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PubMed2001

Dynamical approach to the microcanonical ensemble.

An analytical method to compute thermodynamic properties of a given Hamiltonian system is proposed. This method combines ideas of both dynamical systems and ensemble approaches to thermodynamics, providing de facto a possible alternative to traditional ensemble methods. Thermodynamic properties are extracted from effective motion equations. These equations are obtained by introducing a general variational principle applied to an action averaged over a statistical ensemble of paths defined on the constant energy surface. The method is applied first to the one-dimensional beta-Fermi-Pasta-Ulam chain and to the two-dimensional lattice straight phi(4) model. In both cases, the method gives a good insight of some of their statistical and dynamical properties.

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PubMed2002

Single-particle entropy in (1+2)-body random matrix ensembles.

Random matrix ensembles defined by a mean-field one-body plus a chaos generating random two-body interaction (called embedded Gaussian orthogonal ensembles of (1+2)-body interactions[EGOE(1+2)]) predict for the entropy defined by the occupation numbers of single-particle states, in the chaotic domain, an essentially one parameter Gaussian form for their energy dependence. Numerical embedded ensemble calculations are compared with the theory. In addition, it is shown that the single-particle entropy, thermodynamic entropy defined by the state density and information entropy defined by wave functions in the mean-field basis for EGOE(1+2) describe the results known for interacting Fermi systems such as those obtained from nuclear shell model.

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PubMed2003

Non-Gaussian random-matrix ensembles with banded spectra.

Non-Gaussian random-matrix ensembles are important in many applications. We propose Monte Carlo and Langevin methods for generating non-Gaussian ensembles and their eigenvalue spectra. We also provide a general framework for analytic studies of the level density in these ensembles. We show that, in general, the level densities exhibit banded spectra, with important implications for mesoscopic systems and complex nuclei. The universality of energy-level fluctuations is confirmed.

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PubMed2004

Ensemble theory for force networks in hyperstatic granular matter.

An ensemble approach for force networks in static granular packings is developed. The framework is based on the separation of packing and force scales, together with an a priori flat measure in the force phase space under the constraints that the contact forces are repulsive and balance on every particle. In this paper we will give a general formulation of this force network ensemble, and derive the general expression for the force distribution P(f). For small regular packings these probability densities are obtained in closed form, while for larger packings we present a systematic numerical analysis. Since technically the problem can be written as a noninvertible matrix problem (where the matrix is determined by the contact geometry), we study what happens if we perturb the packing matrix or replace it by a random matrix. The resulting P(f) 's differ significantly from those of normal packings, which touches upon the deep question of how network statistics is related to the underlying network structure. Overall, the ensemble formulation opens up a different perspective on force networks that is analytically accessible, and which may find applications beyond granular matter.

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PubMed2006

Simulation of the density of states in isothermal and adiabatic ensembles.

This paper provides a unified treatment of the fundamental methods used to obtain the density of states via molecular simulations with isothermal ensembles (IEs) and adiabatic ensembles (AEs). Our analysis and results show that provides a natural bridge to go back and forth between IE and AE simulation data. They also underline the difference between the density of states of potential energy macrostates and that of total energy macrostates Omega, even though both provide access to the thermodynamic properties of the system. Visited-states approaches and transition matrix methods are described and applied to the Lennard-Jones fluid to target omega and Omega as functions of energy and volume macrostates. It is shown that one can obtain omega via a generalized acceptance-ratio formula that is applicable regardless of the conditions at which the ensemble is simulated. In this way, one can obtain while performing conventional IE or AE simulations, and do it at no extra cost and with a higher accuracy than is achievable with histogram methods.

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PubMed2006

Force generation in small ensembles of Brownian motors.

The motility of certain gram-negative bacteria is mediated by retraction of type IV pili surface filaments, which are essential for infectivity. The retraction is powered by a strong molecular motor protein, PilT, producing very high forces that can exceed 150 pN. The molecular details of the motor mechanism are still largely unknown, while other features have been identified, such as the ring-shaped protein structure of the PilT motor. The surprisingly high forces generated by the PilT system motivate a model investigation of the generation of large forces in molecular motors. We propose a simple model, involving a small ensemble of motor subunits interacting through the deformations on a circular backbone with finite stiffness. The model describes the motor subunits in terms of diffusing particles in an asymmetric, time-dependent binding potential (flashing ratchet potential), roughly corresponding to the ATP hydrolysis cycle. We compute force-velocity relations in a subset of the parameter space and explore how the maximum force (stall force) is determined by stiffness, binding strength, ensemble size, and degree of asymmetry. We identify two qualitatively different regimes of operation depending on the relation between ensemble size and asymmetry. In the transition between these two regimes, the stall force depends nonlinearly on the number of motor subunits. Compared to its constituents without interactions, we find higher efficiency and qualitatively different force-velocity relations. The model captures several of the qualitative features obtained in experiments on pilus retraction forces, such as roughly constant velocity at low applied forces and insensitivity in the stall force to changes in the ATP concentration.

