A 3D mathematical model for the prediction of mucilage dynamics

We illustrate a three-dimensional mathematical model for the prediction of biological processes that typically occur in a sea region with minor water exchange. The model accounts for particle transport due to water motion, turbulent diffusion and reaction processes and we use a fractional-step approach for discretizing the related different terms.     

Generalized mathematical model of the dynamics of consolidation processes with relaxation

Filtration consolidation of salt-saturated porous media is modeled taking into account time-space nonlocality effects. Asymptotic approximations of problem solutions for excess head are found, an algorithm of numerical modeling of the process dynamics within the framework of the model is proposed, and the results of numerical experiments are presented. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 5, pp. 25–34, September–October 2008.     

A mathematical model for non-linear dynamics of conservative systems with non-homogeneous boundary conditions

In this work a transition into a chaotic dynamics of plates with unmovable boundary conditions along a plate contour and subjected to a longitudinal impact action modeled as a rectangular type loading of infinite length in time is studied. The well-known T. von Kármán equations governing behaviour of flexible isotropic plates have been applied. Finite-difference approximation of order O(h⁴) allowed to transform the problem from PDEs to ODEs. We have shown and discussed how the investigated plate vibrations are transmitted into chaotic dynamics through a period doubling bifurcation. Furthermore, essential influence of boundary conditions on bifurcations number is illustrated, and for all investigated problems the Feigenbaum constant estimation is reported.     

A mathematical model of a searching surveillance system with a group structure

The synthesis of models for searching for different search problems is described. For a search system consisting of groups of spherical search units, a mathematical model of the search is constructed.     

A mathematical model of the OLAP cubes

In 1993, E. Codd introduced a concept of an OLAP (online analytical processing) system, which includes 12 rules of representing data for the user. As can be seen from the name, such systems are designed for analyzing data in an interactive mode. Hence, the basic goal of OLAP means is to represent large amount of data in the form convenient for the end-user analysis. Currently, the representation of data in the form of multidimensional cubes is a de facto standard of user work with large amount of data. In this paper, basic concepts of the OLAP systems are introduced and, then, formalized in terms of the lattice theory. In the frame-work of this formalization, the optimality (in terms of the amount of data stored) of the representation of the OLAP cubes by closed lattices or by quotient lattices (which are equivalent to the former) is proved.     

A mathematical model of planning in the prefrontal cortex

The prefrontal cortex (PFC) is involved in many complex cognitive functions such as problem-solving, planning, reasoning, and decision-making. However, the biological mechanisms of these computations are not clear. To understand these mechanisms, we theoretically consider the experimental result of a path-planning task by Mushiake et al. using a mathematical model referred to as the potential network model. The simulation results show that our model can take the correct path in most trials, regardless of the goal positions and the block patterns in the task. Furthermore, our model reproduces the characteristics of the neuronal activity in both the PFC and the primary motor cortex. This study reveals that although the potential network model is abstract, it can be useful in modelling higher brain functions. This work was presented in part at the 12th International Symposium on Artificial Life and Robotics, Oita, Japan, January 25–27, 2007     

Asymptotic behaviour of a mathematical model of hematopoietic stem cell dynamics

We deeply researched into the asymptotic behaviour of a numerical method adapted for the solution of mathematical model of hematopoiesis which describes the dynamics of a stem cell population. We investigated the stationary solutions of the original model by their numerical approximation: we proved the existence of a numerical stationary solution that provides a good approximation to the nontrivial equilibrium solution of the problem. Also, we presented a numerical simulation which confirms this behaviour.     

基于空域加扰的保密无线通信统一数学模型及其窃密方法

基于空域加扰的方法如人工噪声、天线阵列随机加权等可以在物理层保障无线通信的安全.二者有着共同的物理实质,即在期望用户方向上传递保密信息,而在其正交方向上发射人工干扰.但由于发射天线个数的限制,该人工干扰在空域并非白噪声,窃听用户可以借助接收多天线技术抑制干扰进而解调秘密信息.本文为上述空域加扰的两种方法建立了一致的数学模型,并且在此基础上,利用通信符号的有限码集特性,提出了一种MUSIC-like窃听算法.仿真结果表明,当窃听者比发射端有更多的天线时,该窃听算法可以有效截获保密信息.     

A mathematical model for spirometry

A model originally designed to fit population growth data was investigated to determine whether it could fit spirometric traces as a function of time in normal and ill humans and in normal rats, obtained, respectively, by spirometer and whole-body plethysmography. The model showed great accuracy when applied to a simple spirometer coupled with an analog-to-digital converter interfaced with a personal computer. It also proved to be a good alternative for the more expensive and less accurate electronic devices, as derivative systems, and may be an attractive method for research and/or diagnostic centers.     

