The Experts below are selected from a list of 34011 Experts worldwide ranked by ideXlab platform
Jon A. Wellner - One of the best experts on this subject based on the ideXlab platform.
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Log-Concavity and Strong Log-Concavity: a review.
Statistics surveys, 2014Co-Authors: Adrien Saumard, Jon A. WellnerAbstract:We review and formulate results concerning log-Concavity and strong-log-Concavity in both discrete and continuous settings. We show how preservation of log-Concavity and strongly log-Concavity on ℝ under convolution follows from a fundamental monotonicity result of Efron (1969). We provide a new proof of Efron's theorem using the recent asymmetric Brascamp-Lieb inequality due to Otto and Menz (2013). Along the way we review connections between log-Concavity and other areas of mathematics and statistics, including concentration of measure, log-Sobolev inequalities, convex geometry, MCMC algorithms, Laplace approximations, and machine learning.
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Strong Log-Concavity is Preserved by Convolution
High Dimensional Probability VI, 2013Co-Authors: Jon A. WellnerAbstract:We review and formulate results concerning strong-log-Concavity in both discrete and continuous settings. Although four different proofs of preservation of strong log-Concavity are known in the discrete setting (where strong log-Concavity is known as “ultra-log-Concavity”), preservation of strong logConcavity under convolution has apparently not been investigated previously in the continuous case.
William Y. C. Chen - One of the best experts on this subject based on the ideXlab platform.
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INTERLACING LOG-Concavity OF THE BOROS-MOLL POLYNOMIALS
Pacific Journal of Mathematics, 2011Co-Authors: William Y. C. Chen, Larry X. W. Wang, Ernest X. W. XiaAbstract:We introduce the notion of interlacing log-Concavity of a polynomial sequence {Pm(x)}m≥0, where Pm(x) is a polynomial of degree m with positive coefficients. This sequence is said to be interlacingly log-concave if the ratios of consecutive coefficients of Pm(x) interlace the ratios of consecutive coefficients of Pm+1(x) for any m ≥ 0. The interlacing log-Concavity of a sequence of polynomials is stronger than the log-Concavity of the polynomials themselves. We show that the Boros-Moll polynomials are interlacingly log-concave. Furthermore, we give a sufficient condition for the interlacing log-Concavity which implies that some classical combinatorial polynomials are interlacingly log-concave.
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Interlacing Log-Concavity of the Boros-Moll Polynomials
arXiv: Combinatorics, 2010Co-Authors: William Y. C. Chen, Larry X. W. Wang, Ernest X. W. XiaAbstract:We introduce the notion of interlacing log-Concavity of a polynomial sequence $\{P_m(x)\}_{m\geq 0}$, where $P_m(x)$ is a polynomial of degree m with positive coefficients $a_{i}(m)$. This sequence of polynomials is said to be interlacing log-concave if the ratios of consecutive coefficients of $P_m(x)$ interlace the ratios of consecutive coefficients of $P_{m+1}(x)$ for any $m\geq 0$. Interlacing log-Concavity is stronger than the log-Concavity. We show that the Boros-Moll polynomials are interlacing log-concave. Furthermore we give a sufficient condition for interlacing log-Concavity which implies that some classical combinatorial polynomials are interlacing log-concave.
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The reverse ultra log-Concavity of the Boros-Moll polynomials
Proceedings of the American Mathematical Society, 2009Co-Authors: William Y. C. ChenAbstract:We prove the reverse ultra log-Concavity of the Boros-Moll polynomials. We further establish an inequality which implies the log-Concavity of the sequence {i!di(m)} for any m > 2, where d i (m) are the coefficients of the Boros-Moll polynomials P m (a). This inequality also leads to the fact that in the asymptotic sense, the Boros-Moll sequences are just on the borderline between ultra log-Concavity and reverse ultra log-Concavity. We propose two conjectures on the log-Concavity and reverse ultra log-Concavity of the sequence {di-i(m)d i+ i(m)/d i (m) 2 } for m > 2.
