The 3rd BRICS
Mathematics Conference
July 21–26, 2019
Innopolis University, Russia
BRICS Mathematics conference is a non‐profit scientific conference to promote mathematical communications among BRICS countries. It is expected to be held among BRICS countries regularly. In 2019, it was organized at Innopolis University, a young Russian higher education institution focused on education and research in the field of IT and Robotics. During the Conference were covered: Pure Mathematics; Applied Mathematics in Computer Science; Probability & Statistics.
Partners
It is a great honor for us to host such a high-level event at Innopolis University, with the participation of countries whose mathematical schools are world leaders. It will be very interesting for us to find innovative ideas that can change the world, and also to share our own vision in the natural sciences. Although our University's primary focus lies in the field of computer science, which is often referred to - not quite correctly - as applied mathematics, all of us are eager to become familiar with new ideas and directions in all areas of modern mathematics.

Such high-level conferences are held quite rarely, and we are happy that, in 2019, this conference will be hosted by Innopolis University, here in Tatarstan. I am sure that it will provide a powerful impetus to our education and research. We will be glad to welcome you to our University.
Alexander Tormasov
Rector of Innopolis University
Previous conferences
The BRICS Mathematics Conference was hold twice.
The 1st BRICS Mathematics Conference took place in the Academy of Mathematics and System Sciences, Chinese Academy of Sciences, August 21st-25th, 2017.

The 2nd conference took place in Brazil, July 23rd –27th, 2018 as an affiliated event of the International Congress of Mathematicians, in Brazil, August 1st-9th, 2018. There were 15 plenary speakers from Brazil, Russia, India, China and South Africa in Pure mathematics, applied mathematics and probability & statistics recommended by mathematics society of each country.

Such conferences provide collaboration between mathematics society in order to share our knowledge, improve skills in research and development and teaching as well.

October 21

*In case you haven't received notification before or on this date on your e-mail means you paper will not be published in "Computer Research and Modelling" journal this december

After final paper submission selected accepted papers will be published in "Computer Research and Modeling" a peer-reviewed Russian journal publishing original research papers and review articles in the field of computer research and mathematical modeling in physics, engineering, biology, ecology, economics, psychology etc.

Committees
Core committee
• Jinyun Yuan (UFPR / Brazil)
• Paolo Piccione (University of São Paulo/ Brazil)
• Ya-xiang Yuan (Chinese Academy of Sciences / China)
• Pingwen Zhang (Peking University / China)
• Neela Nataraj (IIT / India)
• A.A. Shananin (MIPT / Russia)
• Belinda Huntley (University of South Africa / Pretoria)
• David Holgate (University of the Western Cape / South Africa)
Scientific committee
• Jinyun Yuan (UFPR / Brasil)
• Gang Tian (PKU / China)
• Mythily Ramaswamy (TIFR-B / India)
• Sudhir R. Ghorpade (IIT-B / India)
• I.A. Taimanov (Sobolev Ins / Russia)
• A.A. Shananin (MIPT / Russia)
• A.V. Bulinski (LMSU / Russia)
• I.B. Petrov (MIPT / Russia)
• A.I. Lobanov (MIPT / Russia)
Organizing committee
• Alexander Tormasov (IU / Russia)
• Sergey Masyagin (IU / Russia)
• Oksana Zhirosh (IU / Russia)
• Konstantin Konkov (MIPT / Russia)
• Yaroslav Kholodov (IU / Russia)
• Nikolay Shilov (IU / Russia)
• Alexey Pavlov (IU / Russia)
• Timur Fazullin (IU / Russia)

Invited speakers
Sergey I. Kabanikhin
Title
Multidimentional Gelfand-Levitan-Krein-Marchenko equations. Theory and Numerics.

Abstract
Hyperbolic equations describing the wave processes are of great concern in many areas of applied mathematics. Waves come through object and deliver information about its structure to the surface of measurements. Solutions of hyperbolic equations can contain non-smooth and singular components. This leads to easier inversion of the operator compared with elliptic and parabolic cases. Usually inverse problems for hyperbolic equations are solved by minimizing the residual functional. Iterative method of minimizing the functional requires the solution of the direct (and, perhaps, adjoint) problem for every iteration of the method. In multidimensional case iterative methods for multidimensional inverse problems are very time-consuming. The Gelfand-Levitan-Krein-Marchenko (GLKM) approach overcomes nonlinearity of the problems – the nonlinear inverse problem reduces to a system of linear integral equations. GLKM method in some sense is the direct method – there is no need to solve the forward problem (no iteration process). In numerical solution of multidimentional GLKM equations we use fast Toeplitz matrix inversion (Levinson, Durbin, Trench, Tyrtyshnikov, Voevodin) and Monte Carlo approach.

Bio
Sergey I. Kabanikhin is Corresponding Member of the Russian Academy of Sciences, Director of the Institute of Computational Mathematics and Mathematical Geophysics SB RAS, Chief Research Scientist of Laboratory of Wave processes of Sobolev Institute of Mathematics SB RAS, Head of Chair of Mathematical Methods of Geophysics of Novosibirsk State University, Chairman of the Scientific Council of the Institute of Computational Mathematics and Mathematical Geophysics SB RAS, member of the Presidium of the Siberian Branch of the Russian Academy of Sciences, member of the Bureau of the Department of Mathematical Sciences of the Russian Academy of Sciences, Chairman of the Commission on supercomputing of Siberian Branch of RAS, Vice-Chairman of the Joint Scientific Council on Mathematics and Informatics SB RAS, a member of the Scientific Council of Sobolev Institute of Mathematics SB RAS, member of the Scientific Board of Mechanics and Mathematics Faculty of the NSU, member of three Councils for the defense of doctoral theses.

S.I. Kabanikhin is the author of more than 200 scientific papers, 15 books and the textbook "Inverse and ill-posed problems", which was acknowledged the best edition of Sobolev Institute of Mathematics in 2008 and entered the list of the 14 best books published in the Siberian Branch of the Russian Academy of Sciences (2009). The textbook was published in Germany in December 2011.
Dayue Chen
Title
Limit theorems for the tagged particle in exclusion processes on regular trees

Abstract
We consider exclusion processes on a rooted d-regular tree. We start from a Bernoulli product measure conditioned on having a particle at the root, which we call the tagged particle. For d>2, we show that the tagged particle has positive linear speed and satisfies a central limit theorem. We give an explicit formula for the speed. As a key step in the proof, we first show that the exclusion process "seen from the tagged particle" has an ergodic invariant measure. The talk is based on a joint paper with Peng Chen, Nina Gantert, Dominik Schmid http://arxiv.org/abs/1811.01035

Bio
Dayue Chen, Professor of Mathematics at Peking University. Dr. Chen received his B.S. degree from Fudan University in 1983, and his Ph.D. degree from the University of California, Los Angeles in 1989. Before joining the faculty of Peking University in 1991, Dr. Chen spent two years at Northwestern University as a visiting assistant professor. He was promoted to the rank of associate professor in 1993 and professor in 1997. He served as Vice Dean of the School of Mathematical Sciences at Peking University (1998-2002 and 2013-2017), Vice President of the Chinese Mathematical Society (2012-2015), and the Editor of Advances in Mathematics (China). He currently serves as the Dean of the School of Mathematical Sciences at Peking University, and the Secretary General of the Chinese Mathematical Society.

Dr. Chen's research field is probability theory. In particular, he is interested in Markov chains, interacting particle systems, percolation and random walks in a random environment, and has published research papers in the Annals of Probability, Stochastic Processes & Their Applications, etc. He has been supported continuously by grants from the NSF China. He participated in many international conferences in probability, and visited UC Berkeley, Mathematical Science Research Institute, Cambridge University, Kobe University, TU Berlin etc. In recent years Dr. Chen was also actively involved in organizing meetings and workshops in Beijing. In past two decades he taught various courses in probability theory and stochastic processes, as well as statistics. He has supervised 32 graduate students, including 7 Ph.D. students.
Alexander S. Holevo
Title
Quantum Shannon Theory

Abstract
The notions of channel and capacity are central to the classical Shannon theory. "Quantum Shannon theory" denotes a subfield of quantum information science which uses operator analysis, convexity and matrix inequalities, asymptotic techniques such as large deviations and measure concentration to study mathematical models of quantum communication channels and their information-processing performance. From the mathematical point of view quantum channels are normalized completely positive maps of operator algebras, the analog of Markov maps in the noncommutative probability theory, while the capacities are related to certain norm-like quantities. In applications noisy quantum channels arise from irreversible evolutions of open quantum systems interacting with environment—a physical counterpart of a mathematical dilation theorem.

It turns out that in the quantum case the notion of channel capacity splits into the whole spectrum of numerical information-processing characteristics depending on the kind of data transmitted (classical or quantum) as well as on the additional communication resources. An outstanding role here is played by quantum correlations — entanglement – inherent in tensor-product structure of composite quantum systems. This talk presents a survey of basic coding theorems providing analytical expressions for the capacities of quantum channels in terms of entropic quantities. We also touch upon recent progress in solution of long-standing problems of additivity and Gaussian optimizers, concerning the entropic quantities of theoretically and practically important class of Bosonic Gaussian channels.

Bio
Alexander S. Holevo graduated from the Moscow Institute of Physics and Technology in 1966, dyploma in «Applied mathematics and computer science». From 1969 works in the Steklov Mathematical Institute, Moscow. Candidate of phys-math sciences — 1969, Doctor of phys-math sciences — 1975, Professor — 1986. Corresponding member of Russian Academy of Sciences -- 2016. List of publications contains nearly 190 titles including five monographs, four of them translated into English and published by the leading foreign Publishing houses (AMS, North Holland, Springer-Verlag, DeGruyter). Scientific interests: noncommutative probability, quantum information and statistical decision theory, mathematical statistics of random processes. Mathematical theory of quantum communication channels was developed, coding theorems of quantum information theory were established, noncommutative statistical decision theory was constructed, the structure of quantum Markov processes was investigated.

