Entropy | Special Issue: Maximum Entropy and Bayesian Methods

Bookmarked Entropy | Special Issue : Maximum Entropy and Bayesian Methods (mdpi.com)
Open for submission now
Deadline for manuscript submissions: 31 August 2017
A special issue of Entropy (ISSN 1099-4300).

Deadline for manuscript submissions: 31 August 2017

Special Issue Editor


Guest Editor

Dr. Brendon J. Brewer

 

Department of Statistics, The University of Auckland, Private Bag 92019, Auckland 1142, New Zealand
Website | E-MailPhone: +64275001336
Interests: bayesian inference, markov chain monte carlo, nested sampling, MaxEnt

Special Issue Information

Dear Colleagues,

Whereas Bayesian inference has now achieved mainstream acceptance and is widely used throughout the sciences, associated ideas such as the principle of maximum entropy (implicit in the work of Gibbs, and developed further by Ed Jaynes and others) have not. There are strong arguments that the principle (and variations, such as maximum relative entropy) is of fundamental importance, but the literature also contains many misguided attempts at applying it, leading to much confusion.

This Special Issue will focus on Bayesian inference and MaxEnt. Some open questions that spring to mind are: Which proposed ways of using entropy (and its maximisation) in inference are legitimate, which are not, and why? Where can we obtain constraints on probability assignments, the input needed by the MaxEnt procedure?

More generally, papers exploring any interesting connections between probabilistic inference and information theory will be considered. Papers presenting high quality applications, or discussing computational methods in these areas, are also welcome.

Dr. Brendon J. Brewer
Guest Editor

Submission

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. Papers will be published continuously (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are refereed through a peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Entropy is an international peer-reviewed Open Access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1500 CHF (Swiss Francs).

No papers have been published in this special issue yet.

Source: Entropy | Special Issue : Maximum Entropy and Bayesian Methods

🔖 The Hypercycle: A Principle of Natural Self-Organization | Springer

Bookmarked The Hypercycle - A Principle of Natural Self-Organization | M. Eigen | Springer (Springer, 1979)
This book originated from a series of papers which were published in "Die Naturwissenschaften" in 1977178. Its division into three parts is the reflection of a logic structure, which may be abstracted in the form of three theses:

A. Hypercycles are a principle of natural self-organization allowing an inte­gration and coherent evolution of a set of functionally coupled self-rep­licative entities.

B. Hypercycles are a novel class of nonlinear reaction networks with unique properties, amenable to a unified mathematical treatment.

C. Hypercycles are able to originate in the mutant distribution of a single Darwinian quasi-species through stabilization of its diverging mutant genes. Once nucleated hypercycles evolve to higher complexity by a process analogous to gene duplication and specialization. In order to outline the meaning of the first statement we may refer to another principle of material self organization, namely to Darwin's principle of natural selection. This principle as we see it today represents the only understood means for creating information, be it the blue print for a complex living organism which evolved from less complex ancestral forms, or be it a meaningful sequence of letters the selection of which can be simulated by evolutionary model games.

Part A in .pdf format.

🔖 Cognition and biology: perspectives from information theory

Bookmarked Cognition and biology: perspectives from information theory (ncbi.nlm.nih.gov)
The intimate relation between biology and cognition can be formally examined through statistical models constrained by the asymptotic limit theorems of communication theory, augmented by methods from statistical mechanics and nonequilibrium thermodynamics. Cognition, often involving submodules that act as information sources, is ubiquitous across the living state. Less metabolic free energy is consumed by permitting crosstalk between biological information sources than by isolating them, leading to evolutionary exaptations that assemble shifting, tunable cognitive arrays at multiple scales, and levels of organization to meet dynamic patterns of threat and opportunity. Cognition is thus necessary for life, but it is not sufficient: An organism represents a highly patterned outcome of path-dependent, blind, variation, selection, interaction, and chance extinction in the context of an adequate flow of free energy and an environment fit for development. Complex, interacting cognitive processes within an organism both record and instantiate those evolutionary and developmental trajectories.

