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Статистический анализ параметров модели эпидемической ситуации
Эпидемиология и вакцинопрофилактика. 2015. Т. 14. № 5(84). С. 13–21.
A calculation method and a variation method of parameters of the epidemic situation model taking into account external risks is proposed. The detailed step-by-step algorithm available in the application EXCEL for the calculation and analysis of the model parameters based on the results of observations is given. The prognosis of the epidemic situation with the estimation of the disease outbreak duration and the total number of population members involved in the outbreak is constructed. We investigated the epidemic situation by an example of reports of a diseases group acute viral respiratory infections-flu in one of the districts of the Moscow region.
Priority areas:
mathematics
Language:
Russian
Богатырев А. Б., Математический сборник 2023 Т. 214 № 3 С. 106–119
Рассматривается клеточное разбиение пространства модулей вещественных кривых рода 2 с отмеченной точкой на единственном вещественном овале. Клетки перечисляются определенными графами, веса которых описывают комплексную структуру на кривой. Показано, что стягивание ребра графа приводит к корневой особенности естественного отображения из весов графа в пространство модулей кривых. ...
Added: August 14, 2026
Богатырев А. Б., Gendron Q., Успехи математических наук 2023 Т. 78 № 1 С. 209–210
Уравнение Пелля-Абеля — это функциональное уравнение вида P²-DQ² = 1, с заданным многочленом D, свободным от квадратов, и неизвестными многочленами P и Q. Мы показываем, что пространство уравнений Пелля-Абеля с фиксированными степенями D и примитивным решением P является комплексным многообразием. Мы описываем его связные компоненты с помощью эффективно вычислимого инварианта. ...
Added: August 14, 2026
Богатырев А. Б., Transactions of the Moscow Mathematical Society 2024 Vol. 85 No. 2 P. 323–337
The best uniform rational approximation of the Sign function on two intervals separated by zero was explicitly found by E. I. Zolotarëv in 1877. The natural extension of this problem to three bands was solved by E. Stiefel in 1961. We indicate the solutions overlooked by the prominent geometer and study their properties. ...
Added: August 14, 2026
Богатырев А. Б., Успехи математических наук 2026 Т. 81 № 3(489) С. 159–160
Предложена простая и эффективно реализуемая формула для изменения абелевых интегралов (включая их периоды) при вариации образующих классической группы Шоттки, представляющей риманову поврехность. ...
Added: August 14, 2026
Gendron Q., Compositio Mathematica 2025 Vol. 161 No. 7 P. 1483–1511
A Pell–Abel equation is a functional equation of the form P^2-DQ^2=1 , with a given polynomial D free of squares and unknown polynomials P and Q. We show that the space of Pell–Abel equations with the degrees of D and of the primitive solution P fixed is a complex manifold. We describe its connected components ...
Added: August 14, 2026
Yu Z., Wang J., Wang Z. et al., Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 2026 Vol. 384 P. 1–16
The integration of data-driven and knowledge-driven approaches in generative geospatial modelling (GGM) is often hindered by their mathematical incompatibilities. Here, we propose a geometric algebra (GA)-based framework that employs a unified multi-vector representation to fuse heterogeneous data and diverse knowledge. The framework facilitates structured reasoning and hypothesis generation through a task-adaptable, five-stage cycle: representation, reasoning, ...
Added: August 13, 2026
Speranski S. O., Математические заметки 2026 Т. 120 № 3 С. 470–483
We show that, in terms of closure ordinals, many infinitary calculi for ‘first-order’ logics of probability (i.e., for languages similar to those in [Abadi & Halpern 1994]) are as hard as possible: the corresponding closure ordinals coincide with the least non-constructive ordinal, denoted by $\omega_1^{\mathrm{CK}}$. ...
Added: August 12, 2026
Ali S., Bocharnikov V., Ratnikov F. et al., Sensors 2026 Vol. 26 No. 16 Article 5024
Large distributed sensor arrays require repeated recalibration as radiation damage, material aging, gain variation, and readout drift alter channel responses. We studied a high-granularity calorimeter as a large sensor array and addressed unsupervised recalibration from two unpaired datasets: a nominal reference response and an aged response with attenuated cell-wise signals. Aging was modeled by a ...
Added: August 11, 2026
Shartova N., Mironova E., Geo Journal 2026 Vol. 91 P. 1–17
The historical timeline of urban development profoundly shapes the contemporary form and functionality of cities. Traditionally, cities were planned with limited consideration for the promotion of a healthy urban environment. Using Nizhny Novgorod, Russia, a city that has evolved from a medieval market town to an industrial centre and later into a multifunctional city with ...
Added: August 9, 2026
Kulev Y., Maksaev A., Promyslov V., Linear Algebra and its Applications 2026 Vol. 730 P. 51–72
The notion of λ-th upper scrambling index was introduced by Huang and Liu in 2010, as a generalization of a notion considered by Akelbek and Kirkland in 2009. For a primitive digraph D, it is defined as the smallest positive integer k such that for every λ vertices of D there exist directed paths of lengths k from these vertices to a common vertex. This ...
Added: August 7, 2026
Kanunnikov A., Promyslov V., Vassilieva E., Electronic Journal of Combinatorics 2024 Vol. 31 No. 3 Article P3.6
Introduced by Goulden and Jackson in their 1996 paper, the matchings-Jack conjecture and the hypermap-Jack conjecture (also known as the b-conjecture) are two major open questions relating Jack symmetric functions, the representation theory of the symmetric groups and combinatorial maps. They show that the coefficients in the power sum expansion of some Cauchy sum for ...
