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Asymptotics and quantization for a mean-field equation of higher order
No full textGiven a regular bounded domain < subset of>2m, we describe the limiting behavior of sequences of solutions to the mean field equation of order 2m, m epsilon 1, [image omitted] under the Dirichlet boundary condition and the bound 0C. We emphasize the connection with the problem of prescribing the Q-curvature
Existence of solutions to a higher dimensional mean-field equation on manifolds
No full textFor m ≥ 1 we prove an existence result for the equation
(-\Delta_g)^m u+\lambda=\lambda\frac{e^{2mu}}{\int_M e^{2mu}d\mu_g}
on a closed Riemannian manifold (M, g) of dimension 2m for certain values of λ
Coefficient groups inducing nonbranched optimal transport
Get PDFIn this work we consider an optimal transport problem with coefficients in a normed Abelian group G, and extract a purely intrinsic condition on G that guarantees that the optimal transport (or the corresponding minimum filling) is not branching. The condition turns out to be equivalent to the nonbranching of minimum fillings in geodesic metric spaces. We completely characterize finitely generated normed groups and finite-dimensional normed vector spaces of coefficients that induce nonbranching optimal transport plans. We also provide a complete classification of normed groups for which the optimal transport plans, besides being nonbranching, have acyclic support. This seems to initiate a new geometric classifications of certainnormed groups. In the nonbranching case we also provide a global version of calibration, i.e. a generalization of Monge-Kantorovich duality
Three Iterations of (d − 1)-WL Test Distinguish Non Isometric Clouds of d-dimensional Points
No full textThe Weisfeiler-Lehman (WL) test is a fundamental iterative algorithm for checking the isomorphism of graphs. It has also been observed that it underlies the design of several graph neural network architectures, whose capabilities and performance can be understood in terms of the expressive power of this test. Motivated by recent developments in machine learning applications to datasets involving three-dimensional objects, we study when the WL test is {\em complete} for clouds of Euclidean points represented by complete distance graphs, i.e., when it can distinguish, up to isometry, any arbitrary such cloud. Our main result states that the (d − 1)-dimensional WL test is complete for point clouds in
d-dimensional Euclidean space, for any d ≥ 2, and only three iterations of the test suffice. Our result is tight for d = 2, 3. We also observe that the d-dimensional WL test only requires one iteration to achieve completeness
Weak holomorphic structures over Kähler manifolds and strong approximation results of curvatures under constraints
No full text
Going Beyond Counting First Authors in Author Co-citation Analysis
Get PDFThe 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
Get PDF“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
Get PDFWe 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
An integrability result for Lp-vector fields in the plane
No full textWe prove that if , then the divergence of an Lp-vector field V on a 2-dimensional domain is the boundary of an integral 1-current if and only if V can be represented as the rotated gradient for a W1,p-map . Such a result extends to exponents the result on distributional Jacobians of Alberti, Baldo, Orlandi (2003
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