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“Informatics and Applications” scientific journalVolume 11, Issue 2, 2017Content Abstract and Keywords About Authors DYNAMIC MODELS OF SYSTEMIC RISK AND CONTAGION
Abstract: Modern financial systems are complicated networks of interconnected financial institutions and default of any of them may have serious consequences for others. The recent crises have shown that complexity and interconnectedness are the major factors of systemic risk, which became the subject of intensive studies usually concentrated on static models. The authors develop a dynamic model based on the so-called structural approach, where defaults are triggered by the exit of some stochastic process from a domain. In the case considered, this is a process defined by the evolution of bank's portfolios values. At the exit time, a bank defaults and a cascade of defaults starts. The authors believe that the distribution of the exit time and the subsequent losses may serve as indicators allowing regulators to monitor the state of the system and take corrective actions in order to avoid contagion in a financial system. The authors model the development of a financial system as a random graph using the preferable attachment algorithm and provide results of numerical experiments on simulated data. Keywords: systemic risk; contagion; scale free network; default ON THE EFFICIENCY OF BRIDGE MONTE-CARLO ESTIMATOR
Abstract: Long-term correlation is a key feature of traffic flows and has a deep impact on network performance. Indeed, the arrival rate can persist on relatively high values for a considerable amount of time, provoking long busy periods and possibly bursts of lost packets. The authors focus on Gaussian processes, well-recognized and flexible traffic models, and consider the probability that the normalized cumulative workload grows at least as the length T of the considered interval. As T increases, such event becomes rare and ad-hoc techniques should be used to estimate its probability. To this aim, the authors present a variant of the well-known conditional Monte-Carlo (MC) method, in which the target probability is expressed as a function of the corresponding bridge process. In more detail, they derive the analytical expression of the estimator, verify its effectiveness through simulations (for different sets of parameters), and investigate the effects of the discretization step. Keywords: Gaussian processes; conditional Monte Carlo; bridge process; rare events; variance reduction MAXIMIZATION OF AVERAGE STATIONARY PROFIT IN M/G/1 QUEUING SYSTEM
Abstract: The problem of optimization of the queue length threshold in a M/G/1 system is considered in terms of maximizing the marginal return received by the system per unit of time. The profit value consists of the following measures: service fee; hardware maintenance fee; cost of service delay; fine for unhandled requests; and fine for system idle. The author formulates the necessary conditions of existence of a finite threshold in an M/G/1 system and prove the statements of necessary and sufficient conditions for threshold optimality and existence of the finite optimal threshold. The author proposes an algorithm for calculating the optimal threshold value and the corresponding maximal profit. The author presents the results of computational experiments that illustrate the work of the proposed algorithm. Keywords: queuing system; threshold management; optimization CLASSIFICATION BY CONTINUOUS-TIME OBSERVATIONS IN MULTIPLICATIVE NOISE II: NUMERICAL ALGORITHM
Abstract: This is the second part of the paper "Classification by continuous-time observations in multiplicative noise I: Formulae for Bayesian estimate" published in "Informatics and Applications," 2017, 11(1). Investigations are aimed at estimation of a finite-state random vector given continuous-time noised observations. The key feature is that the observation noise intensity is a function of the estimated vector, which makes useless the known results in the optimal filtering. In the first part of the paper, the required estimate is obtained both in the explicit integral form and as a solution to a stochastic differential system with some jump processes in the right-hand side. The second part contains a numerical algorithm of the estimate approximate calculation together with its accuracy analysis. An example illustrating the performance of the proposed estimate is also presented. Keywords: optimal filtering; identifiability; recursive scheme; approximation order; time discretization PARTICIPANTS' INFORMATION AWARENESS AND EXISTENCE OF EQUILIBRIUM IN POSITIONAL ITERATION GAMES OF MANY PLAYERS
Abstract: In positional games, dynamical decision-making models are studied for the situation when there is
a conflict of interests and participants know the current position of the game. Each player is able to control the
dynamical system partially. The control strategy chosen by a player is a function defined on the system's phase
space. Players check the system's movement and obtain an implicit idea about strategies applied by their partners.
