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Generalized Centrality Measures for Multiplex Networks: Combining Node Attributes and Group Dynamics
Procedia Computer Science. 2025. Vol. 266. P. 818–824.
Many complex systems are best represented as multilayer or multiplex networks, where nodes are connected through multiple types of links across different layers. This layered structure introduces additional challenges for identifying central elements, as traditional centrality measures typically assume a single-layer network. The paper introduces a new centrality framework for multiplex networks that accounts for both vertex attributes and group-mediated influence, offering a refined approach to identifying critical nodes in multilayer systems. Additionally, we introduce a block concept, combining weights, node parameters, and inter-layer group effects into a unified analytical model. The model is applied to the Florence families dataset.
Basalaev A., Rarovskii A., Journal of Singularities 2026 Vol. 30 P. 61–80
Saito theory associates to an isolated singularity rich structure that plays an important role in mirror symmetry. In this note we construct Saito theory for A and D type Landau-Ginzburg orbifolds. Namely, for the pairs (f,G), where f defines an isolated singularity of A and D type and G is a group of symmetries of ...
Added: September 1, 2026
Rybakov M., Shkatov D., Journal of Logic and Computation 2026 Vol. 36 No. 6 Article exag026
We prove Pi-1-1-hardness, and thus lack of recursive axiomatizability, of constant-domain modal predicate logics defined by a class of Dedekind complete linear Kripke frames containing a frame with an infinitely increasing chain of worlds. The result holds even for the language with one unary predicate letter, one propositional letter, and two individual variables. ...
Added: September 1, 2026
Селянин Ф. И., Moscow Mathematical Journal 2026 Vol. 26 No. 2 P. 167–187
Minkowski mixed volume of n subpolytopes D1,…,Dn of a polytope P⊂Rn clearly does not exceed the normalized volume n!Vol(P). Equality holds if and only if the subpolytopes are interlaced, i.e., each proper face F⊊P intersects at least dim(F)+1 of the polytopes Di. Efficiently computing mixed volumes for more general collections of subpolytopes is crucial for estimating the complexity of numerically solving polynomial systems.
Motivated by relaxing the bound dim(F)+1 to dim(F), we ...
Added: August 31, 2026
Kazaryan M., Dunin-Barkowski P., Bychkov B. et al., International Mathematics Research Notices 2026 Vol. 14 Article rnag146
We prove a recent conjecture of the fourth named author with P. Norbury that states a system of universal polynomial relations among the kappa classes on the moduli spaces of algebraic curves. The proof involves localization and materialization analysis of the spin Gromov–Witten theory of the projective line and is dictated by Z 2 -equivariant ...
Added: August 31, 2026
Kazaryan M., Dunin-Barkowski P., Bychkov B. et al., Communications in Mathematical Physics 2026 Vol. 407 No. 69
We prove that for any initial data on a genus zero spectral curve the cor responding correlation differentials of topological recursion are KP integrable. As an application we prove KP integrability of partition functions associated via ELSV-type formulas to the r-th roots of the twisted powers of the log canonical bundles ...
Added: August 31, 2026
Gromov V., Переслегин С. Б., Переслегина Е. Б. et al., СПб.: Полакс, 2026.
Механизм происходящих в мире изменений носит эволюционный, а не экологический характер. Иначе говоря, Человечество столкнулось с кризисом развития, который имеет три независимые составляющие: кризис индустриального общества (фазовый кризис), кризис научного мышления (эпистемный кризис) и кризис формата существования разума (социосистемный кризис). Доклад посвящён аспектам этого триединого кризиса и возможным путям его преодоления, не сводящимся к первичному ...
Added: August 31, 2026
Devyatov R. A., Mathematical notes 2026 Vol. 119 No. 3 P. 782–786
Let G/B be a flag variety over ℂ, where G is a simple algebraic group with a simply laced Dynkin diagram, and B is a Borel subgroup. We say that the product of classes of Schubert divisors in the Chow ring is multiplicity free if it is possible to multiply it by a Schubert class ...
