forth. Then drugs would seem likely to act more efficiently if they
could participate in such action. Note that this is in strong
contrast to designing drugs using classical molecular dynamic
models of molecules with classical potential functions then docking
the classical model molecules with classical ligands. This may be a
rough approximation to a dance of quantum-classical transitions in
the Poised Realm by small molecule effectors, natural or drugs,
acting on larger, supracritical, more classical target ligands. In
short, small molecules and drugs may perform best if poised in the
Poised Realm between quantum and classical behavior, able to become
classical by hydrogen or van der Waals forces to ligands, altering
<k> into the supracritical, chaotic, classical behavior
regime. It follows that drugs can act by having <k> values
that are lower than critical ER giant component graphs, or more
accurate than ER, chemical network structures we can use for drug
design, and by ligation to a target, lower the total <k>
value moving target+adduct to lower X values, hence more quantum
behaviors to inactivate the target+adduct molecule by altering from
classical to quantum behaviors. This is in stark contrast to the
standard view of a drug as a classical object binding to and
blocking binding of a small molecule to a target molecule, e.g.,
blocking estrogen from binding to the estrogen receptor. Here,
instead, estrogen may be made more "quantum" by binding a drug to
estrogen itself, lowering its <k> value, so it less readily
becomes classical on binding the estrogen receptor, and hence is
unable to act. Conversely, to increase the activity of estrogen, we
might seek to increase its <k> value by an adduct that
increases estrogen+adduct mean <k>, so the total system
becomes classical more readily by motion outward on the x-axis.
[0160] Thus, the Poised Realm affords a truly new way to think
about blocking or activating biological drug target molecules,
quite independently, or together with, binding to the "binding
site" of the target considered as a classical molecule.
Importantly, moving the target+adduct to a lower mean <k>
than critical, hence more rapid decoherence may be feasible by
adducts that bind at MANY sites on the target, e.g., without loss
of generality, estrogen molecule, IN ADDITION to also binding in
the binding site of estrogen. Then the number of ways to "block"
the action of estrogen, or by making estrogen+adduct more classical
hence enhance estrogen's activity, are likely to be increased
compared to classical considerations of blocking only the binding
site of estrogen. Thus many more candidate drugs per target become
possible.
[0161] In further consideration of the above, an adduct binding not
necessarily at, but also near the binding site of a larger
molecule, such as the estrogen receptor as a nonlimiting example,
may alter the local quantum Poised Realm behavior of that part of
the receptor, rendering it more quantum, hence blocking the
receptor from binding, or becoming more classical hence rendering
it more able to bind. Again the number of drugs that may bind near
the binding site and accomplish this adds to those that classically
bind the binding site, and so increase the number of potential
drugs affecting estrogen-estrogen receptor interactions.
[0162] With respect to turning a drug on or off, some embodiments
include stopping and starting the activities of roughly critical
small molecules in the cell by inducing recoherence via, without
limitation, laser light in their absorption bands. Organic
biological molecules often absorb in the infrared and very far
infrared. Infrared radiation, about 1000-3000 nanometers, can
penetrate substantially into the human body. Thus we can induce
recoherence of small molecules in the body, using the information
obtained from the specific absorption and emission spectrum of each
small organic molecule, and hence directly "address" specific
molecules in the body to affect the quantum or classical or Poised
Realm behavior of that specific molecule in the body. Some
embodiments use energy ranges that reach only the skin or a bit
under it (e.g., using visible, infrared, or far infrared light).
Other embodiments use light that penetrates more deeply (e.g.,
using longer wavelengths, with the obvious proviso that damage to
tissues must not be done). Avoiding damage may be obtainable in
general by modulating the timing and spectral distribution
frequencies of the incident photons.
[0163] Similarly, given a drug that is, roughly, critical, some
embodiments increase its "classical" action by inducing decoherence
via the Anti-Zeno effect or generalizations, or decrease its effect
by inducing recoherence by driving its quantum degrees of freedom
with, without limitation, laser light in the infrared or longer
wavelengths, where the drug has absorption bands, or for topical
skin treatment or other topical treatments, with light in the
visible.
[0164] The above use of recoherence and decoherence to tune a
drug's position in the Poised Realm can be used to obtain optimal
drug action by controlling behavior in the Poised Realm.
[0165] Thus, small molecules and drugs may act best, not
classically, but by being poised in the Poised Realm where a smooth
transition to classicity is achieved upon binding adducts to move
the drug further toward order and quantum Poised Realm behavior.
This may allow the drug to gradually anneal to a classical or near
classical Poised Realm state in binding to the larger protein or
other drug target. We can tune this annealing by tuning where the
drug is on the x-axis and by infrared radiation to tune decoherence
and recoherence.
[0166] Furthermore, like real annealing where a metal is heated,
hammered, then quenched repeatedly so that it finds micro-crystal
rearrangements to ever deeper potential wells and becomes and ever
harder metal, and in analogy to simulated annealing in a finite
time using both "cooling" and "heating" to tune the free energy
surface to avoid poor local minima on a classical potential, we can
"anneal" repeatedly our drug to its small, perhaps critical, or
larger more supracritical target. In particular, upon binding to a
supracritical target ligand, a small critical drug, will, through
hydrogen bonds, become on average more supracritical, hence
classical, and "freeze" into a more rigid behavior, but in
decohering make use of the Poised Realm quantum behaviors which can
explore quantum possibilities and find good potential wells. By
repeatedly inducing coherence with infrared radiation, then
allowing decoherence multiple times, a better ultimate binding of
drug to target may be obtainable.
[0167] Finally, if drug and target are both roughly critical where
decoherence is power law slow and not exponential fast in the
ordered and chaotic regimes, and partially in the Poised Realm, we
can use infrared to longer wavelengths radiation, as noted above,
to help prevent decoherence and sustain the Poised Realm behavior
not sustainable by photon showers from within the cell.
[0168] Determining Coherence and Order of Candidate Drug
Molecules.
[0169] As discussed above, degree of order can be determined by the
absorption/emission spectrum of a drug or organic molecule via the
level spacing distribution. The degree of coherence can also be
determined by absorption band widening due to decoherence. If
critical quantum molecules decohere less easily than supracritical
ones like polycyclic hydrocarbons, the critical molecules and
presumably small biologically active organic molecules with
<k> near 1.8445, or more realistic chemical structures,
should show less band broadening than polycyclic hydrocarbons or
Buckmeisterfullerenes with <k>=3. More, Buckminsterfullerene
or other X axis chaotic molecules may decohere exponentially and
more rapidly exponentially as they are more chaotic, so exhibit a
Quantum Anti-Zeno effect more readily than critical organic
molecules. So too may polycyclic hydrocarbons compared to more
critical organic molecules subjected to natural selection.
[0170] Finally, we can assess criticality, subcriticality or
supracriticality on the x-axis for the molecular structure of a
drug, adduct, target, and drug+target or drug+adduct+target, via
the eigen value spectrum of its adjacency matrix for its energy
levels, from which one can deduce the absorption and emission
spectrum of the above drug, drug+target, or drug+target+adduct.
These predictions can then be tested experimentally by measuring
absorption bands by any means known in the art.
[0171] It will be clear to those of ordinary skill in the art that
it is possible to test any molecule, or set of molecules in an
assemblage for their position both on the X axis alone and in the
poised realm generally. Here we use three independent approaches,
alone or together. First, we use a quantum network model to
determine position of any molecule on the X axis, hence also any
set of independent molecules. Second, we measure the absorption and
or emission spectrum distribution to establish, as noted elsewhere
in this patent application, the position of the molecule or
molecules, on the X axis. Third, we measure the decoherence rate,
ranging from a power law for a critical position on the X axis to
an exponential whose rate can vary on the X axis, and to
intermediate decay forms that are mixtures of power law and
exponential behaviors as described in this patent application.
[0172] It will be clear to those of ordinary skill in the art, that
if the molecule being studied or set of molecules being studied are
behaving in a classical fashion, they can be stimulated by any
means known in the art, including appropriately tuned laser
wavelengths, as described in this patent application, to behave in
the Poised Realm, or quantum coherent behavior may be obtained in
the limit of total recoherence or reflowering of quantum
amplitudes. It may often be necessary to stimulate such Poised
Realm behavior to assess experimentally by absorption/emission
spectral distributions and decoherence rates, the position of the
molecule or a set of molecules on the X axis.
[0173] However, in general, organic molecules are quantum in their
behavior as is well known in the art to spectroscopists, hence no
stimulation as in the above paragraph will typically be needed.
[0174] In general, if the absorption/emission spectra of the
different molecules are all uniquely different the set of molecules
can be measured for their position on the X axis simultaneously by
measuring the spectra of each molecule and the total set of
molecules.
[0175] More generally, for assemblies of molecules, the
absorption/emission spectra may reflect inter-atomic or
inter-molecular interactions, but both the absorption/emission
spectrum of the assembly, and its decoherence rate can still be
measured to asses the position of the assembly as a whole on the X
axis. Here if there is a distribution of positions on the X axis by
different parts of the assemblage, this will show up as different
absorption/emission spectral distributions by the different
components of the assembly. These can be deconvoluted, trivially if
the spectral lines for each molecule are unique, and those due to
inter-atomic and inter-molecular interactions are unique for any
pairs of molecules or small interacting subsets of molecules in the
assembly. More complex spectral distributions can also be
deconvolved because we know the ratios of the different molecules
and their binding partners in the assembly, without limitation, a
macromolecular assembly such as a neurotransmitter receptor and its
complex of molecules in a synapse.
[0176] With the above, we can study drugs that are known to be
effective, and/or evolved biomolecules, compared to random and in
particular unevolved organic molecules to test the locations of in
vitro or in vivo drugs or evolved organic molecules on the X axis
and in the Poised Realm, compared to "random" organic molecules. In
one non-limiting experiment, unevolved organic molecules from
chrodronaceous meteorites, such as the famous Murchison meteorite,
which has been shown to have at least 14,000 distinct organic
molecules, are used to test differences in the poised realm between
evolved and unevolved molecules. Since the meteorite dates from
about the origin of the planet earth, these molecules are clearly
abiotic. In addition, collections of known natural abiotic and
synthesized organic molecules are widespread, including in
Beilstein, and in the libraries of pharmaceutical companies,
including, without limitation, combinatorial chemistry libraries.
In addition, we incorporate by reference Origins of Order by Stuart
Kauffman, Oxford University Press, which describes a means to
generate large libraries of organic molecules titled "random
chemistry" which can be used to obtain unevolved organic
molecules.
[0177] In one experiment, approximately 1500 FDA approved drugs
available from the Johns Hopkins Chemical Compound library is used
to determine how they cluster in the poised realm. Specifically,
the position on the x-axis of the poised realm is determine using
methods described herein for each of the 1500 approved drugs. These
are in turn compared to a random library of compounds, such as
those available from compound databases (e.g., Beilstein) or from
the Murchison meteorite. The experiment can demonstrate whether
molecules having drug action cluster around a specific value on the
x-axis. For example, they may cluster around the critical point
discussed above.
[0178] Quantum Reservoir Computer
[0179] One embodiment utilizing a system operating in the poised
realm is quantum reservoir computer, which is an embodied quantum
variation of a classical reservoir computer known in the art. In
this embodiment, the nodes within the reservoir are physical
entities having at least one quantum degree of freedom that is
capable of coupling (e.g., via superposition of states) to quantum
degrees of freedom in other nodes in the reservoir. Unlike current
quantum computers that utilize qubits, a quantum reservoir computer
does not require that all elements (i.e., nodes) in the reservoir
be fully quantum coherent. Rather, the quantum parallelism in the
system is exploited in a self-organizing manner. Thus, the system
can, in some embodiments, operate at room temperature.
[0180] The reservoir of the quantum reservoir computer can be
viewed as a collection of weakly interacting discrete quantum
degrees of freedom. The reservoir may comprise any fixed number of
physical entities (referred to herein as "nodes") having at least
one quantum degree of freedom. In one embodiment, the nodes are
chromophores, which may including a biological chromophore such as
a photosynthetic unit (e.g., chlorophyll, with or without it's
accompanying antenna proteins), a non-biological organic
chromophore (e.g., highly conjugated organic compounds), or an
inorganic chromophore such as an inorganic metal complex. In one
embodiment, chromophores are selected having a relatively long, but
finite, coherence lifetime (e.g., as is found in chlorophyll).
[0181] In another embodiment, the nodes in the reservoir are spins
or magnetic moments. Any known spin or magnetic systems may be
used, including for example paramagnetic or ferromagnetic compounds
or nanostructures. In one embodiment, an artificial spin system
such as is the commercially available in the D-WAVE system may be
used, which utilizes superconducting current to simulate spins.
[0182] In some embodiments, the quantum reservoir can be tuned to
achieve a desired coherence time. For example, decoherence may be
added by applying a random noise potential. The system may be tuned
into the desired Poised-realm state by adjusting this potential.
This way, a quantum reservoir is realized that is not fully
coherent, but has a very long coherence time. Repeated measurements
of this system reset its quantum coherence, which decays very
slowly. Thus, this system can be kept coherent for a sufficiently
long time, so that superposition states stay alive for the time
intervals of single calculation steps.
[0183] The quantum degrees of freedom utilized in the reservoir may
be any degree of freedom that may be coupled between the nodes as
well as coupled to an input and output signal. Non-limiting
examples of quantum degrees of freedom include electronic
excitation states, quantum spin (e.g., electron spin and nuclear
spin), quantum angular momentum, and quantum linear momentum.
[0184] With reference to FIG. 8, a plurality of nodes 200 are
contained within or on a substrate 210. In some embodiments, the
nodes 200 are fixed in or on the substrate. For example, a glass,
silicon, or mica wafer may be used as a substrate 210 and the nodes
200 are adsorbed or deposited onto the surface of the substrate
210. In other embodiments, the nodes 200 are free to move within
the substrate 210. For example, in some embodiments, the substrate
210 may include a liquid medium within which the nodes 200 are
dispersed or dissolved. In some embodiments, the nodes 200 are
distributed in a regular array (such as by using established
microfabrication techniques). In other embodiments, the nodes 200
are randomly distributed.
