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Memory reprocessing in corticocortical and hippocampocortical neuronal ensembles.

Hippocampal cells that fire together during behaviour exhibit enhanced activity correlations during subsequent sleep, with some preservation of temporal order information. Thus, information reflecting experiences during behaviour is re-expressed in hippocampal circuits during subsequent 'offline' periods, as postulated by some theories of memory consolidation. If the hippocampus orchestrates the reinstatement of experience-specific activity patterns in the neocortex, as also postulated by such theories, then correlation patterns both within the neocortex and between hippocampus and neocortex should also re-emerge during sleep. Ensemble recordings were made in the posterior parietal neocortex, in CA1, and simultaneously in both areas, in seven rats. Each session involved an initial sleep episode (S1), behaviour on a simple maze (M), and subsequent sleep (S2). The ensemble activity-correlation structure within and between areas during S2 resembled that of M more closely than did the correlation pattern of S1. Temporal order (i.e. the asymmetry of the cross-correlogram) was also preserved within, but not between, structures. Thus, traces of recent experience are re-expressed in both hippocampal and neocortical circuits during sleep, and the representations in the two areas tend to correspond to the same experience. The poorer preservation of temporal firing biases between neurons in the different regions may reflect the less direct synaptic coupling between regions than within them. Alternatively, it could result from a shift, between behavioural states, in the relative dominance relations in the corticohippocampal dialogue. Between-structure order will be disrupted, for example, if, during behaviour, neocortical patterns tend to drive corresponding hippocampal patterns, whereas during sleep the reverse occurs. This possibility remains to be investigated.

Animals↗

The Ensembl analysis pipeline.

The Ensembl pipeline is an extension to the Ensembl system which allows automated annotation of genomic sequence. The software comprises two parts. First, there is a set of Perl modules ("Runnables" and "RunnableDBs") which are 'wrappers' for a variety of commonly used analysis tools. These retrieve sequence data from a relational database, run the analysis, and write the results back to the database. They inherit from a common interface, which simplifies the writing of new wrapper modules. On top of this sits a job submission system (the "RuleManager") which allows efficient and reliable submission of large numbers of jobs to a compute farm. Here we describe the fundamental software components of the pipeline, and we also highlight some features of the Sanger installation which were necessary to enable the pipeline to scale to whole-genome analysis.

Base Sequence↗

The Ensembl Web site: mechanics of a genome browser.

The Ensembl Web site (http://www.ensembl.org/) is the principal user interface to the data of the Ensembl project, and currently serves >500,000 pages (approximately 2.5 million hits) per week, providing access to >80 GB (gigabyte) of data to users in more than 80 countries. Built atop an open-source platform comprising Apache/mod_perl and the MySQL relational database management system, it is modular, extensible, and freely available. It is being actively reused and extended in several different projects, and has been downloaded and installed in companies and academic institutions worldwide. Here, we describe some of the technical features of the site, with particular reference to its dynamic configuration that enables it to handle disparate data from multiple species.

Animals↗

Identification of candidate disease genes by EST alignments, synteny, and expression and verification of Ensembl genes on rat chromosome 1q43-54.

We aligned Incyte ESTs and publicly available sequences to the rat genome and analyzed rat chromosome 1q43-54, a region in which several quantitative trait loci (QTLs) have been identified, including renal disease, diabetes, hypertension, body weight, and encephalomyelitis. Within this region, which contains 255 Ensembl gene predictions, the aligned sequences clustered into 568 Incyte genes and gene fragments. Of the Incyte genes, 261 (46%) overlapped 184 (72%) of the Ensembl gene predictions, whereas 307 were unique to Incyte. The rat-to-human syntenic map displays rearrangement of this region on rat chr. 1 onto human chromosomes 9 and 10. The mapping of corresponding human disease phenotypes to either one of these chromosomes has allowed us to focus in on genes associated with disease phenotypes. As an example, we have used the syntenic information for the rat Rf-1 disease region and the orthologous human ESRD disease region to reduce the size of the original rat QTL to only 11.5 Mb. Using the syntenic information in combination with expression data from ESTs and microarrays, we have selected a set of 66 candidate disease genes for Rf-1. The combination of the results from these different analyses represents a powerful approach for narrowing the number of genes that could play a role in the development of complex diseases.

Animals↗

Critical behavior of the two-dimensional spin-diluted Ising model via the equilibrium ensemble approach.

The equilibrium ensemble approach to disordered systems is used to investigate the critical behavior of the two-dimensional Ising model in the presence of quenched random site dilution. The numerical transfer matrix technique in semi-infinite strips of finite width, together with phenomenological renormalization and conformal invariance, is particularly suited to putting the equilibrium ensemble approach to work. A method by which to extract with great precision the critical temperature of the model is proposed and applied. A more systematic finite-size scaling analysis than in previous numerical studies has been performed. A parallel investigation, along the lines of the two main scenarios currently under discussion, namely, the logarithmic corrections scenario (with critical exponents fixed in the Ising universality class) versus the weak universality scenario (critical exponents varying with the degree of disorder), is carried out. In interpreting our data, maximum care is constantly taken to be open to both possibilities. A critical discussion shows that an unambiguous discrimination between the two scenarios is still not possible on the basis of the available finite-size data.

