Book
Материалы XII Международного семинара "Дискретная математика и её приложения" имени академика О.Б. Лупанова (Москва, МГУ, 20-25 июня 2016г.)
Closed classes of three-valued logic, generated by periodical functions taking values from the set {0,1} are considered. Criteria of basis exitstence and finite basis existence for classes generated by periodical functions with period of the form p^k (p is fixed prime number, k is arbitrary natural number) are obtained.
Different generalizations of Markov's theorem conserning inversion complexity of Boolean functions systems are considered.
We prove existence and uniqueness of a solution to the problem of minimizing the logarithmic energy of vector potentials associated to a d-tuple of positive measures supported on closed subsets of the complex plane. The assumptions we make on the interaction matrix are weaker than the usual ones, and we also let the masses of the measures vary in a compact subset of ℝ+ d. The solution is characterized in terms of variational inequalities. Finally, we review a few examples taken from the recent literature that are related to our results.
Currently, the tasks of ensuring the quality and stability of the provided IT services are extremely topical. In the operation of the composite applications, the problem of increasing the effectiveness of incident management is a complex technical problem, the solution of which requires the use of the simulation methods. In the work, the integration platform Ensemble of InterSystems Company was considered as a basis for designing integration solutions. Given the architectural features of the integration platforms, a mathematical model of the incident management process in the Ensemble integration platform is proposed. This mathematical model was used to develop algorithms for identifying and classifying incidents. The results of the work can be used in the design and development of incident management information systems, as well as in organizing the work of technical support services for IT companies
Proceedings include extended abstracts of reports presented at the III International Conference on Optimization Methods and Applications “Optimization and application” (OPTIMA-2012) held in Costa da Caparica, Portugal, September 23—30, 2012.
A “Network Analysis” section was arranged at the XVIIIth Interna- tional Academic Conference on Economic and Social Development at the Higher School of Economics on 11–12 April 2017. For the third year, this section invited scholars from sociology, political science, management, mathematics, and linguistics who use network analysis in their research projects. During the sessions, speakers discussed the development of mathematical models used in network analysis, studies of collaboration and communication networks, networks’ in- uence on individual attributes, identifcation of latent relationships and regularities, and application of network analysis for the study of concept networks.
The speakers in this section were E. V. Artyukhova (HSE), G. V. Gra- doselskaya (HSE), M. Е. Erofeeva (HSE), D. G. Zaitsev (HSE), S. A. Isaev (Adidas), V. A. Kalyagin (HSE), I. A. Karpov (HSE), A. P. Koldanov (HSE), I. I. Kuznetsov (HSE), S. V. Makrushin (Fi- nancial University), V. D. Matveenko (HSE), A. A. Milekhina (HSE), S. P. Moiseev (HSE), Y. V. Priestley (HSE), A. V. Semenov (HSE), I. B. Smirnov (HSE), D. A. Kharkina (HSE, St. Petersburg), C. F. Fey (Aalto University School of Business), and F. López-Iturriaga (Uni- versity of Valladolid).
We study di erences in structural connectomes between typically developing and autism spectrum disorders individuals with machine learning techniques using connection weights and network metrics as features. We build linear SVM classi er with accuracy score 0:64 and report 16 features (seven connection weights and nine network node centralities) best distinguishing these two groups.
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.
The problem of minimizing the root mean square deviation of a uniform string with clamped ends from an equilibrium position is investigated. It is assumed that the initial conditions are specified and the ends of the string are clamped. The Fourier method is used, which enables the control problem with a partial differential equation to be reduced to a control problem with a denumerable system of ordinary differential equations. For the optimal control problem in the l2 space obtained, it is proved that the optimal synthesis contains singular trajectories and chattering trajectories. For the initial problem of the optimal control of the vibrations of a string it is also proved that there is a unique solution for which the optimal control has a denumerable number of switchings in a finite time interval.
For a class of optimal control problems and Hamiltonian systems generated by these problems in the space l 2, we prove the existence of extremals with a countable number of switchings on a finite time interval. The optimal synthesis that we construct in the space l 2 forms a fiber bundle with piecewise smooth two-dimensional fibers consisting of extremals with a countable number of switchings over an infinite-dimensional basis of singular extremals.
This proceedings publication is a compilation of selected contributions from the “Third International Conference on the Dynamics of Information Systems” which took place at the University of Florida, Gainesville, February 16–18, 2011. The purpose of this conference was to bring together scientists and engineers from industry, government, and academia in order to exchange new discoveries and results in a broad range of topics relevant to the theory and practice of dynamics of information systems. Dynamics of Information Systems: Mathematical Foundation presents state-of-the art research and is intended for graduate students and researchers interested in some of the most recent discoveries in information theory and dynamical systems. Scientists in other disciplines may also benefit from the applications of new developments to their own area of study.
In this paper, we construct a new distribution corresponding to a real noble gas as well as the equation of state for it.