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Existence and consistency of Wasserstein barycenters
Probability Theory and Related Fields. 2017. P. 901–917.
Loubes J., Le Gouic T.
Based on the Fréchet mean, we define a notion of barycenter corresponding to a usual notion of statistical mean. We prove the existence of Wasserstein barycenters of random probabilities defined on a geodesic space (E, d). We also prove the consistency of this barycenter in a general setting, that includes taking barycenters of empirical versions of the probability measures or of a growing set of probability measures.
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
Karpenko I., Философия науки и техники 2024 Т. 29 № 2 С. 74–87
The article analyzes the idea of a multiplicity of worlds as virtual ones. Gained its popularity in the second half of the 20th century, such an approach states that the universe can be considered as information – as a set of bits and logical operations with them (or as program code).
The hypothesis substantiates the information ...
Added: September 25, 2024
Geng R., Kubler F., Journal of Mathematical Economics 2023 Vol. 107 Article 102866
Non-convexities and discrete choices have become important modeling tools in modern macroeconomics. Unfortunately, the existence of competitive equilibria in the presence of such non-convexities is not always ensured, and most results on the existence of equilibrium that can be found in the literature do not directly apply to models used in applications.
In this paper, we explain ...
Added: December 1, 2023
Sergey S. Ketkov, European Journal of Operational Research 2024 Vol. 313 No. 2 P. 602–615
This study addresses a class of linear mixed-integer programming (MILP) problems that involve uncertainty in the objective function parameters. The parameters are assumed to form a random vector, whose probability distribution can only be observed through a finite training data set. Unlike most of the related studies in the literature, we also consider uncertainty in ...
Added: October 31, 2023
Prozumentik K. V., Философия и культура 2020 № 3 С. 45–57
This article is dedicated to one of the key problems of social philosophy – the phenomenon of human alienation. The subject of this research is the ontological grounds of alienation. The goal consists in determination of the existential foundation of alienation as a complicated socio-ontological phenomenon, as well as differentiation of the narrow and broad ...
Added: October 18, 2023
Bogachev V., Popova S., Известия Иркутского государственного университета. Серия: Математика 2023 Vol. 44 P. 19–30
We study metrizability of compact sets in spaces of Radon measures with the weak topology. It is shown that if all compacta in a given completely regular topological space are metrizable, then every uniformly tight compact set in the space of Radon measures on this space is also metrizable. It is proved that the property ...
Added: September 13, 2023
Measures of conflict, basic axioms and their application to the clusterization of a body of evidence
Andrey G. Bronevich, Alexander E. Lepskiy, Fuzzy Sets and Systems 2022 Vol. 446 P. 277–300
There are several approaches for evaluating conflict within belief functions. In this paper, we develop one of them based on axioms and show its connections to the decomposition approach. We describe a class of conflict measures satisfying this system of axioms and show that measuring conflict can be realized through the clusterization of a body ...
Added: August 27, 2022
Frolov K., Философия науки 2021 Т. 88 № 1 С. 13–29
The main thesis of the article is that the idea of A. Meinong's interpretation of the
concept of existence as an eccentric and deliberately implausible concept that implies absurd
consequences is unjustified. The author shows that, being correctly presented, this
approach not only does not contradict our typical and natural intuitions, but corresponds to
them more than any other ...
Added: December 14, 2021
Frolov K., Философия науки 2020 Т. 87 № 4 С. 15–28
The main point of the article is that the Russellian analysis of the concept of existence does
not provide a significant economy of ontology in comparison with the Meinongian one. The reason
lies in the unavoidable need to preserve the possibility of numerical distinguishing between various
nonexistent (unrealized) objects. For example, Sherlock Holmes is definitely not the same ...
Added: December 14, 2021
Porus V. N., Russian Studies in Philosophy 2020 Vol. 58 No. 3 P. 200–213
Contemporary philosophical anthropology fluctuates
between, on the one hand, the positivist rejection of
the metaphysically loaded concepts of “essence” and
“existence” in their theoretical constructions and, on
the other, the essentialist traditions in which these concepts have played and continue to play a decisive role.
Positivism rejects the ethical component of philosophical anthropology, reducing it to relativism. Essentialism
nourishes the metaphysical ...
Added: October 12, 2020
Ischenko N. I., История философии 2020 Т. 25 № 2 С. 55–68
A competent acquaintance with Martin Heidegger’s major works, such as “Being and Time”, is impossible without understanding the primeval methodological foundations of this German thinker, – or, in other words, without comprehending the principal connection between his existential analysis and the destruction of the European metaphysical knowledge. The inevitable connection of ontic and ontological levels ...
Added: July 11, 2020
Ischenko N. I., Антиномии 2018 Т. 18 № 3 С. 27–46
The subject of this article is Heidegger's existentially-ontological consideration of human being (Dasein) as the transcending structure. This article proves the conclusion that the interpretation of Heidegger's intentional consciousness as "transcendence"
means going beyond Husserl's phenomenology. Consequently, raising an issue of intentionality as a specific kind of Being (rather than cognition) Heidegger in contrast with Husserl ...
Added: October 21, 2018
Boissard E., Le Gouic T., Annales de l'institut Henri Poincare (B) Probability and Statistics 2014 P. 539–563
In this work, we provide non-asymptotic bounds for the average speed of convergence of the empirical measure in the law of large numbers, in Wasserstein distance. We also consider occupation measures of ergodic Markov chains. One motivation is the approximation of a probability measure by finitely supported measures (the quantization problem). It is found that ...
Added: October 13, 2018
Boissard E., Le Gouic T., Loubes J., Bernoulli: a journal of mathematical statistics and probability 2015 P. 740–759
In this paper, we tackle the problem of comparing distributions of random variables and defining a mean pattern between a sample of random events. Using barycenters of measures in the Wasserstein space, we propose an iterative version as an estimation of the mean distribution. Moreover, when the distributions are a common measure warped by a ...
Added: October 13, 2018