Keywords: differential game; positional iteration game; program control; positional strategy; counter strategy; punishment strategy; guaranty strategy; Nash equilibrium situation; Pareto effectiveness MODELING THE SIGNAL-TO-INTERFERENCE RATIO IN A MOBILE NETWORK WITH MOVING DEVICES
Abstract: The goal of the study is to analyze the signal-to-interference ratio (SIR) for device-to-device interaction of devices communication in the 5th generation mobile networks, taking into account the movement of the receiving and transmitting devices in the service area. The SIR value at the receiver of the associated pair is studied as a time-varying random process, and the mathematical model of motion is given by a kinetic equation taking into account the given average speed of the devices, their spatial density, and the maximum allowable communication radius. The measures of performance quality were studied by numerical analysis using SIR simulation of a key channel. The measures are the following: the signal interruption probability for the receiver-transmitter pair, the probability density function of the random variables for the duration of the availability period, and the period of absence of communication. It is shown that the signal interruption probability grows logarithmically as either the average device speed or the number of devices in the service area increases. Keywords: wireless network; signal-to-interference ratio; device-to-device; stochastic geometry; motion model; kinetic equation; performance measure; signal interruption probability HIGH-DENSITY MULTIVARIATE REFERENCE REGION
Abstract: The paper considers the principles of construction of multivariate reference regions. An original method of construction of a region on the basis of areas of high density of points and approximation of data distribution with a mixture of normal distributions is suggested. To estimate the threshold for the probability density, the bootstrap method is used. As an experiment, the paper considers the problem of description and use of the reference region for predicting the type of urinary stones. Real data treatment demonstrated the benefits of the proposed solutions. Keywords: multivariate reference region; high-density region; bootstrap method; multivariate normal APPLICATION OF QUASI-RANDOM ENSEMBLE CALCULATIONS FOR DETERMINATION OF CLIMATE MODEL OPTIMAL PARAMETERS
Abstract: By analyzing a randomly generated set of runs, each 2000 years in length, the author has considered the uncertainty in 12 mixing and transport parameters. Constructing a quantitative measure for the model error made it possible to address both the inverse problem of estimation of model parameters and the direct problem of model predictions. The results represent an attempt at tuning a three-dimensional climate model by a strictly defined procedure which, nevertheless, considers the whole of the appropriate parameter space. The modeling approach is thus to match model outputs to observations while model inputs (parameters) are initially only weakly constrained. Keywords: global climate model; model parameters estimation; latin hypercube ON MODIFICATION OF THE MEAN SQUARED ERROR LOSS FUNCTION FOR SOLVING NONLINEAR HETEROSCEDASTIC ERRORS-IN-VARIABLES PROBLEMS
Abstract: The paper considers the problem of finding the optimal parameters of a nonlinear regression model accounting for errors in both dependent and independent variables. The errors of different measurements are assumed to belong to different probability distributions with different variances. A modified mean squared error- based loss function is derived and analyzed for this case. In the computational experiment, the measurements of the laser's radiation power as a nonlinear function of the resonator's transparency are used to compare the parameters vectors minimizing the presented loss function and the classical mean squared error. The convergence of the parameters minimizing the presented loss function to the optimal parameters for the classical loss function is studied. In addition, some values of the parameters are considered to be "true" ones and are used to generate synthetic data using the physical model and Gaussian noise, which is then used to study the convergence of the parameters minimizing the presented and the classical loss function, respectively, as the function of the noise parameters. Keywords: errors-in-variables models; heteroscedastic errors; symbolic regression; nonlinear regression PERSONAL SEMANTIC OPEN DIGITAL LIBRARY LibMeta. CONSTRUCTION OF THE CONTENT. INTEGRATION WITH LOD SOURCES
Abstract: Semantic technologies development has brought digital libraries to the level where a meaningful representation of the content of digital libraries came to the forefront. At the same time, it is necessary to limit it in terms of a certain subject area. The paper describes the libraries content construction with a thesaurus supporting the domain terminology within the developed system LibMeta. The personal semantic open digital library LibMeta provides the functionality of the construction of the library content in accordance with the specific requirements. LibMeta supports users working with resources of digital libraries and their collections in a certain subject area.