[0185] In one non-limiting example, the nodes 200 are
photosynthetic units that are deposited on a mica substrate using
adsorption from solution. One such technique is described in
Scheuring et al., The EMBO Journal (2004) 23:4127-4133, which is
incorporated herein by reference in its entirety. In this
technique, cell membranes containing photosynthetic units from
Rhodospirillum photometricum are dissolved into dodecylmaltoside
solution. The resulting extract is placed on freshly cleaved mica
using an adsorption buffer drop. The resulting structure includes a
plurality of photosynthetic units distributed across the surface of
the mica.
[0186] The quantum reservoir described above may be used to build a
non-algorithmic computational architecture based on the principles
of neural networks, such as echo state networks or liquid state
machines. The general idea is (i) to drive a random, large, fixed
quantum recurrent neural network with an input signal, thereby
inducing in each node within the reservoir to produce a nonlinear
response signal, and (ii) produce a desired output signal by a
trainable linear combination of all of these response signals.
[0187] In some embodiments, the input signals comprise a quantum
driving force that couple to one or more quantum degrees of freedom
of the nodes 200. Non-limiting examples of suitable input signals
include photons, electrons, and electrical or magnetic fields. In
one embodiment, the input signal is supplied to all nodes 200. For
example, with reference to FIG. 8, a laser 220 may send laser
pulses 240 of appropriate frequency to couple to a quantum degree
of freedom in the nodes 200.
[0188] To translate a real-world classical input to the quantum
mechanical input signal 240, an input processor module 250 may be
provided. This module comprises a traditional algorithmic computer,
such as a general purpose computer, that receives a classical input
signal 260 and drives the input signal generator (e.g., laser 220)
based on the classical input signal 260. For example, a
time-varying analog electrical signal may be provided to the input
processor module 250, which then translates that signal into
appropriate time-varying driving of the signal generator 220. Thus,
a time-varying classical input 260 results in a time-varying
quantum input signal 240 being supplied to the nodes 200. For
example, time-varying current or voltage may be provided to the
input processor module 250, which then drives laser 220 to produce
a corresponding time-varying change in pulse frequency, light
frequency, or intensity of laser light 240 being supplied to the
nodes 200.
[0189] In response to the quantum stimulation and the quantum
coupling of the nodes 200 to each other, nodes 200 may radiate out
a quantum response signal, such as scattered photons. Each node 200
can radiate an output signal and that signal may radiate in
multiple directions. Some embodiments provide a detector 270 that
detects the time-varying output signals 280. In the case of
scattered photons, the output signals may be detected using
photodetectors or a spectrometer. In some embodiments, the detector
270 includes an array of subdetectors in order to detect output
signals 280 emitted in different directions. Other suitable
detectors may include a nuclear magnetic resonance detector or an
electron paramagnetic detector.
[0190] The result of the detection described above is a plurality
of time-varying output signals. The multiplicity of the signals may
be provided by detecting the time variation of a variety of
parameters, such as the time variation of a plurality of
frequencies of scattered photons or the time variation of photons
scattered in a plurality of directions. The plurality of output
signals may then be relayed to an output processor module 290. The
output processor module 290 applies weights or other signal
processing algorithms to the plurality of output signals to produce
a single output signal 300. This module comprises a traditional
algorithmic computer, such as a general purpose computer, that
receives the plurality of output signals from the detector 270 and
calculates the output signal 300.
[0191] The weights or other signal processing algorithm used to
derive the output signal 300 from the plurality of outputs 280
produced by the nodes 200 may be determined using one or more
training procedures, such as is known in classical reservoir
computing. One example of such a training method is depicted by the
flowchart in FIG. 9. At block 400, a time-varying input signal for
which there is a known, desired output is provided to the quantum
reservoir as discussed above. At block 410, a plurality of
time-varying output signals is received by a detector as discussed
above. These signals as well as the desired final output are sent
to the output processor module. The output processor module
determines a weighted combination or a set of weighted combinations
of the plurality of output signals that will produce the desired
final output. In one embodiment, the weighted combination of
outputs is a linear combination. In other embodiments, more
complicated functional forms are utilized. In some embodiments, the
output processor module determines the optimal functional form.
Once a suitable combination is determined that produces the desired
output, the corresponding weights are stored in memory.
[0192] At block 440, it is determined whether there is any
additional training data (i.e., another known input-output
combination). If so, the procedure returns to block 400 for input
of the additional data. When block 420 is reached, the appropriate
combination weights are determined that produces the desired output
that is also consistent with all previous training data. The new
weights are updated into memory at block 440. If no more training
data is supplied, the procedure proceeds to block 450, where a set
of input data having no known output is supplied to the quantum
reservoir. The stored combination weights are applied to the
plurality of output signals in order to produce the final
output.
[0193] In one non-limiting example, the above described quantum
reservoir computer may be implemented using a simulated spin
system, such as provided by D-WAVE. The commercially available
D-WAVE computer contains a plurality of qubits consisting of
superconducting currents that simulate spin. The inputs and outputs
are electrical current. In its intended mode of operation, the
D-WAVE computer operates using only fully quantum coherent qubits
and non-time-varying input (i.e., a traditional quantum computer
approach). However, in the present context, all simulated spins,
including those that are not fully quantum coherent are used as
nodes for the quantum reservoir. Furthermore, a time-varying input
signal and plurality of output signals is provided. With a proper
J.sub.ij and h.sub.i set, the D-Wave Hamiltonian:
Hp = i = 1 N h i .sigma. i 2 + .SIGMA. i , j J ij .sigma. i 2
.sigma. j 2 , ##EQU00019##
can be guided through a finite size version of the metal-insulator
transition. At various low temperatures, the interplay of thermal
decoherence and the spectrum can be determined to achieve the
properties necessary for use as a quantum reservoir.
[0194] Trans-Turing Machine
[0195] In What Is Life, 1944, E. Schrodinger guessed that genes
would be "solids" with quantum mechanical chemical bonds, and for
our purposes now, guessed that the gene would not be a periodic
crystal, for these were "dull" but would be an aperiodic crystal
that contained a microcode for the organism. DNA is exactly such an
aperiodic crystal. The microcode does not "describe" the generation
of the organism or its maintenance, but accomplishes these by
organized behaviors of matter and energy coordinated by the
"information" in the aperiodic crystal, plus, as it turns out, the
entire cell as an open far from equilibrium thermodynamic
system.
[0196] The information is "embodied" and culminates in building and
maintaining an organism.
[0197] The embodied sense of information in Schrodinger's statement
may be contrasted with Shannon and Kolmogorov information. The
former consists in the entropy of an ensemble of messages, in some
finite alphabet, in a Source. The latter is the shortest program
that will output a given sequence of symbols in a prestated
alphabet. Both Shannon and Kolmogorov information measures tell us
how much information we have, but not what information "is." All we
have is syntax. Nor is there, by design, any "coming into being" of
the information in question, nor any semantics of that information
on Shannon or Kolmogorov. Thus, Shannon and Kolmogorov information
is not embodied, is free of matter and energy, free of specific
classical physics causal consequences that may be biologically
functional in a cell or organism, and seems to float in the air, a
third constituent of the universe with matter and energy.
[0198] In contrast, Schrodinger's sense of the aperiodic crystal
containing a microcode for the organism has within it in an
unarticulated way, the ideas of the processes engendered by the
microcode, (plus the cell as an open thermodynamic system), hence
the semantics of the code, that is, the specific processes, whether
quantum, open quantum, poised realm, or classical specific causal
consequences, it engenders. More, matter and energy are explicit in
the processes engendered by the microcode. Information on a
Schrodinger sense is embodied with matter and energy, not floating
free as a third constituent of the universe.
[0199] The essential feature of the aperiodic crystal is broken
symmetries, as in the DNA molecule with its essentially arbitrary
sequence of bases, A,C,T,G along the aperiodic double helix.
[0200] Information in an aperiodic solid or any system combining
quantum, classical and Poised Realm processes, is typically, but
not always, embodied in the broken symmetries of the system. In
particular, it is the broken symmetries of the Hamiltonian of the
classical, poised realm and the quantum systems with its classical
physics borne Hamiltonian which may have many broken symmetries,
which embody information, classical, Poised Realm, and quantum
matter and energy, with a semantics that is the processes that are
enabled by the constraints contained in the Hamiltonians (or other
constraints in the dynamics of the classical, Poised realm and
quantum degrees of freedom). More these broken symmetries
constitute constraints on the release of energy. But "work" is the
very constrained release of energy into a few degrees of freedom,
(Atkins). Thus classically, this constrained release of energy is
work, not heat or entropy. This information has a fundamental
semantics in engendering processes that carry out thermodynamical
work. Such processes underlie any system capable of complex,
diverse organized behavior built from a series of classical actions
serving specific useful purposes, however defined. (We turn to
candidate definitions of "useful purpose"="function"="task" below.)
The information or code engendering such processes has an embodied
meaning in this sense of purposeful (e.g. in terms of survival and
reproductive success) systems performing classical actions, quantum
and Poised Realm behaviors. A code has to endogenously engender
these classical actions (e.g., DNA), by constraining the flow of
matter and energy, to be embodied information. The reason we stress
"classical behavior" is the fact that as quantum or Poised Realm
quantum amplitudes propagate, nothing "real" happens in the "real
classical world."
[0201] The philosopher Immanuel Kant defined an organized being as
that in which the parts exist (in the universe) for and by means of
the whole, and the whole exists for and by means of the parts. A
simple example is a collectively autocatalytic set of peptides, a
concept invented in 1971 by Kauffman ( ) Gonen Ashkenazi at Ben
Gurion University in Beer Sheba Israel has a nine peptide (small
protein) collectively autocatalytic set. No peptide in the set
catalyzes its own formation. Rather, each peptide catalyzes the
formation of one or more other peptides among the nine peptides
from fragments of those peptides. The nine peptide set achieves
autocatalytic "catalytic closure" because all the nine peptides
have their formation from their fragments catalyzed by at least one
of the nine peptides in the nine peptide set. Catalytic closure is
precisely an example of Kant's Organized being. The parts exist (in
the universe) for and by means of the whole nine peptide
autocatalytic set, and the whole collectively autocatalytic set
exists for and by means of the parts. Call such a Kantian system,
"Autonomous". Given an autonomous system we can define the function
of a part by the role it plays in sustaining the existence of the
whole in the universe. Note that the explanatory arrows from upward
from the parts to the whole, and downward from the whole to the
parts whose behaviors the whole organises.
[0202] Given an autonomous system a natural sense of
purpose=function=task is given by those quantum, poised realm,
and/or classical consequences of the parts that sustain the whole
in existence in the universe. Note that the function of the heart
is to pump blood, not make heart sounds or wiggle water in the
pericardial sac. Similarly, the function of one of the nine
peptides is to catalyse the appropriate reaction, not wiggle water
in the medium. The function of a part is a subset of its
consequences, only definable as above. Given the concept of
autonomy, we can see part of the reason Shannon and Kolmogorov
information are inadequate if powerful. They are syntactic only,
have no specific causal consequences associated with the bits in
the bit string, thus CAN have no function in sustaining the
autonomy of a system that gets to exist in the universe. We will
use autonomy with Trans-Turing systems below as one means to solve
the famous Frame problem of computer science.
[0203] Thus, ultimately for the information to have effects in the
decoherent "real world", some variables of a quantum, Poised Realm,
and/or classical system must ultimately become classical.
[0204] The complex Hamiltonians available in Poised Realm Systems,
open to quantum, Poised Realm and classical inputs and acting on
their worlds via quantum, Poised Realm and classical outputs, are
constraints that can have many broken symmetries so contain a great
amount of embodied information enabling a high diversity of
quantum, poised and classical information processing and acting in
the world of the system.
[0205] We show below that such a system is not a universal Turing
Machine, nor a classical "machine," but much richer.
[0206] First we begin with a seminal paper by Dennis Salahub and
coworkers, (JACS) that is a first major step toward Trans-Truing
systems. de la Lande, JACS (2011) 133:3883-3894, incorporated
herein by reference in its entirety. Salahub et al. considered a
simple system of many nuclei and electrons in two potential wells,
(FIG. 6 in Salahub). Here the X axis is a reaction coordinate. The
Y axis is energy. Two potential wells, A and B lie in this plane,
and overlap, the right hand ascending branch of the A well crosses
the left hand ascending branch of the B well. The nuclei are at
this crossing in the initial state, called the "seam region" and
consist in a superposition of states, A and not A, B and not B.
Nuclei are heavier than electrons, so, using a version of the
Lindblat operator, the nuclei decohere to classicity rapidly and,
essentially at the same time, fall either into well A or well B.
They have passed from quantum superpositions to classical nuclei in
one of two displaced potential wells. The immediate consequence is
that the electron cloud responds DIFFERENTLY according to whether
the nuclei have decohered to well A or to well B. Thus, as we claim
in general for Trans-Turing Systems, as some quantum degrees of
freedom decohere to classicity, (or are measured), that ALTERS the
behavior of the remaining quantum degrees of freedom. This is an
essential step toward Trans-Turing systems.
[0207] Note next that in a slightly more refined model, the many
nuclei would decohere to classicality in some temporal order and,
say, spatial relation. The result is that the now increasing number
of classical nuclei will have an ever changing classical
Hamiltonian as additional nuclei become classical and interact with
one another dynamically, ignoring or not the electron cloud. Thus
in a Trans-Turing system, as quantum degrees of freedom decohere to
classiciality, or are measured, the classical Hamiltonian changes
and exhibits NON-Random Behavior. But that non random behavior IS
the classical system itself behaving under the ever changing
Hamiltonian, which may move the system on the X axis. In turn, as a
generalization of the fact that decoherence into well A versus well
B alters the effects of the nuclei on the electron cloud, the
behavior of the many nuclei in possible temporally altering
behavior, non-randomly alters the effects on the quantum degrees of
freedom. Then in the Poised Realm, some of the quantum degrees of
freedom can be in superposition states, hence exhibit constructive
and destructive interference. By our discussion above, high
amplitudes, or amplitudes with high energy and moduli,
preferentially decohere. Or, if quantum measured, by the Fermi
Golden rule, high amplitudes preferentially are measured. In either
case, the altered quantum behavior via constructive and destructive
interference and by the Born rule for pure or mixed states, has the
consequences that non-random changes are made in which quantum
degrees of freedom decohere or are measured and become classical in
the next short time interval. In turn this again alters the
classical Hamiltonian via the newly classical degrees of freedom,
which again alters the quantum and Poised Realm degrees of freedom
hence which amplitudes decohere to classical behavior or are
measured to classical behavior preferentially next. Conversely,
REcoherence of classical degrees of freedom, without limitation by
driving with a laser light, alters which classical degrees of
freedom become quantum, thereby altering non-randomly the classical
Hamiltonian and altering non-randomly the consequent poised realm
open quantum behaviors and quantum behaviors of the Trans-Turing
system.
