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At least 19 recordsLinked to original sources
PubMed2006

Nonequilibrium statistical physics with fictitious time.

Problems in nonequilibrium statistical physics are characterized by the absence of a fluctuation dissipation theorem. The usual analytic route for treating these vast class of problems is to use response fields in addition to the real fields that are pertinent to a given problem. This line of argument was introduced by Martin, Siggia, and Rose. We show that instead of using the response field, one can, following the stochastic quantization of Parisi and Wu, introduce a fictitious time. In this extra dimension a fluctuation dissipation theorem is built in and provides a different outlook to problems in nonequilibrium statistical physics.

Journal Article↗
PubMed2003

New theoretical expressions for the five adsorption type isotherms classified by BET based on statistical physics treatment.

New theoretical expressions to model the five adsorption isotherm types have been established. Using the grand canonical ensemble in statistical physics, we give an analytical expression to each of five physical adsorption isotherm types classified by Brunauer, Emett, and Teller, often called BET isotherms. The establishment of these expressions is based on statistical physics and theoretical considerations. This method allowed estimation of all the mathematical parameters in the models. The physicochemical parameters intervening in the adsorption process that the models present could be deduced directly from the experimental adsorption isotherms by numerical simulation. We determine the adequate model for each type of isotherm, which fixes by direct numerical simulation the monolayer, multilayer, or condensation character. New equations are discussed and results obtained are verified for experimental data from the literature. The new theoretical expressions that we have proposed, based on statistical physics treatment, are rather powerful to better understand and interpret the various five physical adsorption type isotherms at a microscopic level.

Journal Article↗
PubMed2006

Loop calculus in statistical physics and information science.

Considering a discrete and finite statistical model of a general position we introduce an exact expression for the partition function in terms of a finite series. The leading term in the series is the Bethe-Peierls (belief propagation) (BP) contribution; the rest are expressed as loop contributions on the factor graph and calculated directly using the BP solution. The series unveils a small parameter that often makes the BP approximation so successful. Applications of the loop calculus in statistical physics and information science are discussed.

Journal Article↗
PubMed2005

The application of statistical physics to evolutionary biology.

A number of fundamental mathematical models of the evolutionary process exhibit dynamics that can be difficult to understand analytically. Here we show that a precise mathematical analogy can be drawn between certain evolutionary and thermodynamic systems, allowing application of the powerful machinery of statistical physics to analysis of a family of evolutionary models. Analytical results that follow directly from this approach include the steady-state distribution of fixed genotypes and the load in finite populations. The analogy with statistical physics also reveals that, contrary to a basic tenet of the nearly neutral theory of molecular evolution, the frequencies of adaptive and deleterious substitutions at steady state are equal. Finally, just as the free energy function quantitatively characterizes the balance between energy and entropy, a free fitness function provides an analytical expression for the balance between natural selection and stochastic drift.

Adaptation, Biological↗
PubMed1988

Analysis of steric partition behavior of molecules in membranes using statistical physics. Application to gel chromatography and electrophoresis.

The principles of statistical physics are used to formulate general expressions for the steric partition behavior of molecules in both random and ordered membrane structures that may be applied to any shape of the solute and/or the volume-excluding element of the membrane. These expressions fully define partitioning in terms of the volume excluded to point molecules and to finite-sized molecules. The mean effective exclusion volume for a molecule is calculated as a function of a global interaction energy, which varies with position, conformation, and orientation of the molecule. It allows consideration of electrostatic and other nonsteric factors. To test the model, specific partition functions are derived for several simple geometries describing the membrane and solute. Frequently, the derived expressions agree with past analyses; however, a new expression describing partitioning within an random network of fibers is derived. It agrees with past results only in the limit of low exclusion volumes. With greater volume exclusions, past results greatly overestimate the partition function. It is applied to gel electrophoresis and chromatography and survives testing with available experimental data. Unlike past analyses, it predicts nonlinear Ferguson plots for agarose gel electrophoresis. In addition, an analytical expression predicting the minimum radius of a sphere excluded from a random fiber matrix is derived, tested, and found to agree with experimental data.

Chromatography, Gel↗
PubMed1999

Application of statistical physics to heartbeat diagnosis.

We present several recent studies based on statistical physics concepts that can be used as diagnostic tools for heart failure. We describe the scaling exponent characterizing the long-range correlations in heartbeat time series as well as the multifractal features recently discovered in heartbeat rhythm. It is found that both features, the long-range correlations and the multifractility, are weaker in cases of heart failure.

Adult↗
PubMedDate not supplied

[Solid interactions in statistical physics of biopolymers].

A short survey is presented of the development of statistical physics of biological macromolecules and its modern state. The main attention is paid to the analysis of the manifestation of scale invariance and fractal properties of biopolymers--DNA and proteins. Phase transitions related to the phase structure of DNA are briefly analysed. A more detailed account is given of phase transitions in globular proteins, denaturation problem, two phases of the melted globule and the theory of heteropolymers included. Some unsolved problems of this field of science and its prospects are discussed.

