Modeling the dynamics of block-and-fault systems and seismicity

A model of block-and-fault system dynamics (a block model) has been developed to analyze how the basic features of seismicity depend on the lithosphere structure in a region under consideration and on the peculiarities of the lithosphere dynamics. The lithosphere in the region is modeled by a system of perfectly rigid blocks divided by infinitely thin fault planes. The viscoelastic interaction between the blocks and with the underlying medium is specified. Displacements and rotations of the blocks at each time are determined so that the whole block system is in a quasi-static equilibrium state. When the ratio of the stress to the pressure exceeds the critical level in some part of a fault zone, a stress drop occurs that is considered in the model as an earthquake. The paper contains a review of results obtained by numerical simulation of the dynamics of different block structures including the structures approximating the lithosphere structure in specific seismic regions. These results suggest that the block model is a useful tool for studying the influence of geometry of faults and motions of blocks on seismicity features.     

Modeling employees behavior in workplace dynamics

During the past years, Cellular Automata (CAs) have been extensively used for modeling of many complex systems and processes with great success. In this paper, we study a Cellular Automaton (CA) model for the influence of employees’ behavior in a parameterized workplace environment taking into account different behavioral characteristics. In specific, we model employees’ interactions based on their influence radius, the degree of their willingness on adaption of organizational norms and the employee's attitude in general in the under study workplace. The proposed CA model is taking into account employee loyalty, a combined statistic of the employee behavior and her/his insistence and company policies applied to the employees so as to restrain unwanted or impose desirable behavioral patterns in correspondence to the organization norms. Conclusively, the CA model facilitates the presentation and simulation of a workplace with a variety of employee behavioral characteristics and under adaptable company policies. Different workplaces were used to illustrate the simulation of employee behavior with CA model. As a result, the proposed model was practically used on two levels, firstly to estimate the workplace robustness and secondly to illustrate workspace dynamics. Finally, the CA model has been utilized to simulate behavioral patterns at a small enterprise in Greece. In specific, based on the employees answers to detailed surveys the CA model was initialized and then applied to describe the behavioral traits of the under study company employees. Finally, the proposed model, in all the examined cases can be utilized in conjunction with applied employee management techniques to facilitate managerial decisions and forecast the impact of employee behavioral changes and company decisions.     

Modeling the dynamics of entangled quantum states

In the study of association of a diatomic molecule, we consider the atoms as quantum particles in an entangle quantum state. The proposed model of association is based on the selection of such states on the principle of their density in the configuration space, which is in exact agreement with the selection by the amplitude of two-particle states. The result of one step of such a selection is presented that was calculated using the collective behavior method. Original Russian Text K.S. Arakelov, Yu.I. Ozhigov, 2008, published in Vestnik Moskovskogo Universiteta. Vychislitel’naya Matematika i Kibernetika, 2008, No. 4, pp. 34–38.     

Modeling hybrid network dynamics under random perturbations

We define stochastic network models based on internal structural dynamics of individual nodes which undergo Markovian switching subject to noise and external shocks. Steady-state stability and reliability criteria are established in closed form and show explicit dependence on system parameters.     

Modeling and control of parafoils based on computational fluid dynamics

The determination of aerodynamic parameters of parafoil canopies has been a crucial issue because it affects the model precision. To calculate the aerodynamic coefficients of a canopy, the lifting-line theory has been used in the traditional method. However, because of the existence of leading-edge incisions, there are some restrictive assumptions in lifting-line theory when one is calculating the aerodynamic coefficients of a canopy. Therefore in this article we calculate the aerodynamic coefficients on the basis of computational fluid dynamics. As an improvement, the effects of a leading-edge incision and trailing-edge deflection are considered. Firstly, lift and drag coefficients are obtained by use of computational fluid dynamics. Then the least-squares method is used to identify incision and deflection factors. Furthermore, an eight-degrees-of-freedom mathematical model of a parafoil system is established on the basis of the parameters obtained. Finally, a novel control algorithm, generalized predictive control based on a characteristic model, is applied to the system. The precision of the model established and the effectiveness of the proposed control method are validated by simulation and airdrop testing.     

Modeling of contact line dynamics for two-phase flow

We introduce a new model for capillary dominated two-phase flow. Numerical computations demonstrate that it is capable of qualitatively capturing the dynamics of contact lines. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Modeling dynamics of cell population molecule expression distribution

This article introduces a novel approach to the study of the dynamics of the molecule expression level of large-size cell populations, whose goal is to understand how individual cell behavior propagates to population dynamics. A hybrid automaton framework is used which allows the simultaneous modeling of the formation and dissociation of cell-to-cell conjugations, and the molecular processes they control. Serial encounters among the cells are described by a stochastic approach under which the cell distribution over the state space is modeled and the dynamics of the state probability density functions is determined. This work is motivated by the investigation of T-cell receptor expression distribution. These receptors are essential for the antigen recognition and the regulation of the immune system. The results are illustrated with examples and validated with real data.     

