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## Classification of k-Primitive Sets of Matrices

SIAM Journal on Matrix Analysis and Applications. 2013. Vol. 34. No. 3. P. 1174-1188.

Protasov V., Logofet D. O., SIAM Journal on Matrix Analysis and Applications 2014 Vol. 35 No. 2 P. 749-764

We study the location of λ2(A), the second positive eigenvalue of a nonnegative matrix A, as the issue of how many positive eigenvalues can be shifted beyond the spectral radius ρ(A) by means of arbitrary changes in elements of one row. The notion of rank-one correction suggests the nearest generalization expanding the changes in one ...

Added: February 19, 2016

Malyshev D., Дискретный анализ и исследование операций 2012 Т. 19 № 3 С. 58-64

An algorithm is implemented in the article for finding the independence number of a n-vertex graph from the class Free({P5,C5, Kp}) in time O(np+O(1)). ...

Added: June 6, 2012

Sandomirskiy F., Segal-Halevi E., / Cornell university. Series arXiv "Computer Science and Game Theory (cs.GT), arXiv:1908.01669". 2019.

A set of objects, some goods and some bads, is to be divided fairly among agents with different tastes, modeled by additive utility-functions. If the objects cannot be shared, so that each of them must be entirely allocated to a single agent, then fair division may not exist. What is the smallest number of objects ...

Added: September 24, 2019

Nesterov Y., Protasov V., SIAM Journal on Matrix Analysis and Applications 2020 Vol. 41 No. 1 P. 1-28

The problem of nding the closest stable matrix for a dynamical system has many
applications. It is studied for both continuous and discrete-time systems and the corresponding
optimization problems are formulated for various matrix norms. As a rule, nonconvexity of these
formulations does not allow nding their global solutions. In this paper, we analyze positive discretetime
systems. They also ...

Added: July 30, 2020

Protasov V., Mathematical Programming 2016 Vol. 156 P. 485-511

We develop an iterative optimization method for finding the maximal and minimal spectral radius of a matrix over a compact set of nonnegative matrices. We consider matrix sets with product structure, i.e., all rows are chosen independently from given compact sets (row uncertainty sets). If all the uncertainty sets are finite or polyhedral, the algorithm ...

Added: February 20, 2016

Protasov V., Functional Analysis and Its Applications 2013 Vol. 47 No. 2 P. 138-147

Asymptotic properties of products of random matrices ξ k = X k …X 1 as k → ∞ are analyzed. All product terms X i are independent and identically distributed on a finite set of nonnegative matrices A = {A 1, …, A m }. We prove that if A is irreducible, then all nonzero ...

Added: February 22, 2016

Branzei S., Sandomirskiy F., / Cornell university. Series arxiv "Computer Science and Game Theory (cs.GT), arXiv:1907.01766". 2019.

We study the problem of allocating divisible bads (chores) among multiple agents with additive utilities, when money transfers are not allowed. The competitive rule is known to be the best mechanism for goods with additive utilities and was recently extended to chores by Bogomolnaia et al (2017). For both goods and chores, the rule produces ...

Added: September 24, 2019

Cvetkovic A., Protasov V., SIAM Journal on Matrix Analysis and Applications 2020 Vol. 41 No. 3 P. 1167-1182

We develop a matrix approach to the Maximal Acyclic Subgraph (MAS) problem by reducing it to finding the closest nilpotent matrix to the matrix of the graph. Using recent results on the closest Schur stable systems and on minimising the spectral radius over special sets of non-negative matrices we obtain an algorithm for finding an ...

Added: July 30, 2020

Malyshev D., Journal of Applied and Industrial Mathematics 2014 Vol. 8 No. 2 P. 245-255

The edge list-ranking problem is a generalization of the classical edge coloring problem, and it is a mathematical model for some parallel processes. The computational complexity of this problem is under study for graph sets closed under isomorphism and deletion of vertices (hereditary classes). Allfinitely defined and minor-closed cases are described for which the problem ...

Added: May 8, 2014

Aziz H., Moulin H., Sandomirskiy F., / Cornell university. Series arXiv "Computer Science and Game Theory (cs.GT), arXiv:1909.00740". 2019.

We consider fair allocation of indivisible items under additive utilities. When the utilities can be negative, the existence and complexity of an allocation that satisfies Pareto optimality and proportionality up to one item (PROP1) is an open problem. We show that there exists a strongly polynomial-time algorithm that always computes an allocation satisfying Pareto optimality ...

Added: September 24, 2019

Barcelona : IEEE, 2017

International Conference on Control, Decision and Information Technologies. ...