Journal Article↗

Response of an ensemble of noisy neuron models to a single input.

Spike timing precision in response to a subthreshold stimulation can be enhanced by noise in ensembles of neurons [X. Pei, L. Wilkens, and F. Moss, Phys. Rev. Lett. 77, 4679 (1996)]. We elucidate the mechanism underlying this phenomenon by computing the membrane potential distributions of ensembles of Hodgkin-Huxley neuron models. For small noise amplitudes, the membrane potential distribution takes on a Gaussian form centered on the resting potential, while for large fluctuations, there is a significant spread to lower potentials. These two regimes are separated by a relatively narrow band where the distributions transit rapidly from the Gaussian-like shapes to the spread ones. We argue that the optimal noise that maximizes the spike timing precision is situated close to this boundary.

Action Potentials↗

Path integrals for the quantum microcanonical ensemble

Path integral representations for the quantum microcanonical ensemble are presented. In the quantum microcanonical ensemble, two operators are of primary interest. First, rhoinsertion mark=delta(E-Hinsertion mark) corresponds to the microcanonical density matrix and can be used to calculate expectation values. Second, Ninsertion mark=Theta(E-Hinsertion mark) can give the number of states with energy E(n) and Theta(x,x('),E)= . A path integral formalism leads to exact integral representations for Omega(x,x('),E) and Theta(x,x('),E). We present both phase space and configuration space forms. For simple systems, such as the free particle and harmonic oscillator, exact solutions are possible. For more complicated systems, expansion schemes or numerical evaluations are required. A perturbative calculation and numerical integration results are presented for the quantum anharmonic oscillator.

Journal Article↗

Three-dimensional ising model in the fixed-magnetization ensemble: A monte carlo study

We study the three-dimensional Ising model at the critical point in the fixed-magnetization ensemble, by means of the recently developed geometric cluster Monte Carlo algorithm. We define a magnetic-field-like quantity in terms of microscopic spin-up and spin-down probabilities in a given configuration of neighbors. In the thermodynamic limit, the relation between this field and the magnetization reduces to the canonical relation M(h). However, for finite systems, the relation is different. We establish a close connection between this relation and the probability distribution of the magnetization of a finite-size system in the canonical ensemble.

Journal Article↗

Equivalence of stationary state ensembles.

We show that the contact process in an ensemble with conserved total particle number, as simulated recently by Tomé and de Oliveira [Phys. Rev. Lett. 86, 5463 (2001)], is equivalent to the ordinary contact process, in agreement with what the authors assumed and believed. Similar conserved ensembles and equivalence proofs are easily constructed for other models.

Journal Article↗

Stochastic resonance of ensemble neurons for transient spike trains: wavelet analysis.

By using the wavelet transformation (WT), I have analyzed the response of an ensemble of N (=1, 10, 100, and 500) Hodgkin-Huxley neurons to transient M-pulse spike trains (M=1 to 3) with independent Gaussian noises. The cross correlation between the input and output signals is expressed in terms of the WT expansion coefficients. The signal-to-noise ratio (SNR) is evaluated by using the denoising method within the WT, by which the noise contribution is extracted from the output signals. Although the response of a single (N=1) neuron to subthreshold transient signals with noises is quite unreliable, the transmission fidelity assessed by the cross correlation and SNR is shown to be much improved by increasing the value of N: a population of neurons plays an indispensable role in the stochastic resonance (SR) for transient spike inputs. It is also shown that in a large-scale ensemble, the transmission fidelity for suprathreshold transient spikes is not significantly degraded by a weak noise which is responsible to SR for subthreshold inputs.

Animals↗

Smectic phases of semiflexible manifolds: constant-pressure ensemble.

We pursue the constant-pressure ensemble approach to elucidate the statistical mechanics of the smectic phases of semiflexible manifolds, such as two-dimensional smectic phases of long semiflexible polymers and three-dimensional lamellar fluid membrane phases. We use this approach to consider in detail sterically stabilized phases of semiflexible polymers in two-dimensional (2D) smectic systems. For these 2D systems, we obtain the universal constants characterizing the entropic repulsion between semiflexible polymers, such as those in the osmotic pressure P=alpha(k(B)T)(4/3)/kappa(1/3)(a-a(min))(5/3) with alpha found here to be congruent with 0.432 (here, a is the smectic phase period, and a(min) and kappa are the polymer cross-sectional diameter and bending rigidity constant, respectively). We address, by numerical simulations and analytic arguments, finite stacks of N semiflexible manifolds, and discuss in detail the practically interesting thermodynamic limit N--> infinity. We show that the thermodynamic limit is quickly approached within the constant-pressure ensemble: Already from numerical simulations involving just few semiflexible polymers under constant isotropic pressure, one can obtain the infinite 2D smectic equation of state within a few percent accuracy. We use our results to discuss the competition of electrostatic and entropic effects in quasi-2D smectic phases of DNA-cationic-lipid complexes. We use our quantitative results to discuss in detail the elasticity, topological defects, anomalous elasticity, and the effects of externally applied tension in sterically stabilized 2D smectic phases of long semiflexible polymers.

