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PubMed2004

Monte Carlo simulations in generalized isobaric-isothermal ensembles.

We present three generalized isobaric-isothermal ensemble Monte Carlo algorithms, which we refer to as the multibaric-multithermal, multibaric-isothermal, and isobaric-multithermal algorithms. These Monte Carlo simulations perform random walks widely in volume space and/or in potential energy space. From only one simulation run, one can calculate isobaric-isothermal-ensemble averages in wide ranges of pressure and temperature. We demonstrate the effectiveness of these algorithms by applying them to the Lennard-Jones 12-6 potential system with 500 particles.

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PubMed2004

Family of generalized random matrix ensembles.

Using the generalized maximum entropy principle based on the nonextensive q entropy, a family of random matrix ensembles is generated. This family unifies previous extensions of random matrix theory (RMT) and gives rise to an orthogonal invariant stable Lévy ensemble with new statistical properties. Some of them are analytically derived.

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PubMed2004

Kinetics of ensembles with variable charges.

Kinetics of particle ensembles with variable charges is investigated. It is shown that the energy of such ensembles is not conserved in the interparticle collisions. The case when the equilibrium charge depends on the particle coordinate is studied, and the collision integral describing the momentum and energy transfer in collisions is derived. Solution of the resulting kinetic equation shows that the system is unstable--the mean thermal energy exhibits explosion-like growth, diverging at a finite time.

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PubMed2005

Cluster synchronization in an ensemble of neurons interacting through chemical synapses.

In networks of periodically firing spiking neurons that are interconnected with chemical synapses, we analyze a cluster state, where an ensemble of neurons are subdivided into a few clusters, in each of which neurons exhibit perfect synchronization. To clarify stability of the cluster state, we decompose linear stability of the solution into two types of stabilities, stability of a mean state and stabilities of clusters. Computing Floquet matrices for these stabilities, we clarify the total stability of the cluster state for any type of neuron and any strength of interaction even if the size of networks is infinitely large. First, we apply this stability analysis to investigating synchronization in the large ensemble of integrate-and-fire (IF) neurons. In one-cluster state we find the change of stability of a cluster, which elucidates that in-phase synchronization of IF neurons occurs with only inhibitory synapses. Then, we investigate entrainment of two clusters of IF neurons with different excitability. IF neurons with fast decaying synapses show low entrainment capability, which is explained by a pitchfork bifurcation appearing in the two-cluster state with change of synapse decay time constant. Second, we analyze a one-cluster state of Hodgkin-Huxley (HH) neurons and discuss the difference in synchronization properties between IF neurons and HH neurons.

Action Potentials↗

PubMed2005

Predictability, bred vectors, and generation of ensembles in space-time chaotic systems.

Spatial configuration of initial errors strongly affects predictability of space-time chaotic systems. The predictability of numerical models can be adjusted by using prepared ensembles of initial conditions. We present a natural way of preparing ensembles based in using finite-amplitude perturbations with varying correlation. This allows one to take into account the underlying dynamics to generate initial perturbations with spatial correlations varying from fully correlated (bred vectors) to random fluctuations.

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PubMed2005

Regularization of dynamics in an ensemble of nondiffusively coupled chaotic elements.

We investigate the dynamics in an ensemble of chaotic elements with nondiffusive coupling. First, we analyze the case of global coupling. The type of coupling we consider leads to the suppression of oscillations in the whole ensemble at a high coupling strength. A distinct feature of this transition from high-dimensional chaos at a low coupling strength to the stationary state is that there is no partially ordered phase characterized by a large number of coexisting synchronized clusters. A two-cluster mode emerges abruptly, replacing the asynchronous mode. We focus on the influence of connectivity on the dynamics in the two-cluster modes and their domains of existence. We introduce a parameter that characterizes the connectivity: the range of coupling. Our computational and analytical results indicate that the most significant changes in the dynamics occur in the case of local coupling, when extra connections are added. By contrast, if the range of coupling is high, even substantial changes in this range have a small influence on the dynamics.

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PubMed2006

Geometric thermodynamic fields and the generalized ensemble in colloidal physics.

The statistical geometry of hard-sphere mixtures, as defined by Speedy and Reiss, is found to lead to a sum rule that is identical in form to the fundamental equation of the generalized ensemble. This leads one to conjecture the specific form of a set of thermodynamic fields entirely defined by ensemble averages of geometric properties of the configurations. The potential for a direct physical understanding of these quantities is discussed and it is noted that they could, therefore, be of crucial significance to our future understanding of colloidal physics. In the presence of an ideal wall, an analogous sum rule is obtained in terms of interfacial geometric properties (the available surface area for insertions at the wall). For this case, which generalizes beyond hard-sphere models, there exists an obvious physical interpretation involving complete wetting at the ideal wall.

