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On a simple connection between Δ-modular ILP and LP, and a new bound on the number of integer vertices
Operations Research Forum. 2024. Vol. 5. Article 32.
In our note, we present a very simple and short proof of a new interesting fact about
the faces of an integer hull of a given rational polyhedron. This fact has a complete
analog in linear programming theory and can be useful to establish new constructive
upper bounds on the number of vertices in an integer hull of a delta-modular polyhedron,
which are competitive for small values of and can be useful for integer linear maximization
problems with a convex or quasiconvex objective function. As an additional
corollary, we show that the number of vertices in an integer hull is bounded by O(n)^n
for delta = O(1). As a part of our method, we introduce the notion of deep bases of a
linear program. The problem to estimate their number by a non-trivial way seems to
be quite challenging.
Inês G., Скороход С. Н., Matteo d. V. et al., Communications in Nonlinear Science and Numerical Simulation 2027 Vol. 164 P. 1–13
The collective dynamics of spiking networks of neurons has been of central interest to both computational
neuroscience and network science. Over the past years, a new generation of neural
population models based on exact reductions (ER) of spiking networks have been developed.
However, most of these efforts have been limited to networks of neurons with simple dynamics
(e.g. the ...
Added: October 29, 2026
Sergey Slavnov, / Series math "arxiv.org". 2026.
A prototypical example of categorial grammars are those based on Lambek calculus, i.e. noncommutative intuitionistic linear logic. However, it has been noted that purely noncommutative operations are often not sufficient for modeling even very simple natural language phenomena. Therefore a number of alternative formalisms are considered in the literature: those using purely ``commutative'' linear logic ...
Added: October 29, 2026
Association for Computational Linguistics, 2026.
While Large Language Models (LLMs) have revolutionized NLP, they remain prone to hallucinations, reasoning “mode-collapse” in open-ended generation, and a lack of factual provenance. The Automated Knowledge Base Construction (AKBC) workshop addresses a key missing piece of the generative era: structured knowledge. Knowledge Bases (KBs) serve as ground truth for fact verification, the semantic backbone ...
Added: October 28, 2026
Nikitiuk B., Lenev D., Pisarev V. et al., Journal of Colloid and Interface Science 2026 Vol. 718 Article 140444
Hypothesis:Accurate determination of interfacial tension values is crucial for many modeling applications in the oil and gas industry. However, many of the presently used empirical and theoretical models show poor prediction accuracy and do not allow for direct consideration of the concentrations of gases and salts dissolved in the system as well as the specific ...
Added: October 28, 2026
Deshchenya V., Nikolay D. Kondratyuk, Sivakova A. et al., Chemical Engineering Sciences 2027 Vol. 337 Article 124616
Accurate prediction of complex formulation viscosity is crucial for the lubricant industry and engineering processes. However, developing generalizable models remains challenging due to the complexity of industrial mixtures and the scarcity of public experimental data, often resulting from corporate proprietary restrictions. This study presents a machine-learning workflow for viscosity estimation from a proprietary pseudonymized dataset, ...
Added: October 28, 2026
Zubov A., Zubov A., Малявко, Я. et al., Computer Physics Communications 2025 Vol. 317 Article 109860
The concept of representative volume (REV, or RVE in material sciences) is the cornerstone of continuum scale models – one needs to get the volume big enough so that it could be represented with an averaged value (scalar, vector or tensorial, etc.). While REV should be established in all larger scale simulations, this is rarely ...
Added: October 28, 2026
Roman Prosvirnin, Suslov A., Aleksei Soldatov et al., Computation 2026 Vol. 14 No. 10 Article 261
Abstract
Safety-aligned language models often encode that a request is harmful yet still comply with it. We turn this gap between internal recognition and observable behavior into an inference-time defense. The proposed activation-steering method uses a multiplicative operator that amplifies the residual-stream component along a harm-recognition direction. Intervention strength scales with the model’s own assessment of ...
