### Book

## 7th International conference "Problems of Mathematical Physics and Mathematical Modelling” (2018) Book of abstracts

The problem of forecasting multidimensional time series and mining rules in them

has received much attention. The hypothesis that a rule may change in the course

of time is also quite common. This paper is focused on mining rules that change

slightly in the course of time. This means that a rule may be replaced only by a

similar rule. In this paper a novel approach for mining slightly changing rules is

introduced. The approach is based on a rule similarity measure, which is used as a

weight of an arc on a rule graph. The process of mining slightly changing rules lies

in optimizing the path in the rule graph.

The process of Bayesian information update is essentially sequential: as a result of observation, a prior information is transformed to a posterior, which is later interpreted as a prior for the next observation, etc. It is shown that this procedure can be unified and parallelized by converting both the measurement results and the original prior information to a special form. Various forms of information representation and relations between them are studied. Rich algebraic properties of the introduced canonical information space allow to efficiently scale Bayesian procedure and adapt it to processing large amounts of distributed data.

The problem of forecasting multidimensional time series and mining rules in them has received much attention. The hypothesis that a rule may change in the course of time is also quite common. This paper is focused on mining rules that change slightly in the course of time. This means that a rule may be replaced only by a similar rule. In this paper a novel approach for mining slightly changing rules is introduced. The approach is based on a rule similarity measure, which is used as a weight of an arc on a rule graph. The process of mining slightly changing rules lies in optimizing the path in the rule graph.

In this paper we consider the analysis of an M/D[y] /1 vacation queue with periodically gated discipline. The motivation of introducing the new periodically gated discipline lies in modeling a kind of contention-based bandwidth reservation mechanism applied in wireless networks. The analysis approach applied here consists of two steps and it is based on appropriately chosen characteristic epochs of the system. We provide approximate expressions for the probability-generating function of the number of customers at arbitrary epoch as well as for the Laplace–Stieljes transform and for the mean of the steady-state waiting time. Several numerical examples are also provided. In the second part of the paper we discuss how to apply the periodically gated vacation model to the non real-time uplink traffic in IEEE 802.16-based wireless broadband networks.

The methods of biomechanical systems design with artificial elements are analyzed. The data of high-precision measurements of all set of the biometric characteristics, determining of biomechanical system is a basis of mathematical model. The calculations allows to predict complications at denture installation.

The Conference “Mathematical Modeling and Computational Physics 2015” is jointly organized by the Joint Institute for Nuclear Research (JINR), Dubna, Russia, the Technical University (TU), Institute of Experimental Physics SAS, the Pavol Jozef Šafárik University (UPJŠ), Košice, Slovakia, and the IFIN-HH, Bucharest, Romania.

The Conference follows the rich traditions of the previous conferences on mathematical modeling, numerical methods and computational physics that have been held in Dubna, Russia and also in Slovakia since 1964, e.g., Computational Modeling and Computing in Physics 1996, Modern Trends in Computational Physics 1998, V. International Congress on Mathematical Modeling 2002, Mathematical Modeling and Computational Physics 2006, 2009, 2011, and 2013. This year Conference is dedicated to the 60th anniversary of JINR.

This paper is devoted to mathematical modelling of the progression and stages of breast cancer. The Consolidated mathematical growth Model of primary tumor (PT) and secondary distant metastases (MTS) in patients with lymph nodes MTS (Stage III) (CoM-III) is proposed as a new research tool. The CoM-III rests on an exponential tumor growth model and consists of a system of determinate nonlinear and linear equations. The CoM-III describes correctly primary tumor growth (parameter T) and distant metastases growth (parameter M, parameter N). The CoM-III model and predictive software: a) detect di erent growth periods of primary tumor and distant metastases in patients with lymph nodes MTS; b) make forecast of the period of the distant metastases appearance in patients with lymph nodes MTS; c) have higher average prediction accuracy than the other tools; d) can improve forecasts on survival of breast cancer and facilitate optimisation of diagnostic tests. The CoM-III enables us, for the rst time, to predict the whole natural history of PT and secondary distant MTS growth of patients with/without lymph nodes MTS on each stage relying only on PT sizes.

We consider certain spaces of functions on the circle, which naturally appear in harmonic analysis, and superposition operators on these spaces. We study the following question: which functions have the property that each their superposition with a homeomorphism of the circle belongs to a given space? We also study the multidimensional case.

We consider the spaces of functions on the m-dimensional torus, whose Fourier transform is p -summable. We obtain estimates for the norms of the exponential functions deformed by a C1 -smooth phase. The results generalize to the multidimensional case the one-dimensional results obtained by the author earlier in “Quantitative estimates in the Beurling—Helson theorem”, Sbornik: Mathematics, 201:12 (2010), 1811 – 1836.

We consider the spaces of function on the circle whose Fourier transform is p-summable. We obtain estimates for the norms of exponential functions deformed by a C1 -smooth phase.