Вісник Київського національного університету імені Тараса Шевченка. Серія: фізико-математичні науки
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Pattern matching by the terms of cache memory limitations
Get PDFA few known techniques of exact pattern matching, such as 2-byte read, skip loop, and sliding search windows, are improved and applied to pattern matching algorithms, performing over 256-ary alphabets. Instead of 2-byte read, we offer “1.5-byte read”, i.e. reading more than 8 but less than 16 bits of two sequential bytes of a text at each iteration of a search loop. This allows us to fit the search table into L1 cache memory, which significantly improves the algorithm performance. Also, we introduce the so-called double skip loop instead of single one, resolve problems caused by endianness of a machine, and adopt the sliding windows technique to our algorithms. The experimental results averaged over 500 runs of algorithms on 40 different computers show that our algorithms outperform all other tested methods for all tested pattern lengths.Key words: pattern matching, Boyer-Moore-Horspool, fast search, text search, sliding windows.Pages of the article in the issue: 56 - 59Language of the article: Ukrainia
Duality theory under model uncertainty for non-concave utility functions
Get PDFThe main goal for this paper is to study the robust utility maximization functional,i.e. sup_{X\in\Xi(x)} inf_{Q\in\mathsf{Q}} E_Q [U(X_T)]; of the terminal wealth in complete market models, when the investor is uncertain about the underlying probabilistic model and averse against both risk and model uncertainty. In the previous literature, this problem was studied for strictly concave utility functions and we extended existing results for non-concave utility functions by considering their concavization.Key words: robust utility maximization functional, minimax problem, concavization.Pages of the article in the issue: 50 - 56Language of the article: Englis
On hyperbolicity and solution properties of the continual models of micro/nanoparticle aggregation and sedimentation in concentrated suspensions
Get PDFIn continual mechanics sedimentation of aggregating particles in concentrated suspensions are determined by the mass and momentum conservation laws for each component of the suspension. The resulting quasilinear system of differential equations governing the flow could be hyperbolic, strongly strictly or weakly hyperbolic depending on the model accepted. The type and Eigenvalues of the matrix influence the characteristics of the pattern formation during the sedimentation that is essential for the model application in modern medical, microbiological and nanofluidic technologies. In this paper the hyperbolicity of the three-phase model of aggregation and sedimentation of micro/nanoparticles is studied.Key words: Aggregation, Sedimentation, Multiphase Continuous Media, Hyperbolic Systems, Eigenvalues, Characteristics.Pages of the article in the issue: 60 - 63Language of the article: Englis
Generalization of the Lighthill problem for the viscous fluid filled tubes with complicated wall rheology
Get PDFA generalization of the Lighthill model of the plane waves propagation along fluid-filled viscoelastic tubes is proposed. The rheological relation of the wall has two relaxation times for strains and stresses. The equations of the generalized model for the averaged pressure, velocity and the cross-sectional area of the tube are obtained. The solution of the equations in the form of the running waves and the dispersion relation are obtained and compared to those for the Lighthill and Shapiro problems, and the viscoelastic Kelvin-Voigt model for the wall material. Numerical calculations for the model parameters corresponded to human circulation system have been carried out. It is shown, the complicated properties of the material allow accounting for both Young and Lame wave modes, and stabilization the modes that were unstable in the case of simpler rheology. The developed model is helpful in performing the numerical calculations on complex models of arterial vasculatures at lower computation time and resources.Key words: viscoelastic tubes, pulse waves, mathematical modeling, wave dispersion.Pages of the article in the issue: 67 - 70Language of the article: Ukrainia
The uniform strong law of large numbers without any assumption on a family of sets
Get PDFWe study the sums of identically distributed random variables whose indices belong to certain sets of a given family A in R^d, d >= 1. We prove that sums over scaling sets S(kA) possess a kind of the uniform in A strong law of large numbers without any assumption on the class A in the case of pairwise independent random variables with finite mean. The well known theorem due to R. Bass and R. Pyke is a counterpart of our result proved under a certain extra metric assumption on the boundaries of the sets of A and with an additional assumption that the underlying random variables are mutually independent. These assumptions allow to obtain a slightly better result than in our case. As shown in the paper, the approach proposed here is optimal for a wide class of other normalization sequences satisfying the Martikainen–Petrov condition and other families A. In a number of examples we discuss the necessity of the Bass–Pyke conditions. We also provide a relationship between the uniform strong law of large numbers and the one for subsequences.Key words: sums of random variables, uniform in a family of sets limit results, strong law of large numbers.Pages of the article in the issue: 39 - 48Language of the article: Ukrainia
Estimation of probability of exceeding a curve by a strictly ?-sub-Gaussian quasi shot noise process
Get PDFIn this paper, we continue to study the properties of a separable strictly ?-sub-Gaussian quasi shot noise process , generated by the response function g and the strictly ?-sub-Gaussian process ? = (?(t), t ? R) with uncorrelated increments, such that E(?(t)??(s))^2 = t?s, t>s ? R. We consider the problem of estimating the probability of exceeding some level by such a process on the interval [a;b], a,b ? R. The level is given by a continuous function f = {f(t), t ? [a;b]}, which satisfies some given conditions. In order to solve this problem, we apply the theorems obtained for random processes from a class V (?, ?), which generalizes the class of ?-sub-Gaussian processes. As a result, several estimates for probability of exceeding the curve f by sample pathes of a separable strictly ?-sub-Gaussian quasi shot noise process are obtained. Such estimates can be used in the study of shot noise processes that arise in the problems of financial mathematics, telecommunication networks theory, and other applications.Key words: shot noise processes, ?-sub-Gaussian processes.Pages of the article in the issue: 49 - 56Language of the article: Ukrainia