Adenosine Triphosphatases↗

PubMed2006

Free-energy calculations with multiple Gaussian modified ensembles.

We present a Monte Carlo algorithm, which samples free energies of complex systems. Less probable configurations are populated with the help of a multitude of additional Gaussian weights and parallel tempering is used for efficient Monte Carlo moves within phase space. The algorithm is easily parallelized and can be applied to a wide class of problems. We discuss algorithmic performance for the case of low-temperature phase separation in two-dimensional and three-dimensional Ising models, where we determine the magnetic interface tension. Multiple Gaussian modified ensemble simulations, unlike multicanonical ensemble simulations do not require a priori knowledge of the free energy and are of similar efficiency as multicanonical ensemble and Wang-Landau simulations.

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PubMed2000

Density-functional theory of inhomogeneous fluids in the canonical ensemble

We present a density-functional approach for dealing with inhomogeneous fluids in the canonical ensemble. A general relation is proposed between the free-energy functionals in the canonical and the grand canonical ensembles. The minimization of the canonical-ensemble free-energy functional gives rise to Euler-Lagrange equations which involve averaged Ornstein-Zernike equations of second and third order. The theory is especially appropriate for systems with a small, fixed number of particles. As an example of application we obtain accurate results for the density profile of a hard-sphere fluid in a closed spherical cavity that contains only a few particles.

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PubMed2001

Inequivalence of ensembles in a system with long-range interactions.

We study the global phase diagram of the infinite-range Blume-Emery-Griffiths model both in the canonical and in the microcanonical ensembles. The canonical phase diagram shows first-order and continuous transition lines separated by a tricritical point. We find that below the tricritical point, when the canonical transition is first order, the phase diagrams of the two ensembles disagree. In this region the microcanonical ensemble exhibits energy ranges with negative specific heat and temperature jumps at transition energies. These results can be extended to weakly decaying nonintegrable interactions.

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PubMed2001

Resolving clusters in chaotic ensembles of globally coupled identical oscillators.

Clustering in ensembles of globally coupled identical chaotic oscillators is reconsidered using a twofold approach. Stability of clusters towards "emanation" of the elements is described with the evaporation Lyapunov exponents. It appears that direct numerical simulations of ensembles often lead to spurious clusters that have positive evaporation exponents, due to a numerical trap. We propose a numerical method that surmounts the spurious clustering. We also demonstrate that clustering can be very sensitive to the number of elements in the ensemble.

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PubMed2002

Spurious interactions, and their correction, in the ensemble-Kohn-Sham scheme for excited States.

We observe that the direct Coulomb (Hartree) term appearing in the ensemble-density-functional theory for excited states contains an unphysical ("ghost") interaction which has to be corrected by the ensemble exchange and correlation functional. We propose a simple additive correction to the conventional ensemble exchange energy in the form of an orbital functional. By treating this corrected exchange energy functional self-consistently within the optimized effective potential method one finds a significant improvement of atomic excitation energies.

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PubMed2003

Stability and ensemble inequivalence in a globally coupled system.

We consider a system of globally coupled rotors, described by a set of Langevin equations, and examine the stability of the incoherent phase. The corresponding Fokker-Planck equation, providing a unified description of microcanonical and canonical ensembles, bears a few solutions, depending upon the ensemble. It is found that the stability of each solution varies differently with the temperature, revealing the inequivalence between the two ensembles. This also suggests a physical explanation of the quasistationarity observed in recent numerical results.

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PubMed2004

Phase synchronization in ensembles of bursting oscillators.

We study the effects of mutual and external chaotic phase synchronization in ensembles of bursting oscillators. These oscillators (used for modeling neuronal dynamics) are essentially multiple time scale systems. We show that a transition to mutual phase synchronization takes place on the bursting time scale of globally coupled oscillators, while on the spiking time scale, they behave asynchronously. We also demonstrate the effect of the onset of external chaotic phase synchronization of the bursting behavior in the studied ensemble by a periodic driving applied to one arbitrarily taken neuron. We also propose an explanation of the mechanism behind this effect. We infer that the demonstrated phenomenon can be used efficiently for controlling bursting activity in neural ensembles.

