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Semantic and sentiment trajectories of literary masterpieces
Chaos, Solitons and Fractals. 2023. Vol. 175. No. 1. Article 113934.
Vasilii A. Gromov, Dang Q. N.
The paper deals with semantic and sentiment trajectories of literary masterpieces (we used corpora of 12 languages of various language families), composed of individual embeddings or n-grams. We ascertain that, for all languages, semantic and sentiment trajectories are markedly chaotic: positive largest Lyapunov exponents; ‘entropy-complexity’ pairs belonging to the ‘chaotic’ area of the respective plane; the distinctive ‘chaotic’ drop of the number of false nearest neighbours at a particular value of an embedding dimension. The Russian language turns out to be more ‘chaotic’ than, for example, the English one; we attribute this fact to the free order of words. The Esperanto language, for various ‘approaches’ to different Indo-European languages. The results do not corroborate its claim to be equidistant from all languages. However, it seems to be equidistant from all Indo-European languages. These characteristics are utilised in order to develop a method to compare styles of an original masterpiece and its translations (to automatically assess translation quality). It appears that machine translations are still worse than human ones, however, for example, the Facebook translation is comparable with them.
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
Avdoshin S.M., Patrushev K. A., Proceedings of the Institute for System Programming of the RAS 2026 No. 4 часть 2 P. 245–256
The cardinality-constrained Markowitz problem is NP-hard and traditionally solved with commercial MIQP solvers. Following the 2022 export restrictions that rendered both commercial MIQP software and cloud quantum platforms (IBM Quantum, D-Wave Leap) inaccessible from the Russian Federation, practitioners require open-source alternatives. This paper systematically compares three solver families for the discrete mean-variance problem: two open-source ...
Added: August 27, 2026
Zaikin A., Vlasenko D., Zakharov D. et al., Diagnostics 2026 Vol. 16 No. 17 P. 1–15
Background/Objectives: Synolitic graphs (SGs) were developed for task-based fMRI, where
edge weights encode the discriminative power of pairwise regional features; whether similar
information can be recovered from resting-state data was untested. We benchmarked
SGs for autism spectrum disorder (ASD) classification using the multisite ABIDE-I dataset
(871 subjects: 403 subjects with ASD, 468 typical controls; 17 sites; CC200 atlas). Methods:
Using ...
Added: August 27, 2026
Melnikov I., Pelinovsky E., Nonlinear Dynamics 2026 No. 114 Article 934
Pyramidal solitons (solitons with more than two inflection points) of the generalized Korteweg–de Vries (KdV) equation are investigated. Necessary and sufficient conditions for the existence of such structures are presented. Within the framework of the generalized Gardner equation — the simplest model that admits pyramidal solitons as solutions — it is shown that these solutions ...
Added: August 27, 2026
Тула: Тульский государственный педагогический университет им. Л.Н. Толстого, 2025.
Сборник содержит материалы, представленные на XXIV Международной конференции «Алгебра, теория чисел, дискретная геометрия и многомасштабное моделирование: современные проблемы, приложения и проблемы истории», посвящённой 110-летию со дня рождения академика Юрия Владимировича Линника и 110-летию со дня рождения профессора Андрея Борисовича Шидловского и 80-летию со дня рождения профессора Геннадия Ивановича Архипова. Материалы конференции будут полезны научным работникам, ...
Added: August 27, 2026
Yerbolova A. S., Tomashchuk K., Kogan A. et al., Complexity 2026 Vol. 2026 No. 1 Article 5519690
Tis paper presents a novel approach to analyzing and grouping natural languages based on the degree of their chaoticity. It clusters 52 languages from 18 language families, according to the value of the entropy–complexity pair, to reveal the chaotic properties of semantic trajectories. Te obtained clusters appear to be closely correlated with the family of ...
Added: February 16, 2026
Vasilii A. Gromov, Quynh Nhu Dang, Alexandra S. Kogan et al., PeerJ Computer Science 2024 Vol. 10 Article e2550
This paper concerns the problem of distinguishing human-written and bot-generated texts. In contrast to the classical problem formulation, in which the focus falls on one type of bot only, we consider the problem of distinguishing texts written by any person from those generated by any bot; this involves analysing the large-scale, coarse-grained structure of the ...
Added: November 14, 2024
Gromov V., Tomashchuk K., Rukavishnikov A., Qubahan Academic Journal 2024 Vol. 4 No. 3
This paper proposes a new algorithm for the multi-step-ahead prediction of chaotic time series within the framework of the clustering-based forecasting paradigm. The introduction of the concept of non-predictable points enabled to avoid the exponential growth of the prediction error as a function of the number of steps ahead, which made it possible to develop ...
Added: September 27, 2024
Vasilii A. Gromov, Philip S. Baranov, Complexity 2023 Vol. 2023 Article 6689371
This paper introduces several novel strategies for multi-step-ahead prediction of chaotic time series. Introducing a concept of “generalized z-vectors” (vectors of nonsuccessive time series observations) makes it possible to generate sets of possible prediction values for each point we are trying to predict. +rough examining these sets, uni8ed predictions are calculated, which are in turn ...
Added: September 22, 2023
Vasilii A. Gromov, Yury N. Beschastnov, Korney K. Tomashchuk, PeerJ Computer Science 2023 Vol. 9 No. Article e1254
The paper deals with a generalized relational tensor, a novel discrete model to store information about a time series, and algorithms (1) to construct the model, (2) to generate a time series from the model, and (3) to predict a time series. The algorithms combine the concept of generalized z-vectors with ant colony optimization techniques. ...
Added: January 31, 2023
Dmitriev A., Kazmina A., Dmitriev V. et al., , in: 14th Chaotic Modeling and Simulation International Conference.: Springer, 2022. P. 121–133.
Added: July 13, 2022
Gromov V., Borisenko E. A., Neural Computing and Applications 2015 Vol. 26 No. 8 P. 1827–1838
Predictive clustering algorithm based upon modified Wishart clustering technique is applied to predict chaotic time series. Concept of predictable and non-predictable observations is introduced in order to distinguish between reliable and unreliable predictions and, consequently, to enhance an ability to predict up to considerable number of positions ahead. Non-predictable observations are easily ascertained in the ...
Added: September 27, 2018