Simulation of a Gaussian stationary process with a stable correlation function with a given reliability and accuracy
Get PDFIn this paper, the representation of random processes in the form of random series with uncorrelated members obtained in the work by Yu. V. Kozachenko, I.V. Rozora, E.V. Turchina (2007) [1]. Similar constructions were studied in the book by Yu. V. Kozachenko and others. [2] in the general case. However, there are additional difficulties in construction of models of specific process, such as, for example, selection of the appropriate basis in L_2(R). In this paper, models are constructed that approximate the Gaussian process with a stable correlation function \rho_{\alpha} (h) = E X_{\alpha}(t + h) X_{\alpha}(t) = B^2 \exp{-d|h|^{\alpha}}, \alpha > 0, d > 0 with parameter , which is a centered stationary process with a given reliability and accuracy in the space L_p ([0,T]). And also the rates of convergence of the models are found, the corresponding theorems are formulated. Methods of representation and main properties of the process with a stable correlation function \rho_2(h) = B^2 \exp{-d|h|^2}, d > 0 are considered. As a basis in the space L_2(T) Hermitian functions are used.Key words: correlation function, simulation, model of the process, accuracy, reliability.Pages of the article in the issue: 89 - 95Language of the article: Ukrainia
On the convergence rate for the estimation of impulse response function in the space Lp(T)
Get PDFThe problem of estimation of a stochastic linear system has been a matter of active research for the last years. One of the simplest models considers a ‘black box’ with some input and a certain output. The input may be single or multiple and there is the same choice for the output. This generates a great amount of models that can be considered. The sphere of applications of these models is very extensive, ranging from signal processing and automatic control to econometrics (errors-in-variables models). In this paper a time-invariant continuous linear system is considered with a real-valued impulse response function. We assume that impulse function is square-integrable. Input signal is supposed to be Gaussian stationary stochastic process with known spectral density. A sample input–output cross-correlogram is taken as an estimator of the response function. An upper bound for the tail of the distribution of the estimation error is found that gives a convergence rate of estimator to impulse response function in the space Lp(T).Key words: impulse response function, linear time-invariant system (LTI), Gaussian process, cross-correlogram. Pages of the article in the issue: 36-41Language of the article: UkrainianThe problem of estimation of a stochastic linear system has been a matter of active research for the last years. One of the simplest models considers a ‘black box’ with some input and a certain output. The input may be single or multiple and there is the same choice for the output. This generates a great amount of models that can be considered. The sphere of applications of these models is very extensive, ranging from signal processing and automatic control to econometrics (errors-in-variables models). In this paper a time-invariant continuous linear system is considered with a real-valued impulse response function. We assume that impulse function is square-integrable. Input signal is supposed to be Gaussian stationary stochastic process with known spectral density. A sample input–output cross-correlogram is taken as an estimator of the response function. An upper bound for the tail of the distribution of the estimation error is found that gives a convergence rate of estimator to impulse response function in the space Lp(T).Key words: impulse response function, linear time-invariant system (LTI), Gaussian process, crosscorrelogram.Pages of the article in the issue: 36 - 41Language of the article: Ukrainia
Methods for modeling the Ornstein-Uhlenbeck process
Get PDFTwo methods of modeling for the Ornstein-Uhlenbeck process are studied in the work. This process has many applications in physics, financial mathematics, biology. Therefore, it is extremely important to have instruments for modeling this process to solve various theoretical and practical tasks. The peculiarity of this process is that it has many interesting properties: it is Gaussian process, is a stationary process, is a Markov process, it is a solution of the Langevin stochastic equation, etc. Each of these properties allows you to apply different methods to this process modeling. We have considered only two methods, although there are many more. One method uses the fact that this process is Gaussian. Another is based on the Fourier expansion. For both of these methods there were specific conditions are obtained when these models satisfy the given levels of accuracy and reliability.Key words: Ornstein–Uhlenbeck process, modeling with given accuracy and reliability, centered gaussian process, Fourier series.Pages of the article in the issue: 24 - 29Language of the article: Ukrainia
Estimates for the distribution of Hölder semi-norms of real stationary Gaussian processes with a stable correlation function
Get PDFComplex random variables and processes with a vanishing pseudo-correlation are called proper. There is a class of stationary proper complex random processes that have a stable correlation function. In the present article we consider real stationary Gaussian processes with a stable correlation function. It is shown that the trajectories of stationary Gaussian proper complex random processes with zero mean belong to the Orlich space generated by the function . Estimates are obtained for the distribution of semi-norms of sample functions of Gaussian proper complex random processes with a stable correlation function, defined on the compact , in Hölder spaces.Key words: stationary Gaussian processes, proper complex random processes, Orlicz spaces, moduli of continuity, Hölder semi-norms.Pages of the article in the issue: 25 - 30Language of the article: Ukrainia