Optimal multitherapy strategy in mathematical model of dynamics of the number of nonuniform tumor cells

Mathematical model of dynamics of the number of tumor cells is considered. A tumor is assumed to consist of two cell types, each being under the influence of a specific chemotherapeutic agent that is capable of destroying cells of this specific type. The laws of growth of the number of all types of cells are considered to be given by logistic equations. The measure of the influence of each chemotherapeutic agent on the tumor is defined by a therapy function. Two types of therapy functions are used: a monotonically increasing function and a nonmonotonic function with a threshold value. In the first case, the higher the concentration of the agent, the stronger its influence on the tumor. In the second case, there exists a certain threshold value of the chemotherapeutic agent concentration: once it is exceeded, therapy efficiency decreases. The variant, when the total amount of each agent has an integral limit, is also studied. Necessary optimality conditions are formulated using the Pontryagin’s maximum principle. They are used as a base for making important conclusions about the character of the optimal therapy strategy. We find numerically solutions to the optimal control problems, when the control is aimed at minimizing the total number of tumor cells for the cases of monotonic and threshold therapy functions, as well as with account of the integral constraints for the amounts of chemotherapeutic agents.     

A mathematical model for integrated diagnostics

The authors expand on the form of the information flow model they introduced previously, (see ibid., vol.8, no.3, p.16-30 (1991)). Compiling the model requires three algorithms for determining higher-order relationships. One of these, the algorithm for computing logical closure, helps to simplify the modeling task. The authors also introduce a hypothetical antitank missile launcher to illustrate concepts and computations presented previously     

A mathematical analysis of the effects of Hebbian learning rules on the dynamics and structure of discrete-time random recurrent neural networks

We present a mathematical analysis of the effects of Hebbian learning in random recurrent neural networks, with a generic Hebbian learning rule, including passive forgetting and different timescales, for neuronal activity and learning dynamics. Previous numerical work has reported that Hebbian learning drives the system from chaos to a steady state through a sequence of bifurcations. Here, we interpret these results mathematically and show that these effects, involving a complex coupling between neuronal dynamics and synaptic graph structure, can be analyzed using Jacobian matrices, which introduce both a structural and a dynamical point of view on neural network evolution. Furthermore, we show that sensitivity to a learned pattern is maximal when the largest Lyapunov exponent is close to 0. We discuss how neural networks may take advantage of this regime of high functional interest.     

A phenomenological mathematical model of the articular cartilage damage

Articular cartilage (AC) is a biological tissue that allows the distribution of mechanical loads and movement of joints. The presence of these mechanical loads influences the behavior and physiological condition of AC. The loads may cause damaged by fatigue through injuries due to repeated accumulated stresses. The aim of this work is to introduce a phenomenological mathematical model of damage caused by mechanical action. It is considered that tissue failure is a consequence of chondrocyte death and matrix loss, taking into account factors modifying fatigue resistance such as age, body mass index (BMI) and metabolic activity. The model was numerically implemented using the finite elements method and the results obtained allowed us to predict tissue failure at different loading frequencies, different damage sites and variations in damage magnitude. Qualitative concordance between numerical results and experimental data led us to conclude that the model may be useful for physicians and therapists as a prediction tool for prescribing physical exercise and prognosis of joint failure.     

A mathematical stochastic model for the particles diffusion in atmosphere

A mathematical model for the analysis of the random diffusion and dispersion of solid particles with arbitrary shape in a steady state flow defined is here proposed. In particular a mathematical model for the drag coefficient C_D is defined including a scalar random parameter suitable to describe the fluctuations of the physical conditions of the gas surface system. The equation of the dynamics of the particles, which is, in the proposed model, a random non-linear differential equation is qualitatively discussed and some quasi-analytical solutions are obtained with the perturbations techniques. Some numerical experiments visualize the gap between the results obtained by the proposed model and the ones obtained by the corresponding deterministic model.     

A mathematical model of collaborative reputation systems

This paper provides a mathematical framework for modelling collaborative reputation systems (CRSs), which are useful in many fields of electronic commerce. A CRS is an algorithm that, at discrete points in time, receives in input from a set of users some ratings of a set of objects and generates a reputation for both the raters and the evaluated objects. Sufficient conditions for the convergence of a CRS are given, using basic results of the fixed point theory, and in particular for a broad class of iterative filtering methods and their related CRSs, generalizing some previous results. Finally, we analyse a simple kind of CRS which allows to use a priori information on the reliability of a subset of raters. Experimental results provide evidence that such CRSs exhibit high level of robustness against unfair raters.     

A mathematical model of dynamically evolving economics

Cybernetics and Systems Analysis -     

A mathematical model of impurity propagation in ventilation networks

The objective of this study is the construction of the numerical mathematical model for the propagation of fine impurities in ventilation networks using gas dynamic equations by the numerical coupling of domains with different dimensions.     

A mathematical model for computer image tracking

A mathematical model using an operator formulation for a moving object in a sequence of images is presented. Time-varying translation and rotation operators are derived to describe the motion. A variational estimation algorithm is developed to track the dynamic parameters of the operators. The occlusion problem is alleviated by using a predictive Kalman filter to keep the tracking on course during severe occlusion. The tracking algorithm (variational estimation in conjunction with Kalman filter) is implemented to track moving objects with occasional occlusion in computer-simulated binary images.