🔖 Thermodynamics of Prediction

Bookmarked Thermodynamics of Prediction (journals.aps.org Phys. Rev. Lett. 109, 120604 (2012))
A system responding to a stochastic driving signal can be interpreted as computing, by means of its dynamics, an implicit model of the environmental variables. The system’s state retains information about past environmental fluctuations, and a fraction of this information is predictive of future ones. The remaining nonpredictive information reflects model complexity that does not improve predictive power, and thus represents the ineffectiveness of the model. We expose the fundamental equivalence between this model inefficiency and thermodynamic inefficiency, measured by dissipation. Our results hold arbitrarily far from thermodynamic equilibrium and are applicable to a wide range of systems, including biomolecular machines. They highlight a profound connection between the effective use of information and efficient thermodynamic operation: any system constructed to keep memory about its environment and to operate with maximal energetic efficiency has to be predictive.

🔖 Statistical Physics of Adaptation

Bookmarked Statistical Physics of Adaptation (journals.aps.org Phys. Rev. X 6, 021036 (2016))
Whether by virtue of being prepared in a slowly relaxing, high-free energy initial condition, or because they are constantly dissipating energy absorbed from a strong external drive, many systems subject to thermal fluctuations are not expected to behave in the way they would at thermal equilibrium. Rather, the probability of finding such a system in a given microscopic arrangement may deviate strongly from the Boltzmann distribution, raising the question of whether thermodynamics still has anything to tell us about which arrangements are the most likely to be observed. In this work, we build on past results governing nonequilibrium thermodynamics and define a generalized Helmholtz free energy that exactly delineates the various factors that quantitatively contribute to the relative probabilities of different outcomes in far-from-equilibrium stochastic dynamics. By applying this expression to the analysis of two examples—namely, a particle hopping in an oscillating energy landscape and a population composed of two types of exponentially growing self-replicators—we illustrate a simple relationship between outcome-likelihood and dissipative history. In closing, we discuss the possible relevance of such a thermodynamic principle for our understanding of self-organization in complex systems, paying particular attention to a possible analogy to the way evolutionary adaptations emerge in living things.

🔖 Meaning = Information + Evolution by Carlo Rovelli

Bookmarked Meaning = Information + Evolution (arxiv.org)
Notions like meaning, signal, intentionality, are difficult to relate to a physical word. I study a purely physical definition of "meaningful information", from which these notions can be derived. It is inspired by a model recently illustrated by Kolchinsky and Wolpert, and improves on Dretske classic work on the relation between knowledge and information. I discuss what makes a physical process into a "signal".

🔖 Irreversibility and Heat Generation in the Computing Process by R. Landauer

Bookmarked Irreversibility and Heat Generation in the Computing Process (ieeexplore.ieee.org)
It is argued that computing machines inevitably involve devices which perform logical functions that do not have a single-valued inverse. This logical irreversibility is associated with physical irreversibility and requires a minimal heat generation, per machine cycle, typically of the order of kT for each irreversible function. This dissipation serves the purpose of standardizing signals and making them independent of their exact logical history. Two simple, but representative, models of bistable devices are subjected to a more detailed analysis of switching kinetics to yield the relationship between speed and energy dissipation, and to estimate the effects of errors induced by thermal fluctuations.

A classical paper in the history of entropy.

🔖 Why Boltzmann Brains Are Bad by Sean M. Carroll

Bookmarked Why Boltzmann Brains Are Bad (arxiv.org)
Some modern cosmological models predict the appearance of Boltzmann Brains: observers who randomly fluctuate out of a thermal bath rather than naturally evolving from a low-entropy Big Bang. A theory in which most observers are of the Boltzmann Brain type is generally thought to be unacceptable, although opinions differ. I argue that such theories are indeed unacceptable: the real problem is with fluctuations into observers who are locally identical to ordinary observers, and their existence cannot be swept under the rug by a choice of probability distributions over observers. The issue is not that the existence of such observers is ruled out by data, but that the theories that predict them are cognitively unstable: they cannot simultaneously be true and justifiably believed.

