1,721,067 research outputs found
Dimostrare è calcolare
No full text"Questo articolo propone un formalismo per la presentazione di dimostrazioni sia su supporto cartaceo, che su supporto elettronico.
Il lavoro trae ispirazione dall'isomorfismo di Curry-Howard tra dimostrazioni costruttive e programmi funzionali.
Algorithms, unaffected by the Schwarz paradox, approximating tangent planes and area of smooth surfaces via inscribed triangular polyhedra
No full textIn this work we provide an algorithm approximating the tangent bivector at a point of a smooth surface through inscribed triangles converging to the point, regardless their form or position with respect to the tangent plane. This result is obtained approximating Jacobian determinants of smooth plane transformations at a point x through nondegenerate triangles converging to x. We can also approximate the area of a portion of a smooth surface, through a slightly modified notion of area of inscribed triangular polyhedra approaching the surface (without any kind of constraint due to the Schwarz paradox)
The convergence of a gesture recognizer and the shape of a plane gesture
Full text linkIn this work we provide the mathematical framework of !FTL, a new gesture
recognition algorithm. This allows us to algebraically quantify the notion of shape for a
smooth planar curve, inspired by the notion of shape of a triangle given previously by
Lester in this same journal. In particular, we approximate every gesture, considered as a
smooth planar curve, by a polygonal path inscribed on that curve. Then, we consider each
triple of consecutive points on that polygonal path as the vertices of a triangle having a
shape. We show that, as the polygonal line pointwise converges to the original gesture, the
corresponding sequence of shapes pointwise converges to a limiting curve of shapes, that we
consider to be the shape of that gesture. We use the Euclidean metric and the Riemann
integral to measure the distance between the shapes of two gestures. The position, scale and
rotation invariances of the shape of a triangle still hold for the shape of a gesture, and this
provides one of the main achievements of !FTL. Finally, we mention, for further research,
that the two dimensional Euclidean notion of shape can be extended to higher dimensional
settings and more general metrics using Clifford numbers
The shape of planar smooth gestures and the convergence of a gesture recognizer
No full textIn this work we provide the mathematical framework of !FTL, a new gesture recognition algorithm. This allows us to algebraically quantify the notion of shape for a smooth planar curve, inspired by the notion of shape of a triangle given previously by Lester in this same journal. In particular, we approximate every gesture, considered as a smooth planar curve, by a polygonal path inscribed on that curve. Then, we consider each triple of consecutive points on that polygonal path as the vertices of a triangle having a shape. We show that, as the polygonal line pointwise converges to the original gesture, the corresponding sequence of shapes pointwise converges to a limiting curve of shapes, that we consider to be the shape of that gesture. We use the Euclidean metric and the Riemann integral to measure the distance between the shapes of two gestures. The position, scale and rotation invariances of the shape of a triangle still hold for the shape of a gesture, and this provides one of the main achievements of !FTL. Finally, we mention, for further research, that the two dimensional Euclidean notion of shape can be extended to higher dimensional settings and more general metrics using Clifford numbers
A strong comparison principle for the p-laplacian
No full textWe consider weak solutions of the differential inequality of p-Laplacian type -(p)u - f(u) <= - Delta(p)v - f(v) such that u <= v on a smooth bounded domain in RN and either u or v is a weak solution of the corresponding Dirichlet problem with zero boundary condition. Assuming that u < v on the boundary of the domain we prove that u < v, and assuming that u equivalent to v equivalent to 0 on the boundary of the domain we prove u < v unless u equivalent to v. The novelty is that the nonlinearity f is allowed to change sign. In particular, the result holds for the model nonlinearity f(s) = s(q) - lambda s(p-1) with q > p - 1
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
!FTL, an articulation-invariant stroke gesture recognizer with controllable position, scale, and rotation invariances
No full textNearest neighbor classifiers recognize stroke gestures by computing a (dis)similarity between a candidate gesture and a training set based on points, which may require normalization, resampling, and rotation to a reference before processing. To eliminate this expensive preprocessing, this paper introduces a vector-between-vectors recognition where a gesture is defined by a vector based on geometric algebra and performs recognition by computing a novel Local Shape Distance (LSD) between vectors. We mathematically prove the LSD position, scale, and rotation invariance, thus eliminating the preprocessing. To demonstrate the viability of this approach, we instantiate LSD for n=2 to compare !FTL, a 2D stroke-gesture recognizer with respect to P, two state-of-the-art gesture recognizers, on a gesture set typically used for benchmarking. !FTL benefits from a recognition rate similar to 1 and P, but a significant smaller execution time and a lower algorithmic complexity
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
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