Added: August 30, 2026
Bayer A., Kuznetsov A., Macrì E., Journal fuer die reine und angewandte Mathematik 2026 Vol. 2026 No. 836 P. 111–162
We give a self-contained and simplified proof of Mukai’s classification of prime Fano threefolds of index 1 and genus g ≥ 6 with at most factorial terminal singularities, and of its extension to higher dimension. ...
Added: August 30, 2026
Bayer A., Kuznetsov A., Macrì E., Compositio Mathematica 2026 Vol. 162 No. 1 P. 59–99
We give a proof of Mukai’s theorem on the existence of certain exceptional vector bundles on prime Fano threefolds. To our knowledge this is the first complete proof in the literature. The result is essential for Mukai’s biregular classification of prime Fano threefolds, and for the existence of semiorthogonal decompositions in their derived categories. Our ...
Added: August 30, 2026
Guseva L., Novikov A., Advances in Mathematics 2026 Vol. 503 Article 111211
We prove that the Kuznetsov–Polishchuk exceptional collections on rational homogeneous spaces of the symplectic groups Sp(2n,C) are full and consist of vector bundles. To achieve this, we construct several classes of complexes, which we call generalized staircase complexes, symplectic staircase complexes and secondary staircase complexes — each of which may be of independent interest. ...
Added: August 30, 2026
Polishchuk A., Rains E., Journal of the Institute of Mathematics of Jussieu 2026 Vol. 25 No. 1 P. 339–373
We prove that for every relatively prime pair of integers (d,r) with r>0, there exists an exceptional pair (O,V) on any del Pezzo surface of degree 4, such that V is a bundle of rank r and degree d. As an application, we prove that every Feigin-Odesskii Poisson bracket on a projective space can be ...
Added: August 30, 2026
Kazhdan D., Polishchuk A., Pure and Applied Mathematics Quarterly 2026 Vol. 22 No. 3 P. 1115–1166
We continue the study of automorphic functions associated with a curve C over the ring k[ε]/(ε²), where k is a finite field, begun in arXiv:2303.16259. Namely, we study an example of theta-lifting in this framework and show that it can be understood in terms of the orbit decomposition of the space of automorphic functions S(SL₂(F)\SL₂(A_C)) ...
Added: August 30, 2026
Kuznetsov A. P., Sataev I. R., Stankevich N., Chaos 2026 Vol. 36 No. 8 Article 083131
A radio-physical system, namely, a two-mode van der Pol generator, is considered. It is shown that this system demonstrates two types of chaos: with one and two zero Lyapunov exponents. The regions of the second type of chaos are surrounded by bifurcation lines of invariant tori doubling. Quasi-periodic structures of various shapes are embedded within ...
Added: August 30, 2026
Shirokov N. A., Rozenblum G., Israel Journal of Mathematics 2026 P. 1–30
We establish that a generalized H\¨older continuous function on an (m−2)-Ahlfors regular compact set in Rm can be approximated by solutions of an elliptic equation, with the rate of approximation determined by the continuity modulus of the function ...
Added: August 29, 2026
Leonidov A., Vasilyev S., Vasilyeva E., Chaos, Solitons and Fractals 2025 Vol. 201 No. 2 Article 117242
Game-theoretic static equilibria in multiagent two-layered consensus/opinion formation noisy binary choice model are studied. Both layers in the model are complete networks. Each player is present in both layers. Agent’s strategies with respect to the layers are interconnected. General asymmetric, symmetric and antisymmetric expectation/quantal response equilibria are analysed. Phase diagram of the model containing various ...
Added: September 26, 2025
Fuad Aleskerov, Tkachev D., , in: Dynamics of Disasters: From Natural Phenomena to Human ActivityVol. 217.: Springer, 2024. Ch. 1 P. 1–13.