Awards: A. A. Markov Prize for the works on the noncommutative probability theory — 1997; Awards of the Russian Academy of Sciences for the best research achievements in 1992, 1995, 2008, 2015; International «Quantum Communication Award» — 1996; A. von Humboldt Research Award — 1999; Claude E. Shannon Award 2016. Invited speaker at the International Congresses of Mathematicians — Berkeley (1986), Madrid (2006), and many other international and national conferences. Member of the Editorial boards of the journals: «Russian mathematical surveys (Uspekhi)», «Sbornik:mathematics», «Theoretical and mathematical physics», «Izvestiya vuzov: Mathematics», «Quantum Information Processing», «Reports on Mathematical Physics».
Ilya D. Shkredov
Title
Additive Combinatorial problems of Number Theory

Abstract
We give a survey on problems from Number Theory that can be solved or were solved by the methods of Additive Combinatorics such as the Green-Tao theorem about arithmetic progressions, the uniform distribution of the Diffie-Hellman sequence, Ostmann conjecture, the distribution of Fermat quotients, exponential sums over multiplicative subgroups, combinatorial problems with continued fractions and so on.

Bio
Ilya Shkredov received his PhD degree in Mathematics in 2005 and Doctor of Sciences degree in 2009. Positions he helds are Main Researcher of Steklov Mathematical Institute, Full Professor of Division of Dynamical Systems at MSU, Full Professor of Division of Discrete Mathematics at MIPT, Leading Researcher of IITP RAS, Correspondent Member of Russian Academy of Science

Scientific interests: Additive Combinatorics; Number Theory; Combinatorial and Ergodic Number Theory; Combinatorial Ergodic Theory; Themes of research: Multi{dimensional generalizations of Szemer edi's theorem; Exponential sums and Fourier analysis; Sum{product phenomenon; Inverse theorems in additive combinatorics; Uniformly distributed sequences; Continued fractions; Ordinary and multiple recurrence.

Grants and prizes. The best scienti c paper of Steklov Mathematical Institute, 2011/2014/2018; P. Deligne's grant 2007 (based on Balsan's fond 2004).
Xiangyu Zhou
Title
Some recent results in several complex variables

Abstract
We'll present our recent solutions of an optimal L^2 extension problem and Demailly's strong openness conjecture on multiplier ideal sheaves, including the backgrounds, applications and further developments in several complex variables and complex geometry.

Bio
Ph.D, 1990, Institute of Mathematics, Chinese Academy of Science. Russian's Doctor of Sciences, 1998, Steklov Mathematical Institute, Russian Academy of Sciences. 1990—1992, Senior Scientific Member, Steklov Mathematical Institute. Professor, 1998, Academy of Mathematics and Systems Science, Chinese Academy of Sciences. Invited Speaker, ICM 2002. Keynote Speaker, Abel Symposium 2013. Plenary Speaker, Asian Mathematical Conference, 2016. National Natural Science Award of China (by the State Council of China), 2004. S.S. Chern Mathematical Prize (by the Chinese Mathematical Society), 2001. Tan Kah Kee Science Award, 2016. Academician, 2013, Chinese Academy of Sciences. Fellow, 2018, TWAS.
Ye Xiangdong
Title
The recent progress on the multiple ergodic

Abstract
The question on the convergence in the mean or pointwisely of the multiple ergodic averages was originated from the elegant ergodic proof by Furstenberg to the well known Szemeredi's theorem (a subset of integers with positive density contains arbitrarily long arithmetic progressions). In this talk I will review the recent progress and present our contributions to the question.

Bio
Xiangdong Ye obtained Ph.D. in Moscow State University in 1991, and he is now a professor of mathematics at the University of Science and Technology of China (USTC). He was the vice president of USTC (2007-2019). Currently, he is the president of the Anhui province mathematical society and the vice president of the Chinese mathematical society. The research field of Xiangdong Ye is ergodic theory and topological dynamics. He has published more than 100 mathematical papers. Jointly with other researchers he obtained the structure theorem of a minimal system involving nilsystems and established the pointwise convergence theorem of multiple ergodic averages for ergodic distal systems. He severs as editors of several international mathematical journals. He obtained S.S. Chen award in 2013 and the State Natural Science award (2) in 2018.
André Weideman
Title

Abstract
Padé approximation is a useful tool for extracting singularity information from a power series. A linear Padé approximant is a rational function and provides information on pole and zero locations in the complex plane. A quadratic Padé approximant has square root singularities and can therefore provide information on branch point locations. In this paper, we discuss numerical aspects of computing quadratic Padé approximants, such as the solution of the coefficients, the effect of ill-conditioning, the problem of spurious branch-points, and the choice of branches for the square root singularity. Applications presented include the computation of a special function and the solution of a nonlinear PDE.

Bio
J.A.C. Weideman is Professor of Applied Mathematics at Stellenbosch University in South Africa. He was born in Bloemfontein, South Africa, and educated at the University of the Orange Free State (UOFS) in the same city. In the period 1980-1999 he occupied academic positions at the UOFS, at MIT (visiting), and at Oregon State University in the USA. At OSU he was promoted to Associate Professor in 1995 before returning to South Africa in 1999 to take up his current position.

Among Weideman's most cited research is an early paper on the numerical solution of the nonlinear Schrцdinger equation, and mid-career papers on software for spectral methods for differential equations as well as an algorithm for the computation of the complex error function. His recent interests incude the numerical inversion of the Laplace transform, contour integral methods for PDEs, and the computation of the Painlevй transcendents in the complex plane. Weideman is associate editor of Numerical Algorithms and Electronic Transactions of Numerical Analysis, and was elected a SIAM Fellow in 2017.
Tertius de Wet
Title
Confidence Intervals for Extreme Pareto-type Quantiles

Abstract
Extreme Value Theory (EVT) is an important branch of statistical inference due to its application in many fields of science and industry. An important problem in EVT is the estimation of extreme quantiles, often quantiles beyond the range of the available data or in tail regions of very sparse data. In this talk a brief introduction to EVT will be given and some traditional approaches to analysing data in an extreme value context will be given. The talk will then focus on estimation of extreme quantiles as well as the construction of confidence intervals for these quantiles. A novel asymptotic pivotal quantity is proposed which is then used to construct new asymptotic confidence intervals that exhibit more accurate coverage probability. The pivotal quantity also allows for the construction of a saddlepoint approximation from which another set of confidence intervals is constructed. Some results on the small sample properties of these confidence intervals are given using simulation and a case study from insurance.
(Joint work with Sven Buitendag, SU and KUL, Belgium and Jan Beirlant, KUL, Belgium)

Bio
Tertius de Wet is Professor of Statistics at Stellenbosch University in South Africa. He was born in Cape Town and studied at North-West University (NWU) in Potchefstroom, South Africa, where he completed his doctorate in 1971. From 1972 to 1978 he was an academic at NWU and from 1979 to 1981 at Rhodes University in Grahamstown, South Africa. During 1972/1973 he was a post-doctoral visitor at the University of Chicago and during 1978/1979 a visiting professor at the University of Iowa. During 1982 to 1999 he was at the Institute for Maritime Technology in Simons Town, South Africa, where he served in various research, consulting and management positions. Since 2000 he has been professor at Stellenbosch University.

His early research was in goodness-of-fit tests and in particular asymptotic distribution theory of quadratic-type test statistics. This is a topic he returned to often in his future research with order statistics based results a golden thread of his work. Further areas of research included robustness and regression quantiles and in more recent years, extreme value theory. Lately he has again returned to weighted quadratic test statistics in order to find optimal weight functions. As a parallel research interest, he does research with a Belgian colleague in Campanology, the study of bells and carillons, focussing on their historical and statistical properties.

He is an elected member of the International Statistical Institute (ISI) and serves since 2010 on the Editorial board of the ISI's premier journal, the ISI Review. He is a fellow and honorary member of the South African Statistical Association and has served as its president and as editor of its journal. He served on the South African Statistics council from 2008 to 2013.
Srinivasan Kesavan
Title
On a degenerate algebraic Riccati equation

Abstract
The existence of solutions to a degenerate algebraic Riccati equation, associated to an optimal control problem with infinite time horizon, is studied. Under some assumptions on the control system, it is possible to select a solution providing a feedback control law which can stabilize the system.

Bio
Srinivasan Kesavan is one of the top mathematicians in India. His research interests include Partial Differential Equations, Homogenization, Control Theory, Isoperimetric inequalities among other things. He has over 50 research papers and several contributions to conference proceedings and popular scientific articles. His four books are highly popular among students and researchers. Among his many recognitions, major ones are Tamil Nadu Scientist Award, C. L. Chandana Award, Fellowships of National Academy of Sciences and Indian Academy of Sciences. He a member of National Board of Higher Mathematics. He is currently serving as the Vice-President of Ramanujan Mathematical Society, India. He has served twice as Secretary (Grants Selection) for the Commission for Developing Countries (CDC) of the International Mathematical Union (IMU). Currently, he is an Adjunct Professor at the Indian Institute of Technology Madras. Prior to that he was Professor at the Institute of Mathematical Sciences, Chennai (until Jan 2016) and the Deputy Director of the Chennai Mathematical Institute during July 2007 — June 2010.

Rajeeva L. Karandikar
Title
Stochastic Calculus Revisited

Abstract
We will revisit Stochastic Calculus and present a treatment that is very natural and follows the path as in measure theory. This facilitates description of the class of predictable integrands that are integrable w.r.t. a semimartingale without any reference to the decomposition of the semimartingale. Also, we will present a version of the martingale representation theorem w.r.t. a vector valued sigma-martingale. We will also discuss enlargements of underlying filtration and present few open problems in this theme.

