A model of a special-purpose computer system

The paper examines some topics of modeling and optimization of distributed data processing in a special-purpose computer system that consists of several on-board digital computers connected into a single local-area network by a multiplex channel. The computational process is organized so that the processor of each on-board computer executes a fixed set of tasks according to a prespecified program. The objective of the study is to model the computational process in the entire system.Translated from Programmno-Apparatnye Stredstva i Matematicheskoe Obespechenie Vychislitel'nykh Sistem, pp. 113–121, 1994.     

A modified epidemiological model for computer viruses

Since the computer viruses pose a serious problem to individual and corporative computer systems, a lot of effort has been dedicated to study how to avoid their deleterious actions, trying to create anti-virus programs acting as vaccines in personal computers or in strategic network nodes. Another way to combat viruses propagation is to establish preventive policies based on the whole operation of a system that can be modeled with population models, similar to those that are used in epidemiological studies. Here, a modified version of the SIR (Susceptible-Infected-Removed) model is presented and how its parameters are related to network characteristics is explained. Then, disease-free and endemic equilibrium points are calculated, stability and bifurcation conditions are derived and some numerical simulations are shown. The relations among the model parameters in the several bifurcation conditions allow a network design minimizing viruses risks.     

A mathematical model for the effect of malicious object on computer network immune system

In this paper, a nonlinear mathematical model is proposed and analyzed to study the effect of malicious object on the immune response of the computer network. Criteria for local stability, instability and global stability are obtained. It is shown that the immune response of the system decreases as the concentration of malicious objects increases, and certain criteria’s are obtained under which it settles down at its equilibrium level. This paper shows that the malicious objects have a grave effect on cyber defense mechanism. The paper has two parts – (i) in the first part a mathematical model is proposed in which dynamics of pathogen, immune response and relative characteristic of the damaged node in the network is investigated, (ii) in second part the effect of malicious object on the immune response of the network has been examined. Finally how and where to use this modeling is discussed.     

A decisional framework system for computer network intrusion detection

This paper presents a multi-attribute decisional framework for computer network intrusion detection. First, a cost model that allows to estimate accurately the damage resulting from a security incident is described. Then, a multi-attribute optimization algorithm is applied to select the optimal decision based on alternatives to remedy such incidents.     

A prolog-based decision support system for computer capacity planning

This paper describes a project to implement a decision support system for computer capacity planning. The system provides an intelligent interface to the various models needed for this type of planning by assisting the user in model formulation, data manipulation, model execution, interpretation and manipulation of results. The implementation strategy is based on the integration of relational model and database management with logic. A modified version of a Prolog interpreter is utilized as the vehicle for this integrated strategy.This research was supported by Sandia National Laboratories Grant No. 56-3737. Sandia is managed by AT&T Technologies for the U.S. Department of Energy.     

Survival probability for a two-dimensional risk model

In this paper, we consider the survival probability for a two-dimensional risk model. We derive a partial integro-differential equation satisfied by the survival probability and prove its differentiability. We obtain explicit expressions for recursively calculating the survival probability by applying the partial integro-differential equation when claims are exponentially distributed.     

A new epidemic model of computer viruses

This paper addresses the epidemiological modeling of computer viruses. By incorporating the effect of removable storage media, considering the possibility of connecting infected computers to the Internet, and removing the conservative restriction on the total number of computers connected to the Internet, a new epidemic model is proposed. Unlike most previous models, the proposed model has no virus-free equilibrium and has a unique endemic equilibrium. With the aid of the theory of asymptotically autonomous systems as well as the generalized Poincare–Bendixson theorem, the endemic equilibrium is shown to be globally asymptotically stable. By analyzing the influence of different system parameters on the steady number of infected computers, a collection of policies is recommended to prohibit the virus prevalence.     

A modified Markov model for the estimation of computer software performance

The model proposed by Trivedo and Shooman [8] is extended and modified by assuming that (1) the error occurrence rate when the machine is running is proportional to the number of errors in the system; (2) the error correction rate has two components, either an error is corrected with correction rate μ₀ or an error is corrected but a new error is created with ineffective correction rate μ₁. The solution of the differential equations corresponding to the model is obtained in closed form.     

