17,379 research outputs found
The Thermodynamics of Network Coding, and an Algorithmic Refinement of the Principle of Maximum Entropy
The principle of maximum entropy (Maxent) is often used to obtain prior
probability distributions as a method to obtain a Gibbs measure under some
restriction giving the probability that a system will be in a certain state
compared to the rest of the elements in the distribution. Because classical
entropy-based Maxent collapses cases confounding all distinct degrees of
randomness and pseudo-randomness, here we take into consideration the
generative mechanism of the systems considered in the ensemble to separate
objects that may comply with the principle under some restriction and whose
entropy is maximal but may be generated recursively from those that are
actually algorithmically random offering a refinement to classical Maxent. We
take advantage of a causal algorithmic calculus to derive a thermodynamic-like
result based on how difficult it is to reprogram a computer code. Using the
distinction between computable and algorithmic randomness we quantify the cost
in information loss associated with reprogramming. To illustrate this we apply
the algorithmic refinement to Maxent on graphs and introduce a Maximal
Algorithmic Randomness Preferential Attachment (MARPA) Algorithm, a
generalisation over previous approaches. We discuss practical implications of
evaluation of network randomness. Our analysis provides insight in that the
reprogrammability asymmetry appears to originate from a non-monotonic
relationship to algorithmic probability. Our analysis motivates further
analysis of the origin and consequences of the aforementioned asymmetries,
reprogrammability, and computation.Comment: 30 page
Physical portrayal of computational complexity
Computational complexity is examined using the principle of increasing
entropy. To consider computation as a physical process from an initial instance
to the final acceptance is motivated because many natural processes have been
recognized to complete in non-polynomial time (NP). The irreversible process
with three or more degrees of freedom is found intractable because, in terms of
physics, flows of energy are inseparable from their driving forces. In
computational terms, when solving problems in the class NP, decisions will
affect subsequently available sets of decisions. The state space of a
non-deterministic finite automaton is evolving due to the computation itself
hence it cannot be efficiently contracted using a deterministic finite
automaton that will arrive at a solution in super-polynomial time. The solution
of the NP problem itself is verifiable in polynomial time (P) because the
corresponding state is stationary. Likewise the class P set of states does not
depend on computational history hence it can be efficiently contracted to the
accepting state by a deterministic sequence of dissipative transformations.
Thus it is concluded that the class P set of states is inherently smaller than
the set of class NP. Since the computational time to contract a given set is
proportional to dissipation, the computational complexity class P is a subset
of NP.Comment: 16, pages, 7 figure
Reaction kinetics in open reactors and serial transfers between closed reactors
Kinetic theory and thermodynamics of reaction networks are extended to the
out-of-equilibrium dynamics of continuous-flow stirred tank reactors (CSTR) and
serial transfers. On the basis of their stoichiometry matrix, the conservation
laws and the cycles of the network are determined for both dynamics. It is
shown that the CSTR and serial transfer dynamics are equivalent in the limit
where the time interval between the transfers tends to zero proportionally to
the ratio of the fractions of fresh to transferred solutions. These results are
illustrated with finite cross-catalytic reaction network and an infinite
reaction network describing mass exchange between polymers. Serial transfer
dynamics is typically used in molecular evolution experiments in the context of
research on the origins of life. The present study is shedding a new light on
the role played by serial transfer parameters in these experiments.Comment: 11 pages, 7 figure
Thermodynamics of Neutral Protein Evolution
Naturally evolving proteins gradually accumulate mutations while continuing
to fold to thermodynamically stable native structures. This process of neutral
protein evolution is an important mode of genetic change, and forms the basis
for the molecular clock. Here we present a mathematical theory that predicts
the number of accumulated mutations, the index of dispersion, and the
distribution of stabilities in an evolving protein population from knowledge of
the stability effects (ddG values) for single mutations. Our theory
quantitatively describes how neutral evolution leads to marginally stable
proteins, and provides formulae for calculating how fluctuations in stability
cause an overdispersion of the molecular clock. It also shows that the
structural influences on the rate of sequence evolution that have been observed
in earlier simulations can be calculated using only the single-mutation ddG
values. We consider both the case when the product of the population size and
mutation rate is small and the case when this product is large, and show that
in the latter case proteins evolve excess mutational robustness that is
manifested by extra stability and increases the rate of sequence evolution. Our
basic method is to treat protein evolution as a Markov process constrained by a
minimal requirement for stable folding, enabling an evolutionary description of
the proteins solely in terms of the experimentally measureable ddG values. All
of our theoretical predictions are confirmed by simulations with model lattice
proteins. Our work provides a mathematical foundation for understanding how
protein biophysics helps shape the process of evolution
Thermodynamic forces, flows, and Onsager coefficients in complex networks
We present Onsager formalism applied to random networks with arbitrary degree
distribution. Using the well-known methods of non-equilibrium thermodynamics we
identify thermodynamic forces and their conjugated flows induced in networks as
a result of single node degree perturbation. The forces and the flows can be
understood as a response of the system to events, such as random removal of
nodes or intentional attacks on them. Finally, we show that cross effects (such
as thermodiffusion, or thermoelectric phenomena), in which one force may not
only give rise to its own corresponding flow, but to many other flows, can be
observed also in complex networks.Comment: 4 pages, 2 figure
Andrzej Pekalski networks of scientific interests with internal degrees of freedom through self-citation analysis
Old and recent theoretical works by Andrzej Pekalski (APE) are recalled as
possible sources of interest for describing network formation and clustering in
complex (scientific) communities, through self-organisation and percolation
processes. Emphasis is placed on APE self-citation network over four decades.
The method is that used for detecting scientists field mobility by focusing on
author's self-citation, co-authorships and article topics networks as in [1,2].
It is shown that APE's self-citation patterns reveal important information on
APE interest for research topics over time as well as APE engagement on
different scientific topics and in different networks of collaboration. Its
interesting complexity results from "degrees of freedom" and external fields
leading to so called internal shock resistance. It is found that APE network of
scientific interests belongs to independent clusters and occurs through rare or
drastic events as in irreversible "preferential attachment processes", similar
to those found in usual mechanics and thermodynamics phase transitions.Comment: 7 pages, 1 table, 44 references, submitted to Int J Mod Phys
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