Bio
Rajeeva Laxman Karandikar is currently the Director of the Chennai Mathematical Institute. Prior to that he was a Professor and the Head of the Delhi Centre of the Indian Statistical Institute. His research interests include Probability theory and Stochastic Processes, Applications of Statistics, and Cryptography. He has made contributions in several areas of probability theory. These include stochastic calculus, semimartingales, pathwise approximations of solutions to Stochastic differential equations, Markov processes, diffusion processes, martingale problems, filtering theory, linear and non-linear, finitely additive probability theory; Stochastic differential equations in infinite dimensions; financial applications of Stochastic processes, option pricing theory; Boltzman equation and associated Stochastic process; psephology in the context of Indian elections; cryptography, design and analysis of block ciphers; Monte Carlo simulation and so on. He has published several papers and authored two books. He has served as Managing Editor and Editor of Sankhya and as an Associate Editor of Annals of Probability.
Tyakal N. Venkataramana
Title
Thin and Arithmetic Monodromy Groups

Abstract
It is an open question as to when monodromy groups associated to families of smooth projective varieties varying over a smooth quasiprojective base is thin or arithmetic. Of special interest are families of varieties which yield hypergeometric functions as period integrals. In the recent past, progress has been made on this question and we review some of the results.

Bio
Tyakal Nanjundiah Venkataramana is a Senior Professor in the School of Mathematics at the Tata Institute of Fundamental Research, Mumbai. His research interests are at the crossroads of algebra, geometry, topology and number theory. More specifically, he works on Lie groups, arithmetic groups, and automorphic forms. Venkataramana's first major work was the extension of G A Margulis's work on arithmeticity of higher rank lattices to the case of groups in positive characteristics. He also has contributions to non-vanishing theorems on cohomology of arithmetic groups, on Lefschetz type theorems on restriction of cohomology on locally symmetric spaces and to arithmeticity of monodromy groups. He has numerous publications in leading international journals including Ann. Math., Invent. Math., Duke Math. J., etc. (list enclosed), and he has been an invited speaker at the International Congress of Mathematicians held at Hyderabad, India, in 2010.

Carlile Lavor
Title
Protein Geometry: from 3D to 5D

Abstract
Protein structure determination using data from Nuclear Magnetic Resonance (NMR) experiments is a fundamental problem in Computational Chemistry. In order to consider the uncertainties in NMR data, we will discuss a new model to represent protein structures using the 5D Conformal Space and a language more powerful than Linear Algebra.

Bio
Carlile Lavor graduated in Mathematics from the University of Campinas, in 1996, and received a Ph.D. in Computer Science from the Federal University of Rio de Janeiro, in 2001. He was Visiting Professor in distinguished institutions like École Polytechnique (2008–2009), Duke University (2013–2014), and Princeton University (2018).

Since 2015, he is a full professor at the University of Campinas. His research efforts to Distance Geometry, in the last 15 years, culminated with the publication of a paper (co-authored by Liberti, Maculan, and Mucherino) in SIAM Review (first issue in 2014), which was awarded the Notable Article Prize from the ACM Computing Reviews in 2015. He is co-author of the books "Euclidean Distance Geometry" and "A Geometric Algebra Invitation to Space-Time Physics, Robotics and Molecular Geometry", both by Springer. Carlile Lavor is the current President of the Brazilian Society of Applied and Computational Mathematics.
Tiago Pereira
Title
Dynamics of Heterogeneous Systems

Abstract
We will talk about Heterogeneously Coupled Maps (HCM). Such systems are determined by a network with heterogeneous degrees. Some nodes, called hubs, are very well connected while most nodes interact with few others. The local dynamics on each node is chaotic, coupled with other nodes according to the network structure. Such high-dimensional systems are hard to understand in full, nevertheless we are able to describe the system over exponentially large time scales. This allows us to establish the emergence of macroscopic behaviour such as coherence of dynamics among hubs of the same connectivity layer, and chaotic behaviour of the poorly connected nodes. The HCM we study provide a paradigm to explain why and how the dynamics of the network can change across layers. This is a joint work with Sebastian van Strien and Matteo Tanzi.

Bio
Professor of Mathematics at the University of Sao Paulo he obtained his Ph.D. in Berlin in 2007 and was a Leverhulme Trust and Marie Curie fellow at Imperial College London. He is an Advanced Newton Fellow of the Royal Society, a fellow of the Serrapilheira Institute, member of the Brazilian Academy of Sciences and a visiting Professor at Imperial College.

A central theme of his research is the collective behavior of interacting dynamical systems. In particular, how the interaction structure can lead to new dynamics across the system.
Bernardo Rodrigues
Title
2-modular representations of finite simple groups as binary linear codes

Abstract
Let $F$ be a finite field of $q$ elements, and $G$ be a transitive group on a finite set $\Omega$. Then there is a $G$-action on $\Omega$, namely a map ${\cdot}\,{:}\,G \times \Omega \longrightarrow \Omega,\, (g,w) \mapsto w^g = g\cdot w,$ satisfying ${w}^{gg'}= {(g\cdot g')\cdot}{w} = g\cdot (g'\cdot w)$ for all $g, g' \in G$ and all $w \in \Omega,$ and that ${w}^{1} = 1\cdot w = w$ for all $w \in \Omega.$
Let $F \Omega = \{f \,|\, f {:}\, \Omega \longrightarrow F\},$ be the vector space over $F$ with basis $\Omega.$ Extending the $G$-action on $\Omega$ linearly, $F\Omega$ becomes an $F G$-module called an $FG$-permutation module. We are interested in finding all $G$-invariant $FG$-submodules, i.e., codes in $F\Omega.$ The elements $f \in F$ are written in the form $f = \sum_{w \in \Omega} a_w \chi_{w}$ where $\chi_w$ is a characteristic function. The natural action of an element $g \in G$ is given by $g(\sum_{w \in \Omega} a_w \chi_{w}) = \sum_{w \in \Omega} a_w \chi_{g(w)}.$ This action of $G$ preserves the natural bilinear form defined by $$\la \sum_{w \in \Omega} a_w \chi_{w}, \sum_{w \in \Omega} b_w \chi_{w} \ra = \sum_{w \in \Omega}a_{w} b_{w}.$$

Using group representation theory in this talk we present a survey on results of ongoing research that aims to realize finite simple groups as permutation groups of automorphisms of binary linear codes. As an illustration we show an instance of a classification result on binary self-dual codes invariant under rank 3 permutation groups of almost simple type. Thus, bringing to the fore an interplay that exists between finite groups, modular representation theory, combinatorial design theory, algebraic graph theory and algebraic coding theory.

Bio
Bernardo Rodrigues was born in Malange, Angola and studied at the Pedagogic University Enrique José Varona in La Habana, Cuba where he earned a Licenciatura in Mathematics and Education (equivalent to an MSc) and moved to the former University of Natal, in Pietermaritzburg, South Africa where he obtained an MSc in 2000 and a PhD in Mathematics in 2003, the latter under the supervision of Jamshid Moori (Natal) and co-supervision of Jennifer Key (Clemson University). He was appointed to the Mathematics Department of Natal University in 2004, where he is became an Associate Professor since 2010, under the new merged University of KwaZulu-Natal.

In the period 1996 – 2002 he was awarded a DAAD-German Academic Exchange Scholarship to take up graduate studies, and in 2017, he was the recipient of a Fulbright Scholar Award and during the period 2016 - 2018 he participated in two Erasmus Mundus Plus Exchange Programmes. Although his early work concerned the theory of finite groups, in particular the study of the extension problem, his current research interests concern with the interplay between Algebraic Coding Theory, Finite Groups, Modular Representation Theory of Finite Groups and Combinatorial Design Theory as well as Computatational Group Theory and Axial Algebras, including both the concrete and the abstract aspects of these subjects. His recent papers involve modular representation of finite simple groups, as well as the application of this to the realization of finite simple groups as permutation groups of automorphisms of linear codes.

He also works in problems related with the construction of non-associative axial algebras related to the sporadic simple groups. He became a member of the editorial board of the journal Afrika Mathematica in 2013 and a Deputy-Editor in 2018. He has supervised eleven postgraduate dissertations, four of them at PhD level. He has held several visiting positions in several African countries, at universities in the United States, Australia, New Zealand and United Kingdom, most frequently at the University of Birmingham in the UK.
Jaqueline Godoy Mesquita
Title
Functional Volterra Stiletjes integral equations and applications

Abstract
In this work, we investigate the functional Volterra-Stieltjes integral equations and their applications. We prove results concerning existence and uniqueness of solutions, prolongation of solutions of functional Volterra-Stieltjes integral equations. Also, we describe a correspondence between the solutions of these equations and the solutions of functional Volterra delta integral equations on time scales. Finally, we present some examples to illustrate our main results.

Bio
Jaqueline Godoy Mesquita completed her PhD in Mathematics in 2012 at the University of São Paulo with a period at the Academy of Sciences of Czech Republic in Prague. She had two post-doctorate positions, one at the Universidad de Santiago de Chile and the other one at University of São Paulo.She held the position of Assistant Professor at University of São Paulo (2013–2015) and is currently Assistant Professor at University of Brasília since 2015. She has won the International Bernd-Aulbach Prize for Students in 2012, awarded by the International Society of Difference Equations. She was selected to participate at the 5th Heidelberg Laureate Forum 2017 and was selected to be an Oberwolfach Leibniz Fellow during 2018. She was elected young affiliated member of TWAS (2018–2022), affiliated member of the Brazilian Academy of Sciences (2018–2022) and regional secretary of the Brazilian Mathematical Society (2017-2019). She is currently a Humboldt fellow at Justus Liebig Universität Giessen, Germany. Her field of interests includes functional differential equations, impulsive differential equations, generalized ordinary differential equations, and dynamic equations on time scales.
Title
Statistical Innovation and Applications in Industrial, Medical and Business Problems

Abstract
It has been observed a great insertion of statistical methodologies in innovation processes, promoting interaction with professionals from governmental and productive sectors, as well as with the community, efficiently directing the interlocution between academia and industry. In this conference, it is presented the main statistical innovation projects that we have been developing in the sense of approximating the academia, the productive sector, and the community. The focus is given to reliability modeling for oil well construction equipment, classification modeling for fraud detection in financial transactions, electro-encephalography modeling, breast cancer modeling, neglected tropical diseases modeling, and communication modeling for mobile phones and autonomous unmanned aerial vehicles.

Bio
Francisco Louzada is a Professor of Statistics at University of São Paulo (USP), and Director of the Center for Mathematical Sciences Applied in Industry (CeMEAI), both in Brazil. His main interests are data science, survival and reliability analysis, and statistical inference and applications. He is Ph.D. from the University of Oxford, UK, M.Sc. from USP, Brazil, and B.Sc. from UFSCar, Brazil.

