Time behavior of stressed nonhierarchical networks

In this paper it is shown, by means of simulation, that interesting time behavior is observed for damaged and overloaded networks, and that adaptive, decentralized intelligence can have a dramatic influence on the overall network performance. The time behavior of nonhierarchical networks is modeled by a system of nonlinear difference equations among global variables, and bistability is shown to exist. Using a simple adaptive control mechanism, it is shown that, depending upon the value of a certain network variable, either limit cycle or steady state behavior results. A few ideas are discussed for applications of nonhierarchical communications to cellular automata and to decision-making systems.     

Single Sample Path-Based Optimization of Markov Chains

Motivated by the needs of on-line optimization of real-world engineering systems, we studied single sample path-based algorithms for Markov decision problems (MDP). The sample path used in the algorithms can be obtained by observing the operation of a real system. We give a simple example to explain the advantages of the sample path-based approach over the traditional computation-based approach: matrix inversion is not required; some transition probabilities do not have to be known; it may save storage space; and it gives the flexibility of iterating the actions for a subset of the state space in each iteration. The effect of the estimation errors and the convergence property of the sample path-based approach are studied. Finally, we propose a fast algorithm, which updates the policy whenever the system reaches a particular set of states and prove that the algorithm converges to the true optimal policy with probability one under some conditions. The sample path-based approach may have important applications to the design and management of engineering systems, such as high speed communication networks.This work was supported in part by     

Study on nitridation processes of β-Ga2O3 single crystal

Nitridated /3-Ga2Os (100) substrate was investigated as the substrate for CaN epitaxial growth.The effects of nitridation temperature and surface roughness of -Ga2O3 wafers on the formation of CaN were studied.     

A Statistical Model for Cellular Proliferation

Abstract

The evolution of a biological system, like a cellular one, is analyzed by constructing a Markov process on a suitable state space. This is performed by the introduction of an infinitesimal generator for the Markov semigroup associated to this process. A measure valued process is then defined in a natural way and it is proved that his first moment satisfies the Sharpe–Lotka system in a distributional sense. Hence the study of the moments of the process is tried. An involved integral equation for the moment generating functional is derived.     

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??We consider probabilistic meanings for some numerical characteristics of single birth processes. Some probabilities of events, such as extinction probability, returning probability, are represented in terms of these numerical characteristics. Two examples are also presented to illustrate the value of the results.     

Pseudo‐R 2’s in the ordinal probit model*

This paper presents an analysis of the combining mechanism for status information postulated by the mathematical formulation of the theory of status characteristics and expectation states. Six lemmas on the basic features of the combining mechanism are derived from the formulation and discussed. Further, four theorems that illustrate the implications of the particular combining mechanism for power and prestige orders are presented and proven.     

On the cut‐off phenomenon for the transitivity of randomly generated subgroups

Consider K ≥ 2 independent copies of the random walk on the symmetric group S_N starting from the identity and generated by the products of either independent uniform transpositions or independent uniform neighbor transpositions. At any time $n\in \mathbb{N}$, let G_n be the subgroup of S_N generated by the K positions of the chains. In the uniform transposition model, we prove that there is a cut‐off phenomenon at time N ln(N)/(2K) for the non‐existence of fixed point of G_n and for the transitivity of G_n, thus showing that these properties occur before the chains have reached equilibrium. In the uniform neighbor transposition model, a transition for the non‐existence of a fixed point of G_n appears at time of order $N^{1+\frac{2}{K}}$ (at least for K ≥ 3), but there is no cut‐off phenomenon. In the latter model, we recover a cut‐off phenomenon for the non‐existence of a fixed point at a time proportional to N by allowing the number K to be proportional to ln(N). The main tools of the proofs are spectral analysis and coupling techniques. © 2011 Wiley Periodicals, Inc. Random Struct. Alg., 2012     

A stochastic model for microtubule length dynamics

In this paper, we use random walk theory to describe the length dynamics of microtubules, one of the principal components of the cytoskeleton. We present a simple two-state model (growing and shrinking) of microtubule length evolution that incorporates a variable rate of switching between the states. Using the generating function technique, we calculate the mean length of microtubule, its variance and diffusion coefficient. We also report analytical and computer simulation results for the mean number of positive monomers in microtubule, and find good qualitative agreement with experimental data.     

A random walker on a ratchet potential: effect of a non Gaussian noise

We analyze the effect of a colored non Gaussian noise on a model of a random walker moving along a ratchet potential. Such a model was motivated by the transport properties of motor proteins, like kinesin and myosin. Previous studies have been realized assuming white noises. However, for real situations, in general we could expect that those noises be correlated and non Gaussian. Among other aspects, in addition to a maximum in the current as the noise intensity is varied, we have also found another optimal value of the current when departing from Gaussian behavior. We show the relevant effects that arise when departing from Gaussian behavior, particularly related to current's enhancement, and discuss its relevance for both biological and technological situations.