Modeling of aortic valve dynamics in a lumped parameter model of left ventricular-arterial coupling

A lumped parameter model of the sub-system of left ventricle, aortic valve, systemic arteries, systemic capillaries and systemic veins was considered during systole. A model of aortic valve dynamics based solely on geometrical and kinematical consideration is defined. The model is described by two geometrical parameters of aortic valve and a few kinematical relationships. The proposed model mimics the incisures in the aortic flow and aortic pressure very well. We showed that the dicrotic notch could be explained by aortic valve closing in terms of a lumped parameter model, without a need for any wave reflection theory. According to the proposed model the effects of aortic valve dynamics on the aortic flow and pressure are mainly limited to the valve opening and closing periods. The model offers a new paradigm for defining a more realistic left ventricle model.      

多层次统计-动力建模及其应用

该文将子波变换技术和平衡态动力理论结合起来，提出了以气候突变点数为核心的代层次气候建模技术。该技术不仅具有纯粹的动力学意义，而且模式的物理意义十分清楚 ，计算简单。     

Modeling futures price dynamics on the RTS and MICEX indices

Reasons for the substantial differences of historical and theoretical futures prices on RTS and MICEX indices are investigated. A model is proposed that considers the observed differences for the modeling of futures prices within the risk assessment of a portfolio of derivatives using the Monte Carlo method.     

Modeling dependence dynamics through copulas with regime switching

Measuring dynamic dependence between international financial markets has recently attracted great interest in financial econometrics because the observed correlations rose dramatically during the 2008–09 global financial crisis. Here, we propose a novel approach for measuring dependence dynamics. We include a hidden Markov chain (MC) in the equation describing dependence dynamics, allowing the unobserved time-varying dependence parameter to vary according to both a restricted ARMA process and an unobserved two-state MC. Estimation is carried out via the inference for the margins in conjunction with filtering/smoothing algorithms. We use block bootstrapping to estimate the covariance matrix of our estimators. Monte Carlo simulations compare the performance of regime switching and no switching models, supporting the regime-switching specification. Finally the proposed approach is applied to empirical data, through the study of the S&P500 (USA), FTSE100 (UK) and BOVESPA (Brazil) stock market indexes.     

Modeling diseases with latency and nonlinear incidence rates: global dynamics of a multi‐group model

In this paper, we perform global stability analysis of a multi‐group SEIR epidemic model in which we can consider the heterogeneity of host population and the effects of latency and nonlinear incidence rates. For a simpler version that assumes an identical natural death rate for all groups, and with a gamma distribution for the latency, the basic reproduction number is defined by the theory of the next generation operator and proved to be a sharp threshold determining whether or not disease spread. Under certain assumptions, the disease‐free equilibrium is globally asymptotically stable if R₀≤1 and there exists a unique endemic equilibrium which is globally asymptotically stable if R₀>1. The proofs of global stability of equilibria exploit a matrix‐theoretic method using Perron eigenvetor, a graph‐theoretic method based on Kirchhoff's matrix tree theorem and Lyapunov functionals. Copyright © 2015 John Wiley & Sons, Ltd.     

HIV dynamics: Modeling,data analysis,and optimal treatment protocols

We present an overview of some concepts and methodologies we believe useful in modeling HIV pathogenesis. After a brief discussion of motivation for and previous efforts in the development of mathematical models for progression of HIV infection and treatment, we discuss mathematical and statistical ideas relevant to Structured Treatment Interruptions (STI). Among these are model development and validation procedures including parameter estimation, data reduction and representation, and optimal control relative to STI. Results from initial attempts in each of these areas by an interdisciplinary team of applied mathematicians, statisticians and clinicians are presented.     

Modeling the dynamics of interest rate volatility with skewed fat-tailed distributions

This paper proposes generalized parametric models of the short-term interest rate that nest one-factor CEV and discrete time GARCH models. The paper estimates the generalized and nested models with skewed fat-tailed distributions to determine the correct specification of the conditional distribution of interest rates. The results indicate that the discrete time models that incorporate the level and GARCH effects into the diffusion function and that accommodate the tail-thickness of the interest rate distribution perform much better than the CEV model in forecasting the future volatility of interest rates. The results also show that the significance of nonlinearity in the drift function relies crucially on the specification of the volatility function.