[0208] The above is the heart of a Trans-Turing System. Its
behavior is NOT determinant, for either by superposition and
constructive and destructive interference plus decoherence
preferentially of high amplitude modes with large moduli, or their
preferential measurement via the Golden rule, the system is
non-determinate. Thus the Trans-Turing system is not algorithmic.
But it is also, in its global behavior, non-random. So the behavior
is not standard closed quantum system quantum random as in the
Schrodinger equation and von Neumann axiomatization of quantum
mechanics. The Trans-Turing system is entirely new.
[0209] In one embodiment, there are six criteria for a system to
exhibit Trans-Turing behavior. First, the system contains quantum
degrees of freedom propagating in short lived superposition states
that decay rapidly due to decoherence. But these short lived
superposition states undergo constructive and destructive
interference and will be one basis for a NON-Determinacy in the
Trans-Turing system when coupled to decoherence to classicality for
all practical purposes, FAPP, or quantum measurement.
[0210] Second, either via decoherence or motion out the X axis or
both, quantum degrees of freedom become classical FAPP or via
quantum measurement, become classical "Simpliciter". Both
decoherence and measurement are acausal and yield the
non-determinant behavior of the Trans-Turing System.
[0211] Third, there are, in addition, coupled classical degrees of
freedom in the TTS.
[0212] Fourth, when quantum degrees of freedom, and either
superposition states or pure states become classical FAPP, or are
measured, that ALTERS in different specific ways the effects of the
now classical degrees of freedom on one another, thus alters the
non-random collective dynamics of the coupled classical degrees of
freedom. In turn this altered non-random classical behavior alters
non-randomly the behavior of remaining quantum degrees of
freedom.
[0213] Fifth, in turn this non-random alteration of the behavior of
the remaining quantum degrees of freedom alters non-randomly which
of the open quantum degrees of freedom decohere or move out the X
axis to classicality FAPP. In particular, higher quantum amplitudes
tend to decohere with higher probability. So non-randomly altered
quantum behavior, including altered constructive and destructive
interference, alters non-randomly which amplitudes become higher,
thus alters non-randomly which amplitudes decohere to classicality
FAPP.
[0214] Sixth, in turn, classical FAPP degrees of freedom can
recohere, for example, driven by a coherent electromagnetic field
whose intensity and period distribution can be tuned non-randomly
thereby injecting information. The recoherent degrees may achieve a
new controlled superposition state, thereby altering non-randomly
the constructive, destructive, and pure states behaviors among
themselves and other quantum amplitudes, thereby non-randomly
affecting which amplitudes achieve higher amplitudes and tend to
decohere, and also non-randomly altering the behaviors of the
coupled classical degrees of freedom in the TTS.
[0215] Evolution itself indicates that Trans-Turing systems are
fully feasible. Mutations in evolving organisms can be quantum
indeterminate. Yet evolution in the 11 fold evolution of the eye,
the convergence of octopus and human camera eye, the convergent
evolution of marsupials and mammals seen in the Tasmanian wolf and
mammalian wolf, the streamlined forms of the porpoise and shark,
all say evolution by natural selection is strongly NON RANDOM.
Thus, the twin pillars of XX century physics, quantum mechanics
with its von Neumann measurement Born rule randomness, and Newton's
and Einstein's classical physics, literally demonstrates that the
evolution of the biosphere itself is not determinate, hence not
algorithmic, but not random. So too, the Trans-Turing System. At
last we can move beyond the classical physics, algorithmic, Turing
machine.
[0216] Trans-Turing Information Processing and Acting by Poised
Realm Systems.
[0217] A Universal Turing Machine consists of an infinite tape a
finite alphabet of discrete symbols written on discrete squares on
the tape, a finite set of discrete states in a reading head. At
each instant, the head is located over one square on the tape. It
responds to the symbol on the tape and its internal state by
staying in place, moving one square to the left, or one square to
the right. It then, depending upon the symbol it read, and its
internal state, erases the symbol on the tape below it and writes a
symbol, changes from its internal state to one of its internal
states, and iterates. All digital algorithms in all computers are
based on the Universal Turing Machine.
[0218] A critical feature of the Universal Turing Machine is its
absolute definiteness. Given an input symbol and a state at a
position of the reading head on the tape, the entire future
behavior of the system is definitely determined. Despite the famous
halting problem, known in the art, the system is algorithmic,
definite and an abstraction of a perfect mechanical classical
machine.
[0219] A second class of computers are classical analogue
computers, where, for example, electric circuits mimic the water
flow in a system of pipes. These systems are entirely classical if
also sometimes chaotic. They may exhibit epistemological
indeterminism in that we do not know the initial state with
infinite accuracy, but not the ontological indeterminism of quantum
mechanics, the Poised Realm, and Trans-turing systems via
decoherence to classicality or quantum measurement of open quantum
and Poised realm systems.
[0220] It will be clear to those of ordinary skill in the art, that
the Poised Realm Systems in described here are neither universal
Turing machines, nor classical variable analogue computers. Rather
Poised Realm Systems utilize quantum, Poised Realm, and classical
degrees of freedom, along with exogenous quantum, Poised Realm, and
classical inputs and outputs from and to the environment. The
quantum degrees of freedom in the Poised Realm are not limited in
any way to quantum COHERENT qubit realizations of Universal Turing
Algorithmic Machines as in conventional quantum computers. Rather
the quantum degrees of freedom create simple or complex quantum
wave patterns, standing or propagating, and, in the Poised Realm,
exhibit both superpositions and a finite number of amplitudes with
finite positive moduli which can become classical degrees of
freedom by decoherence or measurement and can recohere to quantum
behaviors, pure or superposition states.
[0221] Constructive and destructive interference occurs among the
quantum degrees of freedom whether fully coherent, or Poised Realm
amplitudes. As described, the sensitivity to decoherence increases
with the energy of an amplitude of one or many single or entangled
quantum degrees of freedom. In short quantum and Poised Realm
amplitude wave crests of amplitudes peak and are likely to decohere
to become classical degrees of freedom.
[0222] As used herein, the phrase "bright idea" refers to quantum
waves whose amplitude moduli are sufficiently great that they have
a high probability of decohering to classical degrees of freedom,
and thereafter modifying the Hamiltonians governing the classical
and quantum behaviors of the system.
[0223] The consequence of one bright idea decohering to classicity
and modifying the Hamiltonians of the quantum, Poised Realm, and
classical system, together with the quantum, Poised Realm and
classical inputs to the system, will be a succession of bright
ideas and modifications of the classical and quantum Hamiltonians
of the Poised Realm system. This dynamics is neither quantum nor
classical, neither determinate, hence not algorithmic, nor random.
The Hamiltonian keeps changing as quantum or Poised Realm degrees
of freedom become classical and classical ones become Poised Realm
or quantum coherent.
[0224] These changes in the Hamiltonians can move the Poised Realm
system on the x-axis from order to criticality to chaos and back,
by its own endogenous dynamics and as driven by quantum Poised
Realm, or classical inputs. Or alternatively, alteration in the
quantum network structure of components of the system can move it
on the x-axis either from quantum Poised Realm behavior to
classical behavior without movement on the y-axis, or with movement
on the y-axis as sensitivity to decoherence and recoherence stimuli
and noise change.
[0225] We discuss next entanglement among quantum and poised realm
degrees of freedom and how the behaviors of those degrees of
freedom can be correlated with the "outside world" via the, in
general, shaped potential wells, created by the classical degrees
of freedom of the system. First quantum entanglement and nonlocal
EPR correlations are fully established. We propose use of fixed or
SHIFTING patterns of entanglement among quantum and poised realm
quantum degrees of freedom in one or a SET OF INTERACTING AND
COUPLED TRANS-TURING SYSTEMS. Such entanglement may be achieved by
any means known or discovered in the art, including infrared photon
couplings among generalized chromophores within one or a set of
Trans-Turing systems. Entanglement means that the quantum degrees
of freedom are a SINGLE CORRELATED SYSTEM. Hence, with quantum
measurement, the measured quantum degrees of freedom of the
entangled quantum degrees of freedom ARE correlated and violate
Bell's inequalities. Recent results demonstrate that the more
degrees of freedom are entangled the GREATER IS THE CORRELATION, in
dramatic opposition to the familiar curse of dimensionality in
classical physics. Thus either measurement of a plurality of
entangled poised realm or quantum degrees of freedom yields a
HIGHLY CORRELATED SET OF NOW CLASSICAL DEGREES OF FREEDOM ENABLING
COORDINATED ACTION BY THE TRANS-TURING SYSTEM INVOLVING MANY, NOW
CLASSICAL, DEGREES OF FREEDOM COUPLED TO ONE ANOTHER AND STABLY
CLASSICAL DEGREES OF FREEDOM WITHIN THE TRANS-TURING SYSTEM.
[0226] As is know in the art, study of random Boolean networks,
RBN, and threshold networks demonstrate a classical physics order,
criticality chaos transition. The discrete analogue of the Lyapunov
exponent, called the Derrida Curve, shows convergent flow in the
ordered regime, neither convergence nor divergence at criticality,
and divergent flow in the chaotic regime. We believe the same
results hold true for Hamiltonian systems of many nonlinearly
coupled variables on the X axis. It is of deep importance that
critical RBN show maximum diversity in their behavior as measured
by SET COMPLEXITY, ( ) a power law distribution of "avalanches of
dynamical change" when a single variable is transiently altered,
which allows maximum controlled communication across a network of
many variables without tipping into uncontrollable chaos where any
noise discoordinates behaviors, yet maximizes useful discrimination
of past events. Critical classical systems are optimal with respect
to the capacity to classify environments and act reliably in the
presence of noise. We propose that single or man coupled CRITICAL
Trans-Turing systems, including coupled by entanglement, will
allow, after decoherence to classicality or measurement, wide
correlation among many now classical degrees of freedom. But more,
because these systems are critical with respect to classical
behaviors, the richest, most diverse, and coordinated actions and
discriminations can occur in such systems.
[0227] Further, in the Poised Realm, critical systems exhibit
fractal amplitudes which, we believe, for a multiparticle system,
may also allow maximal Poised Realm coordination of, for example
and without limitation, entangled quantum and Poised Realm degrees
of freedom in one or a plurality of coupled Trans-Turing
systems.
[0228] Because critical Poised Realm systems resist decoherence
best via power law decoherence rather than exponential, they
should, by the Fermi Golden rule, or preferential decoherence of
high modulus amplitudes, tend to transfer quantum energy to
classical energy efficiently.
[0229] Consider a classical particle in a box. If we measure its
position and momentum we know nothing of the shape of the box! But
a quantum wave process in a potential well "knows" in an analogue
embodied sense, the boundary conditions constituted by the
potential well. This may show up, without limitation, in the eigen
values of its energy levels. Thus quantum wave processes, and
Poised Realm quantum wave processes in a classical potential, know
the `CONTEXT" OF THAT POTENTIAL.
[0230] Now consider the contrast of a digital representation of
music in a room by dividing the room into tiny volumes and using a
bit series to represent the music, versus a set of 1000 differently
shaped drum heads well placed in the room, so "tuned" to sense the
music in the room by their joint patterns of vibration, i.e. the
eigenfunction modes of the drum heads. But the drum heads are not
coupled. Now consider a plurality of entangled quantum or poised
realm degrees of freedom which decohere to classicality or are
measured. They ARE ONE quantum state, they "know" their classical
potential surface context. Now, if that surface is tuned to reflect
and span the outside world in some more or less organized way, the
measured or decoherent hence now classical degrees of freedom "know
the "outside world".
[0231] The next step is to realize that the decoherence to
classicality or measurement process, in reflecting the classical
Hamiltonian of the classical degrees of freedom is both the TUNING
OF THE QUANTUM WAVE FUNCTIONS to the world outside, like the drum
heads, but also the Measurement" bias provided by the classical
Hamiltonian of the system as a "measuring instrument. The resulting
classical degree of freedom of a single or many entangled degrees
of freedom is "the answer", as is a pointer reading in a standard
quantum measurement. We will use this below to attempt to solve the
Frame problem in algorithmic Turing systems.
[0232] It will be clear to those of ordinary skill in the art, that
movement of the Poised Realm System only on the x-axis altering the
quantum network structure, or in any other way noted above or more
generally, can result in quantum, and quantum Poised Realm degrees
of freedom becoming more or entirely classical, thereby altering
the quantum network and further modifying the position of the
Poised Realm system on the x-axis, and by becoming classical, these
degrees of freedom can also alter the Hamiltonians of the
classical, quantum and Poised Realm degrees of freedom, again
inducing motion on the x-axis by endogenous or input driven
signals.
[0233] Because of quantum, Poised Realm and classical outputs of
the system to the environment, actions will be taken by the Poised
Realm system on its world, by virtue of the Poised Realm system and
the quantum, Poised Realm, and classical input "information" it
receives. Thus, the Poised Realm system is an embodied, non-Turing,
non-determinate, non-algorithmic, non classical non-random
analogue, information processing and acting system that embodies
information "analysis," action, and information within the Poised
Realm System enabled by the symmetries and broken symmetries of its
Hamiltonians, classical and quantum, quantum network structure and
driving by quantum or Poised Realm inputs which may move the system
on the x and y axes. The broken symmetries of the Hamiltonians can
constitute the "tuning" of the quantum "drum heads" if tuned by
coupling to the outside world, in one or a plurality of
Trans-Turing systems.
[0234] Because the classical variables of the Poised Realm system
may be endERGONIC or exogONIC processes, these may, in general, be
linked into work cycles. Poised realm systems can "build things" by
being capable of carrying out thermodynamical work in the context
described above.
[0235] Design and Evolutionary Selection of Desirable Poised Realm
Systems.