He is a single and joint author of 06 books and various publications in statistical peer-reviewed journals. He is an elected member of the International Statistical Institute (ISI), and he is an Editor of Sankhya A (Springer), and Editor-in-Chief of Springer book series SpringerBriefs in Statistics - ABE. He has served as President of the Brazilian Statistical Association (ABE) and member of the Directory of the Brazilian Chapter of the International Society for Bayesian Analysis (ISBA), and he is a former Editor-in-Chief of the Brazilian Journal of Probability and Statistics (ABE/IMS). Prof. Louzada has provided consulting, training and technological transferring of statistical methodologies for more than 50 companies and institutions. More details can be found in www.mwstat.com/franciscolouzada
Regular speakers
Cong Sun

Title

New stepsizes for the gradient method

Abstract
Based on the idea of coordination transformation, we proposed a new stepsize update strategy for the gradient method, which is the extension of Yuan's stepsize from 2-dimension to 3-dimension. For 3-dimensional convex quadratic function minimization problems, it guarantees to find the optimal solution in 5 iterations. We also modified the strategy to improve the performance. We proved that, for 3-dimensional convex quadratic function minimization problems, the new modified gradient method terminates in finite iterations; for general dimensional problems, it converges R-linearly. Numerical tests show good performances of the proposed method compared to the states of the art.

Jac Weideman

Title

Locating Complex Singularities: Numerics and Applications

Abstract
For numerical computation, a power series representation of a function is typically truncated to a polynomial. Being an entire function, a polynomial cannot reveal much of the singularity structure of the underlying function other than perhaps the distance to the nearest singularity in the complex plane. The same remarks apply to Fourier series and truncated Fourier series. In the first part of the talk we survey some numerical strategies for uncovering additional singularity information. This includes Padé and Fourier-Padé approximations, both of the linear and the quadratic varieties. We discuss numerical implementations, stability, and pitfalls. Our test examples include meromorphic functions as well as functions with branch-point singularities. In the second part of the talk, we apply these techniques to trace the singularities of some nonlinear PDEs in the complex plane.

Ya-Xiang Yuan

Title

Efficient Optimization Algorithms For Large-scale Data Analysis

Abstract
Optimization models are ubiquitous in data analysis. This talk first reviews two efficient Newton type methods based on problem structures: 1) semi-smooth Newton methods for composite convex programs and its application to large-scale semi-definite program problems and machine learning; 2) an adaptive regularized Newton method for Riemannian Optimization. Next, a few parallel optimization approaches are discussed: 1) parallel subspace correction method for a class of composite convex program; 2) parallelizable approach for linear eigenvalue problems; 3) parallelizable approach for optimization problems with orthogonality constraint.

Alexander Bulinski

Title

Feature Selection and Statistical Estimation of Mutual Information

Abstract
Along with a brief survey of various methods employed in the feature selection theory we develop the recent papers and to study statistical estimation of mutual information and other divergences. Such estimates are used for identification of relevant factors having impact on a random response. This research direction is very important, e.g., for analysis of biological and medical data. Theoretical results describing the asymptotic behaviour of statistics under consideration are supplemented with computer simulations. Special attention is paid to the so-called mixed models comprising the widely used logistic regression.

Ekaterina Bulinskaya

Title

Isotropic multidimensional catalytic branching random walk with regularly varying tails

Abstract
The study completes a series of the author's works devoted to spread of particles population in supercritical catalytic branching random walk (CBRW) on a multidimensional lattice. The CBRW model describes evolution of a system of particles combining their random movement with branching (reproduction and death) which only occurs at fixed points of the lattice. The set of such catalytic points is assumed finite and arbitrary. In the supercritical regime the size of population, initiated by a parent particle, increases exponentially with positive probability. The rate of the spread depends essentially on the distribution tails of the random walk jump. If the jump distribution has "light tails", the "population front", formed by the most distant from the origin particles, moves linearly in time and the limiting shape of the front is a convex surface. When the random walk jump has independent coordinates with a semi-exponential distribution, the population spreads with a power rate in time and the limiting shape of the front is a star-shape non-convex surface. So far, for regularly varying tails ("heavy" tails), we considered the problem of the scaled front propagation assuming independence of components of the random walk jump.

Elena Dyakonova , Doudou Li , Vladimir Vatutin and Mei Zhang

Title
Branching processes in random environment with immigration stopped at zero

Abstract
We consider branching processes allowing immigration and evolving in a random environment. In such a process individuals reproduce independently of each other according to offspring distributions which vary in a random manner from one generation to the other. In addition, a number of immigrants join each generation independently on the development of the population and according to the laws varying at random from generation to generation. A formal definition of the process looks as follows. Let ∆ = (∆1, ∆2) be the space of all pairs of probability measures on N0 = {0, 1, 2, . . .}. Supplying ∆ with the componentwise metric of total variation we obtain a Polish space. Let Q = {F, G} be a two-dimensional random vector with independent components F := (F({j}), j = 0, 1, ...), G := (G({j}), j = 0, 1, ...) taking values in ∆, and let Qn = {Fn, Gn}, n = 1, 2, . . . , be a sequence of independent copies of Q. The infinite sequence E = {Q1, Q2, ...} is called a random environment.

Giriraj Methi and Anil Kumar

Title

Numerical Solution of Linear and Higher order Delay Differential Equations using Coded Differential Transform Method

Abstract
Aim of the paper is to obtain numerical solution of linear and higher order delay differential equations (DDEs) using Coded differential transform method (CDTM). We have applied CDTM on few delay problems to show efficiency of proposed method. The CDTM will give approximate series solution. Numerical results and error analysis are presented to show that proposed method is suitable for solving DDE's.

Mythily Ramaswamy, Jean-Pierre Raymond and Arnab Roy

Title

Boundary Feedback stabilization of heat conducting fluid flow

Abstract
The Boussinesq system - Navier-Stokes equations coupled with heat equation, in two dimension with mixed boundary conditions will be studied for feedback stabilization using finite dimensional boundary controls. Numerical implementation of the controls will be discussed.

David Holgate

Title

Topogenous orders and related families of maps

Abstract
A topogenous order is an order relation imposed on the subobject lattices of objects in a given category - for instance on all subspaces of topological spaces. These orders generalise closure, interior and neighbourhood operators and provide a mechanism for studying topological properties in a general category. In this talk we introduce various families of maps which are defined by means of a topogenous order on a general category, study their properties and give some examples. In the standard case of topological spaces they give open, closed, final and initial maps.

Jinyun Yuan

Title
Numerical Linear Algebra in Data Science

Abstract
In this talk we shall give a survey talk on possible applications of numerical linear algebra, such as matrix factorizations, low rank approximation, biorthogonization, eigenvalue problem, least squares, and SVD in data science. Also mention some future possible research issues.

Rakesh Kumar and Subir Das

Title

Impulsive effects on exponential stability of inertial BAM neural network with mixed time-varying delays via matrix measure approach

Abstract
The present article is investigating the effects of time-varying impulses on exponential stability to a unique equilibrium point of inertial BAM neural networks with mixed time-varying delays. A suitable variable transformation is chosen to transform the original system into the system of first order differential equation. The fixed point theory of homeomorphism has been implemented to find the distributed delay-dependent sufficient condition which assured the system has a unique equilibrium point. In order to study the impulsive effects on stability problems, the time-varying impulses including stabilizing and destabilizing impulses are considered with the transformed system. Based on the matrix measure approach and the extended impulsive differential inequality for a time-varying delayed system, we have derived sufficient criteria in matrix measure form which ensure the exponential stability of the system towards an equilibrium point for two classes of activation functions. Further, different convergence rates of the system's trajectories have been discussed for the cases of time-varying stabilizing and destabilizing impulses using the concept of an average impulsive interval. Finally, the efficiency of the theoretical results has been illustrated by providing two numerical examples.

Alexander Shananin

Title

Inverse problems in models of resorse distributions

Abstract
We consider some problems of mathematical economics related with integral geometry and complex analysis. These problems are motivated by substitution of production factors in industry.
We describe several models of resources distribution and discuss the inverse problems for the generalized Radon transform arising in these models. We give a simple explicit range characterization for a Radon transform and we apply it to show that the most popular production functions are compatible with these models. Besides, we give a necessary condition and a sufficient condition for solvability of the model identification problem in the form of appropriate moment problem. These conditions are formulated in terms of rhombic tilings.

Maksim Muratov and Igor Petrov

Title

Application of fractures mathematical models in exploration seismology problems simulation by grid-characteristic method

Abstract
In real problems of exploration seismology we deal with a heterogeneity of the nature of elastic waves interaction with the surface of a fracture by the propagation through it. The fracture is a complex heterogeneous structure. In some places the surfaces of fractures are places in some distance between themselves and are separated by filling fluid or emptiness, in some places we can observe the gluing of surfaces, when under the action of pressure forces the fracture surfaces are closely adjoined to each other. In addition, fractures can be classified by the nature of saturation: fluid or gas. Obviously, for such a large variety in the structure of fractures, one can not use the only one model that satisfies for all cases.

Ramazan Bagaev, Vasily Golubev and Yulia Golubeva

Title

Full-wave 3D earthquake simulation with the double-couple model and the grid-characteristic method

Abstract
One of the destroying natural processes is the initiation of the regional seismic activity. The gradual accumulation of stresses in the geological massif is changed to the sharp slippage along the existing fault. It leads to the large number of human deaths. A lot of efforts have been made to develop precise and robust methods for the estimation of the seismic stability of buildings. In this report we present the results of the advanced source model application to the simulation of the seismic initiation process with the grid-characteristic method. 3D full-wave simulation was carried out. The spatial and temporal distributions of stresses were obtained. Dynamic and kinematic characteristics of first arrivals were successfully compared with the previously published data.

