Exact field-driven interface dynamics in the two-dimensional stochastic Ising model with helicoidal boundary conditions

We investigate the interface dynamics of the two-dimensional stochastic Ising model in an external field under helicoidal boundary conditions. At sufficiently low temperatures and fields, the dynamics of the interface is described by an exactly solvable high-spin asymmetric quantum Hamiltonian that is the infinitesimal generator of the zero range process. Generally, the critical dynamics of the interface fluctuations is in the Kardar-Parisi-Zhang universality class of critical behavior. We remark that a whole family of RSOS interface models similar to the Ising interface model investigated here can be described by exactly solvable restricted high-spin quantum XXZ-type Hamiltonians. (C) 2012 Elsevier B.V. All rights reserved.

Polymorphic toxin systems: Comprehensive characterization of trafficking modes, processing, mechanisms of action, immunity and ecology using comparative genomics

Background: Proteinaceous toxins are observed across all levels of inter-organismal and intra-genomic conflicts. These include recently discovered prokaryotic polymorphic toxin systems implicated in intra-specific conflicts. They are characterized by a remarkable diversity of C-terminal toxin domains generated by recombination with standalone toxin-coding cassettes. Prior analysis revealed a striking diversity of nuclease and deaminase domains among the toxin modules. We systematically investigated polymorphic toxin systems using comparative genomics, sequence and structure analysis. Results: Polymorphic toxin systems are distributed across all major bacterial lineages and are delivered by at least eight distinct secretory systems. In addition to type-II, these include type-V, VI, VII (ESX), and the poorly characterized "Photorhabdus virulence cassettes (PVC)", PrsW-dependent and MuF phage-capsid-like systems. We present evidence that trafficking of these toxins is often accompanied by autoproteolytic processing catalyzed by HINT, ZU5, PrsW, caspase-like, papain-like, and a novel metallopeptidase associated with the PVC system. We identified over 150 distinct toxin domains in these systems. These span an extraordinary catalytic spectrum to include 23 distinct clades of peptidases, numerous previously unrecognized versions of nucleases and deaminases, ADP-ribosyltransferases, ADP ribosyl cyclases, RelA/SpoT-like nucleotidyltransferases, glycosyltranferases and other enzymes predicted to modify lipids and carbohydrates, and a pore-forming toxin domain. Several of these toxin domains are shared with host-directed effectors of pathogenic bacteria. Over 90 families of immunity proteins might neutralize anywhere between a single to at least 27 distinct types of toxin domains. In some organisms multiple tandem immunity genes or immunity protein domains are organized into polyimmunity loci or polyimmunity proteins. Gene-neighborhood-analysis of polymorphic toxin systems predicts the presence of novel trafficking-related components, and also the organizational logic that allows toxin diversification through recombination. Domain architecture and protein-length analysis revealed that these toxins might be deployed as secreted factors, through directed injection, or via inter-cellular contact facilitated by filamentous structures formed by RHS/YD, filamentous hemagglutinin and other repeats. Phyletic pattern and life-style analysis indicate that polymorphic toxins and polyimmunity loci participate in cooperative behavior and facultative 'cheating' in several ecosystems such as the human oral cavity and soil. Multiple domains from these systems have also been repeatedly transferred to eukaryotes and their viruses, such as the nucleo-cytoplasmic large DNA viruses. Conclusions: Along with a comprehensive inventory of toxins and immunity proteins, we present several testable predictions regarding active sites and catalytic mechanisms of toxins, their processing and trafficking and their role in intra-specific and inter-specific interactions between bacteria. These systems provide insights regarding the emergence of key systems at different points in eukaryotic evolution, such as ADP ribosylation, interaction of myosin VI with cargo proteins, mediation of apoptosis, hyphal heteroincompatibility, hedgehog signaling, arthropod toxins, cell-cell interaction molecules like teneurins and different signaling messengers.

Entropy Production in Nonequilibrium Systems at Stationary States

We present a stochastic approach to nonequilibrium thermodynamics based on the expression of the entropy production rate advanced by Schnakenberg for systems described by a master equation. From the microscopic Schnakenberg expression we get the macroscopic bilinear form for the entropy production rate in terms of fluxes and forces. This is performed by placing the system in contact with two reservoirs with distinct sets of thermodynamic fields and by assuming an appropriate form for the transition rate. The approach is applied to an interacting lattice gas model in contact with two heat and particle reservoirs. On a square lattice, a continuous symmetry breaking phase transition takes place such that at the nonequilibrium ordered phase a heat flow sets in even when the temperatures of the reservoirs are the same. The entropy production rate is found to have a singularity at the critical point of the linear-logarithm type.