[0236] Consider first the simulation by digital computers with
algorithms, of Poised Realm systems with desired inputs and with
outputs. One use of such algorithms is to design Poised Realm
systems with input output behaviors that are desired, in rough
parallel to the fully computerized design process of the 777 Boeing
jet. A second broad application of such algorithms is in any of the
many evolutionary selective algorithms that operate on a given
algorithmic representation of the behavior of a Poised Realm
system, and makes any kind of use of any kind of "heritable
variations" and selection of the behaviors of such Poised Realm
systems to achieve input/output and internal behaviors that are
desired. For example, on rugged fitness landscapes, "long jumps" by
big mutations are preferable when fitness is low, but local
variations are more effective when fitness is high, in speeding
evolution and avoiding trapping on poor local optimal. Genetic
Algorithms are just one such evolutionary algorithm known in the
art. But algorithmic Turing simulations cannot constitute the real
behavior of a Trans-Turing system, for Turing systems are classical
physics and Trans-Turing Systems are not.
[0237] A broad second way to design or evolve desired Poised Realm
systems uses without limitation, liposome vesicles with chemical
reactions, and chemical constituents in its interior and exterior
milieu. With reference to FIG. 10, liposomes contain phospholipid
molecules 700 that organize into a bilayer that forms a vesicle
with aqueous regions on the inside and outside of the bilayer.
Included herein are both unilamelar and multilamelar vesicles. In a
Trans-Turing system, the vesicles comprise chromophores 710,
including generalized chromophores defined above, in the broad
sense (e.g., including chromophores coupled to one another) by
binding to beta barrels or other bilipid spanning molecules in the
liposome membrane so that the chromophores are inside, or outside
or both, of the liposomes and can communicate by broadcast or more
specifically with one another, quantum, Poised Realm and classical
inputs. The quantum and poised realm degrees of freedom within one
liposome or a plurality of liposomes constituting a Trans-Turing
system or plurality of such systems may or may not be entangled, as
described above. The vesicles can be divided in any way to daughter
vesicles with or without replenishment of chemical constituents,
and selected for desired Poised Realm behaviors as embodied
physical systems. Such systems are both embodied, not
representational as are Turing systems, achieve functional closure
as autonomous systems, and thus are not simulated on an algorithmic
computer, but are embodied systems that exist and behave in the
universe.
[0238] Generally, to form liposomes with proteins embedded in the
bilipid layer a further classical approach is to isolate the
protein of interest (generally overexpressed) from living cells, by
destroying the cell integrity. Integral membrane proteins are
associated to membranes which are broken during the cell
destruction but reseal to form lipid vesicles (containing membrane
proteins) or membrane fragments.
[0239] At this point these membranes (containing proteins) are
solubilized with excess detergent and sometimes a synthetic lipid
(e.g. POPC) to form mixed micelles (detergent+cell
lipids+POPC+membrane proteins). In each concrete case, it is
routine to find the best detergent for solubilizing the protein
without destabilizing its 3D structure and interaction with very
proximal lipids. Typical examples are sodium cholate, and
octyl-glucoside, digitonin, dodecyl maltoside, and
Triton-X-100.
[0240] Now the detergent can be removed by dialysis or gel
filtration chromatography or adsorption on biobeads or simply by
dilution. Detergent is preferentially removed due to its higher
solubility in water. The product are lipid vesicles (possibly
containing some cell lipids) containing the protein of interest.
The typical size is 50-100 nm. But the presence of the protein can
affect the size. These integral-protein-containing liposomes are
called "proteoliposomes". The procedure to prepare liposomes in
this way is called "detergent depletion method".
[0241] At first approximation, proteins are oriented 50% inward and
50% outward, so for every vectorial application, 50% of protein is
not active.
[0242] Further discussion of liposome manufacturing techniques
suitable to make the structures described herein may be found in
Silvius, J. R. (1992) Solubilization and Functional Reconstitution
of Biomembrane Components. Annu. Rev. Biophys. Biomol. Struct. 21,
323-348 and J.-L. Rigaud, B. Pitard, D. Levy. Reconstitution of
membrane proteins into liposomes: application to energy-transducing
membrane proteins. Biochimica et Biophysica Acta 1231 (1995)
223-246, both of which may be incorporated herein by reference in
its entirety. Examples are described in: Goodwin M g, Jackson J b,
Electrochromic Responses Of Carotenoid Absorbency Bands In Purified
Light-Harvesting Complexes From Rhodobacter-Capsulatus
Reconstituted Into Liposomes, Biochimica Et Biophysica Acta Volume:
1144 Issue: 2 Pages: 191-198 Published: SEP 13 1993; Jackson Jb,
Goodwin Mg, Electrochromic Responses Of Bacteriochlorophyll
Absorbency Bands In Purified Light-Harvesting Complexes Of
Rhodobacter-Capsulatus Reconstituted Into Liposomes, Biochimica Et
Biophysica Acta Volume: 1144 Issue: 2 Pages: 199-203 Published: SEP
13 1993; and Kobayashi M, Fujioka Y, Mori T, Terashima M, Suzuki H,
Shimada Y, Saito T, Wang Z Y, Nozawa T, Reconstitution of
photosynthetic reaction centers and core antenna-reaction center
complexes in liposomes and their thermal stability, Bioscience
Biotechnology And Biochemistry Volume: 69 Issue: 6 Pages: 1130-1136
Published: June 2005; all of which are incorporated herein by
reference in their entirety.
[0243] In order to make giant liposome vesicles, GVs, the vesicles
produced as above are dried over an electrode and after application
of alternate current, GVs are formed, and they contain the integral
membrane protein in the membrane. This is a variant of the
"electroswelling method". See Philippe Girard, Jacques Pecreaux,
Guillaume Lenoir, Pierre Falson, Jean-Louis Rigaud, Patricia
Bassereau, A New Method for the Reconstitution of Membrane Proteins
into Giant Unilamellar Vesicles, Biophysical Journal--1 Jul. 2004
(Vol. 87, Issue 1, pp. 419-429), which is incorporated herein by
reference in its entirety. Alternatively, the proteoliposomes
formed after detergent depletion can be lyophylized and hydrated
without stirring. This corresponds to a sort of "natural swelling"
method that should give protein-containing giant vesicles.
[0244] Liposomes can bud as is known in the art. By budding in the
presence of free and covalently anchored chromophores linked
thereby to betabarrel proteins in the aqueous medium or other
similar molecules, these chromophores will melt into the membrane
and become anchored there. Thus the density per liposome of
chromophores, and their spectral characteristics can be altered.
Since coupling of two chromophores depends upon emission of a
quantum by one chromophore whose size can be absorbed by the
second, tuning the chromophore absorption spectra and ratios in a
liposome partially controls the topology of the quantum network,
hence position of the liposome system on the x-axis.
[0245] Here, rather than using a genetic algorithm of any kind REAL
EVOLUTION of embodied liposomes coupled or not, or any other
embodied systems capable of any kind of reproduction, division,
heritable variation and selection after Darwin, can be used to
evolve desired input, Trans-Turing "computation" and output
behaviors, quantum, Poised Realm, and classical.
[0246] It will be clear to one of ordinary skill in the art that
one preferred embodiment of the current invention is able to evolve
a population of single or interacting Trans-Turing systems to
achieve with more or less success, a high diversity of success
criteria or figures of merit. In general, one approach to this is
to use any one or combination of the wide variety of known in the
art methods for evolution of such devices. The Holland Genetic
Algorithm and its many variants are but one set of examples.
[0247] In the broadest terms, the inputs to a Trans-Turing system
can be any single or combination of coherent quantum behaviors,
poised realm behaviors, or classical behaviors of single or many
degrees of freedom. The outputs can similarly be any one or a
plurality of quantum coherent, poised realm or classical degrees of
freedom. In general, only classical degrees of freedom, including
quantum measured degrees of freedom without their being a limiting
example, can serve as readily sampled outputs.
[0248] In general, the inputs to the quantum system will be
transformed into the outputs of the Trans-Turing system. The
Trans-turing system, may, like a feed forward neural net, have no
internal dynamical attractors including potential wells, or it may
have potential wells of the classical variables which are capable
of such behavior, without limitation, because they typically can
exhibit dissipative dynamics. These alternative attractors,
including without limit, potential wells, can be used to classify
diverse inputs, including those which are constant in time, into
the different attractors of the classical variables of the
Trans-turing system, where which attractor is attained for some
period of time depends in general on the initial state of the
Trans-Turing system as well as its inputs.
[0249] As an entirely non-limiting example of such input-output and
classification by a Trans-Turing system achieved by any form of
evolutionary search, we consider a Trans-turing system consisting
of a single liposome containing chlorophyll and surrounding antenna
proteins. As a non-limiting example, the antenna protein or any
other molecule like it, will float in the liposome lipid bilayer.
In general, rafting will occur bringing the diverse chlorophyll and
antenna proteins into proximity, for example without limitation by
van der Waals forces. In general any such molecule has a longer
axis. Without limitation, use red and green quantum dots or
fluorescent dyes to label the two defined "head" and "tail" ends of
the long axis of such a molecule as chlorophyll wrapped by the
antenna protein.
[0250] Then by any means known in the art, the orientation of any
two or more labeled chlorophyll and antenna proteins in the lipid
bilayer can easily be assessed by standard techniques. Thus, it
will be clear to those of ordinary skill in the art, that for a
plurality of two or more red and green labeled molecules, here,
without limitation, taken to be chlorophyll molecules each wrapped
by its labeled red and green antenna protein, the relative
orientations and distances among these molecules floating in the
liposome membrane can be assessed. These classical degrees of
freedom, without limitation, ca be taken as one possible out of
indefinitely many, classical "output variables".
[0251] We note that the success criterion, or "figure of merit" may
be a steady state of our output variables or any time varying
dynamical behaviors, and the input variables may be steady states,
time varying states, stationary statistical distributions or
non-stationary distributions. Here we consider the simplest case of
steady inputs and their mapping to steady outputs.
[0252] Without limitation, we take as a concrete example of input
variables two lasers with different wavelengths that shine on the
single liposome. The intensity ratio and wavelengths of these laser
lights can be taken as an input "spectrum". For N input laser
frequencies there is an N dimensional input space.
[0253] As a second classical variable input set we take sound
vibrations at two or more frequencies in which the ratio of the
power intensities of the different frequencies, and those
frequencies themselves can be changed to cover an N dimensional
input space for N input frequencies.
[0254] For either the quantum laser, or classical sound vibration
input spectrum, for each point in the N dimensional input space,
the relative orientations and distances of the red and green
labeled, without limitation, chlorophyll and antenna protein
complexes can be asses by light scattering, image analysis or any
other means including mathematical analysis of the orientations and
distances among the output red and green labeled molecules which
may raft together to various degrees in the bilipid layer.
[0255] A mapping from input space to the output variables whose
relative positions constitute an output space can now be
established.
[0256] Without limitation, it may be desired to achieve a
Trans-turing system that maps each point in the input space to a
unique point, bijectively, in the output space. Alternatively it
may be desired to "classify" subsets of the input space to the SAME
output point in the output space. In general this classification
can arise if the Trans-Turing system has attractors such as a
plurality of two or more potential wells that are expressed in two
different stable or statistically discriminable behaviors of the
output variables.
[0257] To achieve such a one to one bijective mapping, or a many to
one classification of the input space to the output space, a
diversity of evolutionary algorithms may be carried out.
[0258] Without limitation, let the Trans-turing systems above be
liposomes with controllable densities of chlorophyll and antenna
proteins dissolved in the bilipid layer, with additional classical
control parameters such as the hypertonicity or hypotonicity of the
medium leading to swelling or shrinking of the liposome, to a
diversity of lipids altering the physical-chemical characteristics
of the liposome bilipid layer and hence the rafting and other
behaviors of the chlorophyll and antenna proteins floating in the
bilipid membrane, hence their collective behaviors under van der
wal and other forces. Other classical inputs can be electric and
magnetic fields, temperature, pressure, and so forth.
[0259] Call these variables, which can be classical, quantum
coherent, or poised realm, the CONTROL PARAMETER SPACE. An
evolutionary search in this "control parameter space" is undertaken
by varieties of evolutionary algorithms, below, to "hill climb" to
points in the control space that optimize the desired input output
behavior of the Trans-turing systems to obtain at least one or a
plurality of Trans-Turing systems that performs as optimally as is
attainable given the complexity of the search space and ruggedness
of the resulting "fitness landscape" i.e. the distribution of the
desired behavior or "figure of merit" across the Control Parameter
Space. As is well known in the art, the success of evolutionary
search by variations alone or with any analogue of recombination,
depends upon the ruggedness of the "fitness landscape" for the
"figure of merit". In general, forms of recombination perform
poorly on quite or very rugged landscapes. Also, when fitness is
low, larger variations in Control space parameters followed by
smaller variations as fitness increases, can optimize evolutionary
search. In addition, the very process of evolutionary search can be
used to establish the statistical features of the fitness landscape
as is known in the art.
[0260] Using these parameters, let an initial population of,
without limitation, 1000 liposome Trans-turing systems be
constructed and tested individually for their input output mapping,
where the initial figure of merit of each liposome Trans-turing
system is established and correlated to the positions of each in
the Control Parameter space.
[0261] Again, without limitation, one or some plurality of the
fittest liposome Trans-Turing systems are used as seeds for a
second generation of liposomes. To be concrete, let, without
limitation, the 100 fittest liposomes be used as this seed. Then
construct from each of these 9 new liposomes differing from it at
defined distances in the Control Parameter space, with the
distances tuned to the current fitness and the ruggedness of the
landscape as it becomes established. This creates a second
generation of liposome Trans turing systems, here without any form
of recombination.
[0262] Iterate the above and assess the figure of merit for the new
second generation of liposome Trans-Turing systems, again pick the
100 best, and form a new 1000 liposome third generation. Iterate
this process as many times as desired, as fitness increases.
[0263] This is the core of an evolutionary search process, here
using liposomes as Trans-Turing systems, and so far without any
analogue of recombination.