🔖 Energy flow and the organization of life | Complexity

Bookmarked Energy flow and the organization of life (Complexity, September 2007)
Understanding the emergence and robustness of life requires accounting for both chemical specificity and statistical generality. We argue that the reverse of a common observation—that life requires a source of free energy to persist—provides an appropriate principle to understand the emergence, organization, and persistence of life on earth. Life, and in particular core biochemistry, has many properties of a relaxation channel that was driven into existence by free energy stresses from the earth's geochemistry. Like lightning or convective storms, the carbon, nitrogen, and phosphorus fluxes through core anabolic pathways make sense as the order parameters in a phase transition from an abiotic to a living state of the geosphere. Interpreting core pathways as order parameters would both explain their stability over billions of years, and perhaps predict the uniqueness of specific optimal chemical pathways.

Download .pdf copy

[1]
H. Morowitz and E. Smith, “Energy flow and the organization of life,” Complexity, vol. 13, no. 1. Wiley-Blackwell, pp. 51–59, 2007 [Online]. Available: http://dx.doi.org/10.1002/cplx.20191

🔖 Evidence for a limit to human lifespan | Nature Research

Bookmarked Evidence for a limit to human lifespan (nature.com)
Driven by technological progress, human life expectancy has increased greatly since the nineteenth century. Demographic evidence has revealed an ongoing reduction in old-age mortality and a rise of the maximum age at death, which may gradually extend human longevity. Together with observations that lifespan in various animal species is flexible and can be increased by genetic or pharmaceutical intervention, these results have led to suggestions that longevity may not be subject to strict, species-specific genetic constraints. Here, by analysing global demographic data, we show that improvements in survival with age tend to decline after age 100, and that the age at death of the world’s oldest person has not increased since the 1990s. Our results strongly suggest that the maximum lifespan of humans is fixed and subject to natural constraints.
[1]
X. Dong, B. Milholland, and J. Vijg, “Evidence for a limit to human lifespan.,” Nature, vol. 538, no. 7624, pp. 257–259, Oct. 2016. [PubMed]

🔖 Hayflick, his limit, and cellular ageing | Nature Reviews Molecular Cell Biology

Bookmarked Hayflick, his limit, and cellular ageing ( Nature Reviews Molecular Cell Biology)
Almost 40 years ago, Leonard Hayflick discovered that cultured normal human cells have limited capacity to divide, after which they become senescent — a phenomenon now known as the ‘Hayflick limit’. Hayflick's findings were strongly challenged at the time, and continue to be questioned in a few circles, but his achievements have enabled others to make considerable progress towards understanding and manipulating the molecular mechanisms of ageing.
[1]
J. Shay and W. Wright, “Hayflick, his limit, and cellular ageing.,” Nat Rev Mol Cell Biol, vol. 1, no. 1, pp. 72–6, Oct. 2000. [PubMed]

🔖 Thermodynamic Uncertainty Relation for Biomolecular Processes, Phys. Rev. Lett. 114, 158101 (2015)

Bookmarked Thermodynamic Uncertainty Relation for Biomolecular Processes (Phys. Rev. Lett. 114, 158101 (2015) - journals.aps.org)
Biomolecular systems like molecular motors or pumps, transcription and translation machinery, and other enzymatic reactions, can be described as Markov processes on a suitable network. We show quite generally that, in a steady state, the dispersion of observables, like the number of consumed or produced molecules or the number of steps of a motor, is constrained by the thermodynamic cost of generating it. An uncertainty ε requires at least a cost of 2k_B T/ε^2 independent of the time required to generate the output.
[1]
A. C. Barato and U. Seifert, “Thermodynamic Uncertainty Relation for Biomolecular Processes,” Physical Review Letters, vol. 114, no. 15. American Physical Society (APS), 15-Apr-2015 [Online]. Available: http://dx.doi.org/10.1103/PhysRevLett.114.158101 [Source]

🔖 Causal Entropic Forces, Phys. Rev. Lett. 110, 168702 (2013)