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The Reverse Ultra Log-Concavity of the Boros-Moll Polynomials
arXiv: Combinatorics, 2008Co-Authors: William Y. C. ChenAbstract:We prove the reverse ultra log-Concavity of the Boros-Moll polynomials. We further establish an inequality which implies the log-Concavity of the sequence $\{i!d_i(m)\}$ for any $m\geq 2$, where $d_i(m)$ are the coefficients of the Boros-Moll polynomials $P_m(a)$. This inequality also leads to the fact that in the asymptotic sense, the Boros-Moll sequences are just on the borderline between ultra log-Concavity and reverse ultra log-Concavity. We propose two conjectures on the log-Concavity and reverse ultra log-Concavity of the sequence $\{d_{i-1}(m) d_{i+1}(m)/d_i(m)^2\}$ for $m\geq 2$.
Adrien Saumard - One of the best experts on this subject based on the ideXlab platform.
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Log-Concavity and Strong Log-Concavity: a review.
Statistics surveys, 2014Co-Authors: Adrien Saumard, Jon A. WellnerAbstract:We review and formulate results concerning log-Concavity and strong-log-Concavity in both discrete and continuous settings. We show how preservation of log-Concavity and strongly log-Concavity on ℝ under convolution follows from a fundamental monotonicity result of Efron (1969). We provide a new proof of Efron's theorem using the recent asymmetric Brascamp-Lieb inequality due to Otto and Menz (2013). Along the way we review connections between log-Concavity and other areas of mathematics and statistics, including concentration of measure, log-Sobolev inequalities, convex geometry, MCMC algorithms, Laplace approximations, and machine learning.
Mohamed S. Kamel - One of the best experts on this subject based on the ideXlab platform.
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ICPR (3) - Shape retrieval using Concavity trees
2004Co-Authors: O. El Badawy, Mohamed S. KamelAbstract:Concavity trees are well-known abstract structures. This paper proposes a new shape-based image retrieval method based on Concavity trees. The proposed method has two main components. The first is an efficient (in terms of space and time) contour-based Concavity tree extraction algorithm. The second component is a recursive Concavity-tree matching algorithm that returns a distance between two trees. We demonstrate that Concavity trees are able to boost the retrieval performance of two feature sets by at least 15% when tested on a database of 625 silhouette images.
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SSPR/SPR - Matching Concavity Trees
Lecture Notes in Computer Science, 2004Co-Authors: Ossama El Badawy, Mohamed S. KamelAbstract:Concavity trees are structures for 2-D shape representation. In this paper, we present a new recursive method for Concavity tree matching that returns the distance between two attributed Concavity trees. The matching is based both on the structure of the tree as well as on the attributes stored at each node. Moreover, the method can be implemented on parallel architectures, and it supports occluded and partial matching. To the best of our knowledge, this is the first work to detail a method for Concavity tree matching. We test our method on 625 silhouettes in the context of shape-based nearest-neighbour retrieval.
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ICPR (3) - Shape representation using Concavity graphs
Object recognition supported by user interaction for service robots, 1Co-Authors: O. El Badawy, Mohamed S. KamelAbstract:In this paper, a new graph data structure for 2-D shape representation is proposed. The new structure is called a Concavity graph, and is an evolution from the already known "Concavity tree". Even though a Concavity graph bears a fundamental resemblance to a Concavity tree, the former is able to describe the shape of multiple objects in an image and their spatial configuration, and is hence inherently more complex. The aim of Concavity graphs is two-fold: first we want to analyze the patterns in a multi-object image in a way that will (1) provide better representation of their shapes, and (2) convey useful information about how they "interact" together. Second, we want our analysis technique to facilitate similarity matching between two images. This paper introduces the new structure and outlines how it can be used for shape representation as well as similarity matching.
Pier Luigi Papini - One of the best experts on this subject based on the ideXlab platform.
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A weakening of Schur-Concavity for copulas
Fuzzy Sets and Systems, 2007Co-Authors: Fabrizio Durante, Pier Luigi PapiniAbstract:The class of copulas satisfying a new property called weak Schur-Concavity is introduced and studied and the relationships of this property with other known notions of Concavity are investigated.
