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PubMed2003

Scaling and universality in continuous length combinatorial optimization.

We consider combinatorial optimization problems defined over random ensembles and study how solution cost increases when the optimal solution undergoes a small perturbation delta. For the minimum spanning tree, the increase in cost scales as delta2. For the minimum matching and traveling salesman problems in dimension d >/= 2, the increase scales as delta3; this is observed in Monte Carlo simulations in d = 2, 3, 4 and in theoretical analysis of a mean-field model. We speculate that the scaling exponent could serve to classify combinatorial optimization problems of this general kind into a small number of distinct categories, similar to universality classes in statistical physics.

Journal Article↗

PubMed2002

Olfactory search at high Reynolds number.

Locating the source of odor in a turbulent environment-a common behavior for living organisms-is nontrivial because of the random nature of mixing. Here we analyze the statistical physics aspects of the problem and propose an efficient strategy for olfactory search that can work in turbulent plumes. The algorithm combines the maximum likelihood inference of the source position with an active search. Our approach provides the theoretical basis for the design of olfactory robots and the quantitative tools for the analysis of the observed olfactory search behavior of living creatures (e.g., odor-modulated optomotor anemotaxis of moths).

Algorithms↗

PubMed2002

Neurotoxic effects of thioflavin S-positive amyloid deposits in transgenic mice and Alzheimer's disease.

Despite extensive deposition of putatively neurotoxic amyloid-beta (Abeta) protein in the brain, it has not been possible to demonstrate an association of Abeta deposits with neuronal loss in Alzheimer's disease (AD), and neuronal loss is minimal in transgenic mouse models of AD. Using triple immunostaining confocal microscopy and analyzing the images with the cross-correlation density map method from statistical physics, we directly compared Abeta deposition, Abeta morphology, and neuronal architecture. We found dramatic, focal neuronal toxicity associated primarily with thioflavin S-positive fibrillar Abeta deposits in both AD and PSAPP mice. These results, along with computer simulations, suggest that Abeta develops neurotoxic properties in vivo when it adopts a fibrillar beta-pleated sheet conformation.

Alzheimer Disease↗

PubMed1997

Fluorescence correlation spectroscopy: diagnostics for sparse molecules.

The robust glow of molecular fluorescence renders even sparse molecules detectable and susceptible to analysis for concentration, mobility, chemistry, and photophysics. Correlation spectroscopy, a statistical-physics-based tool, gleans quantitative information from the spontaneously fluctuating fluorescence signals obtained from small molecular ensembles. This analytical power is available for studying molecules present at minuscule concentrations in liquid solutions (less than one nanomolar), or even on the surfaces of living cells at less than one macromolecule per square micrometer. Indeed, routines are becoming common to detect, locate, and examine individual molecules under favorable conditions.

Biophysics↗

PubMed2001

New method of estimating inbreeding in large semi-isolated populations with application to historic Britain.

The purpose of this paper is to introduce a new method of estimating inbreeding in large, relatively isolated, populations over historic times, to demonstrate its application, and indicate some of its limitations and future developments. The method is based on the "paradox" of genealogy, and requires only that the variation of the population size be known, at least reasonably well, over an extended historic period. In this study a method has been developed to model this "paradox" which allows an estimation of the minimum level of inbreeding necessary for a given population curve in terms of values of Pearl's coefficients for each generation. As an example, the method is applied to the population of Britain. It is found that the frequency of siblings occurring in the same generation of a pedigree varies with the population size according to the Fermi-Dirac equation of statistical physics. The effect of introducing a single known estimate of inbreeding into the model is to make the otherwise diverse results for both the actual numbers of ancestors in a generation and the corresponding coefficients of inbreeding to converge.

Consanguinity↗

PubMed2006

Computing Bayes factors using thermodynamic integration.

In the Bayesian paradigm, a common method for comparing two models is to compute the Bayes factor, defined as the ratio of their respective marginal likelihoods. In recent phylogenetic works, the numerical evaluation of marginal likelihoods has often been performed using the harmonic mean estimation procedure. In the present article, we propose to employ another method, based on an analogy with statistical physics, called thermodynamic integration. We describe the method, propose an implementation, and show on two analytical examples that this numerical method yields reliable estimates. In contrast, the harmonic mean estimator leads to a strong overestimation of the marginal likelihood, which is all the more pronounced as the model is higher dimensional. As a result, the harmonic mean estimator systematically favors more parameter-rich models, an artefact that might explain some recent puzzling observations, based on harmonic mean estimates, suggesting that Bayes factors tend to overscore complex models. Finally, we apply our method to the comparison of several alternative models of amino-acid replacement. We confirm our previous observations, indicating that modeling pattern heterogeneity across sites tends to yield better models than standard empirical matrices.

