Community Detection in Multi-Layer Networks

In the scope of the current thesis we review and analyse networks that are formed by nodes with several attributes. We suppose that different layers of communities are embedded in such networks, besides each of the layers is connected with nodes' attributes. For example, examine one of a variety of online social networks: an user participates in a plurality of different groups/communities – schoolfellows, colleagues, clients, etc. We introduce a detection algorithm for the above-mentioned communities. Normally the result of the detection is the community supplemented just by the most dominant attribute, disregarding others. We propose an algorithm that bypasses dominant communities and detects communities which are formed by other nodes' attributes. We also review formation models of the attributed networks and present a Human Communication Network (HCN) model. We introduce a High School Texting Network (HSTN) and examine our methods for that network

Numerical Evaluation of Wind Speed Influence on Accident Toxic Spill Consequences Scales

This study aims to evaluate numerically the influence of wind speed on scales of environmental harmful consequences caused by accidentally spilled toxic liquid evaporated from the surface of a free-form outlined spill spot. A coupled problem of the gas-dynamic movement of a toxic air-mixture cloud in the surface layer of the atmosphere under the influence of wind and a negative toxic inhalation impact on a human in an accident zone is solved by means of mathematical modelling and computer experiment. Physical processes of toxic liquid evaporation from the spill spot, formation of a mixture of toxic gas with the incoming air, and further dispersion of a hazardous gaseous chemical in the atmosphere under various wind speed conditions are investigated. A three-dimensional non-stationary mathematical model of the turbulent movement of a gas-air mixture is used for obtaining distribution of relative mass concentration of toxic gas impurities in time and space. The model takes into account the complex terrain, compressibility of the gas flow, three-dimensional and non-stationary nature of actual physical processes, different toxic properties of chemical substances, and arbitrary contour shape of the toxic spill spot. A probabilistic harmful impact model based on using a modernized probit analysis method is used to obtain fields of the conditional probability of a fatal human injury resulting from toxic gas inhalation. This model extracts relative mass concentration of toxic gas that could cause negative impact on humans at any control point during calculation time step exposition, collects integral toxic dose values from the multicomponent gas mixture dynamics model, calculates a value of the probit function for the corresponding toxic inhalation dose dangerous factor, and automatically assesses the human fatal injury conditional probability using partial cubic Hermitian spline. This technique allows environmental safety experts assessing the scale of considered type technogenic accident consequences numerically depending on wind speed conditions and elaborating the means to mitigate them to acceptable levels

Оптимізація на загальній множині перестановок зі знаком

A general signed permutation set is introduced. Approaches to optimization on it that are based on its mapping into the Euclidean space are considered. In the scope of the study, properties of the Euclidean combinatorial set and its convex hull - the general signed permutohedron are derived. They include set’s cardinality, an irreducible H-representation of the polyhedron, its dimension, the vertex and adjacency vertex criteria, and the number of combinatorially nonisomorphic polyhedra of a fixed dimension. The behavior of some classes of functions over the general signed permutation set is investigated. Functional-analytical representations of this set are constructed including polyhedral-superspherical and strict superspherical. Explicit solutions of a linear problem and a projection problem over the general signed permutation set are presented. The research allows applying continuous methods to optimization on the discrete set and obtaining both exact and approximate solutions with accuracy estimates.Введено общее множество перестановок со знаком и рассмотрены подходы к оптимизации на нем, основанные на погружении в арифметическое евклидово пространство. В рамках исследования изучены свойства этого евклидового комбинаторного множества и его выпуклой оболочки (общего многогранника перестановок со знаком), такие как мощность множества, несводимое H-представление многогранника, его размерность, критерии и смежности вершин, а также количество комбинаторно неэквивалентных многогранников фиксированной размерности. Исследованы особенности поведения нескольких классов функций на общем множестве перестановок со знаком. Построен ряд функционально-аналитических представлений этого множества, включая полиэдрально-суперсферическое и строгое суперсферическое. Приведены явные решения линейной задачи и задачи проектирования на множество перестановок со знаком. Проведенное исследование позволяет применять непрерывные методы к оптимизации на дискретном множестве и получать как точные, так и приближенные решения оптимизационных задач с оценкой точности.Уведено загальну множину перестановок зі знаком і розглянуто підходи до оптимізації на ній, що ґрунтуються на зануренні в арифметичний евклідів простір. У межах дослідження вивчено властивості евклідової комбінаторної множини та її опуклої оболонки (загального багатогранника перестановок зі знаком), такі як потужність множини, незвідне H-подання багатогранника, його вимірність, критерії вершин та суміжності вершин, а також кількість комбінаторно нееквівалентних багатогранників фіксованої вимірності. Досліджено особливості поведінки кількох класів функцій на загальній множині перестановок зі знаком. Побудовано ряд функціонально-аналітичних подань цієї множини, у тому числі поліедрально-суперсферичне і строге суперсферичне. Наведено явні розв’язки лінійної задачі та задачі проектування на множину перестановок зі знаком. Проведене дослідження дозволяє застосовувати неперервні методи до оптимізації на дискретній множині й отримувати як точні, так і наближені розв’язки оптимізаційних задач з оцінкою точності