Biophysical Phenomena↗

Pseudounitary symmetry and the Gaussian pseudounitary ensemble of random matrices.

Employing the currently discussed notion of pseudo-Hermiticity, we define a pseudounitary group. Further, we develop a random matrix theory that is invariant under such a group and call this ensemble of pseudo-Hermitian random matrices the pseudounitary ensemble. We obtain exact results for the nearest-neighbor level-spacing distribution for (2 x 2) PT-invariant Hamiltonian matrices that have forms, approximately Sln(1/S) near zero spacing for three independent elements and approximately S for four independent elements. This shows a level repulsion in a marked distinction with an algebraic form S(beta) in the Wigner surmise. We believe that this paves the way for a description of varied phenomena in two-dimensional statistical mechanics, quantum chromodynamics, and so on.

Journal Article↗

Stochastic formulation of sampling dynamics in generalized ensemble methods.

The fundamental relations of the sampling process in the multicanonical ensemble and simulated tempering have been studied in the expanded ensembles formalism. The simulated tempering is identified as the multicanonical sampling with the generalized weight determined by a Laplace transform of the temperature weight. The characteristic dynamics of both sampling methods has been verified in the stochastic formulation of the sampling process. Our study gives a necessary and sufficient condition for the weights to realize a uniform sampling in the energy and temperature spaces. Based on the stochastic model, robust force biased iteration schemes have been proposed to allow automatic determinations of uniform sampling weights.

Journal Article↗

Monte Carlo simulation of the nematic-isotropic transition in an isothermal-isobaric ensemble.

Monte Carlo simulation of a system consisting of 512 cylindrically symmetric particles interacting with each other via a potential which has an isotropic, density dependent part as well as an anisotropic part has been used to simulate the nematic state. The usual Metropolis algorithm is used and the particles are allowed to have translational degrees of freedom along with the orientational one. The simulation has been carried out in an isothermal-isobaric (NPT) ensemble and the multiple histogram technique of Ferrenberg-Swendsen with appropriate modification for the NPT ensemble has been used. The results reveal realistic values of the pseudo-spinoidal temperature and pressure as well as that for the pressure dependence of the nematic-isotropic transition temperature.

Journal Article↗

Resonance overlap, secular effects, and nonintegrability: an approach from ensemble theory.

The time evolution of a classical multiresonance nonintegrable Hamiltonian system with few degrees of freedom is analyzed on the ensemble level. Time-dependent perturbation analysis is applied to the Liouville equation to determine the most secular series for the time evolution of the expectation value of some physical observables. In contrast to the so-called lambda(2) t expansion for thermodynamic systems, which is well known in nonequilibrium statistical physics, we find a square root of lambda t expansion in small nonintegrable systems with few degrees of freedom. This asymptotic expansion exists only on the level of ensemble but not on the level of trajectories. Moreover, the time symmetry of this expansion is broken as in nonequilibrium statistical mechanics. The relation of the Chirikov overlapping criterion to our approach is discussed.

Journal Article↗

1/f noise in the two-body random ensemble.

We show that the spectral fluctuations of the two-body random ensemble exhibit 1/f noise. This result supports a recent conjecture stating that chaotic quantum systems are characterized by 1/f noise in their energy level fluctuations. After suitable individual averaging, we also study the distribution of the exponent alpha in the 1/ f(alpha) noise for the individual members of the ensemble. Almost all the exponents lie inside a narrow interval around alpha=1, suggesting that also individual members exhibit 1/f noise, provided they are individually unfolded.

Journal Article↗

Augmented moment method for stochastic ensembles with delayed couplings. I. Langevin model.

By employing a semianalytical dynamical mean-field approximation theory previously proposed by the author [H. Hasegawa, Phys. Rev. E 67, 041903 (2003)], we have developed an augmented moment method (AMM) in order to discuss dynamics of an N -unit ensemble described by Langevin equations with delays. In an AMM, original N -dimensional stochastic delay differential equations (SDDEs) are transformed to infinite-dimensional deterministic DEs for means and correlations of local as well as global variables. Infinite-order DEs arising from the non-Markovian property of SDDE, are terminated at the finite level m in the level-m AMM (AMMm), which yields (3+m)-dimensional deterministic DEs. Model calculations have been made for linear and nonlinear Langevin models. The stationary solution of AMM for the linear Langevin model with N=1 is nicely compared to the exact result. In the nonlinear Langevin ensemble, the synchronization is shown to be enhanced near the transition point between the oscillating and nonoscillating states. Results calculated by AMM6 are in good agreement with those obtained by direct simulations.

Action Potentials↗