更新风险模型中破产概率的一个局部结果

进一步研究延迟更新风险模型,在假定个体索赔额是重尾分布的前提下得到了破产概率的一个局部等价式R(x,x z]～z/ρμ^-F(x),其中F表示索赔额的分布函数,μ为其均值,ρ表示模型的安全负荷系数,极限过程是x→∞．并且对Sparre Anderson模型作了推广,得到了相应的结果．     

Survival probability and ruin probability of a risk model

In this paper, a new risk model is studied in which the rate of premium income is regarded as a random variable, the arrival of insurance policies is a Poisson process and the process of claim occurring is p-thinning process. The integral representations of the survival probability are gotten. The explicit formula of the survival probability on the infinite interval is obtained in the special casc cxponential distribution.The Lundberg inequality and the common formula of the ruin probability are gotten in terms of some techniques from martingale theory.     

A novel computer virus model and its dynamics

In this paper, we propose a novel computer virus propagation model and study its dynamic behaviors; to our knowledge, this is the first time the effect of anti-virus ability has been taken into account in this way. In this context, we give the threshold for determining whether the virus dies out completely. Then, we study the existence of equilibria, and analyze their local and global asymptotic stability. Next, we find that, depending on the anti-virus ability, a backward bifurcation or a Hopf bifurcation may occur. Finally, we show that under appropriate conditions, bistable states may be around. Numerical results illustrate some typical phenomena that may occur in the virus propagation over computer network.     

A connectionist model using probability data as weights and parameters

Based on the concept of virtual lateral inhibition [1,2], a two layered connectionist model is developed, and its properties explored. This model is called LIBRA/RX. The flow of acitivation in this model is described by a set of 3N ordinary nonlinear differential equations, where N is the number of nodes on the nets' upper level. The mathematical properties of the equations are explored, and in particular, the dynamics of the net is demonstrated to be convergent in nearly all cases. The model has thus far been employed in the task of pattern recognition, and more recently in control tasks [3]. In the task of pattern recognition, the lower level or input nodes represent the possible features, and the upper level or output nodes represent the possible classes of patterns. This model uses the probabilities of the pattern classes given the features, and the features given the pattern classes as weights. The prior probabilities of the features and pattern classes also appear as parameters—thus, no learning need be involved. Examples of the nets use in classifying patterns are presented and discussed.     

Equilibrium probability calculations for a discrete-time bulk queue model

Many problems in management science and telecommunications can be solved by the analysis of aD ^X/D^m/1 queueing model. In this paper, we use the zeros, both inside and outside the unit circle, of the denominator of the generating function of the model to obtain an explicit closed-form solution for the equilibrium probabilities of the number of customers in the system. The moments of the number of customers in the queue or in the system are also studied. When there are infinitely many zeros outside the unit circle, we propose an approximation method using polynomials. This method yields correct values for a finite number of the probabilities, the number depending on the degree of the polynomial approximation.     

A delayed computer virus propagation model and its dynamics

In this paper, we propose a delayed computer virus propagation model and study its dynamic behaviors. First, we give the threshold value R₀ determining whether the virus dies out completely. Second, we study the local asymptotic stability of the equilibria of this model and it is found that, depending on the time delays, a Hopf bifurcation may occur in the model. Next, we prove that, if R₀ = 1, the virus-free equilibrium is globally attractive; and when R₀ < 1, it is globally asymptotically stable. Finally, a sufficient criterion for the global stability of the virus equilibrium is obtained.     

Calibration of the default probability model

In this paper, we study the calibration problem for the Merton–Vasicek default probability model [Robert Merton, On the pricing of corporate debt: the risk structure of interest rate, Journal of Finance 29 (1974) 449–470]. We derive conditions that guarantee existence and uniqueness of the solution. Using analytical properties of the model, we propose a fast calibration procedure for the conditional default probability model in the integrated market and credit risk framework. Our solution allows one to avoid numerical integration problems as well as problems related to the numerical solution of the nonlinear equations.     

An interactive method for parametric identification of the mathematical model of a parachute system using computer graphics

A simple mathematical model of the motion of a parachute system in space is described and an interactive algorithm for parametric identification of the model is proposed. The algorithm selects the model parameters that minimize the deviation of the calculated dependences from experimental observations on the computer graphic monitor.Moscow. Translated from Dinamicheskie Sistemy, No. 10, pp. 106–111, 1992.