Amino Acid Sequence↗

PubMed1992

A program for the application of the radial distribution function to cluster analysis in cell biology.

The radial distribution function g(r) is one measure of spatial pattern commonly used in statistical physics to analyze the structure of liquids and has been used in several cellular systems. The graphs of the radial distribution function present three different functional forms. The first form indicates a random distribution; in the second form the graph is characteristic of the cluster distribution; and the third type is characteristic of substantial order. The Funct-G program uses the coordinates (x,y) of each point on m photographs to calculate the radial distribution function g(r) and produce a histogram to analyze graphically this function and to define the distribution model.

Cell Biology↗

PubMed1993

Estimation of the parameters of a binary Markov random field on a graph with application to fibre type distributions in a muscle cross-section.

Methods are discussed for the estimation of the parameters of a binary Markov random field (BMRF) defined on a graph. The standard method is maximum pseudo-likelihood (MPL) estimation. Maximum likelihood (ML) estimation has been hampered in the past by the intractability of the likelihood function. Recently Markov chain Monte Carlo (MCMC) methods have been introduced for ML estimation. In this paper a new method for Monte Carlo maximum likelihood is described. It is used for the estimation of the parameters of a simple model (the Ising model of statistical physics). As an application the distribution of fibre types in a cross-section of human muscle is analysed.

Animals↗

PubMed2002

Biophysical study of the globular organisation of interphase chromosomes.

The globular model of interphase chromosomes is studied using methods involving the statistical physics of polymers. An interphase chromatid is represented as a flexible chain of structural sub-units, or superdomains (SDs). Each SD is simulated as a number of chromatin fibre loops fixed at a nuclear matrix core. A chain of SDs is further folded in the nucleus in a compact conformation owing to volumetric interactions between SDs. The algorithm used is extended to incorporate the chain anchorage at different points. Excluded volume effects are taken into account in Monte Carlo simulation at both the SD and whole chromosome level. A variety of structures is observed in computer experiments. The simulation results correlate with the available experimental data.

Biophysics↗

PubMed2006

Dodgson condensation, alternating signs and square ice.

Starting with the numbers 1,2,7,42,429,7436, what is the next term in the sequence? This question arose in the area of mathematics called algebraic combinatorics, which deals with the precise counting of sets of objects, but it goes back to Lewis Carroll's work on determinants. The resolution of the problem was only achieved at the end of the last century, and with two completely different approaches: the first involved extensive verification by computer algebra and a huge posse of referees, while the second relied on an unexpected connection with the theory of 'square ice' in statistical physics. This paper, aimed at a general scientific audience, explains the background to this problem and how subsequent developments are leading to a fruitful interplay between algebraic combinatorics, mathematical physics and number theory.

Journal Article↗

PubMed1999

Superadditive correlation.

The fact that correlation does not imply causation is well known. Correlation between variables at two sites does not imply that the two sites directly interact, because, e.g., correlation between distant sites may be induced by chaining of correlation between a set of intervening, directly interacting sites. Such "noncausal correlation" is well understood in statistical physics: an example is long-range order in spin systems, where spins which have only short-range direct interactions, e.g., the Ising model, display correlation at a distance. It is less well recognized that such long-range "noncausal" correlations can in fact be stronger than the magnitude of any causal correlation induced by direct interactions. We call this phenomenon superadditive correlation (SAC). We demonstrate this counterintuitive phenomenon by explicit examples in (i) a model spin system and (ii) a model continuous variable system, where both models are such that two variables have multiple intervening pathways of indirect interaction. We apply the technique known as decimation to explain SAC as an additive, constructive interference phenomenon between the multiple pathways of indirect interaction. We also explain the effect using a definition of the collective mode describing the intervening spin variables. Finally, we show that the SAC effect is mirrored in information theory, and is true for mutual information measures in addition to correlation measures. Generic complex systems typically exhibit multiple pathways of indirect interaction, making SAC a potentially widespread phenomenon. This affects, e.g., attempts to deduce interactions by examination of correlations, as well as, e.g., hierarchical approximation methods for multivariate probability distributions, which introduce parameters based on successive orders of correlation.