Added: January 17, 2018

Kalyagin V.A., Koldanov A.P., Koldanov P.A. et al., Physica A: Statistical Mechanics and its Applications 2014 Vol. 413 No. 1 P. 59-70

A general approach to measure statistical uncertainty of different filtration techniques for market network analysis is proposed. Two measures of statistical uncertainty are introduced and discussed. One is based on conditional risk for multiple decision statistical procedures and another one is based on average fraction of errors. It is shown that for some important cases ...

Added: July 19, 2014

М. : ИКИ РАН, 2011

Added: March 26, 2013

Sirotkin D., Malyshev D., Дискретная математика 2017 Т. 29 № 3 С. 114-125

Задача о независимом множестве для заданного обыкновенного графа состоит в вычислении размера наибольшего множества его попарно несмежных вершин. Предлагается новый способ редукции графов. С его помощью получено новое доказательство NP-полноты задачи о независимом множестве в классе планарных графов и доказана NP-полнота данной задачи в классе плоских графов, имеющих только треугольные внутренние грани, с максимальной степенью ...

Added: September 7, 2017

Goldengorin B. I., European Journal of Operational Research 2009 Vol. 198 No. 1 P. 102-112

Added: July 31, 2012

М. : Физматлит, 2013

Conference is devoted to application of the integrated models and soft computing in artificial intelligence. ...

Added: May 26, 2013

Shmid A., Novopashin M. A., Berezin A. A., IOSR Journal of Computer Engineering (IOSR-JCE) 2017 Vol. 19 No. 3 P. 113-121

The paper deals with the Forrester’s approach to analysis of heart electrical dynamics based on the hypothesis that heart belongs to the class of Complex Systems and its dynamics can be described by coupled Van der Pol differential equations with a time lag. The chain of such equations suggested by Ginzburg and Landau was used ...

Added: June 13, 2018

Springer, 2020

This volume offers a collection of carefully selected, peer-reviewed papers presented at the BIOMAT 2019 International Symposium, which was held at the University of Szeged, Bolyai Institute and the Hungarian Academy of Sciences, Hungary, October 21st-25th, 2019. The topics covered in this volume include tumor and infection modeling; dynamics of co-infections; epidemic models on networks; ...

Added: March 11, 2021

Malyshev D., Alekseev V., Дискретный анализ и исследование операций 2008 Т. 15 № 1 С. 3-10

Доказывается полиномиальная разрешимость задачи о независимом множестве для бесконечного семейства подмножеств класса планарных графов. ...

Added: August 31, 2012

Blakeway S., Gromov D., Gromova E. et al., Vestnik Sankt-Peterburgskogo Universiteta, Prikladnaya Matematika, Informatika, Protsessy Upravleniya 2019 Vol. 15 No. 1 P. 22-38

We describe a novel game-theoretic formulation of the optimal mobile agents’ placement problem which arises in the context of Mobile Ad-hoc Networks (MANETs). This problem is modelled as a sequential multistage game. The definitions of both the Nash equilibrium and cooperative solution are given. A modification was proposed to ensure the existence of a Nash ...

Added: March 13, 2020

Boissard E., Le Gouic T., Loubes J., Bernoulli: a journal of mathematical statistics and probability 2015 P. 740-759

In this paper, we tackle the problem of comparing distributions of random variables and defining a mean pattern between a sample of random events. Using barycenters of measures in the Wasserstein space, we propose an iterative version as an estimation of the mean distribution. Moreover, when the distributions are a common measure warped by a ...

Added: October 13, 2018

Vyalyi M., Дискретная математика 1991 Т. 3 № 3 С. 35-45

Added: October 17, 2014

Kotelnikova M. V., Aistov A., Вестник Нижегородского университета им. Н.И. Лобачевского. Серия: Социальные науки 2019 Т. 55 № 3 С. 183-189

The article describes a method that allows to improve the content of disciplines of the mathematical cycle by dividing them into invariant (general) and variable parts. The invariants were identified for such disciplines as «Linear algebra», «Mathematical analysis», «Probability theory and mathematical statistics» delivered to Bachelors program students of economics at several universities. Based on ...

Added: January 28, 2020

Malyshev D., Journal of Applied and Industrial Mathematics 2020 Vol. 14 No. 4 P. 706-721

The edge coloring problem for a graph is to minimize the number of colors that are sufficient to color all edges of the graph so that all adjacent edges receive distinct colors. The computational complexity of the problem is known for all graph classes defined by forbidden subgraphs with at most 6 edges. We improve ...

Added: January 30, 2021