Observable and hidden singular features of large fluctuations in nonequilibrium systems

We study local features, and provide a topological insight into the global structure of the probability density distribution and of the pattern of the optimal paths for large rare fluctuations away from a stable state. In contrast to extremal paths in quantum mechanics, the optimal paths do {\it not} encounter caustics. We show how this occurs, and what, instead of caustics, are the experimentally observable singularities of the pattern. We reveal the possibility for a caustic and a switching line to start at a saddle point, and discuss the consequences.Comment: 10 pages, 3 ps figures by request, LaTeX Article Format (In press, Phys. Lett. A

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

Ventilation system at the cinema hall with different viewer loading

Ventilation system at the cinema hall is tough, but very interesting and exciting task. Cinema hall it is the place which thousands of people visiting every day. The main purpose of the ventilation system at the cinema hall is creating the perfect microclimate conditions. The cinema hall which is considered in this Bachelor thesis located in the Saint Petersburg. It is the part of the big entertainment centre in the Saint-Petersburg. So this is the real existing cinema hall. The aim of this Bachelor thesis is to study energy efficiency of the ventilation system at the cinema hall which is counting on 300 persons. In this Bachelor thesis there is also the assessment of the quality of microclimate at the cinema hall through making measurements of the temperature level and the values of the air humidity. Results of this bachelor thesis could be applied into the Russian construction area and in the future will be useful for the HVAC engineers in Russia

Pattern recognition in bistable networks

Present study concerns the problem of learning, pattern recognition and computational abilities of a homogeneous network composed from coupled bistable units. An efficient learning algorithm is developed. New possibilities for pattern recognition may be realized due to the developed technique that permits a reconstruction of a dynamical system using the distributions of its attractors. In both cases the updating procedure for the coupling matrix uses the minimization of least-mean-square errors between the applied and desired patterns

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