Added: August 7, 2026
Vlassov V., JAMA - Journal of the American Medical Association 2026 P. 1–6
Importance Elevated low-density lipoprotein cholesterol (LDL-C) is a modifiable risk factor for cardiovascular disease, the leading cause of premature death worldwide. Assessing the LDL-C–related burden is critical for guiding prevention and treatment strategies.
Objectives To estimate the global, regional, and national burden of ischemic heart disease and ischemic stroke attributable to elevated LDL-C (relative to 35-54 mg/dL) from ...
Added: August 4, 2026
Spiridonov V. P., Belousov N. M., Sarkissian G. A., Analysis and Mathematical Physics 2026 Vol. 16 Article 96
Hyperbolic hypergeometric integrals are defined as Barnes-type integrals of products of hyperbolic gamma functions. Their reduction to ordinary hypergeometric functions is well known. We study in detail their degeneration to complex hypergeometric functions. Namely, using uniform bounds on the integrands, we prove that the univariate hyperbolic beta integral and the conical function degenerate to two-dimensional ...
Added: August 4, 2026
Gayfullin S., Kikteva V., Results in Mathematics 2026 Vol. 81 No. 5 Article 146
In this paper we obtain a criterion of flexibility for an affine complexity-zero horospherical variety. This result generalizes previously known results on flexibility of normal horospherical varieties, horospherical varieties with an action of a semisimple group, and non-normal toric varieties. ...
Added: August 3, 2026
Lunts V., Функциональный анализ и его приложения 2026 Т. 60 № 3 С. 127–129
Доказано, что канонические полуортогональные разложения производной категории диаграммной схемы индуцируют аналогичные разложения подкатегории совершенных комплексов. ...
Added: August 3, 2026
Belomestny D., Gasnikov A., Gladin E. et al., Russian Mathematical Surveys 2026 Vol. 81 No. 4(490) P. 3–90
Reinforcement learning (RL) is increasingly grounded in tools from probability, optimization, and operator theory. This survey organizes the mathematical structures that underpin the design and analysis of modern algorithms in RL. We begin from Markov decision processes (MDPs) and the Bellman operators, emphasizing contraction mappings, monotonicity, and fixed-point theory that yield convergence guarantees and rates ...
Added: August 3, 2026
A. Radomskii, Mathematical notes 2026 Vol. 119 No. 6 P. 1136–1147
We obtain an upper bound for the sum $\sum_{n\leq N} (a_{n}/\varphi (a_{n}))^{s}$, where $\varphi$ is Euler's totient function, $s\in\mathbb{N}$, and $a_{1},\ldots, a_{N}$ are positive integers (not necessarily distinct) with some restrictions. As applications, for any $t>0$, we obtain an upper bound for the number of $n\in [1,N]$ such that $a_{n}/ \varphi (a_{n})> t$. ...
Added: July 31, 2026
Maghsoohi A., Pavlov V., Rouse P. et al., Health Care Management Science 2026 Vol. 29 No. 37
As the numbers of older people (65 +) rise globally, the pressure on acute hospitals to provide efficient and effective care while addressing resource inequities increases. In this study we introduce Recognising Episodes of Acute Complexity in Health (REACH), a novel Automatic Machine Learning (AutoML)-based predictive model that prioritises older patients and assigns them to complex ...
Added: July 30, 2026
Абызов А. Н., Буутай П. Н., Математика и теоретические компьютерные науки 2026 Т. 4 № 2 С. 4–75
This paper is expository and methodological in nature and is devoted to the development of E.I. Zolotarev’s ideas embedded in his approach to the proof of the quadratic reciprocity law (1872). We consider extensions of Zolotarev’s approach to abstract number rings presented in the work of A. Brunyate and P.L. Clark (2015), and to finite ...
Added: July 30, 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
Bolbachan V., / Series math "arxiv.org". 2024.
Chow polylogarithms are some special functions arising in explicit description of the Beilinson regulator map. The most interesting functional equation for this function reflects its vanishing on the boundary in the Bloch's cycle complex. We show that this functional equation formally follows from more simple ones, namely skew-symmetry, functoriality and multiplicativity.
To prove this, we study ...
Added: July 16, 2026
Bolbachan V., / Series math "arxiv.org". 2024.
Let K be a field of characteristic zero. We prove that its motivic cohomology in degree m−1 and weight m is rationally isomorphic to the cohomology of the polylogarithmic complex. This gives a partial extension of A. Suslin theorem describing the indecomposable K3 of a field. ...
Added: July 16, 2026
Panov V., Ryabchenko A., / Series arXiv "stat.ME". 2026. No. 2607.05048.
This paper investigates the problem of statistical inference for a mixture distribution consisting of a discrete and a continuous component, with a particular focus on the class of rational-infinitely divisible distributions. We consider non-parametric estimation of both components of the mixture as well as the quasi-L{é}vy measure, assuming that the mixture belongs to the class ...
Added: July 9, 2026
Konakov V., Kucher D., Mammen E., / Series arXiv "math". 2026. No. 2606.11142v1.
In this paper, we construct strong approximations for discrete-time Markov chains weakly converging to continuous diffusion processes, as well as for their perturbed counterparts. Under the assumption of bounded coefficients, we construct closely coupled versions of these processes on a shared probability space. In particular, for both non-degenerate and degenerate cases, we maximize the probability ...
Added: June 11, 2026