1,721,002 research outputs found
Cortically Based Optimal Transport
Full text linkWe introduce a model for image morphing in the primary visual cortex V1 to perform completion of missing images in time. We model the output of simple cells through a family of Gabor filters and the propagation of the neural signal accordingly to the functional geometry induced by horizontal connectivity. Then we model the deformation between two images as a path relying two different outputs. This path is obtained by optimal transport considering the Wasserstein distance geodesics associated to some probability measures naturally induced by the outputs on V1. The frame of Gabor filters allows to project back the output path, therefore obtaining an associated image stimulus deformation. We perform a numerical implementation of our cortical model, assessing its ability in reconstructing rigid motions of simple shapes
Intelligent Machines and Mathematics
Full text linkL'attività è stata realizzata come Giornata Indam. Nell’ultima decade le procedure di apprendimento automatico (Machine Learning e in particolare Deep Learning) hanno fatto importanti e significativi progressi che hanno avuto un enorme impatto nella tecnologia e nella società. Lo scopo dell'incontro è di avere una presentazione di alcuni aspetti e problemi dell'intelligenza artificiale che sono legati alla matematica, sia nelle loro declinazioni teoriche che applicative
Geometric and Harmonic Analysis with Interdisciplinary Applications
No full textProgetto di mobilità internazionale con una rete di 19 tra università e centri di ricerca. Il nodo coordinatore è l'università di bolonga. Il Principal coordinator contact è la Professoressa Giovanna Citti del dipartimento di matematica dell'università di bologna
Uniform Gaussian Bounds for Subelliptic Heat Kernels and an Application to the Total Variation Flow of Graphs over Carnot Groups
Full text linkIn this paper we study heat kernels associated with a Carnot
group G, endowed with a family of collapsing left-invariant
Riemannian metrics σε which converge in the Gromov-
Hausdorff sense to a sub-Riemannian structure on G as ε→
0. The main new contribution are Gaussian-type bounds on
the heat kernel for the σε metrics which are stable as ε→0
and extend the previous time-independent estimates in [16].
As an application we study well posedness of the total variation
flow of graph surfaces over a bounded domain in a step
two Carnot group (G; σε ). We establish interior and boundary
gradient estimates, and develop a Schauder theory which are
stable as ε → 0. As a consequence we obtain long time
existence of smooth solutions of the sub-Riemannian flow
(ε = 0), which in turn yield sub-Riemannian minimal surfaces
as t → ∞
Geometric and Harmonic Analysis with Interdisciplinary Applications
No full textGHAIA will promote excellence through mobility to the world leader Universities in pure and applied mathematical
research: Princeton University, Mit, Yale, Johns Hopkins, the Universities of California, of Texas, of Houston, of
Pittsburgh, the Washington University (St. Louis), and the Worchester Polytechnical Institute, the Academia Sinica, the
University of Buenos Aires have joined the consortium. European researchers will have the extraordinary opportunity
to work in their exciting environment as well as receiving visiting researchers from south America. Moreover two
selected enterprises have joined the consortium, allowing intersectorial mobility: Marposs and GMV, leaders in the
strategic sectors of EU industry of precision equipments for automatic inspection, and of satellite navigation
SUB-RIEMANNIAN HEAT KERNELS AND MEAN CURVATURE FLOW OF GRAPHS.
Full text linkWe introduce a sub-Riemannian analogue of the Bence-Merriman-Osher algorithm (Merriman et al., 1992 [42]) and show that it leads to weak solutions of the horizontal mean curvature flow of graphs over sub-Riemannian Carnot groups. The proof follows the nonlinear semi-group theory approach originally introduced by L.C. Evans (1993) [27] in the Euclidean setting and is based on new results on the relation between sub-Riemannian heat flows of characteristic functions of subgraphs and the horizontal mean curvature of the corresponding graph
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
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