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Lines in hypergraphs
Combinatorica. 2013. Vol. 33. No. 6. P. 633–654.
Beaudou L., Bondy A., Chen X., Chiniforooshan E., Chudnovsky M., Chvátal V., Fraiman N., Zwols Y.
One of the De Bruijn-Erdős theorems deals with finite hypergraphs where every two vertices belong to precisely one hyperedge. It asserts that, except in the perverse case where a single hyperedge equals the whole vertex set, the number of hyperedges is at least the number of vertices and the two numbers are equal if and only if the hypergraph belongs to one of simply described families, near-pencils and finite projective planes. Chen and Chvátal proposed to define the line uv in a 3-uniform hypergraph as the set of vertices that consists of u, v, and all w such that {u;v;w} is a hyperedge. With this definition, the De Bruijn-Erdős theorem is easily seen to be equivalent to the following statement: If no four vertices in a 3-uniform hypergraph carry two or three hyperedges, then, except in the perverse case where one of the lines equals the whole vertex set, the number of lines is at least the number of vertices and the two numbers are equal if and only if the hypergraph belongs to one of two simply described families. Our main result generalizes this statement by allowing any four vertices to carry three hyperedges (but keeping two forbidden): the conclusion remains the same except that a third simply described family, complements of Steiner triple systems, appears in the extremal case.
Shipilov F., Barnyakov A., Ivanov A. et al., / Series Physics "arxiv.org". 2026.
A fast simulation of the detector response is a vital task in high-energy physics (HEP). Traditional Monte-Carlo methods form the backbone of modern particle physics simulation software but are computationally expensive. We present a machine-learning-based approach to fast simulation of the Focusing Aerogel Ring Imaging Cherenkov (FARICH) detector response. Given a particle track and momentum, ...
Added: May 19, 2026
Dorovskiy A., / Series arXiv "math". 2026.
In this paper the structural stability of generic families of vector fields of the PC-HC class on the two-dimensional sphere is proved. A classification of these families up to moderate equivalence in neighborhoods of their large bifurcation supports is presented, based on such invariants as the configuration and the characteristic set. The realization lemma is proved. ...
Added: May 14, 2026
Taletskii D., / Series arXiv "math". 2026.
A vertex subset of a graph is called a \textit{distance-$k$ independent set} if the distance between any two of its distinct vertices is at least $k + 1$. For all $n,k \geq 1$, we determine the minimum possible number of inclusion-wise maximal distance-$k$ independent sets among all $n$-vertex trees. It equals~$n$ if $n \leq k ...
Added: May 1, 2026
Ovcharenko M., / Series arXiv "math". 2026.
We introduce an explicit class of tempered Laurent polynomials in the sense of Villegas and Doran--Kerr in n⩽4 variables including all Landau--Ginzburg models for smooth Fano threefolds with very ample anticanonical class. We check that it contains Landau--Ginzburg models for various Fano fourfolds which are complete intersections in smooth toric varieties and Grassmannians of planes, ...
Added: April 30, 2026
Derkacheva A., Sakirkina M., Kraev G. et al., /. 2026.
Comprehensive data on natural hazards and their consequences are crucial for effective for risk assessment, adaptation planning, and emergency response. However, many countries face challenges with fragmented, inconsistent, and inaccessible data, particularly regarding local-scale events. To address this data gap in Russia, we developed an end-to-end processing pipeline that scrapes news from various online sources, ...
Added: April 28, 2026
Pilé I., Deng Y., Shchur L., / Series arXiv "math". 2026. No. 2604.10254.
We investigate the spatial overlap of successive spin configurations in Markov chain Monte Carlo simulations using the local Metropolis algorithm and the Svendsen-Wang and Wolff cluster algorithms. We examine the dynamics of these algorithms for two models in different universality classes: the Ising model and the Potts model with three components. The overlap of two ...
Added: April 20, 2026
Zlotnik Alexander, / Series arXiv "math". 2026. No. 2602.03481v1.
