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Probability laws in multi-dimensional noisy HK-models
Journal of Physics: Conference Series. 2021. Vol. 1740. No. 1. P. 1–6.
Bolychev A., Manita A.
The classical Hegselmann-Krause opinion dynamics model is known for the simplicity of its interaction rules and for the striking complexity of its collective behavior observed in computer simulations. The nonlinearity of the dynamics makes an analytical study of the model a very hard task. Recently there is some interest in introducing a random noise in the HK dynamics. In our study we focus on exact analysis of probability laws for a noisy HK model and give a detailed description of distribution transformations related to such systems. Our results shed some light on a long-time behavior of the noisy HK model and open new possibilities for future analytical and numerical studies in this area
Kupavskii A., Noskov F., Forum of Mathematics, Sigma 2026 Vol. 14 Article 124
We call a family of $s$ sets $\{F_1, \ldots, F_s\}$ a sunflower with $s$ petals if, for any distinct $i, j \in [s]$, one has $F_i \cap F_j = \cap_{u = 1}^s F_u$. The set $C = \cap_{u = 1}^s F_u$ is called the {\it core} of the sunflower. It is a classical result of ...
Added: October 8, 2026
Flamarion M. V., Pelinovsky E., Chaos, Solitons and Fractals 2026 Vol. 213 No. 2 Article 119245
This article concerns the study of modulational instability in the rotated-modified Gardner–Whitham (rmGW) equation. This model incorporates both quadratic and cubic nonlinearities, similarly to the Gardner equation, while also retaining the fully dispersive character of the Whitham equation together with a large-scale dispersive term analogous to that in the Ostrovsky equation. Using a classical multiple-scale asymptotic expansion, we ...
Added: October 8, 2026
Люксембург А. А., УРСС, 2005.
Изучается возможность автоматизированного построения математических теорий. Рассматривается дедуктивная система, основанная на языке логики предикатов первого порядка, объектами системы являются математические выражения или формулы, которые описывают математические объекты или их свойства. В дедуктивной системе выводятся математические определения и теоремы. Для доказательства теорем используются методы автоматического доказательства. Разработан алгоритм, выводящий часть формул системы. Для решения задачи используется аппарат математической ...
Added: October 7, 2026
Bernardin C., Gonçalves P., Olla S., Mathematical Physics Analysis and Geometry 2024 Vol. 27 No. 7
We consider the macroscopic limit for the space-time density fluctuations in the open symmetric simple exclusion in the quasi-static scaling limit. We prove that the distribution of these fluctuations converge to a gaussian space-time field that is delta correlated in time but with long-range correlations in space. ...
Added: October 6, 2026
Bernardin C., Chhaibi R., Najnudel J. et al., Probability Theory and Related Fields 2026 Vol. 195 P. 1823–1875
We study the celebrated Shiryaev-Wonham filter (Wonham, W.M., in J. Soc. Ind. Appl. Math. 347–369, 1964) in its historical setup, where the hidden Markov jump process has two states. We are interested in the weak noise regime for the observation equation. Interestingly, this becomes a strong noise regime for the filtering equations. Earlier results of ...
Added: October 5, 2026
Ismailov A., Spiridonov V., Успехи математических наук 2026 Т. 81 № 5 С. 183–184
Получена новая формула для цепной дроби Аски–Вильсона в форме отношения двух q-гипер-геометрических рядов. ...
Added: October 5, 2026
Abdulkhaev K., Shirokov D., Advances in Applied Clifford Algebras 2026 Vol. 36 P. 1–21
In this paper, we present explicit formulas for the inverse and determinant in geometric (Clifford) algebras over vector spaces of dimension n = 7. The derivation of these formulas is made possible by generalizing the concept of conjugation to basis conjugation operations. We further develop a general method for constructing such formulas over odd-dimensional spaces ...
Added: October 4, 2026
Kuninets A., IEEE Transactions on Information Theory 2026 P. 1–1
In this work we study the applicability of Quasi-Cyclic Subfield Subcodes of Dual Elliptic (QC-SSDE) codes for integration into code-based cryptographic schemes. Detailed algorithms are provided for constructing parity-check matrices as well as block-circulant parity-check matrices for this family of codes, accompanied by empirical results that enable the construction of QC-SSDE codes with predetermined dimensions. ...
Added: October 3, 2026
Medvedev G., Alexandrov Artem, Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 2026 Vol. 114 Article 044102
Graphons are measurable functions used to describe the asymptotic behavior of convergent graph families. Originally motivated by problems in combinatorics and graph theory, graphons have found numerous applications in the modeling and analysis of dynamical processes on networks. In this work, we use graphons to formulate the Ising model on convergent graph sequences, which include ...
Added: October 2, 2026
Pochinka O., Baranov D., Nozdrinova E., Теоретическая и математическая физика 2026 Т. 229 № 1 С. 3–14
The Birman–Williams problem on describing the planetary link of a fibered knot K in S^3 has been partially solved. Using Nielsen's theory for the classification of periodic surface homeomorphisms and its close relationship with the theory of gradient-like diffeomorphisms, it is proved that the planetary link of the trefoil (the unique periodic fibered knot of genus ...
Added: October 2, 2026
Lubashevsky I., Lubashevskiy V., Physica D: Nonlinear Phenomena 2026 Vol. 498 Article 135441
We develop a novel cloud-function formalism describing the dynamical relationship between sensory-information processing in large-scale brain networks (supraliminal processing) and the content of the mental representation of an observed object. The formalism combines elements of neural field theory for large-scale neural activity with the spatial characteristics of perceived objects and their embedding in the environment ...
