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Spectral simplex method
Mathematical Programming. 2016. Vol. 156. P. 485–511.
Protasov V.
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 finds the matrix with maximal/minimal spectral radius within a few iterations. It is proved that the algorithm avoids cycling and terminates within finite time. The proofs are based on spectral properties of rank-one corrections of nonnegative matrices. The practical efficiency is demonstrated in numerical examples and statistics in dimensions up to 500. Some generalizations to non-polyhedral uncertainty sets, including Euclidean balls, are derived. Finally, we consider applications to spectral graph theory, mathematical economics, dynamical systems, and difference equations.
Shipilov F., Barnyakov A., Ivanov A. et al., / Series Physics "arxiv.org". 2026.
A fast simulation of the detector response is a vital task in high-energy physics (HEP). Traditional Monte-Carlo methods form the backbone of modern particle physics simulation software but are computationally expensive. We present a machine-learning-based approach to fast simulation of the Focusing Aerogel Ring Imaging Cherenkov (FARICH) detector response. Given a particle track and momentum, ...
Added: May 19, 2026
Dorovskiy A., / Series arXiv "math". 2026.
In this paper the structural stability of generic families of vector fields of the PC-HC class on the two-dimensional sphere is proved. A classification of these families up to moderate equivalence in neighborhoods of their large bifurcation supports is presented, based on such invariants as the configuration and the characteristic set. The realization lemma is proved. ...
Added: May 14, 2026
Taletskii D., / Series arXiv "math". 2026.
A vertex subset of a graph is called a \textit{distance-$k$ independent set} if the distance between any two of its distinct vertices is at least $k + 1$. For all $n,k \geq 1$, we determine the minimum possible number of inclusion-wise maximal distance-$k$ independent sets among all $n$-vertex trees. It equals~$n$ if $n \leq k ...
Added: May 1, 2026
Ovcharenko M., / Series arXiv "math". 2026.
We introduce an explicit class of tempered Laurent polynomials in the sense of Villegas and Doran--Kerr in n⩽4 variables including all Landau--Ginzburg models for smooth Fano threefolds with very ample anticanonical class. We check that it contains Landau--Ginzburg models for various Fano fourfolds which are complete intersections in smooth toric varieties and Grassmannians of planes, ...
Added: April 30, 2026
Derkacheva A., Sakirkina M., Kraev G. et al., /. 2026.
Comprehensive data on natural hazards and their consequences are crucial for effective for risk assessment, adaptation planning, and emergency response. However, many countries face challenges with fragmented, inconsistent, and inaccessible data, particularly regarding local-scale events. To address this data gap in Russia, we developed an end-to-end processing pipeline that scrapes news from various online sources, ...
Added: April 28, 2026
Qin X., Deng Y., Shchur L. et al., / Series arXiv "math". 2026. No. 2603.02962.
We perform a Monte Carlo analysis of the Ising model on many three-dimensional lattices. By means of finite-size scaling we obtain the critical points and determine the scaling dimensions. As expected, the critical exponents agree with the three-dimensional Ising universality class for all models. The irrelevant field, as revealed by the correction-to-scaling amplitudes, appears to ...
Added: April 20, 2026
Pilé I., Deng Y., Shchur L., / Series arXiv "math". 2026. No. 2604.10254.
We investigate the spatial overlap of successive spin configurations in Markov chain Monte Carlo simulations using the local Metropolis algorithm and the Svendsen-Wang and Wolff cluster algorithms. We examine the dynamics of these algorithms for two models in different universality classes: the Ising model and the Potts model with three components. The overlap of two ...
Added: April 20, 2026
Zlotnik Alexander, / Series arXiv "math". 2026. No. 2602.03481v1.
We deal with the global in time weak solutions to the 1D compressible Navier-Stokes system of equations for large discontinuous initial data and nonhomogeneous boundary conditions of three standard types. We prove the Lipschitz-type continuous dependence of the solution $(\eta,u,\theta)$, in a norm slightly stronger than $L^{2,\infty}(Q)\times L^2(Q)\times L^2(Q)$, on the initial data $(\eta^0,u^0,e^0)$ in a ...
Added: April 18, 2026
Ustyuzhanin V., / Series Econometrics "arxiv". 2026.
This paper proposes Covariate-Balanced Weighted Stacked Difference-in-Differences (CBWSDID), a design-based extension of weighted stacked DID for settings in which untreated trends may be conditionally rather than unconditionally parallel. The estimator separates within-subexperiment design adjustment from across-subexperiment aggregation: matching or weighting improves treated-control comparability within each stacked subexperiment, while the corrective stacked weights of Wing et ...
Added: April 3, 2026
Medvedev V., / Series arXiv "math". 2026.
We investigate the interplay between the dimension of the space of static potentials and the geometric and topological structure of the underlying static three-manifold. A partial classification of boundaryless static manifolds is obtained in terms of this dimension. We also treat the case of static manifolds with boundary. In particular, we prove that if a ...
