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The role of deliberate practice in the acquisition of expert performance
 Psychological Review
, 1993
"... The theoretical framework presented in this article explains expert performance as the end result of individuals ' prolonged efforts to improve performance while negotiating motivational and external constraints. In most domains of expertise, individuals begin in their childhood a regimen of ef ..."
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Cited by 633 (13 self)
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for a minimum of 10 years. Analysis of expert performance provides unique evidence on the potential and limits of extreme environmental adaptation and learning. Our civilization has always recognized exceptional individuals, whose performance in sports, the arts, and science is vastly superior
Good ErrorCorrecting Codes based on Very Sparse Matrices
, 1999
"... We study two families of errorcorrecting codes defined in terms of very sparse matrices. "MN" (MacKayNeal) codes are recently invented, and "Gallager codes" were first investigated in 1962, but appear to have been largely forgotten, in spite of their excellent properties. The ..."
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Cited by 741 (23 self)
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. The decoding of both codes can be tackled with a practical sumproduct algorithm. We prove that these codes are "very good," in that sequences of codes exist which, when optimally decoded, achieve information rates up to the Shannon limit. This result holds not only for the binarysymmetric channel
From Sparse Solutions of Systems of Equations to Sparse Modeling of Signals and Images
, 2007
"... A fullrank matrix A ∈ IR n×m with n < m generates an underdetermined system of linear equations Ax = b having infinitely many solutions. Suppose we seek the sparsest solution, i.e., the one with the fewest nonzero entries: can it ever be unique? If so, when? As optimization of sparsity is combin ..."
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Cited by 423 (37 self)
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A fullrank matrix A ∈ IR n×m with n < m generates an underdetermined system of linear equations Ax = b having infinitely many solutions. Suppose we seek the sparsest solution, i.e., the one with the fewest nonzero entries: can it ever be unique? If so, when? As optimization of sparsity
Local Exponents of Primitive Digraphs
, 1998
"... A digraph G = (V; E) is primitive if, for some positive integer k, there is a u ! v walk of length k for every pair u; v of vertices of V . The minimum such k is called the exponent of G, denoted exp(G). The local exponent of G at a vertex u 2 V , denoted exp G (u), is the least integer k such that ..."
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of characterizing the exponent set ESn = fexp(G) : G 2 Pn g, where Pn is the set of all primitive digraphs of order n, has been completely settled. We define the i th local exponent set ESn (i) := fexp G (i) : G 2 Pn g for each i, 1 i n, and show that ESn (1) has a characterization which closely parallels
Primitive Digraphs with the Largest Scrambling Index
, 2008
"... The scrambling index of a primitive digraph D is the smallest positive integer k such that for every pair of vertices u and v, there is a vertex w such that we can get to w from u and v in D by directed walks of length k; it is denoted by k(D). In [1] we gave the upper bound on k(D) in terms of the ..."
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Cited by 3 (0 self)
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of the order and the girth of a primitive digraph D. In this paper, we characterize all the primitive digraphs such that the scrambling index is equal to the upper bound.
Expander Codes
 IEEE TRANSACTIONS ON INFORMATION THEORY
, 1996
"... We present a new class of asymptotically good, linear errorcorrecting codes based upon expander graphs. These codes have linear time sequential decoding algorithms, logarithmic time parallel decoding algorithms with a linear number of processors, and are simple to understand. We present both random ..."
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Cited by 346 (10 self)
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We present a new class of asymptotically good, linear errorcorrecting codes based upon expander graphs. These codes have linear time sequential decoding algorithms, logarithmic time parallel decoding algorithms with a linear number of processors, and are simple to understand. We present both
Codes and Decoding on General Graphs
, 1996
"... Iterative decoding techniques have become a viable alternative for constructing high performance coding systems. In particular, the recent success of turbo codes indicates that performance close to the Shannon limit may be achieved. In this thesis, it is showed that many iterative decoding algorithm ..."
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Cited by 359 (1 self)
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Iterative decoding techniques have become a viable alternative for constructing high performance coding systems. In particular, the recent success of turbo codes indicates that performance close to the Shannon limit may be achieved. In this thesis, it is showed that many iterative decoding algorithms are special cases of two generic algorithms, the minsum and sumproduct algorithms, which also include noniterative algorithms such as Viterbi decoding. The minsum and sumproduct algorithms are developed and presented as generalized trellis algorithms, where the time axis of the trellis is replaced by an arbitrary graph, the "Tanner graph". With cyclefree Tanner graphs, the resulting decoding algorithms (e.g., Viterbi decoding) are maximumlikelihood but suffer from an exponentially increasing complexity. Iterative decoding occurs when the Tanner graph has cycles (e.g., turbo codes); the resulting algorithms are in general suboptimal, but significant complexity reductions are possible compared to the cyclefree case. Several performance estimates for iterative decoding are developed, including a generalization of the union bound used with Viterbi decoding and a characterization of errors that are uncorrectable after infinitely many decoding iterations.
On the Girth of Digraphs
 Discrete Math
, 1998
"... It was conjectured by Caccetta and Haggkvist in 1978 that the girth of every digraph with n vertices and minimum outdegree r is at most dn=re. The conjecture was proved for r = 2 by Caccetta and Haggkvist, for r = 3 by Hamidoune and for r = 4; 5 by Ho'ang and Reed. In this paper, the followi ..."
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Cited by 11 (3 self)
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It was conjectured by Caccetta and Haggkvist in 1978 that the girth of every digraph with n vertices and minimum outdegree r is at most dn=re. The conjecture was proved for r = 2 by Caccetta and Haggkvist, for r = 3 by Hamidoune and for r = 4; 5 by Ho'ang and Reed. In this paper
PROBLEMS AND RESULTS ON 3CHROMATIC HYPERGRAPHS AND SOME RELATED QUESTIONS
 COLLOQUIA MATHEMATICA SOCIETATIS JANOS BOLYAI 10. INFINITE AND FINITE SETS, KESZTHELY (HUNGARY)
, 1973
"... A hypergraph is a collection of sets. This paper deals with finite hypergraphs only. The sets in the hypergraph are called edges, the elements of these edges are points. The degree of a point is the number of edges containing it. The hypergraph is runiform if every edge has r points. A hypergraph i ..."
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Cited by 317 (0 self)
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with chromatic number 2 were first investigated systematically by M i 11 e r (who used the term property B) in the case of infinite edges. There now is a large literature of this subject both for finite and infinite sets. The main idea behind our investigations is that being simple or being a clique imposes
Results 1  10
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12,137