[0264] Recombination can be implemented by taking two or a
plurality of members of the chosen seed set, here 100 liposomes,
and forming the new generation by considering the Euclidian or, for
discrete Control Parameters in the control parameter space, the
Normalized Compression Distance, between any two or any pair of
more than two members of the seed set. New points can be chosen at
any distance from any one liposome toward any other single or set
of liposomes in the control parameter space, by simple means known
in the art. This is a kind of "sharing of information" among the
seed set to form the next generation for evolutionary search. In
general, too much sharing is unfavorable on a rugged multipeaked
landscape where it may cause trapping of all on poor local optima.
Thus as the structure of the landscape is discovered using means
known in the art, by the evolutionary sampling process itself, the
preferred ratio of mere variation and "generalized recombination or
"sharing" can be tuned to optimally search the landscape.
[0265] By these means, for any input space, output space and figure
of merit, Trans-turing systems well adapted to any single figure of
merit can be attained.
[0266] More generally, there may be more than a single figure of
merit, where the relative importance of the different figures of
merit are unknown. Here the standard solution concept is "Global
Pareto Optimality", i.e. points in the Control Parameter Space
where no motion can occur that increases ONE figure of merit
without lowering one or more other figures of merit. Among such
Pareto optimal points, the global pareto optimal set is such that
no other Pareto optimal points are "better" on any of the figures
of merit that the Global Pareto Optmal Points. In general, each
figure of merit creates its own smooth or rugged fitness landscape,
and the search for global pareto optimal points can be difficult,
but in general is possible. A theorem proves that among the Global
Pareto optimal points, each global optima of any one of the figure
of merit fitness landscapes is one of the Global Pareto optimal
points. Thus if finding a global optimum of a single figure of
merit is feasible or even easy on smooth landscapes, finding some
Global Pareto Optimal points is readily achieved.
[0267] It will be clear to those of ordinary skill in the art, that
these evolutionary search processes can be used for any form of
Trans-turing system, whether liposomes, nanofabricated with
nanotubes or constructed in any other ways.
[0268] The same evolutionary search processes generalize to a
plurality of two or more Trans-Turing systems which are coupled in
any way, classically, by entanglement, or in other ways of coupling
quantum coherent degrees of freedom or poised realm degrees of
freedom. To use our concrete example of an output space generalized
to M liposomes, there is now an N.times.M input space and an
N.times.M output space, and an N.times.M Control Parameter space
for N control parameters per trans-turing system. The same
evolutionary procedures apply, with the figure of merit able to be
far more complex because it now involves possible steady state and
for any single Trans-Turing system or plurality of them, complex
classical, poised realm and quantum coherent behaviors.
[0269] Quantum dots, as known in the art, absorb and emit photons.
Large dots absorb in the red, small dots in the blue. So smaller
dot sizes changes the absorption spectrum toward shorter wave
lengths. Quantum dots have a number of higher excited states
emitting, by Fermi's Golden Rule, preferentially their largest
quanta as they fall from their higher energy states to their ground
states. This can allow quantum dots of different sizes to be
coupled by photon exchanges in liposomes or more generally in any
setting including nano-fabrication in Trans-Turing systems.
[0270] Similarly, quite subcritical chromophore coupled systems
with small trees will absorb and emit photons that are shorter
wavelength than larger trees closer on the x-axis to critical.
These absorption spectra can be tested. The distribution of tree
sizes in a liposome or on a nanodevice will tune the overall
connectivity of the entire system, hence position on the x-axis.
Again, the presence of multiple energy levels per quantum tree of
various tree sizes can allow the trees to communicate by emitted
and absorbed photons in a tunable way.
[0271] For liposomes, exposure to hypotonic and hypertonic
solutions will swell or shrink the liposome altering the proximity
of chromophores hence their photon mediated connectivity, hence
position on the x-axis. Swollen liposomes will be further left on
the x-axis than the same liposome if shrunk in a hypertonic
solution.
[0272] In one nonlimiting preferred mode of evolution of Poised
Realm systems, the liposome contains an autocatalytic set of
polymers and catalysts that catalyze a sequence of chemical
reactions to create the building blocks of the polymers Recent work
by Serra has shown that under these conditions, autocatalytic set
and liposome division SYNCRHONIZE, enabling the open ended
evolution demonstrated by Szathmary et al. in silico. This is a
generalization of Ashkenazi's nine peptide autocatalytic set, now
experimentally achieved. We will call such systems Poised Realm
Protocells, subject to heritable variation. Natural selection and
even co-evolution of such systems in defined or variable
environments can be carried out to achieve Poised Realm protocells
with desired input, output and internal behaviors. More, such
systems will interact not only by catalysis, but by myriad
classical causal features enabling Darwinian preadaptations and the
emergence of novel functions, as discussed by Kauffman in his books
Investigations and Reinventing the Sacred. Because these systems,
like evolution in general, marry quantum, poised realm, and
classical degrees of freedom, and are autonomous Kantian systems
with top down and bottom up causality, they escape mere
reductionism, and can show emergent behaviors. For example swim
bladders in some fish with a tunable ratio of air and water allow
neutral buoyancy in the water column. Paleontologists believe that
these arose as unused causal consequences of the lungs of lung fish
as Darwinian preadaptations, or exaptations. In Reinventing the
Sacred Kauffman shows that we cannot prestate the state space of
the evolving biosphere, hence further we cannot know the boundary
conditions on selection, so we cannot have entailing law. But more,
the swim bladder, which arose due to selection in a population of
fish for good function AS A SWIM BLADDER, HAD THE FURTHER PROPERTY
THAT, ONCE IT EXISTED, IT CONSTITUTED AN ADJACENT POSSIBLE EMPTY
NICHE. A bacterium might evolve only able to live in swim bladders,
like a bacterium only able to live in the lungs of sheep. BUT NOTE
THAT NO SELECTION AT ALL ACTED TO CREATE THE SWIM BLADDER AS A NEW
ADJACENT POSSIBLE EMPTY NICHE! The new empty adjacent possible
niche, "just arose". But this means something astonishing: the
biosphere is literally building, without selection, the very
possibilities it will become.
[0273] In an exactly parallel fashion, evolving and coevolving
Trans-Turing Protocells can and will undergo Darwinian
preadaptations and create "emergent" adjacent possible empty niches
for more such Trans-Turing Protocells. By these means, and those
below, the frame problem of Turing machines and computer science
can be solved: novel functionalities and solutions to problems can
be found under appropriate selective conditions.
[0274] It will be clear to those of ordinary skill in the art, that
any platform, beyond liposomes, that can hold "generalized
chromophores" in a changing or fixed spatial arrangement, can be
used. In particular, if these can grow and divide spontaneously or
non-spontaneously, and in any form undergo "heritable variations"
needed for evolution or even open ended evolution, populations of
Poised Realm Systems that can be selected for desired behaviors can
be obtained and evolved.
[0275] In addition to Trans-Turing protocells that can evolve, this
invention can be used in another way to evolve single or coupled
Trans-Turing systems for desired behaviors. Specifically,
Trans-Turing systems can be nanofabricated or micro or
macrofabricated. An evolutionary procedure can be carried out by an
embodied version of something like the Genetic algorithm, but,
because embodied, beyond it. Here a population of a plurality of
single or coupled Trans-Turing systems, without loss of generality,
nanofabricated ones, can be tested for a desired behavior. The best
one or a subset of the initial population can then be used in a
variety of ways to construct a second generation which might
include the best one or plurality of the first generation, and
small mutant variants of these Trans-Turing systems. Over a
succession of generations, as the evolve and by interacting with
one another, co-evolve, improve performance can be sought. Because
these systems are embodied and have real Poised realm and classical
consequences in the physical world, they evolve in it without
digitally representing that world, as in Turing machines and the
Holland Genetic algorithm. Thus, the famous and unsolved "frame
problem" which bedevils Turing systems, does not even arise for
these embodied systems, for they evolve without digitally or
algorithmically representing their worlds.
[0276] By use of direct design, the use of digital algorithms both
to simulate and evolve in silico, as described above, or
nanofabrication of embodied Trans-Turing systems, alone or coupled
sets of them, nanotechnology can design/evolve and co-evolve and
build Poised Realm devices with desirable properties, including
input and output behaviors that are trans-Turing in their
information processing. Such systems are not algorithmic in the
Turing sense, nor classical physics analogue computers which at
most have epistemological indeterminism via deterministic chaos,
while Trans-Turing systems have ontological non-determinism, yet
analyze input quantum, Poised Realm, and classical data, have
"bright ideas" that become classical degrees of freedom, alter
Hamiltonians or quantum network topology, hence position on the
x-axis by endogenous dynamics and due to quantum, Poised Realm, and
classical inputs, yield a sequence of bright ideas and sequences of
data analyses and quantum, Poised Realm, and classical actions on
the world by the embodied information processing, hence SEMANTIC
system. In one embodiment of this invention, Trans-Turing
Protocells are Kantian Organized Systems and achieve Kepa Ruiz
Mirazo's "autonomy" such that the parts exist in the universe for
and by means of the whole, and the whole exists in the universe for
and by means of the parts whose behaviors it organizes. We call
these "Autonomous Trans-Turing systems". They will be of use in
affording a natural definition below of R. Ashby's "Essential
Variables" as an internal goal state of a Trans-Turing system or
coupled set of Trans-Turing systems.
[0277] It will be clear now, that such novel systems exhibit
dynamics that are neither Schrodinger closed system quantum
mechanical, nor classical deterministic dynamics. THE SYSTEMS ARE
NEITHER DETERMINISTIC, hence are non-algorithmic, and are NOT
random. These Poised Realm Trans-Turing systems exhibit novel
dynamics allowing entirely novel information processing, internal
behaviors, and output behaviors among quantum, Poised Realm, and
classical degrees of freedom.
[0278] Embodied Poised Realm Systems can Form Communicating and
Acting Networks.
[0279] Poised realm systems, without loss of generality, liposomes
or nanotechnology devices, or otherwise, can form arbitrary
networks in which quantum or Poised Realm, or classical degrees of
freedom can be communicated between Poised Realm systems such that
they interact as a "community". Coupling can be by any means known
in the art, including broadcast, waveguides directing photons
emitted by one Poised Realm system and directed to one or a
plurality of other Poised Realm systems, use of quantum wires,
fiber optic cables, carbon nanotubes or any other means of
communication. As noted above the quantum and Poised Realm degrees
of freedom may be quantum entangled. More, recent work shows that
such an entangled system can alter which degrees of freedom are
entangled. Because quantum measurement or decoherence to
classicality constitutes the formation of correlated sets of now
classical variables via that entanglement, and the pattern of
entanglement can change, we can think of this as a kind of
"shifting of attention" by the Trans-Turing system or coupled set
of Trans-turing systems. After the entangled degrees of freedom
shift, a different set of quantum or poised realm variables become
classical with consequences for the coordinated behaviors of the
classical and Poised realm aspects of the system.
[0280] By such communication, communities of Poised Realm Systems
can perform tasks and information processing and acting that no
single Poised Realm system can attain.
[0281] More co-evolution and other "adaptive procedures" or
community assembly procedures, analogous to community assembly in
ecology, can be used to obtain Poised Realm communities with
desired properties. Among these may be a maximal power efficiency
per unit "fuel" or energy input to the Poised Realm devices, at a
finite displacement from equilibrium. Recent results suggest that
bacteria grow at a rate that maximizes biomass production per unit
fuel, here glucose, as input to the system. This picks a specific
displacement from thermodynamic equilibrium as optimal with respect
to power efficiency per unit fuel for such systems. We here
generalize this to Poised Realm systems performing any kinds of
tasks with optimum power efficiency per unit fuel.
[0282] Ecologists suspect a similar maximum power efficiency for
ecosystems. We can evolve communities of Poised Realm systems to
maximize a power efficiency per unit "input," energy, or
information as described below, or both or more general success
criteria.
[0283] As noted above, Critical Trans-Turing systems and either
preferential decoherence of high amplitudes to classical degrees of
freedom or quantum measurement and Fermi's Golden rule, coupled
with the mere power law decoherence of Critical poised realm
systems, implies that maximum power transfer from quantum to
classical degrees of freedom can be obtained. Maximum power
efficiency may be attainable.
[0284] Using Essential Variables to Enable Goal Behavior.
[0285] In Design for a Brain by Ross Ashby, 1960s, Ashby designed a
self-repairing algorithmic system, the homeostat. He considers a
system of N variables, discrete variables and discrete time. He
designates a subset, E<N, of these as "Essential Variables,"
each of which must be kept with "bounds" given the range of values
of each variables. Call this bounded region the "Alive Box." The
system must keep within the Alive Box. Note that in an Kantian
Autonomous system that gets to exist in the universe, the means of
parts and the whole by which the Autonomous system sustains itself
constitutes its Essential variables.
[0286] The N variables comprise a dynamical system with state cycle
dynamical attractors and basins of attractions draining into each
state cycle as is known in the art. See Kauffman's Origin of Order
as a nonlimiting example.
[0287] The system is released from an initial state, flows to an
attractor and either does or does not keep within the Alive Box. If
yes, the system remains in that attractor of the N variables. If
not, it reinitiates at a random state in the state space and flows
to an attractor. Again if the system stays within the Alive Box, it
remains in that attractor, if not the process is iterated.
[0288] If the system fails to remain in the Alive box after some
number of random initial states, Ashby implements a "step change"
in a parameter to one of the variables. This step change can change
the "phase space portrait" of where the basins of attraction and
attractors are located.
[0289] Again, the system is released from random initial states and
if it remains for one of these in the Alive Box, the system stops.
Otherwise after a number of initial states have been sampled, a
step parameter is again changed. The process is iterated until a
value of the parameters is found that allows at least one attractor
of the N variable system to keep within the Alive Box.
[0290] These ideas are fully applicable to Poised Realm systems. A
subset of the classical variables are designated as essential
variables.
[0291] In continuous nonlinear dynamical systems with attractors
and parameters, at a bifurcation point in parameter space, new
attractor(s) may appear, old ones disappear, and the locations of
basins of attraction draining continuous trajectories into
attractors may change.