Biophysical Phenomena↗
PubMed2002

Random graph coloring: statistical physics approach.

The problem of vertex coloring in random graphs is studied using methods of statistical physics and probability. Our analytical results are compared to those obtained by exact enumeration and Monte Carlo simulations. We critically discuss the merits and shortcomings of the various methods, and interpret the results obtained. We present an exact analytical expression for the two-coloring problem as well as general replica symmetric approximated solutions for the thermodynamics of the graph coloring problem with p colors and K-body edges.

Journal Article↗
PubMed2000

Mapping of statistical physics to information theory with application to biological systems.

The problem of achieving a mapping of formalisms in statistical physics and theoretical biology to information theory is discussed using an example for canonical ensembles. We extend the meaning of the Handscomb Monte-Carlo method to a general recipe for the transformation from a "configuration" space to a "sentence" space. The ensemble of "sentences" and its corresponding source uncertainty function are introduced. A possible mapping procedure based on a generalization of the Handscomb representation is described. For a biological illustration, we present a way to introduce a pathway representation to describe metabolic processes in living systems.

Animals↗
PubMed2005

Colloids as model systems for problems in statistical physics.

Owing to their mesoscopic length scales, colloidal suspensions provide ideal model systems suitable for addressing many problems in the field of statistical physics. Exemplarily, we highlight the versatile nature of such systems by discussing experiments with stochastic resonance and a practical realization of a recently proposed ratchet cellular automaton.

Algorithms↗
PubMed2005

A docking analysis of the statistical physics of protein-protein recognition.

We describe protein-protein recognition within the frame of the random energy model of statistical physics. We simulate, by docking the component proteins, the process of association of two proteins that form a complex. We obtain the energy spectrum of a set of protein-protein complexes of known three-dimensional structure by performing docking in random orientations and scoring the models thus generated. We use a coarse protein representation where each amino acid residue is replaced by its Voronoï cell, and derive a scoring function by applying the evolutionary learning program ROGER to a set of parameters measured on that representation. Taking the scores of the docking models to be interaction energies, we obtain energy spectra for the complexes and fit them to a Gaussian distribution, from which we derive physical parameters such as a glass transition temperature and a specificity transition temperature.

Biophysics↗
PubMed2003

Statistical-physical model for foliage clutter in ultra-wideband synthetic aperture radar images.

Analyzing foliage-penetrating (FOPEN) ultra-wideband synthetic aperture radar (SAR) images is a challenging problem owing to the noisy and impulsive nature of foliage clutter. Indeed, many target-detection algorithms for FOPEN SAR data are characterized by high false-alarm rates. In this work, a statistical-physical model for foliage clutter is proposed that explains the presence of outliers in the data and suggests the use of symmetric alpha-stable (SalphaS) distributions for accurate clutter modeling. Furthermore, with the use of general assumptions of the noise sources and propagation conditions, the proposed model relates the parameters of the SalphaS model to physical parameters such as the attenuation coefficient and foliage density.

Journal Article↗
PubMed1999

Statistical physics and physiology: monofractal and multifractal approaches.

Even under healthy, basal conditions, physiologic systems show erratic fluctuations resembling those found in dynamical systems driven away from a single equilibrium state. Do such "nonequilibrium" fluctuations simply reflect the fact that physiologic systems are being constantly perturbed by external and intrinsic noise? Or, do these fluctuations actually, contain useful, "hidden" information about the underlying nonequilibrium control mechanisms? We report some recent attempts to understand the dynamics of complex physiologic fluctuations by adapting and extending concepts and methods developed very recently in statistical physics. Specifically, we focus on interbeat interval variability as an important quantity to help elucidate possibly non-homeostatic physiologic variability because (i) the heart rate is under direct neuroautonomic control, (ii) interbeat interval variability is readily measured by noninvasive means, and (iii) analysis of these heart rate dynamics may provide important practical diagnostic and prognostic information not obtainable with current approaches. The analytic tools we discuss may be used on a wider range of physiologic signals. We first review recent progress using two analysis methods--detrended fluctuation analysis and wavelets--sufficient for quantifying monofractual structures. We then describe recent work that quantifies multifractal features of interbeat interval series, and the discovery that the multifractal structure of healthy subjects is different than that of diseased subjects.

Biophysical Phenomena↗
PubMed2006

Performance analysis of LVQ algorithms: a statistical physics approach.

