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PubMed1999

Fractal behavior in quantum statistical physics.

The properties of an ideal gas of spinless particles are investigated by using the path integral formalism. It is shown that the quantum paths exhibit a fractal character which remains unchanged in the relativistic domain provided the creation of new particles is avoided, and the Brownian motion remains the stochastic process associated with the quantum paths. These results are obtained by using a special representation of the Klein-Gordon wave equation. On the quantum paths the relation between velocity and momentum is not the usual one. The mean square value of the velocity depends on the time needed to define the velocity and its value shows the interplay between pure quantum effects and thermodynamics. The fractal character is also investigated starting from wave equations by analyzing the evolution of a Gaussian wave packet via the Hausdorff dimension. Both approaches give the same fractal character in the same limit. It is shown that the time that appears in the path integral behaves like an ordinary time, and the key quantity is the time interval needed for the thermostat to give to the particles a thermal action equal to the quantum of action. Thus, the partition function calculated via the path integral formalism also describes the dynamics of the system for short time intervals. For low temperatures, it is shown that a time-energy uncertainty relation is verified at the end of the calculations. The energy involved in this relation has not a thermodynamic meaning but results from the fact that the particles do not follow the equations of motion along the paths. The results suggest that the density matrix obtained by quantification of the classical canonical distribution function via the path integral formalism should not be totally identical to that obtained via the usual route.

Journal Article↗
PubMed2003

Statistical physics of RNA folding.

We discuss the physics of RNA as described by its secondary structure. We examine the static properties of a homogeneous RNA model that includes pairing and base stacking energies as well as entropic costs for internal loops. For large enough loop costs the model exhibits a thermal denaturation transition which we analyze in terms of the radius of gyration. We point out an inconsistency in the standard approach to RNA secondary structure prediction for large molecules. Under an external force a second-order phase transition between a globular and an extended phase takes place. A Harris-type criterion shows that sequence disorder does not affect the correlation length exponent while the other critical exponents are modified in the glass phase. However, at high temperatures, on a coarse-grained level, disordered RNA is well described by a homogeneous model. The characteristics of force-extension curves are discussed as a function of the energy parameters. We show that the force transition is always second order. A reentrance phenomenon relevant for real disordered RNA is predicted.

Journal Article↗
PubMed2005

Statistical physics models for nacre fracture simulation.

Natural biological materials such as nacre (or mother-of-pearl), exhibit phenomenal fracture strength and toughness properties despite the brittle nature of their constituents. For example, nacre's work of fracture is three orders of magnitude greater than that of a single crystal of its constituent mineral. This study investigates the fracture properties of nacre using a simple discrete lattice model based on continuous damage random thresholds fuse network. The discrete lattice topology of the proposed model is based on nacre's unique brick and mortar microarchitecture, and the mechanical behavior of each of the bonds in the discrete lattice model is governed by the characteristic modular damage evolution of the organic matrix that includes the mineral bridges between the aragonite platelets. The analysis indicates that the excellent fracture properties of nacre are a result of their unique microarchitecture, repeated unfolding of protein molecules (modular damage evolution) in the organic polymer, and the presence of fiber bundle of mineral bridges between the aragonite platelets. The numerical results obtained using this simple discrete lattice model are in excellent agreement with the previously obtained experimental results, such as nacre's stiffness, tensile strength, and work of fracture.

Animals↗
PubMed2001

The Ising model in physics and statistical genetics.

Interdisciplinary communication is becoming a crucial component of the present scientific environment. Theoretical models developed in diverse disciplines often may be successfully employed in solving seemingly unrelated problems that can be reduced to similar mathematical formulation. The Ising model has been proposed in statistical physics as a simplified model for analysis of magnetic interactions and structures of ferromagnetic substances. Here, we present an application of the one-dimensional, linear Ising model to affected-sib-pair (ASP) analysis in genetics. By analyzing simulated genetics data, we show that the simplified Ising model with only nearest-neighbor interactions between genetic markers has statistical properties comparable to much more complex algorithms from genetics analysis, such as those implemented in the Allegro and Mapmaker-Sibs programs. We also adapt the model to include epistatic interactions and to demonstrate its usefulness in detecting modifier loci with weak individual genetic contributions. A reanalysis of data on type 1 diabetes detects several susceptibility loci not previously found by other methods of analysis.

Algorithms↗
PubMed1986

Brief survey of scope and limitations of quantum and statistical mechanical methods.

An attempt is made to delineate the scope and limitations, and future perspectives, of the theoretical methods being applied increasingly to various aspects of drug design and associated problems. The two methods of approach, quantum mechanics and statistical physics (Monte Carlo, Molecular Dynamics), are used to evaluate such properties as electron density distribution, structure and conformation, intermolecular interactions, etc. for isolated molecules and their autoassociates, and for interactions with the environment (e.g., solvent, receptor molecules). The validity of such calculations, dependent on factors such as geometrical optimalization, correlation energy and differing approximations of the form of the wave function, is illustrated in the case of enol-keto tautomerism of nitrogen heterocycles, relevant to the biological (including chemotherapeutic) activities of some nucleoside analogues. Intermolecular interactions, including the role of solvent, are assessed for purine and pyrimidines. The scope of the Molecular Dynamics methods is exemplified by its application to the mode of action of lysozyme.