Added: October 27, 2026
Aleksei Samarin, Nazarenko A., Nazarenko D. et al., Big Data and Cognitive Computing 2026 Vol. 10 No. 11 P. 1–52
Camera traps are a key tool for non-invasive wildlife monitoring, yet models trained on existing benchmarks often generalize poorly to new regions due to domain shift, class imbalance, and natural variability in illumination, season, and background. We introduce PACTraD, a benchmark of 116,973 annotated camera trap images collected in a protected area of the Baikal ...
Added: October 27, 2026
IEEE, 2026.
Proceedings of the X Scientific School "Dynamics of Complex Networks and their Applications"
(DCNA'2026) contain papers of reports of scientists and specialists in the field of intelligent technologies,
engineering education, research and design of complex networks.
DCNA'2026 was held from 10 to 12 September 2026 in Moscow, Russia, as a part of the International
Forum on Artificial Intelligence and ...
Added: October 26, 2026
Maddalena L., Yildiz B., Del Vecchio Blanco F. et al., Scientific data 2026 P. 1–20
We addressed the task of chemical characterization of the aerosol emitted by heated tobacco products (HTPs) and of the smoke emitted by conventional/commercial cigarettes, usually adopted as a reference. Emphasis was placed on quantifying constituents for enabling the identification of novel compounds through targeted and untargeted analyses, and the evaluation of reductions in toxicant exposure under ...
Added: October 26, 2026
Flamarion M. V., Pelinovsky E., Wave Motion 2027 Vol. 148 Article 103867
We consider the interaction of two solitary waves in the modified Benjamin–Bona–Mahony
(mBBM) equation in a regime where a small parameter measures the departure from the classical
modified Korteweg–de Vries (mKdV) equation. A regular perturbation method is used to
analyze the modification of the two-soliton wave field induced by the weak non-integrability of
the mBBM equation. We show that, ...
Added: October 23, 2026
Obsie E. Y., Zhan Y., Liu Y., Engineering Research Express 2026 Article 7
Maintaining plant health is crucial for crop quality, food security, and agricultural productivity. Although deep learning methods have shown strong potential for species, disease, and severity classification, most existing approaches tackle these tasks separately, failing to exploit shared representations and interdependencies among them. Furthermore, the variability of disease symptoms, such as subtle differences in size, ...
Added: October 22, 2026
Lev Pyatko, Sergey Aksenov, Regular and Chaotic Dynamics 2026 Vol. 31 No. 5 P. 794–813
In the circular restricted three-body problem, families of periodic and quasi-periodic orbits exist in the vicinity of the libration points and are of significant interest for practical applications. This work presents a neural network-based algorithm for orbit construction and station-keeping, applicable to both periodic and quasi-periodic orbits near collinear libration points. The method employs a ...
Added: October 19, 2026
Vorontsova T., М.: Академия, 2025.
The textbook has been prepared in accordance with the requirements of the federal state educational standards for secondary vocational education and is intended for studying the professional modules “Information Security in Information and Telecommunication Systems and Networks Using Software and Hardware‑Software Tools, Including Cryptographic Protection Tools” and “Information Security in Automated Systems Using Software and ...
Added: October 19, 2026
Gribanov D., Khayaleyev T., Cherniavskii M. et al., , in: ESA'2026: Proceedings of the 34th Annual European Symposium on Algorithms.: Schloss Dagstuhl – Leibniz-Zentrum für Informatik, Dagstuhl Publishing, 2026. Ch. 388 P. 25:1–25:22.
We study the standard-form ILP problem max{c⊤x:Ax=b,x∈Zn≥0}, where A∈Zk×n has full row rank. We obtain refined FPT algorithms parameterized by k and Δ, the maximum absolute value of a k×k minor of A. Our approach combines discrepancy-based dynamic programming with matrix discrepancy bounds in Komlós' setting. Let κk denote the maximum discrepancy over all matrices with k columns whose columns have Euclidean norm at most 1. Up to polynomial ...
Added: August 24, 2026
Kolesnikov A., Popova S., / Series arXiv "math". 2024.
We consider the problem of optimal exchange which can be formulated as a kind of optimal transportation problem. The existence of an optimal solution and a duality theorem for the optimal exchange problem are proved in case of completely regular topological spaces. We show the connection between the problem of optimal exchange and the optimal ...
