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223
A Theory of Program Size Formally Identical to Information Theory
, 1975
"... A new definition of programsize complexity is made. H(A;B=C;D) is defined to be the size in bits of the shortest selfdelimiting program for calculating strings A and B if one is given a minimalsize selfdelimiting program for calculating strings C and D. This differs from previous definitions: (1) ..."
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Cited by 380 (15 self)
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) programs are required to be selfdelimiting, i.e. no program is a prefix of another, and (2) instead of being given C and D directly, one is given a program for calculating them that is minimal in size. Unlike previous definitions, this one has precisely the formal 2 G. J. Chaitin properties of the entropy
Entanglement of Formation of an Arbitrary State of Two Qubits
, 1998
"... The entanglement of a pure state of a pair of quantum systems is defined as the entropy of either member of the pair. The entanglement of formation of a mixed state ρ is defined as the minimum average entanglement of a set of pure states constituting a decomposition of ρ. An earlier paper [Phys. Rev ..."
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Cited by 200 (0 self)
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states of this system and shows how to construct entanglementminimizing purestate decompositions. PACS numbers: 03.65.Bz, 89.70.+c 1 Entanglement is the peculiar feature of quantum mechanics that allows, in principle, feats such as teleportation [1] and dense coding [2] and is what Schrödinger called
Deterministic computation of complexity, information and entropy
 in Proceedings of the IEEE International Symposium on Information Theory, p. 326, Inst. of Electr. and Electron
, 1998
"... Abstract A new measure of string complexity [3] for finite strings is presented based on a specific recursive hierarchical string production process (c.f. [2] ). From the maximal bound we deduce a relationship between complexity and total information content. Given an alphabet A and prefixfree co ..."
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Cited by 4 (1 self)
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Abstract A new measure of string complexity [3] for finite strings is presented based on a specific recursive hierarchical string production process (c.f. [2] ). From the maximal bound we deduce a relationship between complexity and total information content. Given an alphabet A and prefix
Computing Invariant Densities And Metric Entropy
, 1999
"... . We present a method for accurately computing the metric entropy (or, equivalently, the Lyapunov exponent) of the absolutely continuous invariant measure for a piecewise analytic expanding Markov map of the interval. We construct atomic measures M supported on periodic orbits up to period M , and ..."
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. We present a method for accurately computing the metric entropy (or, equivalently, the Lyapunov exponent) of the absolutely continuous invariant measure for a piecewise analytic expanding Markov map of the interval. We construct atomic measures M supported on periodic orbits up to period M
ENTROPY MAXIMISATION PROBLEM FOR QUANTUM AND RELATIVISTIC PARTICLES
"... In this paper we are interested in the maximisation problem for the quantum or nonquantum entropy functional (1.1) H(g):= ..."
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In this paper we are interested in the maximisation problem for the quantum or nonquantum entropy functional (1.1) H(g):=
Entropy based nearest neighbor search in high dimensions
 In Proc. 17th Ann. ACMSIAM Symposium on Discrete Algorithm
, 1195
"... In this paper we study the problem of finding the approximate nearest neighbor of a query point in the high dimensional space, focusing on the Euclidean space. The earlier approaches use localitypreserving hash functions (that tend to map nearby points to the same value) to construct several hash ..."
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Cited by 51 (5 self)
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(1/g). Alternatively we can build a data structure of size Õ(n1/(1−ρ)) to answer queries in Õ(d) time. By applying this analysis to the locality preserving hash functions in [17, 21, 6] and adjusting the parameters we show that the c nearest neighbor can be computed in time Õ(nρ) and near linear
EntropyEnergy Balance in Noisy Quantum Computers
, 2003
"... rmodynamically stable (LTS) if no local modi cation of it yields a state with lower speci c free energy. It can be shown that any GTS state is also LTS, but the converse is generally false. States that are LTS but not GTS are referred to as metastable states. An apt example comes from laser ph ..."
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rmodynamically stable (LTS) if no local modi cation of it yields a state with lower speci c free energy. It can be shown that any GTS state is also LTS, but the converse is generally false. States that are LTS but not GTS are referred to as metastable states. An apt example comes from laser
Learning Decision Rules Using an Evolutionary Algorithm and EntropyBased Discretization
, 1998
"... Introduction One of the most promising directions in Knowledge Discovery in Databases (KDD) [4] is induction of decision rules. During the last two decades many methods e.g. AQfamily [9], CN2 [1] or C4.5 [10] were proposed. The advantages of the rulebased approach to KDD include natural represent ..."
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Introduction One of the most promising directions in Knowledge Discovery in Databases (KDD) [4] is induction of decision rules. During the last two decades many methods e.g. AQfamily [9], CN2 [1] or C4.5 [10] were proposed. The advantages of the rulebased approach to KDD include natural
An Algorithm To Compute The Topological Entropy Of A Unimodal Map
, 1997
"... if f i (c) c: The initial word e 1 : : : e n of the kneading invariant will be denoted by K n (f ). Dene the cutting times [Bruin, 1995] as S 0 = 1 and S k = minfn > S k 1 ; e n 6= e n S k 1 g: Next let M(n) = (m i;j ) n i;j=2 be the n 1 n 1matrix given by m i;j = 8 > > > ..."
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if f i (c) c: The initial word e 1 : : : e n of the kneading invariant will be denoted by K n (f ). Dene the cutting times [Bruin, 1995] as S 0 = 1 and S k = minfn > S k 1 ; e n 6= e n S k 1 g: Next let M(n) = (m i;j ) n i;j=2 be the n 1 n 1matrix given by m i;j = 8 > > >
Results 1  10
of
223