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97
Tangencies between families of disjoint regions in the plane
, 2010
"... Let C be a family of n convex bodies in the plane, which can be decomposed into k subfamilies of pairwise disjoint sets. It is shown that the number of tangencies between the members of C is at most O(kn), and that this bound cannot be improved. If we only assume that our sets are connected and vert ..."
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Cited by 1 (0 self)
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Let C be a family of n convex bodies in the plane, which can be decomposed into k subfamilies of pairwise disjoint sets. It is shown that the number of tangencies between the members of C is at most O(kn), and that this bound cannot be improved. If we only assume that our sets are connected
On the Connected Components of the Space of Line Transversals to a Family of Convex Sets
 Discrete Comput. Geom
, 1997
"... Let L be the space of line transversals to a finite family of pairwise disjoint compact convex sets in R 3 . We prove that each connected component of L can itself be represented as the space of transversals to some finite family of pairwise disjoint compact convex sets. Introduction Let A be a f ..."
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Cited by 3 (2 self)
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Let L be the space of line transversals to a finite family of pairwise disjoint compact convex sets in R 3 . We prove that each connected component of L can itself be represented as the space of transversals to some finite family of pairwise disjoint compact convex sets. Introduction Let A be a
doi:10.1155/2007/26249 Research Article New Inequalities on Fractal Analysis and Their Applications
"... Two new fractal measures M∗s and Ms ∗ are constructed from Minkowski contents M∗s and Ms∗. The properties of these two new measures are studied. We show that the fractal dimensions Dim and ̂δ can be derived from M∗s and Ms∗, respectively. Moreover, some inequalities about the dimension of product se ..."
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Two new fractal measures M∗s and Ms ∗ are constructed from Minkowski contents M∗s and Ms∗. The properties of these two new measures are studied. We show that the fractal dimensions Dim and ̂δ can be derived from M∗s and Ms∗, respectively. Moreover, some inequalities about the dimension of product
POUR L'OBTENTION DU GRADE DE DOCTEUR ÈS SCIENCES PAR
"... 2010 to my wife, Joyce, and my family... Résumé ..."
On the Helly Number for Hyperplane Transversals to Unit Balls
 In Branko Grunbaum Festschrift, G. Kalai and
"... We prove some results about the Hadwiger problem of finding the Helly number for line transversals of disjoint unit disks in the plane, and about its higherdimensional generalization to hyperplane transversals of unit balls in ddimensional Euclidean space. These include (a) a proof of the fact tha ..."
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Cited by 5 (2 self)
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that the Helly number for unit disks in the plane is 5. 1 Introduction In 1955, Hadwiger [11] posed the problem of determining the smallest number k with the property that if every collection of k members of a family of n k pairwise disjoint unit disks in the plane are met by a line, then all
New Techniques for Geographic Routing
, 2006
"... As wireless sensor networks continue to grow in size, we are faced with the prospect of emerging wireless networks with hundreds or thousands of nodes. Geographic routing algorithms are a promising alternative to tradition ad hoc routing algorithms in this new domain for pointtopoint routing, but ..."
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As wireless sensor networks continue to grow in size, we are faced with the prospect of emerging wireless networks with hundreds or thousands of nodes. Geographic routing algorithms are a promising alternative to tradition ad hoc routing algorithms in this new domain for pointtopoint routing
Theoretical Foundations of Equitability and the Maximal Information Coefficient
, 2014
"... The maximal information coefficient (MIC) is a tool for finding the strongest pairwise relationships in a data set with many variables [1]. MIC is useful because it gives similar scores to equally noisy relationships of different types. This property, called equitability, is important for analyzing ..."
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The maximal information coefficient (MIC) is a tool for finding the strongest pairwise relationships in a data set with many variables [1]. MIC is useful because it gives similar scores to equally noisy relationships of different types. This property, called equitability, is important for analyzing
DOI: 10.1007/s0052600302104
, 2003
"... Abstract. We give a new proof of regularity of biharmonic maps from fourdimensional domains into spheres, showing first that the biharmonic map system is equivalent to a set of bilinear identities in divergence form. The method of reverse Hölder inequalities is used next to prove continuity of sol ..."
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Abstract. We give a new proof of regularity of biharmonic maps from fourdimensional domains into spheres, showing first that the biharmonic map system is equivalent to a set of bilinear identities in divergence form. The method of reverse Hölder inequalities is used next to prove continuity
1Generalized Signal Alignment: On the Achievable DoF for MultiUser MIMO TwoWay Relay Channels
"... Abstract—This paper studies the achievable degrees of freedom (DoF) for multiuser multipleinput multipleoutput (MIMO) twoway relay channels, where there are K source nodes, each equipped with M antennas, one relay node, equipped with N antennas, and each source node exchanges independent message ..."
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Abstract—This paper studies the achievable degrees of freedom (DoF) for multiuser multipleinput multipleoutput (MIMO) twoway relay channels, where there are K source nodes, each equipped with M antennas, one relay node, equipped with N antennas, and each source node exchanges independent
Query Evaluation with Constant Delay
"... I am grateful to Luc Segoufin who kindly accepted me to be his PhD student. He introduced me to the problem of query enumeration and encouraged me to look for the answers to all the questions that emerged during our collaboration. He was a truly great advisor, always supportive and available for dis ..."
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Parents, who directed me to follow the scientific path and where fully supportive at all times. Thanks to all the members of LSV – it was a pleasure working with You. I would like to thank the awesome people whom I have been working with in the same office on the 4th floor. Without all the nice riddles
Results 1  10
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