The Experts below are selected from a list of 1380 Experts worldwide ranked by ideXlab platform
Cristian V Ciobanu - One of the best experts on this subject based on the ideXlab platform.
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the Incomplete Beta Function law for parallel tempering sampling of classical canonical systems
Journal of Chemical Physics, 2004Co-Authors: Cristian Predescu, M Predescu, Cristian V CiobanuAbstract:We show that the acceptance probability for swaps in the parallel tempering Monte Carlo method for classical canonical systems is given by a universal Function that depends on the average statistical fluctuations of the potential and on the ratio of the temperatures. The law, called the Incomplete Beta Function law, is valid in the limit that the two temperatures involved in swaps are close to one another. An empirical version of the law, which involves the heat capacity of the system, is developed and tested on a Lennard-Jones cluster. We argue that the best initial guess for the distribution of intermediate temperatures for parallel tempering is a geometric progression and we also propose a technique for the computation of optimal temperature schedules. Finally, we demonstrate that the swap efficiency of the parallel tempering method for condensed-phase systems decreases naturally to zero at least as fast as the inverse square root of the dimensionality of the physical system.
Enrique Arribas - One of the best experts on this subject based on the ideXlab platform.
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nonlinear oscillator with power form elastic term fourier series expansion of the exact solution
Communications in Nonlinear Science and Numerical Simulation, 2015Co-Authors: Augusto Belendez, Jorge Frances, Tarsicio Belendez, Sergio Bleda, Carolina Pascual, Enrique ArribasAbstract:Abstract A family of conservative, truly nonlinear, oscillators with integer or non-integer order nonlinearity is considered. These oscillators have only one odd power-form elastic-term and exact expressions for their period and solution were found in terms of Gamma Functions and a cosine-Ateb Function, respectively. Only for a few values of the order of nonlinearity, is it possible to obtain the periodic solution in terms of more common Functions. However, for this family of conservative truly nonlinear oscillators we show in this paper that it is possible to obtain the Fourier series expansion of the exact solution, even though this exact solution is unknown. The coefficients of the Fourier series expansion of the exact solution are obtained as an integral expression in which a regularized Incomplete Beta Function appears. These coefficients are a Function of the order of nonlinearity only and are computed numerically. One application of this technique is to compare the amplitudes for the different harmonics of the solution obtained using approximate methods with the exact ones computed numerically as shown in this paper. As an example, the approximate amplitudes obtained via a modified Ritz method are compared with the exact ones computed numerically.
W. T. Sulaiman - One of the best experts on this subject based on the ideXlab platform.
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Functional Inequalities for Incomplete Beta Function
Journal of the Indian Mathematical Society, 2014Co-Authors: W. T. SulaimanAbstract:In the present paper several new integral inequalities concerning the Incomplete Beta Function are proved.
Jesus S. Dehesa - One of the best experts on this subject based on the ideXlab platform.
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Generalization of Stam Inequalities leading to generalized Fisher-Rényi Complexity Measures
2018Co-Authors: Steeve Zozor, David Puertas-centeno, Jesus S. DehesaAbstract:Information-theoretic inequalities play a fundamental role in numerous scientific and technological areas: they generally express the impossibility to have a complete description of a system via a finite number of information measures. They gave rise to the design of various quantifiers of the internal complexity of a (quantum) system. In this presentation, I will introduce a parametric Fisher–Rényi complexity, named (p, β, λ)-Fisher–Rényi complexity, based on both an extension of the Fisher information and the Rényi entropies of a probability density Function ρ characteristic of the system. This complexity measure quantifies the balance of the spreading and the gradient contents of ρ, and has the three main properties of a statistical complexity: the invariance under translation and scaling transformations, and a universal bounding from below. The latter is precisely on the core of this presentation, generalizing the so-called Stam inequality, which lowerbounds the product of the Shannon entropy power and the Fisher information of a probability density Function. An extension of this inequality was already proposed by Bercher and Lutwak, a particular case of the general one, where the three parameters are linked, allowing to determine the sharp lower bound and the associated probability density with minimal complexity. Using the notion of differential-escort deformation, we are able to determine the sharp bound of the complexity measure even when the three parameters are decoupled. In addition, we determine the probability distribution that saturates the inequality, this last one involving an inverse Incomplete Beta Function. Finally, the complexity measure is calculated for various quantum-mechanical states of the harmonic and hydrogenic systems, which are the two main prototypes of physical systems subject to a central potential.
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On Generalized Stam Inequalities and Fisher-Rényi Complexity Measures
Entropy, 2017Co-Authors: Steeve Zozor, David David Puertas-centeno, Jesus S. DehesaAbstract:Information-theoretic inequalities play a fundamental role in numerous scientific and technological areas (e.g., estimation and communication theories, signal and information processing, quantum physics,... ) as they generally express the impossibility to have a complete description of a system via a finite number of information measures. In particular, they gave rise to the design of various quantifiers (statistical complexity measures) of the internal complexity of a (quantum) system. In this paper, we introduce a three-parametric Fisher–Rényi complexity, named (p, β, λ)-Fisher–Rényi complexity, based on both a two-parametic extension of the Fisher information and the Rényi entropies of a probability density Function ρ characteristic of the system. This complexity measure quantifies the combined balance of the spreading and the gradient contents of ρ, and has the three main properties of a statistical complexity: the invariance under translation and scaling transformations, and a universal bounding from below. The latter is proved by generalizing the Stam inequality, which lowerbounds the product of the Shannon entropy power and the Fisher information of a probability density Function. An extension of this inequality was already proposed by Bercher and Lutwak, a particular case of the general one, where the three parameters are linked, allowing to determine the sharp lower bound and the associated probability density with minimal complexity. Using the notion of differential-escort deformation, we are able to determine the sharp bound of the complexity measure even when the three parameters are decoupled (in a certain range). We determine as well the distribution that saturates the inequality: the (p, β, λ)-Gaussian distribution, which involves an inverse Incomplete Beta Function. Finally, the complexity measure is calculated for various quantum-mechanical states of the harmonic and hydrogenic systems, which are the two main prototypes of physical systems subject to a central potential.
Cristian Predescu - One of the best experts on this subject based on the ideXlab platform.
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the Incomplete Beta Function law for parallel tempering sampling of classical canonical systems
Journal of Chemical Physics, 2004Co-Authors: Cristian Predescu, M Predescu, Cristian V CiobanuAbstract:We show that the acceptance probability for swaps in the parallel tempering Monte Carlo method for classical canonical systems is given by a universal Function that depends on the average statistical fluctuations of the potential and on the ratio of the temperatures. The law, called the Incomplete Beta Function law, is valid in the limit that the two temperatures involved in swaps are close to one another. An empirical version of the law, which involves the heat capacity of the system, is developed and tested on a Lennard-Jones cluster. We argue that the best initial guess for the distribution of intermediate temperatures for parallel tempering is a geometric progression and we also propose a technique for the computation of optimal temperature schedules. Finally, we demonstrate that the swap efficiency of the parallel tempering method for condensed-phase systems decreases naturally to zero at least as fast as the inverse square root of the dimensionality of the physical system.