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PubMed2006

Unconditional two-mode squeezing of separated atomic ensembles.

We propose schemes for the unconditional preparation of a two-mode squeezed state of effective bosonic modes realized in a pair of atomic ensembles interacting collectively with optical cavity and laser fields. The scheme uses Raman transitions between stable atomic ground states and under ideal conditions produces pure entangled states in the steady state. The scheme works both for ensembles confined within a single cavity and for ensembles confined in separate, cascaded cavities.

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PubMed2006

Ensemble-based discriminant learning with boosting for face recognition.

In this paper, we propose a novel ensemble-based approach to boost performance of traditional Linear Discriminant Analysis (LDA)-based methods used in face recognition. The ensemble-based approach is based on the recently emerged technique known as "boosting". However, it is generally believed that boosting-like learning rules are not suited to a strong and stable learner such as LDA. To break the limitation, a novel weakness analysis theory is developed here. The theory attempts to boost a strong learner by increasing the diversity between the classifiers created by the learner, at the expense of decreasing their margins, so as to achieve a tradeoff suggested by recent boosting studies for a low generalization error. In addition, a novel distribution accounting for the pairwise class discriminant information is introduced for effective interaction between the booster and the LDA-based learner. The integration of all these methodologies proposed here leads to the novel ensemble-based discriminant learning approach, capable of taking advantage of both the boosting and LDA techniques. Promising experimental results obtained on various difficult face recognition scenarios demonstrate the effectiveness of the proposed approach. We believe that this work is especially beneficial in extending the boosting framework to accommodate general (strong/weak) learners.

Algorithms↗

PubMed2006

Accuracy/diversity and ensemble MLP classifier design.

The difficulties of tuning parameters of multilayer perceptrons (MLP) classifiers are well known. In this paper, a measure is described that is capable of predicting the number of classifier training epochs for achieving optimal performance in an ensemble of MLP classifiers. The measure is computed between pairs of patterns on the training data and is based on a spectral representation of a Boolean function. This representation characterizes the mapping from classifier decisions to target label and allows accuracy and diversity to be incorporated within a single measure. Results on many benchmark problems, including the Olivetti Research Laboratory (ORL) face database demonstrate that the measure is well correlated with base-classifier test error, and may be used to predict the optimal number of training epochs. While correlation with ensemble test error is not quite as strong, it is shown in this paper that the measure may be used to predict number of epochs for optimal ensemble performance. Although the technique is only applicable to two-class problems, it is extended here to multiclass through output coding. For the output-coding technique, a random code matrix is shown to give better performance than one-per-class code, even when the base classifier is well-tuned.

Algorithms↗

PubMed2005

Clustering ensembles: models of consensus and weak partitions.

Clustering ensembles have emerged as a powerful method for improving both the robustness as well as the stability of unsupervised classification solutions. However, finding a consensus clustering from multiple partitions is a difficult problem that can be approached from graph-based, combinatorial, or statistical perspectives. This study extends previous research on clustering ensembles in several respects. First, we introduce a unified representation for multiple clusterings and formulate the corresponding categorical clustering problem. Second, we propose a probabilistic model of consensus using a finite mixture of multinomial distributions in a space of clusterings. A combined partition is found as a solution to the corresponding maximum-likelihood problem using the EM algorithm. Third, we define a new consensus function that is related to the classical intraclass variance criterion using the generalized mutual information definition. Finally, we demonstrate the efficacy of combining partitions generated by weak clustering algorithms that use data projections and random data splits. A simple explanatory model is offered for the behavior of combinations of such weak clustering components. Combination accuracy is analyzed as a function of several parameters that control the power and resolution of component partitions as well as the number of partitions. We also analyze clustering ensembles with incomplete information and the effect of missing cluster labels on the quality of overall consensus. Experimental results demonstrate the effectiveness of the proposed methods on several real-world data sets.

Algorithms↗

PubMed2007

Ensemble tracking.

We consider tracking as a binary classification problem, where an ensemble of weak classifiers is trained online to distinguish between the object and the background. The ensemble of weak classifiers is combined into a strong classifier using AdaBoost. The strong classifier is then used to label pixels in the next frame as either belonging to the object or the background, giving a confidence map. The peak of the map and, hence, the new position of the object, is found using mean shift. Temporal coherence is maintained by updating the ensemble with new weak classifiers that are trained online during tracking. We show a realization of this method and demonstrate it on several video sequences.

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