Stochastic competitive learning in complex networks

Competitive learning is an important machine learning approach which is widely employed in artificial neural networks. In this paper, we present a rigorous definition of a new type of competitive learning scheme realized on large-scale networks. The model consists of several particles walking within the network and competing with each other to occupy as many nodes as possible, while attempting to reject intruder particles. The particle's walking rule is composed of a stochastic combination of random and preferential movements. The model has been applied to solve community detection and data clustering problems. Computer simulations reveal that the proposed technique presents high precision of community and cluster detections, as well as low computational complexity. Moreover, we have developed an efficient method for estimating the most likely number of clusters by using an evaluator index that monitors the information generated by the competition process itself. We hope this paper will provide an alternative way to the study of competitive learning.

Network-based stochastic semisupervised learning

Semisupervised learning is a machine learning approach that is able to employ both labeled and unlabeled samples in the training process. In this paper, we propose a semisupervised data classification model based on a combined random-preferential walk of particles in a network (graph) constructed from the input dataset. The particles of the same class cooperate among themselves, while the particles of different classes compete with each other to propagate class labels to the whole network. A rigorous model definition is provided via a nonlinear stochastic dynamical system and a mathematical analysis of its behavior is carried out. A numerical validation presented in this paper confirms the theoretical predictions. An interesting feature brought by the competitive-cooperative mechanism is that the proposed model can achieve good classification rates while exhibiting low computational complexity order in comparison to other network-based semisupervised algorithms. Computer simulations conducted on synthetic and real-world datasets reveal the effectiveness of the model.

Optimal mean-variance control for discrete-time linear systems with Markovian jumps and multiplicative noises

In this paper, we consider the stochastic optimal control problem of discrete-time linear systems subject to Markov jumps and multiplicative noises under two criteria. The first one is an unconstrained mean-variance trade-off performance criterion along the time, and the second one is a minimum variance criterion along the time with constraints on the expected output. We present explicit conditions for the existence of an optimal control strategy for the problems, generalizing previous results in the literature. We conclude the paper by presenting a numerical example of a multi-period portfolio selection problem with regime switching in which it is desired to minimize the sum of the variances of the portfolio along the time under the restriction of keeping the expected value of the portfolio greater than some minimum values specified by the investor. (C) 2011 Elsevier Ltd. All rights reserved.

PERFORMANCE EVALUATION OF RESOURCE-AWARE BUSINESS PROCESSES USING STOCHASTIC AUTOMATA NETWORKS

In this work, we study the performance evaluation of resource-aware business process models. We define a new framework that allows the generation of analytical models for performance evaluation from business process models annotated with resource management information. This framework is composed of a new notation that allows the specification of resource management constraints and a method to convert a business process specification and its resource constraints into Stochastic Automata Networks (SANs). We show that the analysis of the generated SAN model provides several performance indices, such as average throughput of the system, average waiting time, average queues size, and utilization rate of resources. Using the BP2SAN tool - our implementation of the proposed framework - and a SAN solver (such as the PEPS tool) we show through a simple use-case how a business specialist with no skills in stochastic modeling can easily obtain performance indices that, in turn, can help to identify bottlenecks on the model, to perform workload characterization, to define the provisioning of resources, and to study other performance related aspects of the business process.

Biological evolution of replicator systems: towards a quantitative approach

The aim of this work is to study the features of a simple replicator chemical model of the relation between kinetic stability and entropy production under the action of external perturbations. We quantitatively explore the different paths leading to evolution in a toy model where two independent replicators compete for the same substrate. To do that, the same scenario described originally by Pross (J Phys Org Chem 17:312–316, 2004) is revised and new criteria to define the kinetic stability are proposed. Our results suggest that fast replicator populations are continually favored by the effects of strong stochastic environmental fluctuations capable to determine the global population, the former assumed to be the only acting evolution force. We demonstrate that the process is continually driven by strong perturbations only, and that population crashes may be useful proxies for these catastrophic environmental fluctuations. As expected, such behavior is particularly enhanced under very large scale perturbations, suggesting a likely dynamical footprint in the recovery patterns of new species after mass extinction events in the Earth’s geological past. Furthermore, the hypothesis that natural selection always favors the faster processes may give theoretical support to different studies that claim the applicability of maximum principles like the Maximum Metabolic Flux (MMF) or Maximum Entropy Productions Principle (MEPP), seen as the main goal of biological evolution.