Added: October 2, 2026
Zlotnik A., Математические заметки 2026 Т. 120 № 6 С. 1005–1009
Численным методам решения систем газодинамических уравнений посвящена обширная литература. Ранее было разработано и успешно апробировано специальное семейство симметричных по пространству консервативных разностных методов, основанных на предварительной кинетической, точнее, квазигазодинамической (КГД), регуляризации этих уравнений. Актуальной задачей является построение численных методов, которые обладают не только свойством консервативности по массе, импульсу и полной энергии, но и удовлетворяют условиям энтропийной ...
Added: October 1, 2026
Vyugin I. V., Sashadhar D., Algebra and Number Theory 2026 P. 1–10
We study the K-Fibonacci sequence Fp modulo prime p. Cardinalities of sets |Fp+Fp| and |Fp⋅Fp| are estimated. We present the method of estimating doubling constant of some m-dimensional recurrent sets in Fp. ...
Added: October 1, 2026
Kuksin S., Dynamical Systems 2026
We study the mixing properties of discrete-time and continuous-time dissipative dynamical systems driven by bounded mixing random forces. The continuous-time systems are
reduced to discrete-time random dynamical systems generated by time-one maps, so that
the main analysis is carried out in the discrete setting. We introduce a class of mixing random forcings whose regular conditional distributions with ...
Added: October 1, 2026
Kuksin S., Shirikyan A., Journal of Dynamics and Differential Equations 2026 P. 1098–1100
The paper deals with the problem of large-time behaviour of trajectories for discrete-time dynamical systems driven by a random noise. Assuming that the phase space is finite-dimensional and compact, and the noise is a Markov process with a transition probability satisfying some regularity hypotheses, we prove that all the trajectories converge to a unique measure ...
Added: October 1, 2026
Potanin B., Dolgikh S., Statistics and Probability Letters 2027 Article 110984
We derive bounds on the gradient and Hessian of the log-CDF, ln F(x), of the multivariate normal distribution. These bounds scale linearly and quadratically in ‖x‖ , respectively, with constants depending only on the covariance matrix. We demonstrate the usefulness of these bounds by proving asymptotic normality of the maximum-likelihood estimator of the multivariate probit ...
Added: October 1, 2026
A. V. Pereskokov, Journal of Mathematical Sciences 2026 Vol. 302 No. 4 P. 531–545
We consider the Zeeman effect problem for the hydrogen atom in a magnetic field using
irreducible representations of the Karasev–Novikova algebra with quadratic commutation
relations. We find the asymptotics of a series of eigenvalues and the corresponding
asymptotic eigenfunctions near the upper boundaries of spectral clusters. ...
Added: October 1, 2026
Levashev V., / Series arXiv "math". 2026. No. 2609.06010.
We prove that continuous A-bilinear pairings on the ring of Laurent series that are invariant under continuous automorphisms coincide, up to a constant, with the pairing given by the residue of a differential form over any commutative associative ring with identity. ...
Added: September 24, 2026
Pyatov P. N., Pivovarov P. A., / Series math "arxiv.org". 2026. No. 2609.06274.
We investigate a special ansats that allows for an iterative solution of the constant Yang-Baxter equation. Testing this ansatz, we construct four sequences of the constant R-matrices. In each sequence the R-matrices act on the tensor squares of vector spaces of linearly growing dimensions. Each R-matrix also depends on a single complex parameter.
By analyzing the ...
Added: September 24, 2026
Medvedev V., / Series arXiv "math". 2026.
We study complete static manifolds with boundary admitting a nowhere-vanishing static potential. Our main result shows that, under a natural lower bound relating the scalar curvature and the boundary mean curvature, a simple static manifold with boundary must in fact have positive scalar curvature, negative boundary mean curvature, and be compact; we also obtain explicit ...
Added: September 19, 2026
Poddiakov A., / Series Social Science Research Network "Social Science Research Network". 2026. No. 7437658.
Clarity of knowledge and reasoning is necessary in many cases. Yet vagueness in scientific thinking related to surprise, curiosity, "ability to engage with not-knowing" (de Freitas) and abductive reasoning is also a crucially important source of scientific creativity which supplements combinatorial logic when dealing with the already known. Starting from studies by C. S. Peirce ...
Added: September 15, 2026
Glutsyuk A., / Series arXiv "math". 2026.
B.Josephson (Nobel Prize, 1973) predicted a tunnelling effect for a system of two superconductors separated by a narrow dielectric (such a system is called Josephson junction): existence of a supercurrent through it and equations governing it. The overdamped Josephson junction is modeled by the family of differential equations on the 2-torus, dθdτ=1ω(cosθ+B+Acosτ), which is known as ...
Added: September 8, 2026
Pochinka O., Shmukler V., / Series math.RT "arXiv:1808.06395 [math.RT]". 2026.
Anosov flows have a long and rich history, firstly motivated by the
study of geodesic flows in negative curvature surface by Anosov and Sinai.
Not every closed manifold admits an Anosov flow for well-known reasons:
the fundamental group of a 3-manifold M admitting an Anosov flow must
have exponential growth, and M must be universally covered by R3. Nevertheless,
there ...
Added: August 31, 2026
Loubenets E. R., / Series arxiv.org "quant-ph". 2026. No. 2607.18050.
In many quantum applications it is important to know whether or not a Bell nonlocal two-qudit state exhibits its nonlocality under correlation scenarios with some given numbers S1,S2≥1 of generalized quantum measurements at two sites. In the present article, we find analytically a new general locality condition sufficient for a nonseparable Werner state with a ...
Added: July 21, 2026