Igor Petrov

Title

Application of grid-characteristic method for mathematical modeling in deformable solid mechanics dynamical problems

Abstract
The grid-characteristic method is a promising numerical method for solving hyperbolic systems of equations, e.g., equations describing elastic and acoustic waves. This method has high precision and allows you to physically correctly simulate wave processes in heterogeneous media. The grid-characteristic method makes it possible to correctly take into account boundary conditions and conditions on surfaces with different physical characteristics. Most fully the advantages of the method are for one-dimensional equations, especially in combination with a fixed difference grid, as in conventional grid-based methods. However, in the multidimensional case using the algorithms of splitting with respect to spatial variables, the author has managed to preserve its positive qualities. The use of the method of Runge – Kutta type, or integro-interpolation method for hyperbolic equations makes it possible to effectively carry out the generalization of methods developed for linear equations, in nonlinear case, in particular, to enforce the difference analogs of the conservation laws, which is important for shock-capturing, for example, discontinuous solutions.

Eugene Tyrtyshnikov

Title

Big Data Numerical Algorithms Using Matrix and Tensor Low Rank Structures

Abstract
In this talk we consider optimization algorithms using low-rank structures in matrices and tensors. We also discuss efficient implementations of the cross-tensor-train procedures and recent developments of theory explaining why these algorithms work so nice in practice. The practical importance of the very approach consists in its paradigm of using only small part of matrix entries that allows one to construct a sufficiently accurate approximation in a fast way for "big data" matrices that cannot be placed in any available computer memory and are accessed implicitly through calls to a procedure producing any individual entry in demand. Besides that, we consider some applications, in particular the new advanced algorithms for numerical solution of the Smoluchowsky-type equations.

Title

Grassmann and Schubert varieties over Finite Fields, with Applications to Coding Theory

Abstract
Consider the Grassmann variety with its canonical Plucker embedding, or more generally a Schubert variety in a Grassmannian with its nondegenerate embedding in a subspace of the Plucker projective space. We can cut it by linear subspaces of a fixed dimension of the ambient projective space, and ask which of the linear sections are "maximal". The term "maximal" can be interpreted in several ways and we will be particularly interested in maximality with respect to the number of points, when working over a finite field. In general, this is an open problem. We will describe several known results in this direction as well as connections to coding theory and some basic questions of multilinear algebra.

Vladimir Konyukhov, Ivan Konyukhov and Anatolii Chekalin

Title

Numerical Simulation, Parallel Algorithms and Software for Performance Forecast of System "Porous-Fractured Reservoir & Producing Pumping Well" During its Commissioning Into Operating Regime

Abstract
Exploitation of the oil producing wells equipped with electrical submersible pumping systems (ESPs) is attended by the interconnected thermo- and hydrodynamic processes in the multiphase flows moving in the porous medium of the oil reservoir, tubes of well and channels of ESP. These processes become significantly non-steady during the commissioning into operation the wells after underground equipment repair. In this case the problem of computer forecast of the interconnected heat and mass transfer in the system "oil reservoir - well - ESP" and the task of correct pump selection for the wells are quite actual. Solution of these problems can be efficiently found numerically. In this report we propose the mathematical model, finite-difference schemes and algorithms for computation of transient thermo- and hydrodynamic processes at the commissioning the unified system including the oil producing well, ESPs and porous-fractured reservoir with bottom water.

Vladimir Konyukhov, Ivan Konyukhov and Anatolii Chekalin

Title

Numerical Modeling And Parallel Computations Of Heat And Mass Transfer During Physical And Chemical Actions On The Non-Uniform Oil Reservoir Developing By System Of Producing And Injecting Wells

Abstract
The subject of this research is mathematical, numerical and computer simulation of thermo- and hydrodynamic processes in the multiphase flows in the system of producing and injecting wells developing the non-uniform oil reservoir with the use of physical and chemical methods for the increasing of oil recovery. Two types of physical-chemical technologies, namely polymer flooding and hydrogel flooding, are considered. In the first case the thickening agent is aqueous polymer solution of the desired concentration injected into the porous reservoir to create the high-viscous moving field. Unlike this technology, the hydrogel flooding is characterized by creation and evolution of the moving hydrogel field directly in porous medium in result of chemical reaction between the water solutions of two gel-forming components which one after another are injected into the oil reservoir with given time interruption.

Sergei Shalagin, Vjacheslav Zakharov and Bulat Eminov

Title

Application of one-type IP-cores for two-dimensional data arrays distributed processing in FPGA-architecture

Abstract
The problem of image processing, two-dimensional data arrays, is being solved through implementing two-dimensional fast Fourier transform (FFT) using single-type hardware modules, namely IP-cores in the Virtex-6 FPGA-architecture. We have also shown the possibility to implement in parallel each stage of the two-dimensional FFT, based on four "butterfly" transforms (BTrs) over four elements of the data array being processed. Estimates have been obtained for the time and hardware complexity of an IP-core implementing a BTr, which is also used in implementing a one-dimensional FFT. The findings can be used to evaluate hardware and time complexity in performing a two-dimensional FFT over an array of a given dimension using both existing and promising distributed computing systems having programmable architectures.

Maria Elovenkova and Alexey Vasyukov

Title

Modeling of textile membrane dynamic deformation and destruction

Abstract
This work is devoted to a mathematical modeling of a thin textile membrane under an intense shock load. The deformation of the membrane and its subsequent destruction are considered. For the detailed consideration of the destruction, the work presents the calculations of individual one-dimensional threads that make up the membrane. The calculations of two-dimensional membrane are also presented for a complex three-dimensional load profile.

Paolo Piccione

Title

Bifurcation Phenomena in Geometric Variational Problems

Abstract
I will review some basic of classical Bifurcation Theory, and then I will discuss a few modern applications in Riemannian Geometry, including minimal and constant mean curvature surfaces, as well as the Yamabe problem.

Ivan Mitskovets, Vladislav Stetsyuk and Nikolay Khokhlov

Title

Overset grids approach for topography modeling in elastic-wave modeling using grid-characteristic method

Abstract
Taking into account the topography of the earth's surface can improve the accuracy of seismic modeling when using real geological data. The presence of topography will cause more complicated seismic wave propagation phenomena, such as diffraction at rough surfaces, complex propagation of Rayleigh wave, and site effects caused by wave interferences. Primary goal of this research is to construct method that implement the free surface on topography, utilizing overlay curved grid for characterization. We investigate workability of GCM approach using overset grids (also known as the Chimera grid approach) in combination of regular rectangular and curvilinear grids. Furthermore, this mechanism allows to reduce computational complexibility by simulating wave propagation in regular, homogeneous physical area using sparse regular rectangle grid, in order to increase digitalization of fractured regions and minimize Courant number. Moreover, the mechanism of the mesh building is simplified.Method validation was performed by comparison with " EX2DDIR 1.0 final " and " specfem2d " software packages at two-dimensional Lamb's problem solving. To demonstrate the capabilities of our method, we calculate the propagation of seismic wave in the solid under wavy free-surface. To validate result of our approach in case of non-trivial topography, we compare it with "specfem2d" solution. There was used 4th-order 6-stage low storage Runge-Kutta scheme, non-regular rectangle grid with same grid dimensions and time step.

Igor Konnov

Title

Gradient projection method with regularization for optimization problems in Hilbert spaces

Abstract
We suggest simple implementable modifications of the gradient projection method for smooth convex optimization problems in Hilbert spaces. Usually, the custom method attain only weak convergence. We prove strong convergence of the new version and establish its complexity estimate, which appears similar to the convergence rate of the weakly convergent version. Preliminary results of computational tests confirm efficiency of the proposed modification.

Anna Andreeva, Andrey Nikolaev and Alexey Lobanov

Title

On elaboration of blood clotting mathematical model

Abstract
Mathematical modeling of the blood coagulation involves some attempts to describe experimental data for coagulation in increasingly comprehensive theoretical frame-works. In vivo injury to the vessel is followed by constriction of the vessel and the formation of a platelet plug. The formation of a fibrin clot occurs through multistage plasma coagulation process providing longevity to the temporary platelet seal. Since the activated platelets play a significant role in the thrombin production dur-ing coagulation, incorporation of the platelet related reactions from the primary coagulation stage into the models of the plasma stage was done. A comprehen-sive "reaction-diffusion-convection" type is necessary for accurate description of the fibrin polymerization in the presence of the platelets. Considering the role of the platelets and the reactions on their surface thrombin generation allows us to model the process of clotting in a whole blood, not only in plasma. Most of the mathemati-cal models for the blood coagulation system have described the fibrin polymeriza-tion in a simplistic manner until recently. The main limitation of the simpli-fied model was that it didn't described the lag period observed in experiments. Au-thors proposed a detailed model of the fibrin polymerization in, based on the current knowledge of molecular mechanisms of this reaction.

Neela Nataraj

Title

Finite element methods for a distributed optimal control problem governed by the von Karman equations

Abstract
Consider the distributed optimal control problem governed by the von Karman equations that describe the deflection of very thin plates defined on a polygonal domain in the plane with box constraints on the control variable. The talk discusses a numerical approximations of the problem that employs conforming and nonconforming finite element methods to discretize the state and adjoint variables. The control is discretized using piecewise constants. A priori error estimates are derived for the state, adjoint and control variables under minimal regularity assumptions on the exact solution. Error estimates in lower order norms for the state and adjoint variables are derived. The lower order estimates for the adjoint variable and a post-processing of control leads to an improved error estimate for the control variable. Numerical results confirm the theoretical results obtained. This is a joint work with J.P. Raymond, Sudipto Chowdhury and Devika Shylaja.

Raoul Nigmatullin

Title

Two Statistical Methods for Quantitative "Reading" of Different Trendless Sequences

Abstract
In this paper, two new statistical methods related to analysis of the trendless sequences (TLS) are described. These statistical methods are rather "universal" and do not use a priori supposition about the model of the chosen noise (Gaussian, "white", "color", "1/f – noise" etc.). Two basic proposed methods, based on the author opinion, can find a wide application in various regions of a science and technics. The first method is based on the "struggle principle" between positive and negative amplitudes. It gives at least 10 quantitative parameters and can be applied for compression of "big data" arrays and for comparison of the pattern and tested sequences. The second method is based on the prove of existence of the discrete geometrical invariants (DGI) of the second and the fourth orders for comparison of random sequences. It allows obtaining from 2N initial data points only 10 quantitative parameters that include the moments and their inter-correlations. With the help of the second method, one can calibrate the different measured equipments based on their random fluctuations of the measured cell. These methods do not use a priory proposed model about the random process and can find a wide application in different branches of science and technology, especially in analysis of different nano-noises, including a quantum noise.