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PubMed2006

Periodic orbits of the ensemble of Sinai-Arnold cat maps and pseudorandom number generation.

We propose methods for constructing high-quality pseudorandom number generators (RNGs) based on an ensemble of hyperbolic automorphisms of the unit two-dimensional torus (Sinai-Arnold map or cat map) while keeping a part of the information hidden. The single cat map provides the random properties expected from a good RNG and is hence an appropriate building block for an RNG, although unnecessary correlations are always present in practice. We show that introducing hidden variables and introducing rotation in the RNG output, accompanied with the proper initialization, dramatically suppress these correlations. We analyze the mechanisms of the single-cat-map correlations analytically and show how to diminish them. We generalize the Percival-Vivaldi theory in the case of the ensemble of maps, find the period of the proposed RNG analytically, and also analyze its properties. We present efficient practical realizations for the RNGs and check our predictions numerically. We also test our RNGs using the known stringent batteries of statistical tests and find that the statistical properties of our best generators are not worse than those of other best modern generators.

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PubMed2000

Manifestation of random phase in a finite ensemble of a turbulent fluid

A field can be specified by a set of spectral coefficients, c(j)(t), relative to an expansion basis. In fluid turbulence, one often assumes the condition that if one were to extract data from an ensemble of realizations, one would find that the average, , would vanish unless i = i('), as in the case of a homogeneous ensemble in which the i's represent wave vectors. We analytically treat an extension to the case in which one has a larger number of coefficients than realizations, introducing intrinsic linear dependences that vitiate the stated condition.

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PubMed2001

Transmission of noise coded versus additive signals through a neuronal ensemble.

Neuronal populations receive signals through temporally inhomogeneous spike trains which can be approximated by an input consisting of a time dependent mean value (additive signal) and noise with a time dependent intensity (noise coded signal). We compare the linear response of an ensemble of model neurons to these signals. Our analytical solution for the mean activity demonstrates the high efficiency of the transmission of a noise coded signal in a broad frequency band. For both kinds of signal we show that the transmission by the ensemble reveals stochastic resonance as well as a nonmonotonous dependence on the driving frequency.

Action Potentials↗

PubMed2001

Kohn-Sham theory for ground-state ensembles.

An electron density distribution n(r) which can be represented by that of a single-determinant ground state of noninteracting electrons in an external potential v(r) is called pure-state v-representable (P-VR). Most physical electronic systems are P-VR. Systems which require a weighted sum of several such determinants to represent their density are called ensemble v-representable (E-VR). This paper develops formal Kohn-Sham equations for E-VR physical systems, using the appropriate coupling constant integration. It also derives local density- and generalized gradient approximations, and conditions and corrections specific to ensembles.

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PubMed2002

Spectroscopy with random and displaced random ensembles.

Because of the time reversal invariance of the angular momentum operator J2, the average energies and variances at fixed J for random two-body Hamiltonians exhibit odd-even- J staggering that may be especially strong for J = 0. It is shown that upon ensemble averaging over random runs, this behavior is reflected in the yrast states. Displaced (attractive) random ensembles lead to rotational spectra with strongly enhanced B(E2) transitions for a certain class of model spaces. It is explained how to generalize these results to other forms of collectivity.

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PubMed2004

Single-photon generation from stored excitation in an atomic ensemble.

Single photons are generated from an ensemble of cold Cs atoms via the protocol of Duan et al. [Nature (London), ()]]. Conditioned upon an initial detection from field 1 at 852 nm, a photon in field 2 at 894 nm is produced in a controlled fashion from excitation stored within the atomic ensemble. The single-quantum character of field 2 is demonstrated by the violation of a Cauchy-Schwarz inequality, namely w(1(2),1(2)|1(1))=0.24+/-0.05 not > or = 1, where w(1(2),1(2)|1(1)) describes the detection of two events (1(2),1(2)) conditioned upon an initial detection 1(1), with w-->0 for single photons.

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PubMed2005

Superradiance and subradiance in an inhomogeneously broadened ensemble of two-level systems coupled to a low-Q cavity.

The collective spontaneous emission of a fully inverted inhomogeneously broadened ensemble of N two-level systems coupled to a single-mode low-Q cavity is investigated numerically using Monte Carlo wave function technique. An intrinsically bi-exponential emission dynamics is found when the time scales of superradiance tau(sr) and inhomogeneous dephasing T2* approximately 1/Deltaomega(inh) become comparable: a fast superradiant is followed by a slow subradiant decay. Experimental configurations using ensembles of quantum dots coupled to optical microcavities are proposed as possible candidates to observe the combined superradiant and subradiant energy relaxation.

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PubMed1995

Signal-to-noise ratio enhancement of cardiac late potentials using ensemble correlation.