Bookmarked Causal Entropic Forces (Phys. Rev. Lett. 110, 168702 (2013) journals.aps.org )
Recent advances in fields ranging from cosmology to computer science have hinted at a possible deep connection between intelligence and entropy maximization, but no formal physical relationship between them has yet been established. Here, we explicitly propose a first step toward such a relationship in the form of a causal generalization of entropic forces that we find can cause two defining behaviors of the human “cognitive niche”—tool use and social cooperation—to spontaneously emerge in simple physical systems. Our results suggest a potentially general thermodynamic model of adaptive behavior as a nonequilibrium process in open systems.
[1]
A. D. Wissner-Gross and C. E. Freer, “Causal Entropic Forces,” Physical Review Letters, vol. 110, no. 16. American Physical Society (APS), 19-Apr-2013 [Online]. Available: http://dx.doi.org/10.1103/PhysRevLett.110.168702 [Source]

 

🔖 How Life (and Death) Spring From Disorder | Quanta Magazine

Bookmarked How Life (and Death) Spring From Disorder by Philip Ball (Quanta Magazine)
Life was long thought to obey its own set of rules. But as simple systems show signs of lifelike behavior, scientists are arguing about whether this apparent complexity is all a consequence of thermodynamics.

This is a nice little general interest article by Philip Ball that does a relatively good job of covering several of my favorite topics (information theory, biology, complexity) for the layperson. While it stays relatively basic, it links to a handful of really great references, many of which I’ve already read, though several appear to be new to me. [1][2][3][4][5][6][7][8][9][10]

While Ball has a broad area of interests and coverage in his work, he’s certainly one of the best journalists working in this subarea of interests today. I highly recommend his work to those who find this area interesting.

References

[1]
E. Mayr, What Makes Biology Unique? Cambridge University Press, 2004.
[2]
A. Wissner-Gross and C. Freer, “Causal entropic forces.,” Phys Rev Lett, vol. 110, no. 16, p. 168702, Apr. 2013. [PubMed]
[3]
A. Barato and U. Seifert, “Thermodynamic uncertainty relation for biomolecular processes.,” Phys Rev Lett, vol. 114, no. 15, p. 158101, Apr. 2015. [PubMed]
[4]
J. Shay and W. Wright, “Hayflick, his limit, and cellular ageing.,” Nat Rev Mol Cell Biol, vol. 1, no. 1, pp. 72–6, Oct. 2000. [PubMed]
[5]
X. Dong, B. Milholland, and J. Vijg, “Evidence for a limit to human lifespan,” Nature, vol. 538, no. 7624. Springer Nature, pp. 257–259, 05-Oct-2016 [Online]. Available: http://dx.doi.org/10.1038/nature19793
[6]
H. Morowitz and E. Smith, “Energy Flow and the Organization of Life,” Santa Fe Institute, 07-Aug-2006. [Online]. Available: http://samoa.santafe.edu/media/workingpapers/06-08-029.pdf. [Accessed: 03-Feb-2017]
[7]
R. Landauer, “Irreversibility and Heat Generation in the Computing Process,” IBM Journal of Research and Development, vol. 5, no. 3. IBM, pp. 183–191, Jul-1961 [Online]. Available: http://dx.doi.org/10.1147/rd.53.0183
[8]
C. Rovelli, “Meaning = Information + Evolution,” arXiv, Nov. 2006 [Online]. Available: https://arxiv.org/abs/1611.02420
[9]
N. Perunov, R. A. Marsland, and J. L. England, “Statistical Physics of Adaptation,” Physical Review X, vol. 6, no. 2. American Physical Society (APS), 16-Jun-2016 [Online]. Available: http://dx.doi.org/10.1103/PhysRevX.6.021036 [Source]
[10]
S. Still, D. A. Sivak, A. J. Bell, and G. E. Crooks, “Thermodynamics of Prediction,” Physical Review Letters, vol. 109, no. 12. American Physical Society (APS), 19-Sep-2012 [Online]. Available: http://dx.doi.org/10.1103/PhysRevLett.109.120604 [Source]

🔖 A de Bruijn identity for discrete random variables by Oliver Johnson, Saikat Guha

Bookmarked A de Bruijn identity for discrete random variables by Oliver Johnson, Saikat Guha (arxiv.org)
We discuss properties of the "beamsplitter addition" operation, which provides a non-standard scaled convolution of random variables supported on the non-negative integers. We give a simple expression for the action of beamsplitter addition using generating functions. We use this to give a self-contained and purely classical proof of a heat equation and de Bruijn identity, satisfied when one of the variables is geometric.