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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.
Poddiakov A., / Series Social Science Research Network "Social Science Research Network". 2026. No. 7437658.
Clarity of knowledge and reasoning is necessary in many cases. Yet vagueness in scientific thinking related to surprise, curiosity, "ability to engage with not-knowing" (de Freitas) and abductive reasoning is also a crucially important source of scientific creativity which supplements combinatorial logic when dealing with the already known. Starting from studies by C. S. Peirce ...
Added: September 15, 2026
Glutsyuk A., / Series arXiv "math". 2026.
B.Josephson (Nobel Prize, 1973) predicted a tunnelling effect for a system of two superconductors separated by a narrow dielectric (such a system is called Josephson junction): existence of a supercurrent through it and equations governing it. The overdamped Josephson junction is modeled by the family of differential equations on the 2-torus, dθdτ=1ω(cosθ+B+Acosτ), which is known as ...
Added: September 8, 2026
Pochinka O., Shmukler V., / Series math.RT "arXiv:1808.06395 [math.RT]". 2026.
Anosov flows have a long and rich history, firstly motivated by the
study of geodesic flows in negative curvature surface by Anosov and Sinai.
Not every closed manifold admits an Anosov flow for well-known reasons:
the fundamental group of a 3-manifold M admitting an Anosov flow must
have exponential growth, and M must be universally covered by R3. Nevertheless,
there ...
Added: August 31, 2026
Очеретяный К. А., Галактика медиа: журнал медиа исследований 2025 Т. 7 № 4 С. 109–126
h as a means, but as an outlet, as a fashion, and a personalization factor, - in other words, as an expansion of ways of presence and influence. It coincides with the trend of emotional design, the production of impressions and affects, which gradually changed the approach at the level of commercial, design- and engineering ...
Added: August 30, 2026
Shabanov N., Kuricheva O., Kurbatova J. et al., / Series Working Papers SSRN "Department of Economics Ca’ Foscari University of Venice". 2026.
The carbon balance of an ecosystem is the difference between Gross Primary Productivity (GPP) and Ecosystem Respiration (Reco) as expressed by Net Ecosystem Exchange (NEE). While remote sensing retrievals of GPP have reached maturity, Reco estimation remains underexplored and ultimately cast bias on NEE. Here we present an end-to-end multi-scale analysis of the mechanism of ...
Added: August 21, 2026
Ponomarenko A., / Series Computer Science "arxiv.org". 2025.
This paper addresses the challenge of merging hierarchical navigable small world (HNSW) graphs, a critical operation for distributed systems, incremental indexing, and database compaction. We propose three algorithms for this task: Naive Graph Merge (NGM), Intra Graph Traversal Merge (IGTM), and Cross Graph Traversal Merge (CGTM). These algorithms differ in their approach to vertex selection ...
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
Piontkovski D., / Series arXiv "math". 2026.
A noncommutative projective variety is defined, following Artin and Zhang, by a graded coherent algebra 𝐴. The category of coherent sheaves is then the quotient qgr(𝐴) of the category of finitely presented graded modules by the subcategory of torsion modules. We consider the categorical and polynomial entropies of the Serre twist, that is, of the ...
Added: June 23, 2026
Piontkovski D., / Series arXiv "math". 2025.
If a symmetric multilinear algebra is weakly nil, then it is Engel. This result may be regarded as an infinite-dimensional analogue of the well-known Jacobian theorem, which states that if a polynomial mapping has a polynomial inverse, then its Jacobian matrix is invertible. This refines a theorem of Gerstenhaber and partially answers a question posed ...
Added: June 23, 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
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
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