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Optimally sparse representation in general (nonorthogonal) dictionaries via ℓ¹ minimization
 PROC. NATL ACAD. SCI. USA 100 2197–202
, 2002
"... Given a ‘dictionary’ D = {dk} of vectors dk, we seek to represent a signal S as a linear combination S = ∑ k γ(k)dk, with scalar coefficients γ(k). In particular, we aim for the sparsest representation possible. In general, this requires a combinatorial optimization process. Previous work considered ..."
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Cited by 626 (37 self)
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Given a ‘dictionary’ D = {dk} of vectors dk, we seek to represent a signal S as a linear combination S = ∑ k γ(k)dk, with scalar coefficients γ(k). In particular, we aim for the sparsest representation possible. In general, this requires a combinatorial optimization process. Previous work
Dictionary of protein secondary structure: pattern recognition of hydrogenbonded and geometrical features
 Biopolymers
, 1983
"... structure ..."
KodairaSpencer theory of gravity and exact results for quantum string amplitudes
 Commun. Math. Phys
, 1994
"... We develop techniques to compute higher loop string amplitudes for twisted N = 2 theories with ĉ = 3 (i.e. the critical case). An important ingredient is the discovery of an anomaly at every genus in decoupling of BRST trivial states, captured to all orders by a master anomaly equation. In a particu ..."
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Cited by 545 (60 self)
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We develop techniques to compute higher loop string amplitudes for twisted N = 2 theories with ĉ = 3 (i.e. the critical case). An important ingredient is the discovery of an anomaly at every genus in decoupling of BRST trivial states, captured to all orders by a master anomaly equation. In a particular realization of the N = 2 theories, the resulting string field theory is equivalent to a topological theory in six dimensions, the Kodaira– Spencer theory, which may be viewed as the closed string analog of the Chern–Simon theory. Using the mirror map this leads to computation of the ‘number ’ of holomorphic curves of higher genus curves in Calabi–Yau manifolds. It is shown that topological amplitudes can also be reinterpreted as computing corrections to superpotential terms appearing in the effective 4d theory resulting from compactification of standard 10d superstrings on the corresponding N = 2 theory. Relations with c = 1 strings are also pointed out.
ERC  A Theory of Equity, Reciprocity and Competition
 FORTHCOMING AMERICAN ECONOMIC REVIEW
, 1999
"... We demonstrate that a simple model, constructed on the premise that people are motivated by both their pecuniary payoff and their relative payoff standing, explains behavior in a wide variety of laboratory games. Included are games where equity is thought to be a factor, such as ultimatum, twoperio ..."
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Cited by 699 (21 self)
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We demonstrate that a simple model, constructed on the premise that people are motivated by both their pecuniary payoff and their relative payoff standing, explains behavior in a wide variety of laboratory games. Included are games where equity is thought to be a factor, such as ultimatum, twoperiod alternating offer, and dictator games; games where reciprocity is thought to play a role, such as the prisoner’s dilemma and the gift exchange game; and games where competitive behavior is observed, such as Bertrand and Cournot markets, and the guessing game.
Planning Algorithms
, 2004
"... This book presents a unified treatment of many different kinds of planning algorithms. The subject lies at the crossroads between robotics, control theory, artificial intelligence, algorithms, and computer graphics. The particular subjects covered include motion planning, discrete planning, planning ..."
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Cited by 1108 (51 self)
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This book presents a unified treatment of many different kinds of planning algorithms. The subject lies at the crossroads between robotics, control theory, artificial intelligence, algorithms, and computer graphics. The particular subjects covered include motion planning, discrete planning, planning under uncertainty, sensorbased planning, visibility, decisiontheoretic planning, game theory, information spaces, reinforcement learning, nonlinear systems, trajectory planning, nonholonomic planning, and kinodynamic planning.
Algorithms for simultaneous sparse approximation. Part II: Convex relaxation
, 2004
"... Abstract. A simultaneous sparse approximation problem requests a good approximation of several input signals at once using different linear combinations of the same elementary signals. At the same time, the problem balances the error in approximation against the total number of elementary signals th ..."
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Cited by 365 (5 self)
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Abstract. A simultaneous sparse approximation problem requests a good approximation of several input signals at once using different linear combinations of the same elementary signals. At the same time, the problem balances the error in approximation against the total number of elementary signals that participate. These elementary signals typically model coherent structures in the input signals, and they are chosen from a large, linearly dependent collection. The first part of this paper proposes a greedy pursuit algorithm, called Simultaneous Orthogonal Matching Pursuit, for simultaneous sparse approximation. Then it presents some numerical experiments that demonstrate how a sparse model for the input signals can be identified more reliably given several input signals. Afterward, the paper proves that the SOMP algorithm can compute provably good solutions to several simultaneous sparse approximation problems. The second part of the paper develops another algorithmic approach called convex relaxation, and it provides theoretical results on the performance of convex relaxation for simultaneous sparse approximation. Date: Typeset on March 17, 2005. Key words and phrases. Greedy algorithms, Orthogonal Matching Pursuit, multiple measurement vectors, simultaneous
Results 1  10
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15,898