Galina Mozhaeva, Diana Dammer, Svetlana Veledinskaya and Eduard Galazhinskiy

Title

The experience of adaptive online platform application for math teaching

Abstract
One of the significant problems of higher education today is the inadequate level of school preparation of university applicants, in particular in mathematics. The way out of this situation seems to be the creation of an adaptive learning system based on special adaptive algorithms that provide a dynamic, data-based building of an individual learning path and takes into account the preparedness, abilities, goals, motivation, and other characteristics of the student.
The report presents the results of the first phase of the project to create an adaptive online platform, implemented in Tomsk State University together with the company Enbisys, including testing the system.

Galina Mozhaeva, Diana Dammer, Svetlana Veledinskaya and Eduard Galazhinskiy

Title

The experience of adaptive online platform application for math teaching

Abstract
One of the significant problems of higher education today is the inadequate level of school preparation of university applicants, in particular in mathematics. The way out of this situation seems to be the creation of an adaptive learning system based on special adaptive algorithms that provide a dynamic, data-based building of an individual learning path and takes into account the preparedness, abilities, goals, motivation, and other characteristics of the student.
The report presents the results of the first phase of the project to create an adaptive online platform, implemented in Tomsk State University together with the company Enbisys, including testing the system.

Ravneet Kaur and Vijay Kumar Kukreja

Title

Finite difference fractional step method for solving Burgers equation

Abstract
Burgers' equation is discussed in this paper using the fractional step method. Approximate solutions are considered in two space dimension with Dirichlet boundary conditions. The finite difference scheme is Lax-Wendroff for spatial derivative and forward for time derivative. The nonlinear term is discretized using the quasi-linearization. A priori bound is proved using Lyapunov functional showing the boundedness of the system. Further, the unique existence of the proposed scheme is discussed with fixed point theorem. The uniqueness of the solution at all the levels is ensured for the proposed scheme with contraction mapping argument. The convergence of the finite difference scheme is ensured with the assumption of the sufficiently smooth solution with ${L^\infty}$ discrete norm. The results for various test problems are compared with exact values and it is clearly shown that results obtained using both the methods are precise and reliable.

Shamil Galiev and Alexander Khorkov

Title

Linear and Nonlinear Optimization Models for Multiple Covering of a Bounded Plane Domain with Circles

Abstract
A numerical method for investigating multiple covering of a convex bounded closed plane domain with circles of given radius is proposed. The problem of multiple covering (k-covering) is considered with restrictions on the minimal possible distances between the centers of circles and without such restrictions. To solve these problems, some integer linear programming (LP) and nonlinear problems are constructed. We use a heuristic solution algorithm for 0–1 LP problems of higher dimensions. An algorithm for finding an approximate number of such circles and the positions of their centers is described. Approximate lower bounds of the circle numbers of the k-covering of the given domain are found. Numerical results demonstrating the effectiveness of the proposed methods are presented.

Title

Extension of Strongin's Global Optimization Algorithm to Continous on a Compact Interval Function

Abstract
From Vanderbei's paper it is known that continuous on a compact interval function is epsilon-Lipschitz and this feature can be used for finding approximately the extremum of function. However, deriving Lipschitz epsilon-constant estimation allowing constructing continuous function minimization algorithms is not easy task. In this paper, we propose extension of Strongin's global optimization algorithm, which not requires a prior knowledge of epsilon-constant estimation, prof its convergence and solve numerical examples.

Raoul Nigmatullin and Praween Agarwal

Title

Direct Evaluation of the Desired Correlations: Verification on Real Data

Abstract
In this extended abstract, a new method for evaluation of the desired correlations is proposed. It allows to evaluate the "content" of the external factors (l=1,2,…,L) setting in the form of data arrays $y_m^(l)(x)$ (m=1,2,…,M) inside the given $Y_m(x)$ function that is supposed to be subjected by the influence of these factors. As contrasted to the conventional correlation analysis, the proposed method allows finding the "influence" functions $b_l(x)$ (l=1,2,…,L) and evaluating the "remnant" array $G_m(x)$ that is remained as a "quasi-independent" part from the influence of the factors $y_m(l)(x)$. The general expression works as a specific "balance" and reproduces the well-knows cases, when $b_l(x) = C_l$ (it is reduced to the linear least square method with $Gm(x)\appr 0$) and coincides with the remnant function $Y_m(x) \appr G_m(x)$, when the influence functions becomes negligible ($b_l(x) \appr 0$). The available data show that the proposed method allows to extract a small signal S(x) from the "pattern" background and it conserves its stability/robustness in the presence of a random fluctuations/noise. The obtained relationships allow to understand deeper the existing correlations and make them more informative, especially in detection of the desired deterministic and stable bonds/laws that can be hidden inside.

Polina Stognii and Igor Petrov

Title

The seismic waves spread in models with the ice field in the Arctic shelf

Abstract
The Arctic region is of great importance for the seismic exploration because great amounts of gas and oil deposits are located there. The geological works in the region are hard because of the presence of different ice constructions, for example, icebergs, ice fields, ice hummocks. They must be taken into consideration while carrying out such geological works. These ice constructions bring in extra wave reflections into the seismograms. This work aims to simulate the real geological works and find out the real influence of the ice field on the wave field and on the seismograms. The influence of multiple waves in the ice layer on the results is being studied. The dependence of the results from the grid step is shown.

Tatyana Shornikova

Title

Models of renewal with by continuous time

Abstract
Background. Presently the problem of construction of discrete model with the use of casual processes on the basis of choice of productive function is well studied and by us, and in different literature. And a model with continuous time is studied less than by virtue of complication of application of approach for a productive function, therefore as impossible actual. A research aim is a construction of model with continuous time on the basis of approach with the use of transformation of Laplace of function of reliability and function of renewal. A basic instrument of research is transformation of Laplace, that allows on occasion to describe the process of renewal simpler as compared to application of integral equalizations, especially in that case, when it gives simple expressions for that in the dictionary of transformations it is possible easily to find an initial function.

Shamil Ishmukhametov, Ismail Amer and Mohammed Alkhalidi Arkan

Title

Comparing different GCD algorithms

Abstract
In our paper we analyze effectiveness of several algorithms of the GCD calculation for pairs of large naturals with respect to their speed, number of iterations and possibility of parallelization of the computation procedure. We involve in our investigation the classical Euclidian GCD Algorithm, the k-ary GCD Algorithm by J. Sorenson and the new Approximating k-ary GCD Algorithm, elaborated by S.~Ishmukhametov. We outline main advantage sides and shortages of each considered algorithm and their application to practical tasks like computations in finite fields used by cryptographers.

Nikolai Suvorov and Mihail Shleymovich

Title

Mathematical model of the biometric iris recognition system

Abstract
Automatic recognition of personal identity by biometric features is based on unique peculiarities or characteristics of people. Biometric identification process consist in making of reference templates and comparison with new input data. Iris pattern recognition algorithms presents high accuracy and low identification errors percent on practice. Iris pattern advantages over other biometric features are determined by its high degree of freedom (nearly 249), excessive density of unique features and constancy. High recognition reliability level is very important because it provides search in big databases. Unlike one-to-one check mode that is applicable only to small calculation count it allows to work in one-to-many identification mode. Every biometric identification system appears to be probabilistic and qualitative characteristics description utilizes such parameters as: recognition accuracy, false acceptance rate and false rejection rate. These characteristics allows to compare identity recognition methods and asses the system performance under any circumstances. This article explains the mathematical model of iris pattern biometric identification and its characteristics. Besides, there are analyzed results of comparison of model and real recognition process.

Ilya Afanasyev and Nikolay Shilov

Title

Challenges in Internet of Robotic Things

Abstract
This paper provides an overview, analysis and challenges of possible solutions for the Internet of Robotic Things (IoRT), discussing the integration of smart spaces and robotic applications.

Marina Alekhina, Oksana Barsukova and Tatyana Shornikova

Title

About complete finite bases in $P_2,$ having an unreliability coefficient 1 for the faults of type 0 at the outputs of elements and containing pairs of special functions

Abstract
We consider the realization of Boolean functions by the circuits from unreliable elements in a complete finite basis containing pairs of special functions. We assume that all elements of a circuit are exposed to the faults type 0 at the outputs with probability $\varepsilon \in (0,1/2)$ independently of each other. The pairs of functions are found whose presence in the basis guarantees the realization of almost any Boolean function by an asymptotically optimal in reliability circuit functioning with unreliability is asymptotically equal to $\varepsilon$ with $\varepsilon \to 0.$

Yuri Vassilevski

Title

Numerical simulation of incompressible flows in time-dependent domains

Andrey Bogatyrev

Title

Ansatz method: dimensional reduction for uniform rational.
Poster speakers
Dimpal Jyoti Mahanta, Pallabi Saikia and Munindra Borah

Title
A study on Chapman-Richards growth model and estimation of it's parameters

Abstract
The main objective of this paper is to discuss the applicability of Chapman Richard growth models in forestry. Integral form and the limiting cases of the Chapman Richard growth model are also discussed along with their varied re-parameterizations. The biological properties of the parameters are studied briefly. Fitting growth data to the Chapman Richards model usually involves some traditional nonlinear optimization methods, which require significant amount of computation. This paper introduces two methods suitable for the models, which demand less computation and can use any growth data. The parameters of these models are estimated using the methods for the top height growth data originated from the Bowmont Norway spruce thinning experiment, sample plot 3661 and the average height of twelve weeping Higan Cherry trees planted in Washington, D.C. Results show that each of the methods, introduced in this paper performed adequately well. The estimated parameters are logically and biologically significant. Finally the methods of estimation established during this work fits satisfactorily and might contend with the existing methods of estimation.