Keywords: semantic library; data model; ontology; data sources; search in LOD MODIFICATED ELLIPSOIDAL CONDITIONALLY OPTIMAL FILTERS FOR NONLINEAR STOCHASTIC SYSTEMS ON MANIFOLDS
Abstract: The analytical synthesis theory for modificated ellipsoidal conditionally optimal filters (MECOF) for nonlinear stochastic systems on manifolds (MStS) based on the nonnormed a posteriori characteristic function is developed. Gaussian and non-Gaussian MStS are considered. The MECOF algorithms are more simple than the ECOF algorithms. The MECOF algorithms are the basis of the software tool "StS-Filter" (version 2017). Keywords: accuracy and sensitivity equations; ellipsoidal approximation and linearization methods (EAM & ELM); ellipsoidal conditionally optimal filter (ECOF); modificated ellipsoidal conditionally optimal filter (MECOF); nonnormed characteristic function; Poisson noise; conditionally optimal filter (COF); Wiener noise SINGLE SERVER QUEUEING SYSTEM WITH DEPENDENT INTERARRIVAL TIMES
Abstract: The paper studies a single server queueing system with an infinite number of positions in the queue and random distribution of the service time. The incoming flow of claims is a Poisson flow with a random intensity. The current intensity value is selected from a finite set with given probabilities at the start of the countdown to the next receipt of the claim. Sequential intensities form a Markov chain of a special kind. Particular cases of such flows are hyperexponential flows and flows arising in the study of Bayesian models of queueing systems with a discrete prior distribution. Considered flows describe well the work of queueing systems operating in a random environment with a finite set of different states and Markov relationship between them. Furthermore, such flows can accurately approximate real flows in data networks. The nonstationary behavior of the queue length is studied. Keywords: Poisson flow; random intensity; hyperexponential flow; Markov chain; single server; queue length STRONG CONSISTENCY OF THE MEAN SQUARE RISK ESTIMATE IN THE INVERSE STATISTICAL PROBLEMS
Abstract: Nonlinear methods of digital signal processing based on thresholding of wavelet coefficients became a popular tool for solving the problems of signal de-noising and compression. This is explained by the fact that the wavelet methods allow much more effective analysis of nonstationary signals than traditional Fourier analysis, thanks to the better adaptation to the functions with varying degrees of regularity Wavelet thresholding risk analysis is an imp ortant practical task, because it allows determining the quality of techniques themselves and the equipment which is being used. In some applications, the data are observed not directly but after applying a linear transformation. The problem of inverting this transformation is usually set incorrectly, leading to an increase in the noise variance. In this paper, the asymptotic properties of the mean square error (MSE) estimate are studied when inverting linear homogeneous operators by means of wavelet vaguelette decomposition and thresholding. The strong consistency of this estimate has been proved under mild conditions. Keywords: wavelets; thresholding; MSE risk estimate; correlated noise; asymptotic normality UNIVERSAL THRESHOLDING IN THE MODELS WITH NON-GAUSSIAN NOISE
Abstract: A common assumption in nonparametric signal estimation is that the signal function belongs to a certain class. For example, it may be piecewise continuous or piecewise differentiable and have a compact support. These assumptions, as a rule, make it possible to economically represent a signal function in a specially selected basis in such a way that the useful signal is concentrated in a relatively small number of large expansion coefficients. Then, threshold processing removes noisy coefficients. Typically, the noise distribution is assumed to be Gaussian. This model has been well studied in the literature and optimal thresholding parameters have been calculated for different classes of signal functions. The paper considers the problem of constructing an estimate for the signal function from the observations containing additive noise, whose distribution belongs to quite a wide class. The authors calculate the values of universal thresholding parameters for which the mean-square risk is close to the minimum. Keywords: thresholding; non-Gaussian noise; mean-square risk
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