1,720,967 research outputs found
Smooth approximation of bi-Lipschitz orientation-preserving ho- meomorphisms
No full textWe show that a planar bi-Lipschitz orientation-preserving homeomorphism can be approximated in the W1,p
norm, together with its inverse, with an orientation-preserving homeomorphism which is piecewise affine or smooth
Eulerian Calculus for the Displacement Convexity in the Wasserstein Distance
No full textIn this paper we give a new proof of the (strong) displacement convexity of a class of integral functionals defined on a compact Riemannian manifold satisfying a lower Ricci curvature bound. Our approach does not rely on existence and regularity results for optimal transport maps on Riemannian manifolds, but it is based on the Eulerian point of view recently introduced by Otto and Westdickenberg [SIAM J. Math. Anal., 37 (2005), pp. 1227–1255] and on the metric characterization of the gradient flows generated by the functionals in the Wasserstein space
On Sudakov's type decomposition of transference plans with norm costs
Get PDFWe consider the original strategy proposed by Sudakov for solving the Monge transportation problem with norm cost \d{\cdot}\min \bigg\{ \int \d{\mathtt T(x) - x} d\mu(x), \ \mathtt T : \R^d \to \R^d, \ \nu = \mathtt T_\# \mu \bigg\},with , probability measures in and absolutely continuous w.r.t. \LL. The key idea in this approach is to decompose (via disintegration of measures) the Kantorovich optimal transportation problem into a family of transportation problems in Z_\a\times\R^d, where \{Z_\a\}_{\a\in\A} \subset \R^d are disjoint regions such that the construction of an optimal map \mathtt T_\a : Z_\a \to \R^d is simpler than in the original problem, and then to obtain by piecing together the maps \mathtt T_\a.
When the norm \d{\cdot} is strictly convex \cite{sudak}, the sets Z_\a are a family of -dimensional segments determined by the Kantorovich potential called optimal rays, while the existence of the map \mathtt T_\a is straightforward provided one can show that the disintegration of \LL (and thus of ) on such segments is absolutely continuous w.r.t. the -dimensional Hausdorff measure \cite{Car:strictly}.
When the norm \d{\cdot} is not strictly convex, the main problems in this kind of approach are two: first, to identify a suitable family of regions \{Z_\a\}_{\a\in\A} on which the transport problem decomposes into simpler ones, and then to prove the existence of optimal maps.
In this paper we show how these difficulties can be overcome, and that the original idea of Sudakov can be successfully implemented.
The results yield a complete characterization of the Kantorovich optimal transportation problem, whose straightforward corollary is the solution of the Monge problem in each set Z_\a and then in . The strategy is sufficiently powerful to be applied to other optimal transportation problems.
The analysis requires \begin{enumerate}\item the study of the transportation problem on directed locally affine partitions \{Z\ka,C\ka\}_{k,\a} of , i.e. sets Z\ka \subset \R^d which are relatively open in their -dimensional affine hull and on which the transport occurs only along directions belonging to a cone C\ka;\item the proof of the absolute continuity w.r.t. the suitable -dimensional Hausdorff measure of the disintegration of \LL on these directed locally affine partitions;\item the definition of cyclically connected sets w.r.t. a family of transportation plans with finite cone costs;\item the proof of the existence of cyclically connected directed locally affine partitions for transport problems with cost functions which are indicator functions of cones and no potentials can be constructed.
\end{enumerate
Smooth approximation of bi-Lipschitz orientation-preserving homeomorphisms
Get PDFWe show that a planar bi-Lipschitz orientation-preserving homeomorphism can be approximated in the W1,p
norm, together with its inverse, with an orientation-preserving homeomorphism which is piecewise affine or smooth
Deterministic particle approximation of aggregation diffusion equations with nonlinear mobility
No full textWe consider a class of aggregation-diffusion equations on unbounded one-dimensional domains with Lipschitz nonincreasing mobility function. We show strong L1-convergence of a suitable deterministic particle approximation to weak solutions of a class aggregation-diffusion PDEs (coinciding with the classical ones in the no vacuum regions) for any bounded initial data of finite energy. In order to prove well-posedness and convergence of the scheme with no BV or no vacuum assumptions and overcome the issues posed in this setting by the presence of a mobility function, we improve and strengthen the techniques introduced in [S. Daneri, E. Radici and E. Runa, Deterministic particle approximation of aggregation-diffusion equations on unbounded domains, J. Differential Equations 312 (2020) 474-517]
Deterministic particle approximation of aggregation-diffusion equations on unbounded domains
No full textWe consider a one-dimensional aggregation-diffusion equation, which is the gradient flow in the Wasserstein space of a functional with competing attractive-repulsive interactions. We prove that the fully deterministic particle approximations with piecewise constant densities introduced in [25] starting from general bounded initial densities converge strongly in L1 to the unique bounded weak solution of the PDE. In particular, the result is achieved in unbounded domains and for arbitrary nonnegative bounded initial densities, thus extending the results in [30,34,35] (in which a no-vacuum condition is required) and giving an alternative approach to [10] in the one-dimensional case, including also subquadratic and superquadratic diffusions. We provide also numerical simulations for the approximation scheme
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
- …