Phool Singh

Title
Double image encryption using equal modulus decomposition and random modulus decomposition in fractional Harley domain

Abstract
Random modulus decomposition and modified equal modulus decomposition are not only asymmetric cryptosystems, but also invulnerable to special attack. A new double image asymmetric cryptosystem using equal modulus decomposition and random modulus decomposition in fractional Harley domain is proposed. An input grayscale image which is bounded with another grayscale image as its phase mask, is transformed via fractional Hartley transform. Equal modulus decomposition is applied on the derived image which leads to get two intermediate images. One is further processed to another fractional Hartley transform followed by random modulus decomposition, whereas other serves as first private key. Random modulus decomposition also results in two images: encrypted image and the second private key. In the decryption process, encrypted image is added with second private key and then subjected to inverse fractional Hartley transform. Resulting image is then added to first private key, and followed by another fractional Hartley transform, thus recovering the double images. One is amplitude and other as argument part of the decrypted image. The cryptosystem is validated for grayscale images of Lena and Cameraman of size 256×256 pixels. Statistical attacks such as correlation distribution, 3D plots, entropy analysis and histograms analysis are performed on the scheme and results show the efficiency of the cryptosystem. Peak-signal-noise-ratio and correlation coefficient are used as statistical metric. Noise attack and special attack on the scheme also establish the robustness of the cryptosystem.

Alexander O. Spiridonov and Evgenii M. Karchevskii

Title
Mathematical and numerical modeling of a drop-shaped microcavity laser

Abstract
We study electromagnetic fields and emission thresholds of a drop-shaped microcavity laser. Spectral characteristics are calculated numerically solving the lasing eigenvalue problem [1] on the basis of the set of Muller boundary integral equations, which we approximate by the Nyström method. This approach leads to a "characteristic equation" for mode frequencies and lasing thresholds of the microcavity of the complicated form.

In contrast with previously investigated by the Nyström method microcavity lasers with smooth contours, the drop has a corner. We propose a new computer implementation of the Nyström method for contours with corners following [2] and taking into account the symmetry of the drop [3]. The computational experiments demonstrate the fast convergence of the method. The convergence of the method was mathematically proved for the microcavity lasers with smooth contours in [4].

Title
On a method of extending the functionality of a microelectromechanical system

Abstract
The article proposes a method of extending the functionality of the microelectromechanical system (MEMS) of the planar group RR-type by using the observed oscillations beats. On the basis of the obtained mathematical model of MEMS, its analysis is carried out and the conditions for the occurrence of beats with information ability are determined. The proposed method provides both the preservation of the resonant mode of operation of the device and the possibility of measuring the second component of the angular velocity of the base.

Angelina Markina and Dmitrii Tumakov

Title
Designing a symmetrical tooth-shaped monopole microstrip antenna with specified characteristics for Wi-Fi applications

Abstract
The problem of designing a well-matched monopole microstrip antenna for Wi-Fi applications is considered. We assume that characteristics of the designed symmetric tooth-shaped antenna are given. The characteristics of the antenna means its electrical characteristics such as the operating frequency range, bandwidth, reflection coefficient and etc.

We make a correlation and regression analysis for the family of monopole tooth-shaped antennas. We construct regression models for the basic electrical characteristics for the solving the design problem. At the next design stage, we determine the design geometric parameters of the antenna a_R, b_R and d_R using regression models for f, BW and R. However, each of the regression models has small errors, so at this stage the antenna in its parameters is close to the parameters of a well-matched antenna. In the next antenna design step, we refine ("improve") the values of its design parameters in order to obtain an antenna with optimal electrical characteristics. For this purpose, we build the objective function and solve its optimization problem. We obtain the antenna with specified characteristics. In particular, we get the most matching antenna by minimizing the reflection coefficient.

Artyom Gumirov, Vjacheslav Zakharov and Bulat Eminov

Title
Hardware-software implementation of pseudorandom sequence generator based on the composition of linear and nonlinear transformations

Abstract
The target of this research is the hardware implementation of pseudorandom sequence generators (hereinafter, the "generators") using the technology of field programmable gate arrays (FPGA). The matters are considered regarding the use of the embedded FPGA hardware resource, i.e., the embedded block memory, including the methods of use and the hardware complexity, to construct generators. The paper presents the implementation of a hardware-software module of the pseudorandom sequence generator with the period of 2^320 – 1. The key feature of the sheet-oriented representation of generators is based on using the embedded block memory FPGA XC3S700A for the algorithmic implementation of pseudorandom sequences (PRS). The generator model is implemented as a stand-alone automaton with the output function based on the composition of linear and nonlinear transformations over a finite field. The automaton transition function is performed on the linear feedback shift register, in which the linear feedback is constructed on a primitive polynomial with the power of n = 320. The generator architecture is described using the hardware description language VHDL. The paper also presents the estimates of the module hardware complexity in the FPGA basis using the embedded block memory of the FPGA XC3S700A chip, in which the n value determining the period of the PRSes to be generated reaches the highest value of 320.

Ilya Pershin and Dmitrii Tumakov

Title
Relationship between base frequency of the Koch-type wire dipole and various dimensions

Abstract
We consider a dipole wire antenna of the Koch type. The antenna consists of a wire dipole with symmetrical arms with respect to the feed point with the geometry similar to the Koch prefractal. The curves forming the arms differ from the classical Koch fractal only by the position of the central vertex. Our goal is to establish the dependence of the frequency on the dimension of the curve forming the arm antenna. We consider various dimensions as characteristics of the curve. The dimensions are Minkowski dimension, information dimension, correlation dimension and Higuchi fractal dimension. We describe algorithms for calculating these dimensions. We review relationships between base frequency of the Koch-type wire dipole and the various dimensions. We make the correlation analysis for the first three Koch-type prefractals.

A K Yadav and Phool Singh

Title

Encryption cum compression of a double image using orthogonal-triangular decomposition (QR decomposition) with column pivoting

Astract
An asymmetric double image encryption cum compression scheme based on orthogonal-triangular decomposition and sparse matrix has been proposed. The proposed cryptosystem is asymmetric in nature as the encryption and decryption processes are different and contrary to symmetric cryptosystems same keys are not used in encryption and decryption processes. The asymmetric nature of the system is due to the QR decomposition which provides a permutation matrix as a cipher text and the product of orthogonal and triangular matrix as the key. The cipher text obtained through this process is a sparse matrix which enables us to store the image by CSR method to give a compressed encrypted data. Thus, a cryptosystem which can be used as a compression algorithm is proposed. To check the efficacy of the scheme 3-D plots, statistical parameters and key sensitivity are analyzed. The Scheme is also analyzed against occlusion and noise attacks. All the numerical simulations validate the security and efficiency of the proposed cryptosystem.

Dmitry Bubnov

Title

Plario – adaptive learning solution for Math

Abstract
Plario is an adaptive learning system, online math tutor for senior high school students and freshmen in colleges and universities. This is a joint project of Tomsk State University and ENBISYS, IT company.

The reason behind Plario creation was the demand to improve academic math knowledge in junior university students. At present moment Plario has its focus on one basic math section: Algebraic expressions simplification. This section was decomposed and presented as a domain ontology/ graph of interconnected skills (competencies), which serves as basis for assessment and adaptive algorithms. Content consists of theoretical material in microdoses and practical exercises with different complexity level. System architects, software engineers and Data Scientists from ENBISYS have developed solution for efficient knowledge mastering considering individual distinctions in each student.

Svetlana Novikova, Natalia Valitova and Elmira Kremleva

Title

Right-hand sides conversion of Takagi-Sugeno system output into the membership function for Mamdani system output

Abstract
When performing soft computations, two fuzzy inference systems are most common: a Takagi-Sugeno system with linear right-hand sides of the rules, and a Mamdani system, where the right-hand side is a fuzzy statement in the form (y is C).

The advantage of Takagi-Sugeno systems is the ability to customize or adjust their parameters by presenting the Sugeno system in the form of a fuzzy neural network for its further learning. The Mamdani system does not have this capability, but its use can be preferable for some tasks.
It would be natural to define such a Mamdani-type fuzzy inference system, which would be identical to a Takagi-Sugeno system in the sense of their responses identity after defuzzification.
The article developed an algorithm that allows researchers to implement this transformation.

Svetlana Novikova, Alexander Snegurenko and Rouzilya Yakhina

Title
Reverse algorithm of dynamic stochastic system parameters calculation on the example of gas turbine aircraft engine control

Abstract
Mathematical and computer simulation is the basis for aircraft engines design. Due to the fuel combustion disturbance, the engine is exposed to random disturbances in the form of Gaussian white noises in real live operation. At the bench test stage, not all system feedbacks can be accurately known. Thus, direct problems describing the engine operation are represented as stochastic differential equations systems with unknown parameters and additive white noises in the right-hand side.

The tasks of operation modes control aircraft engines relate to inverse problems. It is necessary to formulate the inverse problem and solve it regarding control parameters to determine the parameters of the engine control. The engine control parameters is described by the direct stochastic model However, due to the fact that some of the parameters are unknown, we will first have to evaluate their values based on system phase characteristics measurements. This greatly complicates the solution. The article developed a method for solving this problem. A computational algorithm is described. The effectiveness of the algorithm is proved by computational experiments.

Stella Lyasheva, Svetlana Novikova and Mikhail Shleymovich

Titile

Neural network modeling for predict the heat of high-energy substances explosion

Abstract
Experiments with detonating substances are not safe, require significant material costs. Preparing the experiment takes a long time. In addition, there is the problem of verifying the reliability of the results obtained, since in each specific experiment the result may depend on many factors, some of which are not always subject to the researcher. The use of computational neural network methods for predicting the properties and parameters of high-energy individual substances will in some cases refuse to conduct full-scale experiments and replace them with computational experiments.

Existing calculated methods hawe a low accuracy. To increase accuracy, it was decided to use neural networks to predict the heat of explosion. For the construction and training of the neural network was chosen analytical platform «Deductor». On the basis of the obtained results, it can be concluded that the use of a neural network showed the best result compared with the computational methods for calculating the heat of explosion.