A Human Communication Network Model

Abstract. A number of attributed formation models based on ErdosRenyi and Barabasi-Albert random graph models are presented. One of them is a Human Communication Network (HCN) model based on time restrictions on face-to-face communication. Construction of this weighted network requires a few numerical parameters and allows to transform any unweighted node attributed network into weighted. This transformation helps solving numerous problems in Network Analysis such as community detection, network topology inference, etc. Understanding nature of human communication networks allows to solve many practical problems starting with fast spreading any information and innovation through the networks and ending with detecting key people, collaboration with whom helps achieving different goals

Kombinatoryczne konfiguracje punktów i politopy

The monograph is dedicated to exploring combinatorial point configurations derived from mapping a set of combinatorial configurations into Euclidean space. Various methods for this mapping, along with the typology and properties of the resultant configurations, are presented. In addition, the study revolves around combinatorial polytopes defined as convex hulls of combinatorial point configurations. The primary focus lies in examining multipermutation and partial multipermutation point configurations alongside their associated combinatorial polytopes known as multipermutohedra and partial multipermutohedra. Our theoretical contributions are substantiated through the proof of theorems and supporting auxiliary statements. Examples and illustrations are included to enhance the comprehension of the material.Monografia poświęcona jest badaniu kombinatorycznych konfiguracji punktowych uzyskanych z odwzorowania zbioru konfiguracji kombinatorycznych na przestrzeń euklidesową. Przedstawiono różne metody tego mapowania, wraz z typologią i właściwościami powstałych konfiguracji. Ponadto badanie dotyczy wielotopów kombinatorycznych zdefiniowanych jako wypukłe kadłuby kombinatorycznych konfiguracji punktowych. Główny nacisk położony jest na badanie konfiguracji punktów multipermutacji i częściowych punktów multipermutacji wraz z powiązanymi z nimi kombinatorycznymi politopami, znanymi jako multipermutoedry i częściowe multipermutoedry. Nasz wkład teoretyczny jest uzasadniony dowodem twierdzeń i wspierającymi je stwierdzeniami pomocniczymi. Aby ułatwić zrozumienie materiału, załączono przykłady i ilustracje

Numerical Evaluation of Wind Speed Influence on Accident Toxic Spill Consequences Scales

This study aims to evaluate numerically the influence of wind speed on scales of environmental harmful consequences caused by accidentally spilled toxic liquid evaporated from the surface of a free-form outlined spill spot. A coupled problem of the gas-dynamic movement of a toxic air-mixture cloud in the atmosphere’s surface layer under the influence of wind and a negative toxic inhalation impact on a human in an accident zone is solved by means of mathematical modelling and computer experiment. A three-dimensional non-stationary mathematical model of the turbulent movement of a gas-air mixture is used for obtaining distribution of relative mass concentration of toxic gas impurities in time and space. A probabilistic impact model based on using a modernized probit analysis method is used to obtain fields of conditional probability of a fatal human injury resulting from toxic gas inhalation. This technique allows environmental safety experts assessing the scale of considered type technogenic accident consequences numerically depending on wind speed conditions and elaborating the means to mitigate them to acceptable levels

Experience in Engineers Training on Multiple Integrals in the Nomotex DLS

The paper discusses a new approach to teaching the discipline “Multiple and curvilinear integrals, series” for engineers, using a new digital information and educational environment “NOMOTEX”, developed at the Department of Computational Mathematics and Mathematical Physics, Bauman Moscow State Technical University. A new methodology for conducting lectures and practical classes for the Multiple Integrals course using Nomotex DLS is presented. The article analysed to the experience of training engineers at the Bauman Moscow State Technical University course on Multiple Integrals, including the advantages of learning using interactive computer visualization of mathematical concepts