An optimal one-weight "filter" is presented for the purpose of improving the signal-to-noise ratio of averaged ECG recordings in the analysis of late potentials. Based on a simple statistical model, the filter is estimated from the ensemble correlation of available beats. The correlation estimator is found by a maximum likelihood procedure in which the observed signal is assumed to have a Gaussian distribution. The performance of the optimal filter is studied in relation to an ensemble with individual or subaveraged beats.

Action Potentials↗

PubMed1998

Ensembles of radial basis function networks for spectroscopic detection of cervical precancer.

The mortality related to cervical cancer can be substantially reduced through early detection and treatment. However, current detection techniques, such as Pap smear and colposcopy, fail to achieve a concurrently high sensitivity and specificity. In vivo fluorescence spectroscopy is a technique which quickly, noninvasively and quantitatively probes the biochemical and morphological changes that occur in precancerous tissue. A multivariate statistical algorithm was used to extract clinically useful information from tissue spectra acquired from 361 cervical sites from 95 patients at 337-, 380-, and 460-nm excitation wavelengths. The multivariate statistical analysis was also employed to reduce the number of fluorescence excitation-emission wavelength pairs required to discriminate healthy tissue samples from precancerous tissue samples. The use of connectionist methods such as multilayered perceptrons, radial basis function (RBF) networks, and ensembles of such networks was investigated. RBF ensemble algorithms based on fluorescence spectra potentially provide automated and near real-time implementation of precancer detection in the hands of nonexperts. The results are more reliable, direct, and accurate than those achieved by either human experts or multivariate statistical algorithms.

Algorithms↗

PubMed2005

An efficient and accurate algorithm for assigning nuclear overhauser effect restraints using a rotamer library ensemble and residual dipolar couplings.

Nuclear Overhauser effect (NOE) distance restraints are the main experimental data from protein nuclear magnetic resonance (NMR) spectroscopy for computing a complete three dimensional solution structure including sidechain conformations. In general, NOE restraints must be assigned before they can be used in a structure determination program. NOE assignment is very time-consuming to do manually, challenging to fully automate, and has become a key bottleneck for high-throughput NMR structure determination. The difficulty in automated NOE assignment is ambiguity: there can be tens of possible different assignments for an NOE peak based solely on its chemical shifts. Previous automated NOE assignment approaches rely on an ensemble of structures, computed from a subset of all the NOEs, to iteratively filter ambiguous assignments. These algorithms are heuristic in nature, provide no guarantees on solution quality or running time, and are slow in practice. In this paper we present an accurate, efficient NOE assignment algorithm. The algorithm first invokes the algorithm in [30, 29] to compute an accurate backbone structure using only two backbone residual dipolar couplings (RDCs) per residue. The algorithm then filters ambiguous NOE assignments by merging an ensemble of intra-residue vectors from a protein rotamer database, together with internuclear vectors from the computed backbone structure. The protein rotamer database was built from ultra-high resolution structures (<1.0 A) in the Protein Data Bank (PDB). The algorithm has been successfully applied to assign more than 1,700 NOE distance restraints with better than 90% accuracy on the protein human ubiquitin using real experimentally-recorded NMR data. The algorithm assigns these NOE restraints in less than one second on a single-processor workstation.

Algorithms↗

PubMed2001

Thermodynamic propensities of amino acids in the native state ensemble: implications for fold recognition.

An amino acid sequence, in the context of the solvent environment, contains all of the thermodynamic information necessary to encode a three-dimensional protein structure. To investigate the relationship between an amino acid sequence and its corresponding protein fold, a database of thermodynamic stability information was assembled that spanned 2951 residues from 44 nonhomologous proteins. This information was obtained using the COREX algorithm, which computes an ensemble-based description of the native state of a protein. It was observed that amino acid types partitioned unequally into high, medium, and low thermodynamic stability environments. Furthermore, these distributions were reproducible and were significantly different than those expected from random partitioning. To assess the structural importance of the distributions, simple fold-recognition experiments were performed based on a 3D-1D scoring matrix containing only COREX residue stability information. This procedure was able to recover amino acid sequences corresponding to correct target structures more effectively than scoring matrices derived from randomized data. High-scoring sequences were often aligned correctly with their corresponding target profiles, suggesting that calculated thermodynamic stability profiles have the potential to encode sequence information. As a control, identical fold-recognition experiments were performed on the same database of proteins using DSSP secondary structure information in the scoring matrix, instead of COREX residue stability information. The comparable performance of both approaches suggested that COREX residue stability information and secondary structure information could be of equivalent utility in more sophisticated fold-recognition techniques. The results of this work are a consequence of the idea that amino acid sequences fold not into single, rigidly stable structures but rather into thermodynamic ensembles best represented by a time-averaged structure.

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