[0292] In a Poised Realm System, the decoherence on the y-axis, or
motion on the x-axis, of a quantum degree of freedom to a classical
degree of freedom can operate on the Hamiltonian, or quantum
network structure of the classical and quantum systems as a
parametric bifurcation parameter. Indeed, continuous variation on
the y-axis from quantum to classical can act as a bifurcation
parameter as do motions on the x-axis or both the X and Y axes. In
addition, quantum or classical parameters can be changed. The
recoherence of a classical degree of freedom, or motion toward
order on the x-axis, can act as a bifurcation parameter to the
classical and quantum Hamiltonians. In addition, inputs, classical
or quantum, may drive the system between attractors or drive the
system so rapidly that attractors are not attained and maintained.
However, the average time spent in the Alive Box is always
definable.
[0293] To create a Poised Realm System "homeostat" we carry out the
processes noted above. The Poised Realm system keeps changing by
decoherence or recoherence of quantum or classical degrees of
freedom, or changes in classical or quantum parameters, or changes
in inputs, until the system maintains itself in the Alive Box.
[0294] This architecture endows the Poised realm system with
"primary drives", i.e., to keep within the Alive Box.
[0295] Choosing Essential Variables.
[0296] As noted above, choosing essential variables is not trivial.
In Poised Realm evolving protocells, examples of Kantian autonomous
Trans-Turing protocells, autonomy itself that maintains the Kantian
organized being in the universe, alone or in the presence of
natural selection for evolving protocells picks the relevant
essential variables and their embodied classical causal
consequences that form a functional closure of tasks by which the
Kantian system sustains itself. These are the variables whose
change increases "fitness" by whatever success criteria is in
operation.
[0297] Note that for embodied Trans-Turing protocells as autonomous
systems, adaptation and preadaptations using existing causal
features of the classical variables for novel functionalities, or
"tasks" that achieve "task" closure in a set of tasks (like a
dividing eukaryote), solves the frame problem. Again, the system
does NOT represent its world digitally. It exists and evolves as an
embodied Trans-Turing System or a coupled plurality of them,
perhaps as a population that evolves or co-evolves, in an
environment. New functions and tasks achieved by new "uses" of
causal features of the classical variables, enabled also by the
Poised Realm and other Trans-Turing features of the system, promote
adaptation. Selection for desired behaviors is then carried out, as
in biology.
[0298] For an evolving population of mutated budding liposomes or
generations of mutant liposomes where the ratio and density of
chromophores with different absorption/emission spectra are varied,
hence varying quantum network connectivity and position on the
x-axis, those variables which strongly alter fitness for the
desired goal are good candidates for essential variables. The same
is true for an evolving population of nanotech devices with similar
mutations in chromophore, carbon nanotube structures and spectra,
and topologies of connections. Those variations which strongly
affect fitness for the desired goal are good candidates for
essential variables.
[0299] Secondary Goals.
[0300] Biology teaches us that evolution can achieve tasks via a
sequence of evolved subtasks. Ontogeny is a prime example. It will
be clear that the embodied Trans-Turing system protocell Autonomous
system(s), in an environment with inputs, classical and quantum,
and outputs acting on the world, classical and quantum, may attain
states and Hamiltonians which can serve as subgoals. Here, the
Essential Variables may or may not be kept within the Alive Box,
but a different, perhaps overlapping set of sub-essential variables
are kept within their own bounds, Secondary Alive Box. From the
Secondary Alive Box, the Poised Realm System can attain the Alive
Box by some variety of "simple" steps. Without limitation, a simple
"step" is to initiate the Poised Realm System in a quantum, Poised
Realm, and classical state which is near that which attains the
Secondary Alive Box, and from this state, the system flows, with or
without decoherence and recoherence of quantum, Poised Realm, and
classical variables that change the classical and quantum
Hamiltonian, readily to the Alive Box sustaining configuration of
the system.
[0301] A partial ordering or hierarchy of Secondary and Tertiary
Alive Box configurations of the Poised Realm system can sometimes
be found, with access via these partial orderings or hierarchical
orderings to the configuration of the Poised Realm system such that
it remains in the Alive Box. The partial ordering leads from a
single or more generality a plurality of Nth level Alive boxes to
one or a plurality of N-1 or lower level N-2, 3, alive boxes.
[0302] Beyond Autonomous Trans-Turing systems undergoing embodied
evolution, there is a second means of perhaps much more rapid
non-biological "learning" of adaptive behavior, goals and subgoals
that solves the frame problem. As a non-limiting example, subdivide
the Essential Variable Alive box into successively smaller
subspaces that contain one another, labeled 1, 2, 3, 4, 5 meaning
"getting better, 1->5" This is an analogue of an emotional human
response to solving a problem where even the "form" of the solution
is unknown hence beyond solution algorithmically due to the frame
problem. Now, we have seen that high amplitudes with high energy
and moduli preferentially decohere, and have called them "bright
ideas". Decoherence or measurement typically leads to decoherence
or measurement of high moduli amplitudes. In turn this leads to a
slight modification of the classical Hamiltonian and results in a
change in the Hamiltonian of the quantum system. A succession of
measurements or decoherence events leads to a succession of "bright
ideas" becoming classical, so a succession of modifications of the
classical Hamiltonian and Hamiltonian of the quantum system. Think
of these decoherence events, or measurement events carried out by
the classical degrees of freedom on the quantum degrees of freedom
in some basis that the classical degrees of freedom constitute as
"asking a question" and getting a classical variable answer in a
single, or entangled set of open quantum or Poised Realm variables
when so measured. The results of the now classical variables may be
to move the system from box 1 in the Alive box toward Box 2, then
3, then finally 5. Call being in the 5 box A Solution. Then the
system has gone through a succession of measurement or decoherence
questions, a sequence of classical variable answers, until it finds
a solution that keeps the system in the "happy" box 5. At that
point, the system either stops changing as in Ashby's case, or uses
the relevant classical variables as a memory store for the solution
given the problem. In order to adapt to different problems in
different "environments", the system may need to "ignore" the
memory classical variables. This may be possible by rendering them
quantum or poised realm again via recoherence. As quantum degrees
of freedom again, they cannot affect the behaviors of the classical
degrees of freedom of the system. The details remain to be worked
out.
[0303] Operant Conditioning of Poised Realm Systems.
[0304] Given the Alive Box and a diversity of Secondary and
Tertiary and higher order Alive Boxes, the Poised Realm system
needs memory classical degrees of freedom. As noted above, such
memory degrees of freedom can arise by decoherence of quantum
degrees of freedom where these degrees of freedom can remain
classical indefinitely. Or they can become classical by measurement
and remain classical including by the quantum zeno effect. Or they
can become classical by motion on the x-axis. Once memory variables
exist, they serve as bifurcation parameters in the classical
Hamiltonian of the total system.
[0305] These Memory classical variables maintain aspects of the
classical, Poised Realm, and quantum Hamiltonians of the total
Poised Realm system such that the Alive box and subboxes can be
attained and sustained.
[0306] Given such Memory variables, the Poised Realm System can
undergo "operant conditioning". Given some input to the system, it
attains a subgoal Alive box from which it can attain the Alive Box.
In the subgoal box, memory classical variables arise by decoherence
on the Y, motion on the x-axis or both X and Y axes, so classical
parameters change, and the system attains the Alive box. Given the
classical state of the now classical memory variables, the system
responds to the inputs from the world by attaining either the
subgoal box, or directly the Alive box.
[0307] Given the Alive Box and decoherence or motion on the x-axis,
of quantum variables to classical Memory variables which can remain
classical for long periods of time, as well as classical variables
which can become partially or completely quantum, both of which
change the Hamiltonian's of the quantum and classical systems,
hence their dynamical behavior, the Alive Box serves as "internal
motivation" as in Ashby's Homeostat, and the Poised Realm system
will search on its own means to use any input stream of quantum or
classical data, its own internal quantum and classical Poised Realm
dynamics, and its outputs--which it may "observe", for example via
sensors, the Poised Realm System will search and often attain a
state that takes the input stream and with or without subgoal
boxes, old or new, achieve a state that remains in the Alive Box.
Thus, the Poised Realm System has "learned" to map some aspects of
the input data stream to specific internal structures and dynamics,
including the memory variables, and learned at the same time to map
the inputs to useful outputs that keep the Poised system in the
Alive Box.
[0308] More on Attention in the Poised Realm System.
[0309] By virtue of the classical Hamiltonian, or any other
classical system, without limitation, a nonlinear dynamical system
capable of order, criticality and chaos, as evidenced by work on
Random Boolean networks, Piecewise linear networks, linear ODE
networks, and Threshold Tan h function networks, and the possible
entangled (and possibly measured entangled) correlated quantum
behavior in the Poised Realm, the system with quantum, Poised
Realm, and classical inputs may "focus attention" on any subset of
its input stream, internal state--which it may sense by sensor
degrees of freedom--and output behavior--which again it may sense.
Thus the Poised Realm system need not be effected by all inputs,
quantum or otherwise. Or that effect may be very minimal, so that
the system "sees" and "responds" to focused aspects of its inputs,
internal states, and outputs. Again we note that shifting patterns
of entanglement, as is known in the art, allow sequential shifting
of the focus of attention.
[0310] By "focusing attention" on any subset of inputs, and
carrying out both data processing and actions coupled to that
input, the total behavior can become relevant, without limitation,
to keeping the system in the Alive Box. Thus, the system can
"notice" features of its environment and actions, and modify its
behavior to keep subgoals attained, or remain within the Alive
Box.
[0311] There is an analogy between a quantum degree of freedom
becoming classical for some period of time and the "step changes in
parameters" advocated by R. Ashby in his "Design for a Brain" to
change the system such that essential variables are kept within
bounds. In addition, there is a similarity between the changes in
the Hamiltonian of a Poised Realm system, when some of its quantum
degrees of freedom become classical, and the preparation of a
quantum system plus is classical components in a quantum experiment
by measurements that make quantum degrees of freedom classical in
the prepared quantum system. In effect, this preparation step can
be thought of as reshaping the classical and quantum Hamiltonians
of the prepared system thereby picking a favored pointer basis.
[0312] This has a bearing on quantum computation where the quantum
algorithm can be thought of as reshaping the Hamiltonian of the
quantum system, which then accumulates high modulus amplitudes in
the vicinity of the solution so that von Neumann consistent
measurement is likely to give the "right answer" after a number of
measurements. Thus, the spontaneous dynamics of a Poised Realm
system where, given the current Hamiltonians of the classical and
quantum system, some amplitudes can "peak" to high moduli and
remain quantum or can decohere preferentially to classical
"answers" to a "question" posed by the current Hamiltonians. Thus,
such Poised Realm systems appear to be non-algorithmic
quantum-Poised Realm-classical computing and "doing" systems.
[0313] In a general sense, what we here call a change in the
Hamiltonian of a quantum and/or classical system when a quantum
degree of freedom decoheres to classicity for all practical
purposes is similar to the Born-Oppenheimer approximation for
"effective Hamiltonians" due to slow and fast changing variables
such as nuclear positions and electron cloud distributions in
molecules. Note that Salahub et al used this approximation in their
paper, as described above.
[0314] The Diversity of Organized Behaviors of Poised Realm
Systems.
[0315] Kauffman introduced Random Boolean networks as models of
genetic regulatory networks in 1967 and 1969 (see Reinventing the
Sacred, by S. Kauffman Oxford UP 1993, 1995, 2000 and Basic Books
2008). These systems, and continuous cousins including piecewise
linear equations by L. Glass, linear code systems by S. Thurner,
and nonlinear threshold networks by M. Andrecut and Kauffman, show
that such systems behave in an ordered regime, a chaotic regime and
an "edge of chaos" critical phase transition.
[0316] Critical networks exhibit remarkable features, ranging from
maximum storage of information (Shmulevich), maximum pairwise
mutual information (Ribeiro et al.), maximum Set Complexity,
explained further below (Galas et al.), maximum power efficiency
(Carteret et al.), maximum capacity to evolve gracefully (Aldana et
al.), maximum capacity to make reliable discriminations of past
events and reliable action in the presence of minor noise, and
maximum capacity in a "society" of networks that can influence one
another to create novel attractor behaviors in the members of the
society or "tissue" or "colony" (Damiana et al.).
[0317] Galas et al. have introduced a new measure of the diversity
of organized processes a classical causal system can carry out,
called set complexity. Consider a random binary string, e.g.,
(10100010). Concatenate this string with itself,
(1010001010100010). Now use a compressor such as gzip to compress
the concatenated string. Since the concatenated random string is
redundant, and of length, here N=8, for the initial string, the
compressor will reduce the concatenated string length 2.times.N, to
length N by eliminating redundancy. Now take two different random
strings length N, and concatenate them and try to compress them.
They cannot be compressed, so remain length 2N. Normalized
Compression Distance is a universal distance measure between
objects such as binary strings. The extent to which two strings,
concatenated, can be compressed is a measure of the similarity
between the strings. That similarity is a distance measure, and is
normalized by dividing by N.
[0318] Set Complexity is a new measure for such objects. Let there
be M such, without loss of generality, binary strings of length N.
Calculate the pairwise normalized compression distance for all
distinct pairs of strings and normalize by the number of pairs to
find the average normalized compression distance among M strings.
Call this average, E. Set Complexity is defined as
SC=E.times.(1-E). This measure is 0 if E=0 or 1 and reaches a
maximum for E=0.5.
[0319] The intuition behind set complexity is that M identical
binary strings must have low set complexity, and also M strings
that are random with respect to one another must have low set
complexity. Thus set complexity reaches a maximum for intermediate
values of E. It is a new measure of the diversity of objects, or,
if the symbols represent actions by variables, e.g., the output
values of N variables in a random Boolean net, it represents the
diversity of organized processes of the classically causal
systems.
[0320] It is exciting that critical Random Boolean Nets sharply
maximize Set Complexity defined over the M states on all state
cycles of the network. In short, the asymptotic behavior of
critical random Boolean nets maximizes the organized diversity of
processes such systems can carry out.
[0321] We extend this definition of set complexity to Poised Realm
Systems. With respect to the classical variables of the system, the
Set Complexity definition is identical. Using the discussion by W.
H. Zurek, Decoherence and the Transition from Quantum to
Classical-Revisited, Los Alamos Science No. 27, 2002, we extend set
complexity to the quantum degrees of freedom of a Poised Realm
system. The mutual information, I, between two quantum systems, S1
and S2 is I(S1,S2)=H(S1)+H(S2)-H(S1,S2). Without loss of
generality, the entropy, H, in the above formulation can be taken
as the von Neumann entropy as is known in the art.
