出生率与年龄段有关的生灭分枝树

本文基于生灭过程的生灭演化机理, 将生物繁衍过程描述为有向随机图过程-随机分枝树, 建立了出生率与年龄段有关的生灭分枝树演化模型. 本文研究了任一节点在不同年龄及临死时刻的出度分布、虚出度分布和拟出度分布, 并证明了拟出度过程是随机时刻终止的Poisson过程, 讨论了首生年龄及相对出生年龄的分布, 给出了任一节点成为孤立节点的概率.     

表面等离子体共振技术在电化学反应过程研究中的应用

简述了表面等离子体共振(SPR)的基本原理,并综述了表面等离子体共振技术在电化学反应过程中的应用。SPR技术可以无需任何标记原位实时地检测分子间的相互作用,也可用于连续监测吸附/脱附和缔合/解离过程。表面等离子共振光谱(SPRS)与电化学技术结合可用来同时表征和处理电极/溶液的界面,在电化学掺杂/去掺杂过程、吸附/脱附反应的研究、痕量物质的检测、薄膜厚度、介电常数的测定等方面的应用已取得了很大的进展。     

Stability and Removal of Benzophenone-Type UV Filters from Water Matrices by Advanced Oxidation Processes

Benzophenone (BP) type UV filters are common environmental contaminants that are posing a growing health concern due to their increasing presence in water. Different studies have evidenced the presence of benzophenones (BP, BP-1, BP-2, BP-3, BP-4, BP-9, HPB) in several environmental matrices, indicating that conventional technologies of water treatment are not able to remove them. It has also been reported that these compounds could be associated with endocrine-disrupting activities, genotoxicity, and reproductive toxicity. This review focuses on the degradation kinetics and mechanisms of benzophenone-type UV filters and their degradation products (DPs) under UV and solar irradiation and in UV-based advanced oxidation processes (AOPs) such as UV/H₂O₂, UV/persulfate, and the Fenton process. The effects of various operating parameters, such as UV irradiation including initial concentrations of H₂O₂, persulfate, and Fe²⁺, on the degradation of tested benzophenones from aqueous matrices, and conditions that allow higher degradation rates to be achieved are presented. Application of nanoparticles such as TiO₂, PbO/TiO₂, and Sb₂O₃/TiO₂ for the photocatalytic degradation of benzophenone-type UV filters was included in this review.     

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.     

Critical comparison of several order-book models for stock-market fluctuations

Far-from-equilibrium models of interacting particles in one dimension are used as a basis for modelling the stock-market fluctuations. Particle types and their positions are interpreted as buy and sel orders placed on a price axis in the order book. We revisit some modifications of well-known models, starting with the Bak-Paczuski-Shubik model. We look at the four decades old Stigler model and investigate its variants. One of them is the simplified version of the Genoa artificial market. The list of studied models is completed by the models of Maslov and Daniels et al. Generically, in all cases we compare the return distribution, absolute return autocorrelation and the value of the Hurst exponent. It turns out that none of the models reproduces satisfactorily all the empirical data, but the most promising candidates for further development are the Genoa artificial market and the Maslov model with moderate order evaporation.