Bistable Gradient Networks II: Storage Capacity and Behaviour Near Saturation

We examine numerically the storage capacity and the behaviour near saturation of an attractor neural network consisting of bistable elements with an adjustable coupling strength, the Bistable Gradient Network (BGN). For strong coupling, we find evidence of a first-order "memory blackout" phase transition as in the Hopfield network. For weak coupling, on the other hand, there is no evidence of such a transition and memorized patterns can be stable even at high levels of loading. The enhanced storage capacity comes, however, at the cost of imperfect retrieval of the patterns from corrupted versions.Comment: 15 pages, 12 eps figures. Submitted to Phys. Rev. E. Sequel to cond-mat/020356

The Effect of Focusing and Caustics on Exit Phenomena in Systems Lacking Detailed Balance

We study the trajectories followed by a particle subjected to weak noise when escaping from the domain of attraction of a stable fixed point. If detailed balance is absent, a _focus_ may occur along the most probable exit path, leading to a breakdown of symmetry (if present). The exit trajectory bifurcates, and the exit location distribution may become `skewed' (non-Gaussian). The weak-noise asymptotics of the mean escape time are strongly affected. Our methods extend to the study of skewed exit location distributions in stochastic models without symmetry.Comment: REVTEX macros (latest version). Two accompanying PS figures, one of which is large (over 600K unpacked

The Escape Problem for Irreversible Systems

The problem of noise-induced escape from a metastable state arises in physics, chemistry, biology, systems engineering, and other areas. The problem is well understood when the underlying dynamics of the system obey detailed balance. When this assumption fails many of the results of classical transition-rate theory no longer apply, and no general method exists for computing the weak-noise asymptotics of fundamental quantities such as the mean escape time. In this paper we present a general technique for analysing the weak-noise limit of a wide range of stochastically perturbed continuous-time nonlinear dynamical systems. We simplify the original problem, which involves solving a partial differential equation, into one in which only ordinary differential equations need be solved. This allows us to resolve some old issues for the case when detailed balance holds. When it does not hold, we show how the formula for the mean escape time asymptotics depends on the dynamics of the system along the most probable escape path. We also present new results on short-time behavior and discuss the possibility of focusing along the escape path.Comment: 24 pages, APS revtex macros (version 2.1) now available from PBB via `get oldrevtex.sty

Genetic Diversity of Historical and Modern Populations of Russian Cattle Breeds Revealed by Microsatellite Analysis

Analysis of ancient and historical DNA has great potential to trace the genetic diversity of local cattle populations during their centuries-long development. Forty-nine specimens representing five cattle breeds (Kholmogor, Yaroslavl, Great Russian, Novgorod, and Holland), dated from the end of the 19th century to the first half of the 20th century, were genotyped for nine polymorphic microsatellite loci. Using a multiple-tube approach, we determined the consensus genotypes of all samples/loci analysed. Amplification errors, including allelic drop-out (ADO) and false alleles (FA), occurred with an average frequency of 2.35% and 0.79%, respectively. A significant effect of allelic length on ADO rate (r2 = 0.620, p = 0.05) was shown. We did not observe significant differences in genetic diversity among historical samples and modern representatives of Kholmogor and Yaroslavl breeds. The unbiased expected heterozygosity values were 0.726–0.774 and 0.708–0.739; the allelic richness values were 2.716–2.893 and 2.661–2.758 for the historical and modern samples, respectively. Analyses of FST and Jost’s D genetic distances, and the results of STRUCTURE clustering, showed the maintenance of a part of historical components in the modern populations of Kholmogor and Yaroslavl cattle. Our study contributes to the conservation of biodiversity in the local Russian genetic resources of cattle

Comparative Study of the Genetic Diversity of Local Steppe Cattle Breeds from Russia, Kazakhstan and Kyrgyzstan by Microsatellite Analysis of Museum and Modern Samples

The comparative molecular genetic study of museum and modern representatives of cattle breeds can help to elucidate the origin and maintenance of historical genetic components in modern populations. We generated the consensus genotypes for 11 microsatellite loci for 24 museum samples of Kalmyk, Kyrgyz, and Kazakh cattle, dated from the first quarter of the 20th century, and compared them with those of modern Kalmyk, Kyrgyz, and Kazakh white-headed breeds. The level of genetic diversity of the modern Kalmyk and Kyrgyz cattle (uHe = 0.771–0.778) was similar to those observed in the museum samples (uHe = 0.772–0.776), while a visible decrease in genetic variability in the modern Kazakh white-headed breed compared to museum Kazakh cattle was detected (uHe = 0.726 and 0.767, respectively). The PCA plot, FST- and Jost’s D-based networks, and STRUCTURE clustering provided strong evidence of the maintenance of the historical genetic background in modern populations of Kalmyk and Kyrgyz cattle. In spite of the allele pool of Kazakh white-headed cattle having undergone great changes compared to the museum Kazakh cattle, several animals still carry the visible aspect of the historical genetic components. Our results can be used for the selection of individuals for the creation of gene banks and may significantly improve the efficiency of conservation programs aimed at preserving genetic diversity in the national genetic resources of cattle

Experiments on critical phenomena in a noisy exit problem.

We consider a noise-driven exit from a domain of attraction in a two-dimensional bistable system lacking detailed balance. Through analog and digital stochastic simulations, we find a theoretically predicted bifurcation of the most probable exit path as the parameters of the system are changed, and a corresponding nonanalyticity of the generalized activation energy. We also investigate the extent to which the bifurcation is related to the local breaking of time-reversal invariance