Drug Compounding↗
PubMed2002

On Wiener filtering and the physics behind statistical modeling.

The closed-form solution of the so-called statistical multivariate calibration model is given in terms of the pure component spectral signal, the spectral noise, and the signal and noise of the reference method. The "statistical" calibration model is shown to be as much grounded on the physics of the pure component spectra as any of the "physical" models. There are no fundamental differences between the two approaches since both are merely different attempts to realize the same basic idea, viz., the spectrometric Wiener filter. The concept of the application-specific signal-to-noise ratio (SNR) is introduced, which is a combination of the two SNRs from the reference and the spectral data. Both are defined and the central importance of the latter for the assessment and development of spectroscopic instruments and methods is explained. Other statistics like the correlation coefficient, prediction error, slope deficiency, etc., are functions of the SNR. Spurious correlations and other practically important issues are discussed in quantitative terms. Most important, it is shown how to use a priori information about the pure component spectra and the spectral noise in an optimal way, thereby making the distinction between statistical and physical calibrations obsolete and combining the best of both worlds. Companies and research groups can use this article to realize significant savings in cost and time for development efforts.

Algorithms↗
PubMed1989

A critical review of the physics and statistics of condoms and their role in individual versus societal survival of the AIDS epidemic.

Condom failure rates for HIV are substantially greater than for pregnancy, even for highly motivated people who may reach the limit set by allowed manufacturing imperfections. This makes condoms ineffective for lifelong protection from HIV-infected sexual partners; therefore, in general, condoms provide inadequate risk reduction for the individual. Nevertheless, they are sufficiently effective that if everyone used condoms, the AIDS epidemic would stop. Quantitative public health goals to reduce the "reproductive rate" of HIV from an estimated 4-12 people infected per infected person to below 1 are needed. Government and scientific testing of condoms could be improved statistically and by utilizing relevant physics.

Acquired Immunodeficiency Syndrome↗
PubMed2006

Maximum independent set on diluted triangular lattices.

Core percolation and maximum independent set on random graphs have recently been characterized using the methods of statistical physics. Here we present a statistical physics study of these problems on bond diluted triangular lattices. Core percolation critical behavior is found to be consistent with the standard percolation values, though there are strong finite size effects. A transfer matrix method is developed and applied to find accurate values of the density and degeneracy of the maximum independent set on lattices of limited width but large length. An extrapolation of these results to the infinite lattice limit yields high precision results, which are tabulated. These results are compared to results found using both vertex based and edge based local probability recursion algorithms, which have proven useful in the analysis of hard computational problems, such as the satisfiability problem.

Journal Article↗
PubMed2004

Dynamics of traffic flow with real-time traffic information.

We studied dynamics of traffic flow with real-time information provided. Provision of the real-time traffic information based on advancements in telecommunication technology is expected to facilitate the efficient utilization of available road capacity. This system has a potentiality of not only engineering for road usage but also the science of complexity series. In the system, the information plays a role of feedback connecting microscopic and macroscopic phenomena beyond the hierarchical structure of statistical physics. In this paper, we tried to clarify how the information works in a network of traffic flow from the perspective of statistical physics. The dynamical feature of the traffic flow is abstracted by a contrastive study between the nonequilibrium statistical physics and a computer simulation based on cellular automaton. We found that the information disrupts the local equilibrium of traffic flow by a characteristic dissipation process due to interaction between the information and individual vehicles. The dissipative structure was observed in the time evolution of traffic flow driven far from equilibrium as a consequence of the breakdown of the local-equilibrium hypothesis.

Journal Article↗
PubMed2000

Information geometry of mean-field approximation.

I present a general theory of mean-field approximation based on information geometry and applicable not only to Boltzmann machines but also to wider classes of statistical models. Using perturbation expansion of the Kullback divergence (or Plefka expansion in statistical physics), a formulation of mean-field approximation of general orders is derived. It includes in a natural way the "naive" mean-field approximation and is consistent with the Thouless-Anderson-Palmer (TAP) approach and the linear response theorem in statistical physics.

Artificial Intelligence↗
PubMed2002

[Assessment of image reconstruction parameters in PET using physical and statistical figures of merit].

The aim of this study was to analyze the recommended OSEM image reconstruction parameters in positron emission tomography (PET). Spatial resolution, signal-to-noise ratio, and contrast were used as physical figures of merit (FOM). For statistical FOMs, the t-value and the area under the receiver operating characteristic (ROC) were employed. The spatial resolution was measured with 21 point sources. The signal-to-noise ratio, the contrast, and the t-value were investigated with a whole-body phantom with hollow spheres inserted. A phantom containing line sources was used for ROC analysis. As result, the reconstruction parameters recommended for visual evaluation lead to images with an adequate lesion detectability. The quantitative reconstruction, however, needs improvement.

Artifacts↗