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» Explicit constructions of RIP matrices and related problems
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BSL
2000
153views more  BSL 2000»
13 years 7 months ago
Combinatorics with definable sets: Euler characteristics and Grothendieck rings
We recall the notions of weak and strong Euler characteristics on a first order structure and make explicit the notion of a Grothendieck ring of a structure. We define partially or...
Jan Krajícek, Thomas Scanlon
KR
2000
Springer
13 years 11 months ago
Representing and Aggregating Conflicting Beliefs
We consider the two-fold problem of representing collective beliefs and aggregating these beliefs. We propose a novel representation for collective beliefs that uses modular, tran...
Pedrito Maynard-Reid II, Daniel J. Lehmann
CORR
2012
Springer
218views Education» more  CORR 2012»
12 years 3 months ago
On the Hardness of Welfare Maximization in Combinatorial Auctions with Submodular Valuations
We present a new type of monotone submodular functions: multi-peak submodular functions. Roughly speaking, given a family of sets F, we construct a monotone submodular function f ...
Shahar Dobzinski, Jan Vondrák
FOCS
2004
IEEE
13 years 11 months ago
Extracting Randomness Using Few Independent Sources
In this work we give the first deterministic extractors from a constant number of weak sources whose entropy rate is less than 1/2. Specifically, for every > 0 we give an expl...
Boaz Barak, Russell Impagliazzo, Avi Wigderson
ADCM
2007
134views more  ADCM 2007»
13 years 7 months ago
Barycentric coordinates for convex sets
In this paper we provide an extension of barycentric coordinates from simplices to arbitrary convex sets. Barycentric coordinates over convex 2D polygons have found numerous appli...
Joe D. Warren, Scott Schaefer, Anil N. Hirani, Mat...