Journal Article↗

PubMed1999

Finite-connectivity systems as error-correcting codes.

We investigate the performance of parity check codes using the mapping onto Ising spin systems proposed by Sourlas [Nature (London) 339, 693 (1989); Europhys. Lett. 25, 159 (1994)]. We study codes where each parity check comprises products of K bits selected from the original digital message with exactly C checks per message bit. We show, using the replica method, that these codes saturate Shannon's coding bound for K-->infinity when the code rate K/C is finite. We then examine the finite temperature case to assess the use of simulated annealing methods for decoding, study the performance of the finite K case, and extend the analysis to accommodate different types of noisy channels. The connection between statistical physics and belief propagation decoders is discussed and the dynamics of the decoding itself is analyzed. Further insight into new approaches for improving the code performance is given.

Journal Article↗

PubMed2000

Cascading parity-check error-correcting codes

A method for improving the performance of sparse-matrix based parity check codes is proposed, based on insight gained from methods of statistical physics. The advantages of this approach are demonstrated on an existing encoding/decoding paradigm suggested by Sourlas. We also discuss the application of the same method to more advanced codes of a similar type.

Journal Article↗

PubMed2000

Thermal, nonequilibrium phase space for networked computers

It is shown that networks of computers can be described by concepts of statistical physics. Computers in a network behave like systems coupled to a thermal reservoir. The role of thermal fluctuations is played by computing transactions. A thermal Kubo-Martin-Schwinger condition arises due to the coupling of a computer to a strong periodic source, namely, the daily and weekly usage patterns of the system.

Journal Article↗

PubMed2000

Algorithmic complexity in the minority game

In this paper, we present our approach for the study of the complexity of Minority Game using tools from thermodynamics and statistical physics. Previous attempts were based on the behavior of volatility, an observable of the financial markets. Our approach focuses on some properties of the binary stream of outcomes of the game. Physical complexity, a magnitude rooted in Kolmogorov-Chaitin theory, allows us to explain some properties of collective behavior of the agents. Mutual information function, a measure related to Shannon's information entropy, was useful to observe a kind of phase transition when applied to the binary string of the whole history of the game.

Journal Article↗

PubMed2000

Difference-quotient turbulence model: analytical solutions for the core region of plane poiseuille flow

The difference-quotient turbulence model and an explanation in terms of fluid dynamics is presented. With this model an analytical theory for the symmetric core region of turbulent plane Poiseuille flow is derived. The equations and the solutions reveal an order/disorder transition with analogies in other scientific fields where statistical physics applies. At moderate Reynolds numbers the time-averaged profile of the downstream mean velocity and a second-order fluctuation correlation are described in terms of Bessel functions of the first type. At the infinite Reynolds number limit these solutions converge toward functions which can be described by simple geometric figures. Experimental data confirm the model results.

Journal Article↗

PubMed2001

Entropy-based analysis of the number partitioning problem.

In this paper we apply the multicanonical method of statistical physics on the number partitioning problem (NPP). This problem is a basic NP-hard problem from computer science, and can be formulated as a spin-glass problem. We compute the spectral degeneracy, which gives us information about the number of solutions for a given cost E and cardinality difference m. We also study an extension of this problem for Q partitions. We show that a fundamental difference on the spectral degeneracy of the generalized (Q>2) NPP exists, which could explain why it is so difficult to find good solutions for this case.

Journal Article↗

PubMed2001

Rotation-induced phase transition in a spherical gravitating system.

Due to the infinite range and singularity of the gravitational force, it is difficult to directly apply the standard methods of statistical physics to self-gravitating systems, e.g., interstellar grains, globular clusters, galaxies, etc. Unusual phenomena can occur, such as a negative heat capacity, unbounded mass, or the gravothermal catastrophe where the equilibrium state is fully collapsed and the entropy is unbounded. Using mean field theory, we investigate the influence of rotation on a purely spherical gravitational system. Although spherical symmetry nullifies the total angular momentum, its square is finite and conserved. Here we study the case where each particle has specific angular momentum of the same magnitude l. We rigorously prove the existence of an upper bound on the entropy and a lower bound for the energy. We demonstrate that, in the microcanonical and canonical ensembles, a phase transition occurs when l falls below a critical value. We characterize the properties of each phase and construct the coexistence curve for each ensemble. Possible applications to astrophysics are considered.

Journal Article↗