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30
PseudoRandom Generation from OneWay Functions
 PROC. 20TH STOC
, 1988
"... Pseudorandom generators are fundamental to many theoretical and applied aspects of computing. We show howto construct a pseudorandom generator from any oneway function. Since it is easy to construct a oneway function from a pseudorandom generator, this result shows that there is a pseudorandom gene ..."
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Cited by 729 (21 self)
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Pseudorandom generators are fundamental to many theoretical and applied aspects of computing. We show howto construct a pseudorandom generator from any oneway function. Since it is easy to construct a oneway function from a pseudorandom generator, this result shows that there is a pseudorandom generator iff there is a oneway function.
Quantum Algorithm For Hilberts Tenth Problem
 Int.J.Theor.Phys
, 2003
"... We explore in the framework of Quantum Computation the notion of Computability, which holds a central position in Mathematics and Theoretical Computer Science. A quantum algorithm for Hilbert’s tenth problem, which is equivalent to the Turing halting problem and is known to be mathematically noncomp ..."
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Cited by 60 (10 self)
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We explore in the framework of Quantum Computation the notion of Computability, which holds a central position in Mathematics and Theoretical Computer Science. A quantum algorithm for Hilbert’s tenth problem, which is equivalent to the Turing halting problem and is known to be mathematically noncomputable, is proposed where quantum continuous variables and quantum adiabatic evolution are employed. If this algorithm could be physically implemented, as much as it is valid in principle—that is, if certain hamiltonian and its ground state can be physically constructed according to the proposal—quantum computability would surpass classical computability as delimited by the ChurchTuring thesis. It is thus argued that computability, and with it the limits of Mathematics, ought to be determined not solely by Mathematics itself but also by Physical Principles. 1
Stability of Tsallis entropy and instabilities of Rényi and normalized Tsallis entropies: A basis for qexponential distributions
 Nonextensive Statistical Mechanics and Its Applications
, 2001
"... A basis for qexponential distributions ..."
Mutual information of population codes and distance measures in probability space
 Phys Rev Lett
, 2001
"... We studied the mutual information between a stimulus and a large system consisting of stochastic, statistically independent elements that respond to a stimulus. The Mutual Information (MI) of the system saturates exponentially with system size. A theory of the rate of saturation of the MI is develop ..."
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Cited by 13 (0 self)
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We studied the mutual information between a stimulus and a large system consisting of stochastic, statistically independent elements that respond to a stimulus. The Mutual Information (MI) of the system saturates exponentially with system size. A theory of the rate of saturation of the MI is developed. We show that this rate is controlled by a distance function between the response probabilities induced by different stimuli. This function, which we term the Confusion Distance between two probabilities, is related to the Renyi αInformation.
Random Heuristic Search
 Theoretical Computer Science
, 1999
"... There is a developing theory of growing power which, at its current stage of development (indeed, for a number of years now), speaks to qualitative and quantitative aspects of search strategies. Although it has been specialized and applied to genetic algorithms, it's implications and applicability a ..."
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Cited by 11 (1 self)
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There is a developing theory of growing power which, at its current stage of development (indeed, for a number of years now), speaks to qualitative and quantitative aspects of search strategies. Although it has been specialized and applied to genetic algorithms, it's implications and applicability are far more general. This paper deals with the broad outlines of the theory, introducing basic principles and results rather than analyzing or specializing to particular algorithms. A few specific examples are included for illustrative purposes, but the theory's basic structure, as opposed to applications, remains the focus. Key words: Random Heuristic Search, Modeling Evolutionary Algorithms, Degenerate Royal Road Functions. 1 Introduction Vose [20] introduced a rigorous dynamical system model for the binary representation genetic algorithm with proportional selection, mutation determined by a rate, and onepoint crossover, using the simplifying assumption of an infinite population. 1 ...