[0322] Using this measure of mutual information I, we compute the
mutual information between, without loss of generality, two quantum
or Poised Realm degrees of freedom, S1 and S2. Then, for a set of
quantum and Poised Realm quantum degrees of freedom in a Poised
realm system, we compute the mean mutual information, E, between
all pairs of quantum degree of freedom ion the Poised Realm System
where E is normalized to a maximum value of 1.0. Quantum Set
Complexity is then E.times.(1-E).
[0323] We define the total classical and quantum set complexity as
Set Complexity (classical)+Set Complexity (quantum). Classical
systems behaving as described by Hamiltonians can be quantized. Not
all classical causal systems are so describable by a Hamiltonian,
for example, random Boolean nets. However, the x-axis for our
kicked quantum rotor, or a kicked quantum oscillator goes from
order, with 0 Lyapunov exponent, to a second order (critical) phase
transition, to chaos for classical Hamiltonian systems. We believe
that the Set Complexity for Hamiltonian systems is maximized for
critical classical Hamiltonian systems whether by motion on the
y-axis, the x-axis or both. We also believe that total set
complexity for a Poised Realm System is maximized for critical
classical and critical quantum and Poised Realm quantum and
classical behaviors. If so, such Poised systems, classical and
quantum can carry out the greatest diversity of organized processes
hence are optimal for many practical applications.
[0324] More generally, total set complexity is maximized for Poised
systems with inputs and outputs somewhere in the Poised Realm, and
can be obtained for optimal task performance.
[0325] Using the above, we have a design criterion for Poised Realm
systems capable of carrying out the maximal information processing,
internally diverse dynamical Poised Realm behaviors, and the
richest Poised Realm actions on the world or in communities of
Poised Realm systems.
[0326] It may be that Poised Realm systems can simultaneously
maximize a power efficiency per unit fuel, in a generalized sense
of fuel as energy, and the diversity of organized behaviors as in
the Set Complexity measures above, by operating along the critical
line in the Poised Realm. Or there may be a more complex trade off
between maximum power efficiency and displacement from equilibrium
and maximum set complexity. Both are open to utilization in single
Poised Realm Systems or communities of Poised Realm systems.
[0327] Possible neurobiological implications: i. We propose that in
the vertebrate brain and even in Box Jellyfish, Trans-Turing
behavior occurs in molecules, probably within synapses, perhaps in
neurotransmitter receptors. We propose that experience, qualia, are
associated with quantum measurement. We propose that entangled
degrees of freedom in even anatomically unconnected synapses
enables a Unity of Consciousness to solve the binding problem of
neurobiology, we propose that the classical behaviors of neurons
and sensory tunes tiny time-space variations of transmembrane
potentials that constitute the classical Hamiltonians that "tune
the drumhead potentials" to cover the external world when
measurement occurs, we propose and answer to Descartes: The mind
acts causally on the brain either by decoherence or measurement,
and can do so repeatedly via recoherence or flowering of quantum
behaviors after measurement.
[0328] Based on this, one conclusion is that molecules, probably in
synapses, comprise evolved Trans-Turing systems. Then we propose
that neural networks of real neurons, coupled with modes of
mechano-sensory or other inputs, can be molded to be potentially
conscious systems capable of practical non-algorithmic problem
solving including solving the frame problem and unity of
consciousness.
[0329] Two approaches to test this are: i. See if neurotransmitter
receptors can carry out quantum measurement and test of anesthetics
freeze them in a classical state such that they cannot measure, so
qualia cannot arise. ii. Select for ease of ether anesthetization
in some organism, say Drosophila melanogaster, until little or no
ether is needed to produce anesthetization. Compare wild type and
mutant proteins for quantum measurement. The wild type should be
able to carry out quantum measurement, the mutant proteins should
not be able to carry out measurement, or able to do so to a so to a
reduced extent perhaps by being frozen classical.
[0330] In a preferred embodiment of Trans-Turing systems we make
use of incorporation of, without limitation, chlorophyll molecules
and their antenna proteins, or other molecules into liposomes,
(1-4). Here the chlorophyll and antenna proteins may be embedded in
the membrane of the liposome and move in the membrane surface.
Alternatively the chlorophyll and antenna proteins may be adfixed
to one or more macromolecular assemblies, or by means known in the
art to artificial nanostructures such as, without limitation,
nanotube structures, and affixed at known positions and
orientations to such nanostructures, for example using streptavidin
and biotin.
[0331] Work on chloroplasts of diverse light harvesting organisms
shows that the average intermolecular distance between
chlorophyll-antenna protein complexes ranges from 10 to 20
angstroms. Coherent energy transfer by quantum coherence ranges up
to 100 nM, (5). These figures set an initial estimate for the
density of chlorophyll antenna complexes that must be incorporated
into a liposome of known surface area and volume, typically on the
order of 1 micron or less in diameter, to achieve the desired
average distances between chlorophyll antenna complexes in the
liposome where these complexes float. By means known in the art,
rafting of such antenna protein complexes as they aggregate in the
liposome membrane can be used, by means known in the art, to
achieve higher densities in local subregions of the liposome
complex's surface membrane.
[0332] An established means known in the art to create liposomes
containing a known and tunable mean density of chlorophyll antenna
complexes is based on a process in which chloroplast membranes are
dissolved in a detergent like sodium deoxycholate along with
phospholipid. The detergent is removed by dialysis, the lipid
reassembles into lipid vesicles, and the proteins and chlorophyll
are incorporated into the bilayers. One can control the ratio of
chlorophyll to surface area simply by varying the amount of lipid
in the mixture. If one wishes, one can purify the reaction centers
ahead of time from a photosynthetic membranes. References to these
procedures are incorporated by reference below, (1-4).
[0333] In an alternative preferred mode of realization of
Trans-Turing systems, noted above, the chlorophyll antenna protein
complexes or other molecules are affixed to a nanotube two or three
dimensional structure of desired structure and affixed to this
using biotin and streptavidin by means known in the art to specific
locations on the nanotube structure. The latter structure with
affixed chlorophyll and antenna protein complexes are then
incorporated into liposomes by dissolving lipids, without
limitation, phospholipids, or any other lipids capable for forming
liposomes, in medium containing the nanostructure with affixed
chlorophyll and antenna complexes. The latter structures are
incorporated into at least some of the newly formed liposomes,
creating Trans Turing systems.
[0334] Alternatively nanotube or other nanostructures with
chlorophyll and antenna proteins, or any other molecules, affixed
e.g. by streptavidin and biotin, may be used to create a
Trans-Turing system without encorporation into a liposome or other
bounding membrane or structure.
[0335] The Trans-Turing systems so constructed can exhibit quantum
coherent behavior in electron transfer among antenna protein
chloroplasts, including entanglement (5). In addition, one must
calculate all possible quantum pathways from antenna chloroplast A
to B. Those pathways that pass through the medium, or "bath" in the
interior of the liposome can induce deocherence, (5). Thus these
systems also live in the quantum-classical poised realm. By means
of incident driving quantum or classical input, for example, and
without limitation, laser light of tuned wavelength and intensity,
recoherence can be induced. Thus these systems can hover in the
poised realm. As noted above, by tuning the random versus periodic
features of the driving stimulus, the degree and rate of
decoherence and recoherence can be controlled.
[0336] In addition coupled quantum systems, can exhibit open
quantum coherent to decoherence to classicality to recoherence
without incident laser light, Ali Nissim, (pc).
[0337] As is known in the art, Sholes Included by reference, (5,6),
Two-Dimensional photon echo (2DPE) spectropscopy has recently
emerged as a practical method for detailed insight into excited
state dynamics. Information in 2DPE spectra includes the TIME
EVOLUTION of decoherence of coherent superpositions of the
absorption bands, which provides a measure of quantum
coherence.
[0338] It will be clear that 2DPE spectropscopy can be used
throughout this patent application for all cases requiring
measurement of power law versus exponential decay of decoherence to
measure criticality (power law decoherence) or ordered or chaotic
position, (exponential decoherence) on the X axis. This is true for
measurements of molecules within Trans-Turing systems as they
behave, hence we can measure decoherence and recoherence in a Trans
turing system or set of coupled Trans-Turing systems. As noted
above in this patent application, deviation away from criticality
in the Poised Realm yields mix forms of decoherence between power
law and exponentials themselves with various decay rates, that can
be used to measure position on the X axis of molecules in
Trans-Turing systems, in situ, or not, and for drug design as noted
above. Thus we can study and follow poised realm behaviors of
molecules in time in Trans-Turing Systems, and in cells with
respect to drug action, and in neural synapses, which may
constitute Trans Turing systems, whose molecules, including
neurotransmitters and their receptors may be in the poised realm
and play a role in conscious and unconscious mental behaviors along
with quantum measurement events in quantum coherent or poised realm
systems.
[0339] We note that spin echo (7) and neutron spin echo (8) can
also be used to measure decoherence.
[0340] More, we note that new means are known in the art to achieve
controlled entanglement of quantum degrees of freedom, (9), hence
entanglement can play a role within and between molecules in one or
a plurality of trans-Turing systems, including possibly
Trans-Turing behaviors in one or more anatomically connected or
unconnected neural synapses. By quantum measurement of one or a
plurality of entangled degrees of freedom in Trans Turing Systems,
where the degree of Einstein-Podolsky-Rosen NON LOCAL quantum
correlations increase with the number of entangled degrees of
freedom, highly correlated behaviors of measured, hence now
classical, degrees of freedom within one, or a plurality of
molecules in a single or set of Trans-Turing Systems, including
possible a set of anatomically unconnected but entangled molecules
in neural synapses, can arise. These correlated now classical
degrees of freedom can have classical causal consequences for the
total single or set of coupled trans-turing systems and their
quantum, poised realm, and classical behaviors.
[0341] The above Trans-Turing systems have classical, quantum
coherent, and poised realm inputs, and outputs, including from and
to other nearby Trans-Turing systems, thereby forming a "society"
of interacting Trans-Turing systems. Without loss of generality,
entanglement among the quantum degrees of freedom in one or a
plurality of trans-turing systems can occur and can be altered,
thereby altering which measured, and now classical degrees of
freedom are highly correlated to act jointly as classical aspects
of the Trans-Turing system on the Trans-Turing system with respect
to its quantum coherent, Poised Realm, and classical degrees of
freedom and act as classical aspects of the outputs of the
Trans-Turing system.
[0342] As noted above, the total behavior of Trans-Turing systems
is not definite, via decoherence to classicality FAPP, or quantum
measurement of coherent or poised realm behaviors, yet not random
due to classical degrees of freedom and their classical
Hamiltonian, plus the changing effects of the changing classical
behaviors on the quantum coherent and Poised Realm behaviors.
[0343] It will be clear to those of ordinary skill in the art,
given our specifications above, that we can obtain organic
molecules in general, or other molecules, calculate their position
of the X order-criticality-chaos axis using the graph theoretical
techniques noted above, test for their position on the X axis, and
in particular for Poised Realm Critical behavior by testing for
power law decoherence at criticality in the Poised Realm, compared
to a gradual conversion to exponential decoherence with different
exponential decay rates as molecules are located on the X axis
further toward order or chaos from criticality. Thus, we can
assemble, in general, molecules of any desired distribution on the
X axis, from all critical, to any other distribution, for
incorporation into liposomes to create Trans-Turing systems.
[0344] Alternatively we can use such molecules in the X axis on
nanofabricated Trans-Turing systems. Or we can use macroscopic
Trans-Turing systems.
[0345] In a preferred embodiment of this invention, the molecules
incorporated into the liposome to create trans-turing systems will
be closely clustered around the critical location in the Poised
Realm. Here we expect a maximum of controllable behavior as the
quantum chaotic domains described above increase in size up to
merging, or not quite merging, into the giant component described
above at Poised Realm criticality. We expect the most complex
Poised Realm behavior here, at the conductor-insulator transition
critical transition described above. More we expect the most
complex computational behavior among critical coupled classical
degrees of freedom, and we expect optimal energy transfer from
quantum modes to classical modes of behavior at criticality based,
as noted elsewhere on Fermi's golden rule of preferential
measurement of those amplitudes with the highest modulus, or
preferential decoherence of amplitudes with large moduli. The
energy will be released into the now classical degree(s) of
freedom.
[0346] Using our graph theoretical calculations, we can synthesize,
or screen for by use of combinatorial chemistry means known in the
art, molecules of any sort, e.g. without limitation, binding a
known ligand, or catalyzing a known reaction, or binding to a
stable analogue of a transition state, at known positions of the X
axis for incorporation into Trans-Turing systems, for the behavior
of molecules in Trans-Turing systems alone or coupled, or drug
candidates. As we noted above, the failure of classical
physics--"lock-key" ideas for combinatorial chemistry, where
Kauffman has the founding international patents filed in 1985, to
yield functional drugs, compared to the success in Japanese
pharmaceutical companies which continue to use medicinal chemistry
techniques, suggests that the medicinal chemistry techniques may
well be, inadvertantly, probing in vivo Poised Realm behaviors,
beyond classical lock-key concepts, in drug discovery. This bears
on our uses of the Poised Realm for drug discovery as described
above.
[0347] Link to Consciousness in the Human Brain, and Coupled
Trans-Turing Systems.
[0348] The human brain has about 10 to the 11 neurons, each with an
average of 600 synapses. Each axon ends on one dendrite. Many
dendrites, each with many synapses, feed into one downstream
neuronal cell. With the arrival of an action potential at a
synapse, neurotransmitter molecules are released, travel across the
synaptic cleft and bind to neurotransmitter receptors. Often this
results, via a complex of molecules including the receptor, in
opening or closing a channel on the post synaptic dendrite, leading
to tiny time/space alterations in the local transmembrane
potential. These alterations travel to the axon hillock of the
neural cell and are summed. If the transmembrane potential
increases to less than about -20 mV, an action potential is likely
to be initiated and travel down the axon to impinge on one or more
downstream synapses.
[0349] Francis Crick, in the Astonishing Hypothesis, (10), points
out that a vast amount of information is thrown away concerning the
behaviors of vastly many molecules in synapses and tiny time space
alterations in dendritic transmembrane potentials to achieve either
firing or not firing of a classical physics action potential.