Added: December 20, 2024
Dmitry V. Gribanov, Dmitry S. Malyshev, Pardalos P. M. et al., Computational Optimization and Applications 2025 Vol. 92 P. 811–861
In this paper, we consider the counting function $\QEnum(y) = |\PC_{y} \cap \ZZ^{n_x}|$ for a parametric polyhedron $\PC_{y} = \{ x \in \RR^{n_x} \colon A x \leq b + B y\}$, where $y \in \RR^{n_y}$. We give a new representation of $\QEnum(y)$, called a \emph{piece-wise step-polynomial with periodic coefficients}, which is a generalization of piece-wise ...
Added: December 6, 2024
Rudenko V., Yudin N., Васин А. А., Компьютерные исследования и моделирование 2023 Т. 15 № 2 С. 329–353
This article reviews both historical achievements and modern results in the field of Markov Decision Process (MDP) and convex optimization. This review is the first attempt to cover the field of reinforcement learning in Russian in the context of convex optimization. The fundamental Bellman equation and the criteria of optimality of policy — strategies based on it, ...
Added: November 29, 2024
Gribanov D., Shumilov I., Malyshev D. et al., Journal of Global Optimization 2024 Vol. 89 P. 1033–1067
In our paper, we consider the following general problems: check feasibility, count the number of feasible solutions, find an optimal solution, and count the number of optimal solutions in P ∩ Zn , assuming that P is a polyhedron, defined by systems Ax ≤ b or Ax = b, x ≥ 0 with a sparse ...
Added: March 6, 2024
Ignatov A., , in: 14th International Conference, OPTIMA 2023, Petrovac, Montenegro, September 18–22, 2023, Revised Selected Papers. Communications in Computer and Information Science (CCIS, volume 1913)Vol. 1913.: Springer, 2023. P. 173–187.
Modeling protein folding, which is the process by which a protein obtains its spacial shape, still remains a challenging problem. Protein geometry might be simplified by using the coarse-grained models. The highest level of simplification is achieved in HP-models where only polarity of amino acid residues is considered, and the unified monomers are located in nodes ...
Added: January 18, 2024
Маршалко Г. Б., Математические вопросы криптографии 2014 Vol. 5 No. 2 P. 87–98
We show that neuron weights used in neural network-based biometric authentication scheme defined in GOST R 52633 standard series contain all the information on biometric data and secret key of the legitimate user. So, the complexity of evaluating (with known tables of neuron weights) the legitimate user's secret key is equivalent to the complexity of evaluating ...
Added: October 7, 2022
Gribanov D., Malyshev D., Siberian Electronic Mathematical Reports 2022 Vol. 19 No. 2 P. 613–626
Let a polytope P be defined by a system Ax ≤ b. We consider the problem to count a number of integer points inside P, assuming that P is ∆-modular. The polytope P is ∆-modular if all the rank sub-determinants of A are bounded by ∆ in the absolute value. We present a new FPT-algorithm, ...
Added: September 19, 2022
Gribanov D., Shumilov I., Dmitry Malyshev et al., Journal of Global Optimization 2024 Vol. 88 P. 591–651
Many papers in the field of integer linear programming (ILP, for short) are devoted to problems of the type $\max\{c^\top x \colon A x = b,\, x \in \ZZ^n_{\geq 0}\}$, where all the entries of $A,b,c$ are integer, parameterized by the number of rows of $A$ and $\|A\|_{\max}$. This class of problems is known under ...
Added: May 10, 2022
Belogaev A., Alexey Elokhin, Krasilov A. et al., IEEE Access 2020 Vol. 8 P. 169010–169023
Intelligent Transportation Systems (ITS) will become an essential part of every city in the near future. They should support various vehicle-to-everything (V2X) applications that improve road safety or even enable autonomous driving. Recently, the European Telecommunications Standards Institute (ETSI) introduced a multi-access (mobile) edge computing concept as a promising solution to satisfy the V2X delay ...
Added: September 18, 2020