Universal geometric approach to uncertainty, entropy and infromation, Phys. Rev. A 59
, 1999
"... It is shown that a unique measure of volume is associated with any statistical ensemble, which directly quantifies the inherent spread or localisation of the ensemble. It is applicable whether the ensemble is classical or quantum, continuous or discrete, and may be derived from a small number of the ..."
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Cited by 6 (0 self)
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It is shown that a unique measure of volume is associated with any statistical ensemble, which directly quantifies the inherent spread or localisation of the ensemble. It is applicable whether the ensemble is classical or quantum, continuous or discrete, and may be derived from a small number of theoryindependent geometric postulates. Remarkably, this unique ensemble volume is proportional to the exponential of the ensemble entropy, and hence provides a novel geometric characterisation of the latter quantity. Applications include unified volumebased derivations of the Holevo and Shannon bounds in quantum and classical information theory, a precise geometric interpretation of thermodynamic entropy for equilibrium ensembles, a geometric derivation of semiclassical uncertainty relations, a new means for defining classical and quantum localization for arbitrary evolution processes, a geometric interpretation of relative entropy, and a new proposed definition for the spotsize of an optical beam. Advantages of ensemble volume over other measures of localization (rootmeansquare deviation, Renyi entropies, and inverse participation ratio) are discussed. PACS Numbers: 03.65.Bz, 03.67.a, 05.45+b, 42.60.Jf I
Tsallis Entropy and Jaynes' Information Theory Formalism
 Braz. J. Phys
, 1999
"... Introduction In spite of its great success, the Statistical Mechanics paradigm based on the BoltzmannGibbs entropy measure seems to be inadequate to deal with many interesting physical scenarios #1,2,3#. Astronomical selfgravitating systems constitute an important illustrative example of these di ..."
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Cited by 6 (0 self)
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Introduction In spite of its great success, the Statistical Mechanics paradigm based on the BoltzmannGibbs entropy measure seems to be inadequate to deal with many interesting physical scenarios #1,2,3#. Astronomical selfgravitating systems constitute an important illustrative example of these di#culties #4#. A considerable e#ort has been devoted by astrophysicists to develop a thermostatistical description of selfgravitating systems along the lines of standard Statistical Mechanics. The failure of those attemps was due to the nonextensivity e#ects associated with the long range of the gravitational interaction #4#. Ten years ago Tsallis proposed a generalization of the celebrated BoltzmannGibbs #BG# entropic measure #5#. The new entropy functional introduced by Tsallis #5# along with its associated generalized thermostatistics #6, 7# is nowadays being hailed as the possible basis of a theorethical framework aproppriate to deal with nonextensive settings #8,9,10#. This ent
Families of Alpha Beta and GammaDivergences: Flexible and Robust Measures of Similarities
, 2010
"... ..."
Particle description of zero energy vacuum. II. Basic vacuum systems
, 2001
"... We describe vacuum as a system of virtual particles, some of which have negative energies. Any system of vacuum particles is a part of a keneme, i.e. of a system of n particles which can, without violating the conservation laws, annihilate in the strict sense of the word (transform into nothing). A ..."
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Cited by 2 (0 self)
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We describe vacuum as a system of virtual particles, some of which have negative energies. Any system of vacuum particles is a part of a keneme, i.e. of a system of n particles which can, without violating the conservation laws, annihilate in the strict sense of the word (transform into nothing). A keneme is a homogeneous system, i.e. its state is invariant by all transformations of the invariance group. But a homogeneous system is not necessarily a keneme. In the simple case of a spin system, where the invariance group is SU(2), a homogeneous system is a system whose total spin is unpolarized; a keneme is a system whose total spin is zero. The state of a homogeneous system is described by a statistical operator with infinite trace (von Neumann), to which corresponds a characteristic distribution. The characteristic distributions of the homogeneous systems of vacuum are defined and studied. Finally it is shown how this description of vacuum can be used to solve the frame problem posed in (I). 1