[0350] We believe it is a sensible hypothesis to "stand the brain
on its head", and ask whether the synapses are the "business end"
of the brain, whose behavior is partially driven by the sensory
inputs and classical physics neural network among the 10 to the
11th neurons and 600 times as many synapses. If so, the synapse
itself may be a Trans-Turing system operating in the Poised Realm,
where decoherence, recoherence, and quantum measurements may
occur.
[0351] We hypothesize that conscious experience is associated with
quantum measurement in coherent or poised realm quantum systems.
The resulting classical degrees of freedom, post measurement, allow
the conscious mind via these classical variables to have classical
physical consequences for the total mind-brain system, answering
Descartes about how mind acts on matter. Measurement is NOT causal,
so mind does not act causally on matter. In addition, decoherence
to classicality FAPP may allow mind to have acausal consequences
for brain.
[0352] The hypothesis that conscious experience, qualia, are
associated with quantum measurement is testable in two ways at
least: i. anesthetics bind to neurotransmitter receptors in
hydrophobic pockets. If the "freeze" neurotransmitters into
classical or classical FAPP behavior such that the
neurotransmitters receptors cannot undergo measurement events,
while in the absence of anesthetics neurotransmitter receptors do
undergo measurement events, that is evidence that conscious
experience, i.e. "qualia", IS associated with quantum measurement.
In addition, fruit flies, Drosophila melaogaster, can be ether
anesthetized. Selection of anesthetization with decreasing ether
doses can yield mutant proteins that, with anesthesia for little or
no ether, may reveal by standard genetics the protein and other
molecules associated with consciousness. Then the mutant proteins
or other molecules can be tested for "freezing" such that they
cannot undergo measurement, while the unselected normal, or wild
type versions of those proteins can undergo quantum measurement.
These experiments can help identify the possibly synaptic molecules
whose quantum and Poised Realm and classical behavior is related to
consciousness. On this view, decoherence to classicality FAPP may
be associated with unconscious actions of mind on brain.
[0353] If these results are obtained, we can construct living
neural networks of controlled network "architecture" and dendritic
synaptic interconnections, graft these to sensor inputs, say,
without limitation, from the Box jelly fish eye and its downstream
neurons as inputs to the above neural net, and effector neurons
acting on artificial output devices, limbs, actuators and so forth.
From these neural systems, or using non-neural general Trans-Turing
systems alone or coupled, including coupled by entanglement, we can
create devices that classify their worlds, solve the frame problem,
and act on their worlds, see just below "Evolving Trans-Turing
Systems."
[0354] More, by entanglement of diverse unconnected or connected
quantum degrees of freedom in diverse synapses, or trans-turing
systems, and quantum measurement of those entangled degrees of
freedom, highly correlated, due to Einstein Podolski Rosen non
local "EPR" quantum effects violating Bell's inequalities will
arise, and the now highly correlated and also now classical degrees
of freedom can be used to act causally on the classical world, as
well as to modify the ongoing behavior of the single or coupled
Trans-Turing systems. Finally, local alterations can alter which
quantum degrees of freedom are entangled, thereby altering: i.
which now classical degrees of freedom are correlated upon their
quantum measurement; ii. if qualia are associated with quantum
measurement, entangled quantum degrees of freedom may yield a unity
of consciousness, that is, a solution to the qualia binding
problem. Shifting patterns of entanglement in effect, shift the
"focus of attention" of the coupled Trans-Turing systems.
[0355] A further feature of note in considering either neural
systems with synapses, or more general networks of Trans Turing
systems arises as follows. Consider a classical physics volume with
a classical physics gas in it. Does measuring the position and
momentum of one classical particle give any insight into the SHAPE
of the volume, or "box"? No. By contrast, a quantum wave behavior
in a classical potential well that serves as its BOUNDARY
CONDITIONS, "feels" or "knows" its boundary conditions which show
up, for example, and without limitation, in the spectrum of its
energy levels. Thus the wave property of a quantum system knows the
SHAPE of its boundary condition potential well.
[0356] Consider by analogy, a room filled with music. Now consider
breaking the room into tiny 3 dimensional volumes and measuring
pressure in each as a function of time, then analyzing these via a
digital "propositional" computer. Compare this to an analogue in
which 1000 differently shaped drum heads are placed around the
music filled room. The spectral (eigenfunction) patterns of
vibration of the diverse drum heads, each reflecting the boundary
conditions arising due to the shape of its drum head, "know" in a
non-propositional and analogue way the music in the room.
Telephones used to work in this way.
[0357] Similarly, consider the tens of billions of synapses in the
brain, where sensory inputs from the world, and classical physics
firing of action potentials, TUNE the tiny time/space synaptic and
local dendritic transmembrane potentials that serve as part of the
potential well, or boundary condition on possible coherent or
Poised Realm quantum wave behaviors among, say, neurotransmitter
receptor molecules. Then the energy levels and other behaviors of
those molecules, or any other relevant quantum or Poised Realm
molecules or components, "Know", the shapes of their potential well
boundary conditions. But this means that proper tuning of those
boundary conditions allow the Poised Realm, hence probably
Trans-Turing behaviors, in the synapsic region to know their
external world. By entanglement of quantum degrees of freedom,
coherent or Poised Realm, in properly tuned sets of potential
wells, and quantum measurement of many entangled quantum degrees of
freedom, tuned and highly correlated qualia are achieved, so a
unity of consciousness is achieved, solving the neural binding
problem. Thus, neural devices made as above may achieve this.
[0358] More generally, the same holds for a plurality of
Trans-Turing systems whose potential wells are constituted in part
by classical degrees of freedom, and which can be tuned, like the
drum heads, to reflect in a coordinated way the "world" around the
set of Trans-Turing systems. They collectively "Know" their
embedding world, and do so in a non-propositional way. In turn, the
lack of a propositional form, allows such evolving Trans Turing
systems, see just below, to solve the Frame problem of computer
science via Darwinian preadaptations and other means.
[0359] Evolving Trans-Turing Systems for Desired Behaviors.
[0360] Trans Turing systems can be studied either by simulation or
by construction of embodied trans-turing systems. In either case,
to "program" a trans-turing system to achieve a desired behavior, a
preferred means is to use some analogue of the Holland Genetic
Algorithm, or more generally an adaptive strategy using generations
of populations of variant Trans-Turing systems, choosing the "best"
subset of the members of each generation, keeping these unmodified
and slightly modified to create a next generation of Trans-Turing
systems, and selecting the fittest by some "figure of merit" or
selection criterion.
[0361] In general, any combination of time constant or time varying
classical, poised realm, and quantum coherent inputs and outputs
can be used to define a figure of merit. As a non-limiting example,
generalized "pattern recognition" on a set of quantum coherent,
e.g. laser, poised realm, e.g. from another Trans-turing system,
and classical inputs can be used as inputs, and output behavior
that classifies these into alternative time constant or time
varying patterns of quantum coherent, poised realm, and classical
outputs can be the figure of merit that is the basis of selection
on successive generations.
[0362] In general, any such mapping of inputs to desired outputs,
classed in any way by the Trans-Turing system, creates a "fitness
landscape" over the space of parameters used to vary the structure
and coupling among the variables in the Trans-Turing system or set
of interacting Trans-Turing Systems. It is well known in the art
that the statistical features of this fitness landscape for any
single figure of merit may be simple and single peaked, or "rugged"
and multipeaked, and even "random" with many local peaks. It is
known in the art that recombination works as an adaptive strategy
on landscapes which are not too rugged (Kauffman, Origins of Order,
Oxford Univ Press 1993 incorporated here by reference, (11)).
[0363] More generally, if there are multiple figures of merit and
their relative importance is not definable, Global Pareto
optimality is, as known in the art, the sensible solution
concept.
[0364] It will be clear to those of ordinary skill in the art, that
TransTuring system may be embodied in self reproducing "protocells"
able to reproduce, and yield heritable variations, thus undergo
adaptive evolution given a figure of merit, and undergo Darwinian
preadaptations, also called Exaptations, (see Kauffman
Investigations, Oxford University Press 2000, and Reinventing the
Sacred, Basic Books, 2008 both incorporated here by reference,
(12,13). Critically, exaptations allow NEW functions to emerge. As
a concrete example, some fish have swim bladders, sacs filled with
air and water, whose ratio determines neutral buoyancy in the water
column. These evolved by preadaptations from the lungs of lung
fish. Here a new function, neutral buoyancy, arose in the
biosphere. This new function SOLVES the "FRAME PROBLEM" in computer
science. The frame problem consists in the following: picture a
robot with a standard digital computer on board. Many features of
the robot and, say room it is in, are described FINITELY and given
"affordances". Here, for example the arm of the robot has a finite
number of described features, each with FINITE LIST of
propositionally defined affordances: Is a, Does A, Needs A, . . . .
The frame problem is this: Given a task, we are NOT guaranteed that
the robot can deduce from the finite list propositionally defined
affordances the solution to the task.
[0365] But preadaptations of Trans-Turing systems that are evolving
or co-evolving, as in the case of the evolution by preadaptation
swim bladders which confer neutral buoyancy in the water column by
the ratio of air and water in the swim bladder, evolved from the
lungs of lung fish, yield the novel function of the swim bladder:
neutral buoyancy. This new function, in general, would never be
represented a finite list of affordances propositionally concerning
the lungs of lung fish. Preadaptations arise in evolving embodied
systems that are Kantian wholes in which the whole where the part
exist for and by means of the whole, and the whole exists for and
by means of the parts. As a non-limiting example, collectively
autocatalytic sets of polymers such as peptides, (14), are such
Kantian wholes. Gonen Ashkenazi, (15), at Ben Gurion University in
Beer Sheeba Israel has a nine peptide collectively autocatalytic
set. Here no peptide catalyzes its own formation, but the formation
of another peptide from smaller peptides that are "food" fed to the
system, and are fragments of the "other" peptide in question. It is
essential that in the collectively autocatalytic set, no peptide
catalyzes its own formation. Calling catalysis of a specific
reaction a catalytic "task", the nine peptide system achieves
CATALYTIC TASK "CLOSURE (11,14). All the reactions that must be
catalyzed ARE catalyzed by some peptide in the collectively
autocatalytic whole.
[0366] A collectively autocatalytic peptide system is an example of
a Kantian whole. The parts exist in the universe by means of the
whole, and the whole exists in the universe by means of the parts
(16).
[0367] Now consider an evolving cell. It too achieves a closure in
a set of tasks. But these are far wider than catalysis, and include
making membranes, vectoring proteins to specific organelles in the
cell, doing work cycles, and reproducing by mitosis.
[0368] The next essential point to realize about the evolution of
Kantian wholes is that each part has consequences. For a
Trans-Turing system these are quantum coherent, poised realm, and
classical. But there is no orderable or finite list of the
consequences of any part alone or with indefinitely many other
parts. Further, for each consequence there is no orderable or
finite list of potential USES of that consequence. Yet, for the
ongoing evolution of the Kantian whole, by heritable variations and
some form of selection, all that is needed is that at least ONE, or
a plurality of consequences of one or a plurality of parts, FIND
SOME USE among their consequences that enhances the fitness of the
Kantian Trans-Turing whole with respect to any figure of merit.
This allows, via quantum and/or poised realm/and or classical
consequences, new functionalities to emerge that are not logically
entailed by a finite list of propositional statements of
affordances of parts of, e.g. a robot or standard computer. The
embodied Trans-Turing system solves the frame problem, never solved
in computer science.
[0369] In one preferred embodiment of this invention, Trans-Turing
systems are part of evolving and coevolving protocells with an
autocatalytic set of polymers, RNA or proteins or any other
polymers, or merely an autocatalytic set of molecules, housed in a
reproducing liposome. Here liposome reproduction has been achieved
experimentally, (17). Collectively autocatalytic sets have been
achieved experimentally. Recent work shows that such sets can
undergo open ended evolution, (18), and if contained in a liposome
that undergoes growth and budding, the autocatalytic set can
typically synchronize its own reproduction with that of the
liposome. (19). In short, Trans-Turing systems capable of evolving
and co-evolving in protocells are now feasible and can evolve to
adapt to a known figure of merit by adaptations or preadaptations,
where the both solve the computer science Frame Problem.
[0370] Craig Ventner has recently created an "artificial cell" with
DNA, RNA and encoded proteins, able to reproduce and create desired
proteins, (20). It will be clear to those of ordinary skill in the
art that such systems can be used to create populations of evolving
Trans-turing systems, using encoded proteins and a metabolism of
smaller organic molecules capable of Poised Realm and Trans-Turing
behavior. The positions of these molecules on the X axis can be
calculated using our graph theoretical procedures, and
experimentally verified using power law versus exponential
decoherence rates.
[0371] More, the artificial cell can embody a genetic regulatory
net of transcription factors which activate and inhibit one
another. This network, (see Kauffman, 1993, Origins of Order), can
be dynamically ordered, critical or chaotic. The most controllable
behavior occurs for critical networks. There is evidence that real
cells are critical, (Nykter et al, (21). This classical critical
behavior can be married to Trans-Turing behavior which is also
critical, to achieve Trans-Turing systems that optimize the
diversity of organized behaviors of the total system. Here the
degree of organization of a causal process can be measured by its
power efficiency per unit fuel, and the choice of which causal
process to consider among a set of interwoven causal processes of
each part of the system can be chosen to maximize Set Complexity,
defined elsewhere in this patent application. This can be
generalized to measure set complexity of the total quantum and
classical aspects of the system, as specified in this patent
application elsewhere.
[0372] In another embodiment of Trans-Turing systems, these can be
constructed using nano-tube structures of arbitrary sizes and two
or three dimensional structure, with chlorophyll and antenna
proteins, or any other atoms of molecules, affixed at known or
variable positions on the nanotube structure, and capable of
quantum coherent, open quantum Poised Realm, and classical
behaviors, to create one or any population of Trans-Turing systems.
By fabrication or any other means, know or in the future known, a
population of similar or increasingly diverse Trans Turing systems
can be constructed, and in parallel with the discussion above, can
be selected by evolution, or co-evolution of interacting identical
or diverse Trans Turing systems, to increasing fitness with respect
to single figures of merit, or, using global pareto optimality, for
optimal solutions to a set of figures of merit where the relative
importance of the plurality of success criteria are not
specifiable.
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