Added: April 3, 2026
Gabdullin N., Androsov I., / Series Computer Science "arxiv.org". 2026.
Label prediction in neural networks (NNs) has O(n) complexity proportional to the number of classes. This holds true for classification using fully connected layers and cosine similarity with some set of class prototypes. In this paper we show that if NN latent space (LS) geometry is known and possesses specific properties, label prediction complexity can ...
Added: April 2, 2026
Vorchik A., / Social Science Research Network. Серия SSRN Working Paper Series "SSRN Working Paper Series". 2026.
This article is devoted to the phenomenon of intrinsic motivation, to understand which two models are proposed. We study how positive/negative intrinsic motivation to work (experienced utility) affects worker's individual labour supply (model I) and the amount of effort they exert (model II). In model I, we use intrinsic motivation to explain the positive/negative slope ...
Added: March 15, 2026
Kolesnikov A., / Series arXiv "math". 2025.
We study Blaschke--Santal{ó}-type inequalities for N>=2 sets (functions) and a special class of cost functions. In particular, we prove new results about reduction of the maximization problem for the Blaschke--Santal{ó}-type functional to homogeneous case (functional inequalities on the sphere) and extend the symmetrization argument to the case of N>2 sets.
We also discuss links to the ...
Added: February 13, 2026
Vorchik A., Мамышев М. А., / Series Social Science Research Network "Social Science Research Network". 2025.
In this paper, we develop a formal mathematical model aimed to explain the Dunning-Kruger effect that beginners systematically overestimate their own competence in various fields of knowledge and activity. We argue that the Dunning-Kruger effect arises from the emotional nature of confidence combined with unknown unknowns that it simply can not take into account due ...
Added: February 11, 2026
Musaev A. U., Vorchik A., / Series Social Science Research Network "Social Science Research Network". 2026.
This paper attempts to model the evolutionary theory of modernization and democratization. The model reflects the key provisions of R. Inglehart and C. Welzel's theory and provides a microfoundation for the adaptation of subjective values to the objective importances of the survival factors and the structure of the labour markets from the perspective of evolutionary ...
Added: February 10, 2026
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
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., Calcolo 2019 Vol. 56 No. 2 P. 1–11
Multiple Perron eigenvectors of non-negative matrices occur in applications, where
they often become a source of trouble. A usual way to avoid it and to make the
Perron eigenvector simple is a regularization of matrix: an initial non-negative matrix
A is replaced by A + "M, where M is a strictly positive matrix and " > 0 is ...
Added: June 12, 2019
Voinov A. S., Linear Algebra and its Applications 2013 Vol. 439 No. 15 P. 1627–1634
Let A = {A_1, ..., A_m} be a set of nonnegative dxd matrices having at least one strictly positive product (all products with no ordering and with repetitions permitted). What is the minimal possible length of their positive product? In other words, what is the minimal number l(A) for which there are indices i_1, ..., ...
Added: March 14, 2017
Protasov V., Voinov A. S., Linear Algebra and its Applications 2017 No. 513 P. 376–408
Multiplicative matrix semigroups with constant spectral radius (c.s.r.) are studied and applied to several problems of algebra, combinatorics, functional equations, and dynamical systems. We show that all such semigroups are characterized by means of irreducible ones. Each irreducible c.s.r. semigroup defines walks on Euclidean sphere, all its nonsingular elements are similar (in the same basis) ...
Added: March 11, 2017
Shitov Y., Linear Algebra and its Applications 2016 Vol. 497 P. 62–65
The max-times algebra is the set R+ of nonnegative reals with operations ⊕:(a,b)→max{a,b} and ⊙:(a,b)→ab. We discuss the property of matrices to be squares of max-times or conventional nonnegative matrices. We prove that there exists a matrix having a conventional nonnegative square root but no max-times square root. Also, we present a set S of cardinality three for which there is a ...
Added: February 23, 2016
Nesterov Y., Protasov V., SIAM Journal on Matrix Analysis and Applications 2013 Vol. 34 No. 3 P. 999–1013
We suggest a new approach to finding the maximal and the minimal spectral radii of linear operators from a given compact family of operators, which share a common invariant cone (e.g., family of nonnegative matrices). In the case of families with the so-called product structure, this leads to efficient algorithms for optimizing the spectral radius ...
Added: February 23, 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
Protasov V., SIAM Journal on Matrix Analysis and Applications 2013 Vol. 34 No. 3 P. 1174–1188
We develop a new approach for characterizing $k$-primitive matrix families. Such families generalize the notion of a primitive matrix. They have been intensively studied in the recent literature due to applications to Markov chains, linear dynamical systems, and graph theory. We prove, under some mild assumptions, that a set of $k$ nonnegative matrices is either ...
Added: February 19, 2016