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To spike or not to spike: the whims of the Wonham filter in the strong noise regime
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 the authors show the appearance of spikes in the filtered process, akin to a metastability phenomenon. This paper is aimed at understanding the smoothed optimal filter, which is relevant for any system with feedback. In particular, we exhibit a sharp phase transition between a spiking regime and a regime with perfect smoothing.
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
Yakovlev K., Puchkin N., Journal of Complexity 2026 Vol. 97
We present a theory for simultaneous approximation of the score function and its derivatives, enabling the handling of data distributions with low-dimensional structure and unbounded support. Our approximation error bounds match those in the literature while relying on assumptions that relax the usual bounded support requirement. Crucially, our bounds are free from the curse of ...
Added: September 30, 2026
Zlotnik A., Mathematical notes 2026 Vol. 120 No. 6 P. 1174–1178
Numerical methods for solving systems of gas dynamic equations are the subject of a vast literature. A special family of spatially symmetric conservative difference methods based on preliminary kinetic, or quasi-gasdynamic (QGD), regularization of these equations was constructed and successfully tested. A pressing issue is the construction of numerical methods that are not only conservative ...
Added: September 30, 2026
Beldiev I., Тимашёв Д. А., Алгебра и анализ 2026 Т. 38 № 5 С. 1–10
An algebraic variety X is called a homogeneous space if there exists a transitive regular action of an algebraic group on X. We prove inequalities between the dimension of a homogeneous space of a linear algebraic group and its Picard number. ...
Added: September 30, 2026
Planche L., Ilina A., Jay F. et al., Molecular Biology and Evolution 2026 Article 235
Admixture between populations is a common feature of human history. Admixture events introduce new genetic variation that can fuel evolution. Characterizing the significance of admixture events on the evolution of populations across various species is of great interest to evolutionary geneticists. Local Ancestry Inference (LAI) methods infer genetic ancestry of an individual at a particular ...
Added: September 30, 2026
Glutsyuk A., Ilyashenko Y., Izvestiya. Mathematics 2026 Vol. 90 No. 1 P. 73–89
We show that a completely non-degenerate B-group is uniquely determined by its factor: two such groups with conformally equivalent factors are Möbius conjugate. A similar property is inherent to the quasi-Fuchsian groups but not to degenerate B-groups. We also study the factor of a B-group as a triple: the main factor, the marked characteristic complex, and a homotopy class of ...
Added: September 30, 2026
Tuzhilin M., Автоматика и телемеханика 2026 № 11 С. 84–97
Предлагается обобщение двух известных инвариантов реальных сетей: степени и кси-центральности. Строится серия центральностей, основанная на матрице Лапласа сети и параметризованная параметром j со следующими свойствами: во-первых, при j = 0, 1 эти центральности совпадают со степенью и ксицентральностью; во-вторых, их распределение хорошо приближается распределением Вейбулла; в-третьих, для реальных сетей они имеют правостороннюю асимметрию, а для ...
Added: September 29, 2026
Melnikov I., Pelinovsky E., Доклады Российской академии наук. Физика, технические науки (ранее - Доклады Академии Наук. Физика) 2026 Т. 529 С. 29–36
Conditions for the emergence of pyramidal solitary waves (solitary waves possessing more than two inflection points) are presented for a family of generalized Korteweg – de Vries (KdV) equations. For the generalized Gardner equation, it is shown that pyramidal solitons are unstable. The decay of initial perturbations close to pyramidal solitary waves is demonstrated numerically. ...
Added: September 29, 2026
Merkulov S., Journal of Pure and Applied Algebra 2026 Vol. 230 P. 1–19
We study the dual cyclic Hochschild complex $Cyc(A,\K)$ of a
(possibly, infinite-dimensional) $A_\infty$-algebra $(A,\mu)$ and prove
that any pre-Calabi-Yau extension $\pi$ of the given $A_\infty$ structure $\mu$ in $A$
induces on the cyclic cohomology of $(A,\mu)$ a representation of a new dg properad of {\em oriented}\, ribbon graphs. We compute the cohomology of that properad in terms of ...
Added: September 29, 2026
Aleksei Samarin, Aleksei Toropov, Kotenko E. et al., , in: Proceedings of the 37th Conference of Open Innovations Association FRUCT, Helsinki, Finland, 14-16 May 2025, Issue 1 (Full Papers)Vol. 37.: Helsinki: FRUCT Oy, 2025. P. 271–277.
This study focuses on improving iris and pupil segmentation in infrared images, a crucial task for gaze-tracking systems. We propose a lightweight image preprocessing approach, which ensures controlled data transformation, effectively eliminating parasitic reflections, noise, and contrast inconsistencies without introducing unwanted artifacts. Our approach employs analytically defined transformations, incorporating local and global filtering techniques to ...
Added: September 19, 2026
Zotov L., Логинов А. В., Ольховский А. А. et al., В кн.: ВОПРОСЫ ТЕОРИИ И ПРАКТИКИ ГЕОЛОГИЧЕСКОЙ ИНТЕРПРЕТАЦИИ ГРАВИТАЦИОННЫХ, МАГНИТНЫХ И ЭЛЕКТРИЧЕСКИХ ПОЛЕЙ 51-я сессия Международного семинара им. Д.Г. Успенского - В.Н. Страхова. Москва, 2025.: Пермский государственный университет, 2025.
One of the major components of the Earth’s polar motion is Chandler wobble with 433-day period. To extract it from observations narrow-band filtering is required. We have developed method which joins Kalman filtering and band-pass filtering in direct time with the phase correction in reversed time. By using Euler-Liouville equation generating resonant CW as a ...
Added: December 10, 2025
Dergunov I., Meinerding C., Schlag C., Management Science 2023 Vol. 69 No. 5 P. 2547–3155
In a parsimonious regime switching model, we find strong evidence that expected consumption growth varies over time. Adding inflation as a second variable, we uncover two states in which expected consumption growth is low, one with high and one with negative expected inflation. Embedded in a general equilibrium asset pricing model with learning, these dynamics ...
Added: September 13, 2022
Djurdjevic V., Ansuini A., Bertolini D. et al., Current Biology 2018 Vol. 28 No. 7 P. 1005–1015
As the popularity of rodents in the vision research continues to grow, some questions remain unanswered. One of the key questions is - can rodents perform a "proper" higher level vision task such as object recognition. In our paper we present the new research findings which demonstrate that, despite having much poorer visual abilities compared ...
Added: December 14, 2020