Title

Constructive modeling of conservative DBMS

Abstract
Conservative DBMSs (with occasional updating of data) characterized by OLAP load with a high proportion of complex queries like "selection - projection - join" type. Commercial DBMSs have high-performance and reliability, but are too expensive (for example, Oracle Database). A good alternative to expensive parallel DBMS in the field of big data is freely distributed foreign open source systems Hadoop and Spark. The objective of this work is analyzing possibilities of developing economical conservative high-volume DBMSs comparable in efficiency by performance/cost criterion with the Spark system while processing a query flow to a database with data amounts of hundreds and more GB on cluster platforms using a regular query processing plan, and also using MySQL and GPU accelerators at the executive level. The basis of the research was adopted methodology constructive system modeling.

Rustam Latypov and Evgeny Stolov

Title

Neural Net as Pseudo-inverse Filter in Speech Coding Problem

Abstract

Ismail Amer and Arkan Mohammed Alkhalidi

Title
Investigation of K-Ary GCD algorithm for natural numbers

Abstract
In our paper we investigate the k-ary Algorithm for finding GCD of long natural numbers. We suggest an effective modification for the Algorithm which gives an essential acceleration for the whole procedure of finding GCD. The common task of GCD calculation plays an important role in different spheres of Number Theory and Cryptography. It has applications in arithmetic of Finite Fields and key generation for the Cryptography.

Title

Statistical Analysis of Associative Stego Messages

Abstract
The article discusses some possibilities of using statistical test (NIST) of randomness and developed tools for statistical analysis of stego messages created by using the associative masking mechanism of finite set of code symbols. Suggestions for further research of associative steganography strength are given.

Rafis Rakhmankulov and Mikhail Shleimovich

Title

Frame extrapolation in video stream using optical flow methods

Abstract
The article presents data on the analysis of interpolation, extrapolation and optical flow methods describing the generation of intermediate frames of a video stream in real time, where next frames are not known. Method was developed to generate additional frames in video steams, to increase frame rate. Unlike others this method is hardware independent. I further show implementation using different technologies like OpenCV, CUDA and OpenCL. I explore performance impact on different resolutions and analyse them. Moreover, I present the ways to further research on this topic.

Razil Enikeev

Title

Last steps of the k-ary GCD algorithm

Abstract
The greatest common divisor (GCD) algorithms are used in cryptography, integer factoring and algebraic computations. The k-ary algorithm is one of the most effective methods to calculate the GCD of large numbers. In this paper we show that two last steps of the k-ary algorithm is redundant. Additionally, this paper describes the modified k-ary algorithm that shows how to get rid of last steps. The modified algorithm can be obtained from the original one by small changes.

Gee Jun Hui Leonidas Yunani and Medvedev Mikhail

Titile

Classifying Steel Defects Using Transfer Learning

Abstract
This paper proposes the application of transfer learning in classifying common surface defects found on hot-rolled steel strips. 3 potential models (Xception, InceptionV3 and InceptionResNetV2) are chosen and evaluated on their accuracy and F1 score using stratified cross validation. The experimental results show that InceptionV3 is able to classify surface defects with a relatively high accuracy and F1 score of over 95% while having a memory efficient architecture suitable for real world applications.

Nikolai Antonov

Title

Random number generator based on the transformation of multiplicative convolution

Abstract
The vast majority of random number generators based on linear feedback shift registers produce pseudorandom sequences with satisfactory or even very good randomness properties, but few number of them are resistant to various cryptographic attacks. This article describes a method for enhancing the cryptographic strength of a linear feedback shift register while maintaining its statistical properties. The main feature of this method is a special transforma-tion performed on register elements. The conducted experiments show that the applying of this transformation does not degrade, and even improves the statis-tical properties of the generated sequences, and makes it difficult to determine the initial state of the registers constituting the generator.

Bulat Eminov and Farid Eminov

Title

The use of the complementary event method in the study of markovian and semi-markovian processes

Abstract
When designing various systems, it becomes necessary to use the apparatus of queueing theory. The use of the complementary event method makes it possible to simply obtain the dependences of the probability of denial of service on the magnitude of the queue size limit. The proposed approach was applied in the study of Markovian and semi-Markovian processes.

Mikhail Volnikov

Title

Simulation of vibrations of a cantilever rod with a vibration damper using the finite difference method

Abstact
The article deals with the mathematical modeling of cantilever beams using the finite difference method. Models have been developed to calculate static and dynamic deflections of consoles, as well as to simulate vibrations with attached vibration dampers.

Alexey Martyshkin, Vitaly Kalashnikov, Dmitry Trokoz, Vyacheslav Boriskin, Tania Pashchenko, Michael Sinev and Valeriya Kormishina

Title

Creating coorpative text editor by using conflict-free replicated data types

Abstract
This article discusses the main difficulties associated with the implementation of applications for co-editing of documents as a distributed system. The most common methods of implementing algorithms for creating a collaborative text editor are listed, such as blocking the edited text segment when it is edited by one co-author; differential three-way merge of changes between clients and the server; use of tree data structures; algorithms based on conflict-free replicated data types with the approach of operational transformations. The main advantages and disadvantages of these methods are given. A variant of implementation using algorithms based on conflict-free replicated data types with the approach of operational transformations is proposed. The ways of solving the main problem - memory consumption – which is typical for this method are considered.

Dina Latypova and Dmitrii Tumakov
Title

Cluster analysis of handwritten numbers

Abstract
The handwritten numbers clustering problem was considered. Clustering was done for 60 thousand images of handwritten numbers contained in the training sample of the MNIST database. Several main clusters were allocated for each digit separately using Kohonen neural network. Common features and characteristics of writing the same numbers were identified. The size and weight of clusters of different numbers were analyzed.

The resulting clusters were analyzed on the test sample of the MNIST database which contains 10 thousand images. The situations of clusters intersection were considered and the main preconditions for such an intersection were identified. On the basis of the obtained results, it was made a conclusion about the reason of the digit images recognition error by artificial intelligence. The algorithm for recognizing handwritten numbers image was proposed.

Title

Mathematical model of the thyroid gland as a megasystem containing a follicle

Abstract
The thyroid gland is an endocrine organ with the function of producing hormones that contribute to the development of the whole organism. The main exchange component is iodine. The gland itself consists of follicles - structural elements of the organ, in which the synthesized thyroid hormone accumulates in a state bound to protein.

The point-like single-chamber mathematical model of the follicle of the thyroid gland is considered. The follicle model is represented by a single camera - the combination of colloid and thyrocytes. In the proposed model, the rate of iodine exchange depends on the volume of the follicle. In turn, the volume of a colloid in the follicle depends on the concentration of treoglobulin and other molecules. Thus, in this model, the rate of exchange of iodine is made dependent on the concentration of substances in the colloid.

Alexandr Kindaev and Alexandr Moiseev

Title

Results of risk modeling in agricultural insurance

Abstract
Insurance is a powerful tool for smoothing losses arising in the course of economic activity. A key element of the review process is to determine the insurance risk insurance for different approaches formation of the insurance premium. Naturally, the more appropriate approach is to determine the risk-based insurance model, with subsequent correction results.

In the previous works as authors the simulation model of process of insurance of a grain yield of cultures is constructed. The assumption that insurance captured all agricultural producers of some compact area was significant assumption of model. Today agricultural insurance captured not all agricultural producers in this connection consideration of influence of coverage of the insurance field on change of insurance tariffs is relevant.

Marina Alekhina and Oksana Barsukova

Title

Asymptotic estimate of the unreliability of circuits in a basis consisting of the Webb function in p3 for faults of type 2 at outputs of elements

Abstract
We consider the problem of the implementation of ternary logic functions by the circuits from unreliable functional elements in full basis consisting of the Webb function. We assume that elements of the circuit pass to fault states independently of each other, and they are exposed to single-type constant faults of type 2 at the outputs (in good condition the basic element implements the function assigned to it, and in the faulty state into which it passes with the probability varepsilon ( varepsilon < 1=2) implements the constant 2). It is shown that under such faults almost any ternary logic function can be implemented by an asymptotically optimal in reliability circuit functioning with the unreliability which is asymptotically equal to 3epsilon with epsilon -> 0.
Attending
Visas
If you need Russian visa to attend the conference, please: Consult the Russian embassy or consulate in your country then contact the office at Innopolis University a.adelshin@innopolis.ru or o.zirosh@innopolis.ru to assist you to apply for the Russian visa and to get invitation from the Innopolis university or from the Ministry of Foreign Affairs of the Russian Federation.

Invitation for the humanitarian visa (applies for scientific technical purposes such as conferences, forums, workshops etc.).

We use Telex system for the invitation. Your data will be telexed directly from the Ministry of Foreign Affairs to the Russian consulate you are going to obtain your visa in. Telex highly increases your chances of obtaining a humanitarian visa.

The procedure itself is quite simple:
1. We prepare the application for the invitation (passport and the additional information such as place of work is required).
2. Documents are electronically approved by Innopolis University and Foreign Affairs Ministry representative. Usually it takes about 1 week.
3. We submit the documents to the Foreign Affairs Ministry representative in Russia. In 2 weeks we have the invitation and Telex number ready.
4. You can apply for a Russian visa.
How to get to Innopolis
Taxi
The road from Kazan to Innopolis takes 40-50 minutes and 1 hour 20 minutes from Kazan International Airport to Innopolis and passes along the M-7 Volga highway. At the exit of the highway there will be a big signpost "Innopolis". You can see the route here. Average trip cost from Kazan — 600 rub, from Airport — 1200 rub using Yandex, Uber or Gett taxi services. Better way to use them is download their apps from Apple Store / Google Play.

Shuttle buses
There are two bus routes from Kazan to Innopolis — 1. "Kombinat Zdorovie" bus stop; 2. "Vostochny" bus station. Here you can see their timetable and route. Ticket price is 100 rub by card. The bus stop you need at Innopolis is "University".
Accomodation
There are plenty of hotels in Kazan: Korston, Art hotel, Luciano, Shalyapin, Ramada Kazan City Center, Double Tree by Hilton, Relita have most convenient locations. You may also stay on Sviyaga Hills resort which is in 5 minutes from Innopolis by car or in Innopolis University Campus which is 3 minutes walk from the Venue.