1,720,963 research outputs found
Linear Lipschitz and C-1 extension operators through random projection
No full textWe construct a regular random projection of a metric space onto a closed doubling subset and use it to linearly extend Lipschitz and C-1 functions. This way we prove more directly a result by Lee and Naor [5] and we generalize the C-l extension theorem by Whitney [8] to Banach spaces. (C) 2020 Elsevier Inc. All rights reserved.AMC
Stability of quasi-entropy solutions of non-local scalar conservation laws
No full textWe prove the stability of entropy solutions of nonlinear conservation laws with respect to perturbations of the initial datum, the space-time dependent flux and the entropy inequalities. Such a general stability theorem is motivated by the study of problems in which the flux P[u](t, x, u) depends possibly non-locally on the solution itself. For these problems we show the conditional existence and uniqueness of entropy solutions. Moreover, the relaxation of the entropy inequality allows to treat approximate solutions arising from various numerical schemes. This can be used to derive the rate of convergence of the recent particle method introduced in Radici and Stra (SIAM J Math Anal 55(3):2001–2041, 2023. https://doi.org/10.1137/21M1462994) to solve a one-dimensional model of traffic with congestion, as well as recover already known rates for some other approximation methods
A PDE approach to a 2-dimensional matching problem
Full text linkWe prove asymptotic results for 2-dimensional random matching problems. In particular, we obtain the leading term in the asymptotic expansion of the expected quadratic transportation cost for empirical measures of two samples of independent uniform random variables in the square. Our technique is based on a rigorous formulation of the challenging PDE ansatz by Caracciolo et al. (Phys Rev E 90:012118, 2014) that linearizes the Monge–Ampère equation
Weak and strong convergence of derivations and stability of flows with respect to MGH convergence
Full text linkThis paper is devoted to the study of weak and strong convergence of derivations, and of the flows associated to them, when dealing with a sequence of metric measure structures (X,d,mn), mn weakly convergent to m. In particular, under curvature assumptions, either only on the limit metric structure (X,d,m) or on the whole sequence of metric measure spaces, we provide several stability results
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Full text link“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
Appropriate Similarity Measures for Author Cocitation Analysis
Full text linkWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
Log-concave measures: recent results and open problems
No full textLog-concave measures arise naturally in the context of probabilistic optimization, as pointed out by Prékopa, and serve the role of a reference measure in infinite dimensional vector spaces for purposes such as gradient flows. They have been thoroughly studied first by Borell, then by Brascamp and Lieb. In this thesis we present the basic theory regarding concave measures (characterization in the finite dimensional case, stability under projection and disintegration, integrability of seminorms, zero-one law), then we present some results such as estimates of the moments and a dichotomy property, proved by Krugova, regarding the differentiability
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