We deal with the global in time weak solutions to the 1D compressible Navier-Stokes system of equations for large discontinuous initial data and nonhomogeneous boundary conditions of three standard types. We prove the Lipschitz-type continuous dependence of the solution $(\eta,u,\theta)$, in a norm slightly stronger than $L^{2,\infty}(Q)\times L^2(Q)\times L^2(Q)$, on the initial data $(\eta^0,u^0,e^0)$ in a ...
Added: April 18, 2026
Medvedev V., / Series arXiv "math". 2026.
We investigate the interplay between the dimension of the space of static potentials and the geometric and topological structure of the underlying static three-manifold. A partial classification of boundaryless static manifolds is obtained in terms of this dimension. We also treat the case of static manifolds with boundary. In particular, we prove that if a ...
Added: April 3, 2026
Gabdullin N., Androsov I., / Series Computer Science "arxiv.org". 2026.
Label prediction in neural networks (NNs) has O(n) complexity proportional to the number of classes. This holds true for classification using fully connected layers and cosine similarity with some set of class prototypes. In this paper we show that if NN latent space (LS) geometry is known and possesses specific properties, label prediction complexity can ...
Added: April 2, 2026
Kolesnikov A., / Series arXiv "math". 2025.
We study Blaschke--Santal{ó}-type inequalities for N>=2 sets (functions) and a special class of cost functions. In particular, we prove new results about reduction of the maximization problem for the Blaschke--Santal{ó}-type functional to homogeneous case (functional inequalities on the sphere) and extend the symmetrization argument to the case of N>2 sets.
We also discuss links to the ...
Added: February 13, 2026
Sorokin K., Beketov M., Онучин А. et al., / arxiv.org. Серия cs.SI "Social and Information Networks ". 2025.
Community detection in complex networks is a fundamental problem, open to new approaches in various scientific settings. We introduce a novel community detection method, based on Ricci flow on graphs. Our technique iteratively updates edge weights (their metric lengths) according to their (combinatorial) Foster version of Ricci curvature computed from effective resistance distance between the ...
Added: January 15, 2026
Радушев Д. О., Dogonasheva O., Gutkin B. et al., Chaos, Solitons and Fractals 2025 Vol. 203 P. 1–11
Partial synchronization plays a crucial role in the functioning of neuronal networks: selective, coordinated activation of neurons enables information processing that flexibly adapts to a changing computational context. Since the structure of coherent activity patterns reflects the network’s current state, developing automated tools to identify them is a key challenge in neurodynamics. Existing methods for ...
Added: November 27, 2025
Vyacheslav V. Chistyakov, / Series arXiv [math.FA] "Functional Analysis". 2019. No. arXiv: 1910.08490.
Let $T\subset\mathbb{R}$, $M$ be a metric space with metric $d$, and $M^T$ be the set of all functions mapping $T$ into $M$. Given $f\in M^T$, we study the properties of the approximate variation $\{V_\varepsilon(f)\}_{\varepsilon>0}$, where $V_\varepsilon(f)$ is the greatest lower bound of Jordan variations $V(g)$ of functions $g\in M^T$ such that $d(f(t),g(t))\le\varepsilon$ for all $t\in T$. The notion of $\varepsilon$-variation ...
Added: October 21, 2019
Beaudou L., Bondy A., Chen X. et al., Electronic Journal of Combinatorics 2015 Vol. 22 No. 1 P. 1–6
A special case of a combinatorial theorem of De Bruijn and Erdős asserts that every noncollinear set of n points in the plane determines at least n distinct lines. Chen and Chávtal suggested a possible generalization of this assertion in metric spaces with appropriately defined lines. We prove this generalization in all metric spaces induced by connected chordal graphs. ...
Added: April 11, 2019
С.А.Чистякова, В.В.Чистяков, В кн.: Труды Математического центра имени Н.И.ЛобачевскогоТ. 54: Теория функций, ее приложения и смежные вопросы.: Каз.: Издательство Казанского математического общества и Академии наук РТ, 2017. С. 399–402.
Given a closed interval $I=[a,b]$ and a metric space $(M,d)$, we introduce a
nondecreasing sequence $\{\nu_n\}$ of pseudometrics on $M^I$ (the set of all
functions from $I$ into $M$), called the {\it joint modulus of variation}. We show that
if two sequences of functions $\{f_j\}$ and $\{g_j\}$ from $M^I$ are such that
$\{f_j\}$ is pointwise relatively compact on $I$, ...