The situation of deep uncertainty is defined by the absence of any statistical evaluations of the situation development. For instance, such situations may include events that occur for the first time. We use scenario analysis to model the potential outcomes of events affecting networks under deep uncertainty. Centrality indices are used to identify vulnerable vertices ...
Added: March 5, 2025
I. Samoylenko, Aleja D., Primo E. et al., Physical Review X 2023 Vol. 13 No. 2 Article 021032
A wealth of evidence shows that real-world networks are endowed with the small-world property, i.e., that the maximal distance between any two of their nodes scales logarithmically rather than linearly with their size. In addition, most social networks are organized so that no individual is more than six connections apart from any other, an empirical ...
Added: July 28, 2023
Kovalenko K., Romance M., Vasilyeva E. et al., Chaos, Solitons and Fractals 2022 Vol. 162 Article 112397
Identifying the most influential nodes in networked systems is of vital importance to optimize their function and control. Several scalar metrics have been proposed to that effect, but the recent shift in focus towards network structures which go beyond a simple collection of dyadic interactions has rendered them void of performance guarantees. We here introduce ...
Added: January 31, 2023
Lepskiy A., Meshcheryakova N., , in: Information Processing and Management of Uncertainty in Knowledge-Based Systems. IPMU 2020* 2. Vol. 1238.: Cham: Springer, 2020. P. 283–296.
We apply Dempster-Shafer theory in order to reveal important elements in undirected weighted networks. We estimate cooperation of each node with different groups of vertices that surround it via construction of belief functions. The obtained intensities of cooperation are further redistributed over all elements of a particular group of nodes that results in pignistic probabilities ...
Added: July 8, 2020
Aleskerov F. T., Yakuba V. I., / NRU Higher School of Economics. Series WP7 "Математические методы анализа решений в экономике, бизнесе и политике". 2020. No. 2323.
We introduce a class of new centrality indices in networks which take into account a para meter of a node, direct and indirect (with fixed length of the path) connections of nodes, and a group influence of nodes to a node. Total influence is evaluated as a linear combination of its components, however, other rules ...
Added: May 30, 2020
Aleskerov F. T., Gavrilenkova I., Швыдун С. В. et al., Group Decision and Negotiation 2020 Vol. 29 No. 3 P. 399–424
Since 9/11, terrorism has become a global issue of the twenty-first century. Terrorist organizations become important actors of world politics as they gain influence on political process and decision-making. Some organizations compete with each other in order to gain more power and influence. We study the distribution of power among terrorist groups using network approach ...
Added: April 19, 2020
Швыдун С. В., В кн.: XIII Всероссийское совещание по проблемам управления ВСПУ-2019: труды.: М.: ИПУ РАН, 2019. С. 1852–1857.
В работе рассматривается задача оценки влияния в сетевых структурах, связи между вершинами в которых могут быть различного типа. Предлагается модель, которая производит оценку попарного влияния вершин друг на друга на каждом уровне взаимодействия с учетом индивидуальных характеристик вершин, а также возможности их непрямого и группового взаимодействия. Процедура оценки итогового влияния вершин осуществляется с использованием известных правил коллективного выбора. Показано ...
Added: October 31, 2019
ŽNIDARŠIČ A., Ferligoj A., DOREIAN P., Network Science 2018 Vol. 6 No. 1 P. 1–33
Social network data are prone to errors regardless their source. This paper focuses on missing data due to actor non-response in valued networks. If actors refuse to provide information, all values for outgoing ties are missing. Partially observed incoming ties to non-respondents and all other patterns for ties between members of the network can be ...
Added: November 2, 2018
Springer, 2019.
Game theory has recently become a useful tool for modeling and studying various
networks. The past decade has witnessed a huge explosion of interest in issues that
intersect networks and game theory. With the rapid growth of data traffic, from any
kind of devices and networks, game theory is requiring more intelligent transformation.
Game theory is called to play ...
Added: September 15, 2018