Learning vector quantization (LVQ) constitutes a powerful and intuitive method for adaptive nearest prototype classification. However, original LVQ has been introduced based on heuristics and numerous modifications exist to achieve better convergence and stability. Recently, a mathematical foundation by means of a cost function has been proposed which, as a limiting case, yields a learning rule similar to classical LVQ2.1. It also motivates a modification which shows better stability. However, the exact dynamics as well as the generalization ability of many LVQ algorithms have not been thoroughly investigated so far. Using concepts from statistical physics and the theory of on-line learning, we present a mathematical framework to analyse the performance of different LVQ algorithms in a typical scenario in terms of their dynamics, sensitivity to initial conditions, and generalization ability. Significant differences in the algorithmic stability and generalization ability can be found already for slightly different variants of LVQ. We study five LVQ algorithms in detail: Kohonen's original LVQ1, unsupervised vector quantization (VQ), a mixture of VQ and LVQ, LVQ2.1, and a variant of LVQ which is based on a cost function. Surprisingly, basic LVQ1 shows very good performance in terms of stability, asymptotic generalization ability, and robustness to initializations and model parameters which, in many cases, is superior to recent alternative proposals.

Algorithms↗
PubMed2005

Statistical physics of grain-boundary engineering.

Percolation theory is now standard in the analysis of polycrystalline materials where the grain boundaries can be divided into two distinct classes, namely "good" boundaries that have favorable properties and "bad" boundaries that seriously degrade the material performance. Grain-boundary engineering (GBE) strives to improve material behavior by engineering the volume fraction c and arrangement of good grain boundaries. Two key percolative processes in GBE materials are the onset of percolation of a strongly connected aggregate of grains, and the onset of a connected path of weak grain boundaries. Using realistic polycrystalline microstructures, we find that in two dimensions the threshold for strong aggregate percolation c(SAP) and the threshold for weak boundary percolation c(WBP) are equivalent and have the value c(SAP) = c(WBP) =0.38 (1) , which is slightly higher than the threshold found for regular hexagonal grain structures, c(RH) =2 sin (pi/18) =0.347... . In three dimensions strong aggregate percolation and weak boundary percolation occur at different locations and we find c(SAP) =0.12 (3) and c(WBP) =0.77 (3) . The critical current in high T(c) materials and the cohesive energy in structural systems are related to the critical manifold problem in statistical physics. We develop a theory of critical manifolds in GBE materials, which has three distinct regimes: (i) low concentrations, where random manifold theory applies, (ii) critical concentrations where percolative scaling theory applies, and (iii) high concentrations, c> c(SAP) , where the theory of periodic elastic media applies. Regime (iii) is perhaps most important practically and is characterized by a critical length L(c) , which is the size of cleavage regions on the critical manifold. In the limit of high contrast epsilon-->0 , we find that in two dimensions L(c) proportional, gc/ (1-c) , while in three dimensions L(c) proportional, g exp [ b(0) c/ (1-c) ] / [c (1-c) ](1/2) , where g is the average grain size, epsilon is the ratio of the bonding energy of the weak boundaries to that of the strong boundaries, and b(0) is a constant which is of order 1. Many of the properties of GBE materials can be related to L(c) , which diverges algebraically on approach to c=1 in two dimensions, but diverges exponentially in that limit in three dimensions. We emphasize that GBE percolation processes and critical manifold behavior are very different in two dimensions as compared to three dimensions. For this reason, the use of two dimensional models to understand the behavior of bulk GBE materials can be misleading.

Journal Article↗
PubMedDate not supplied

A physical statistics theory for detectability of target signals in noisy images. I. Mathematical background, empirical review, and development of theory.

This paper addresses the physical probability of finding, by random chance of noise fluctuations, false-positive events in the background field of view of a noisy image. The signal levels of these random events are characterized by a general noise power spectrum; if they are comparable in magnitude with that of a true target signal, averaged over an area equal to that of the true target signal, then the false-positive events obscure the confidence of the true signal identification. The theory shows that the statistics of this phenomenon depend very strongly, and with distinct threshold behavior, upon the generalized power-signal-to-noise ratio of the true target signal; the behavior depends only weakly upon other factors, e.g., the background field of view area examined with respect to the true target area. Evaluation of even the simplest model of detection confidence, based upon this theory, yields several immediate results. The predicted SNR at threshold is approximately 3.5, with a variation of +/- 0.5 from 10%-95% confidence-of-detection levels. The theory is applied also to systems where display or intrinsic signal detection properties, rather than system inputs, limit the statistics. In this case, the theory predicts, in agreement with experiments, contrast-limiting effects of 1% contrast for the human eye vision system and 5% contrast for typical TV displays of scintigraphic images. When experimental detectability studies of numerous investigators all are converted to a uniform specification of the output power-average-signal-to-noise ratio, then the theoretical predictions here give an excellent description of all major aspects of the empirical results.

False Positive Reactions↗
PubMed2000

Statistical physics of regular low-density parity-check error-correcting codes

A variation of Gallager error-correcting codes is investigated using statistical mechanics. In codes of this type, a given message is encoded into a codeword that comprises Boolean sums of message bits selected by two randomly constructed sparse matrices. The similarity of these codes to Ising spin systems with random interaction makes it possible to assess their typical performance by analytical methods developed in the study of disordered systems. The typical case solutions obtained via the replica method are consistent with those obtained in simulations using belief propagation decoding. We discuss the practical implications of the results obtained and suggest a computationally efficient construction for one of the more practical configurations.

Journal Article↗