Added: August 29, 2017
Vyacheslav V. Chistyakov, Svetlana A. Chistyakova, Studia Mathematica 2017 Vol. 238 No. 1 P. 37–57
Given a subset $T$ of the reals $R$ and a metric space $M$, we introduce a nondecreasing sequence $\{\nu_n\}$ of pseudometrics on $M^T$ (the set of all functions from $T$ into $M$), called the joint modulus of variation. We prove that if two sequences $\{f_j\}$ and $\{g_j\}$ of functions from $M^T$ are such that $\{f_j\}$ ...
Added: May 11, 2017
Vyacheslav V. Chistyakov, Svetlana A. Chistyakova, Journal of Mathematical Analysis and Applications 2017 Vol. 452 No. 2 P. 970–989
We introduce a pseudometric TV on the set M^X of all functions mapping a rectangle X on the plane R^2 into a metric space M, called the total joint variation. We prove that if two sequences {fj} and {gj} of functions from M^X are such that {fj} is pointwise precompact on X, {gj} is pointwise ...
Added: April 13, 2017
Vyacheslav V. Chistyakov, Svetlana A. Chistyakova, / Series math "arxiv.org". 2016. No. 1601.07298.
Given a subset T of real numbers and a metric space M, we introduce a nondecreasing sequence {v_n} of pseudometrics on the set M^T of all functions from T into M, called the joint modulus of variation. We prove that if two sequences of functions {f_j} and {g_j} from M^T are such that {f_j} is ...
Added: February 12, 2016
Ponomarenko A., Avrelin N., Naidan B. et al., , in: DATA ANALYTICS 2014, The Third International Conference on Data Analytics.: [б.и.], 2014. P. 125–130.
Similarity searching has a vast range of applications in various fields of computer science. Many methods have been proposed for exact search, but they all suffer from the curse of dimensionality and are, thus, not applicable to high dimensional spaces. Approximate search methods are considerably more efficient in high dimensional spaces. Unfortunately, there are few ...
Added: October 15, 2014
Yury M., Ponomarenko A., Vladimir K. et al., Lecture Notes in Computer Science 2012 No. 7404 P. 132–147
We propose a novel approach for solving the approximate nearest neighbor search problem in arbitrary metric spaces. The distinctive feature of our approach is that we can incrementally build a non-hierarchical distributed structure for given metric space data with a logarithmic complexity scaling on the size of the structure and adjustable accuracy probabilistic nearest neighbor ...
Added: October 1, 2013
Chistyakov V., Nonlinear Analysis 2010 Vol. 72 No. 1 P. 15–30
The notion of a modular is introduced as follows. A (metric) modular on a set X is a function w:(0,∞)×X×X→[0,∞] satisfying, for all x,y,z∈X, the following three properties: x=y if and only if w(λ,x,y)=0 for all λ>0; w(λ,x,y)=w(λ,y,x) for all λ>0; w(λ+μ,x,y)≤w(λ,x,z)+w(μ,y,z) for all λ,μ>0. We show that, given x0∈X, the set Xw={x∈X:limλ→∞w(λ,x,x0)=0} is a ...
Added: January 25, 2013
Chistyakov V., Nonlinear Analysis 2010 Vol. 72 No. 1 P. 1–14
The notion of a modular is introduced as follows. A (metric) modular on a set X is a function w:(0,∞)×X×X→[0,∞] satisfying, for all x,y,z∈X, the following three properties: x=y if and only if w(λ,x,y)=0 for all λ>0; w(λ,x,y)=w(λ,y,x) for all λ>0; w(λ+μ,x,y)≤w(λ,x,z)+w(μ,y,z) for all λ,μ>0. We show that, given x0∈X, the set Xw={x∈X:limλ→∞w(λ,x,x0)=0} is a ...
Added: September 26, 2012
Delon J., Salomon J., Sobolevski A., Journal of Mathematical Sciences 2012 Vol. 181 No. 6 P. 782–791
We consider a minimum-weight perfect matching problem on the line and establish a "bottom-up" recursion relation for partial minimum-weight matchings. ...
Added: May 11, 2012