The Experts below are selected from a list of 31056 Experts worldwide ranked by ideXlab platform
Boris A Malomed - One of the best experts on this subject based on the ideXlab platform.
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dynamics of one dimensional quantum droplets
Physical Review A, 2018Co-Authors: G E Astrakharchik, Boris A MalomedAbstract:The structure and dynamics of one-dimensional binary Bose gases forming quantum droplets is studied by solving the corresponding amended Gross-Pitaevskii equation. Two physically different regimes are identified, corresponding to small droplets of an approximately Gaussian shape and large ``puddles'' with a broad flat-top plateau. Small droplets collide quasielastically, featuring the solitonlike behavior. On the other hand, large colliding droplets may merge or suffer fragmentation, depending on their relative velocity. The frequency of a breathing excited state of droplets, as predicted by the dynamical Variational Approximation based on the Gaussian ansatz, is found to be in good agreement with numerical results. Finally, the stability diagram for a single droplet with respect to shape excitations with a given wave number is drawn, being consistent with preservation of the Weber number for large droplets.
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numerical realization of the Variational method for generating self trapped beams
Optics Express, 2018Co-Authors: Erick I Duque, Servando Lopezaguayo, Boris A MalomedAbstract:: We introduce a numerical Variational method based on the Rayleigh-Ritz optimization principle for predicting two-dimensional self-trapped beams in nonlinear media. This technique overcomes the limitation of the traditional Variational Approximation in performing analytical Lagrangian integration and differentiation. Approximate soliton solutions of a generalized nonlinear Schrodinger equation are obtained, demonstrating robustness of the beams of various types (fundamental, vortices, multipoles, azimuthons) in the course of their propagation. The algorithm offers possibilities to produce more sophisticated soliton profiles in general nonlinear models.
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staggered and moving localized modes in dynamical lattices with the cubic quintic nonlinearity
Physical Review E, 2008Co-Authors: A Maluckov, Ljupco Hadzievski, Boris A MalomedAbstract:Results of a comprehensive dynamical analysis are reported for several fundamental species of bright solitons in the one-dimensional lattice modeled by the discrete nonlinear Schrodinger equation with the cubic-quintic nonlinearity. Staggered solitons, which were not previously considered in this model, are studied numerically, through the computation of the eigenvalue spectrum for modes of small perturbations, and analytically, by means of the Variational Approximation. The numerical results confirm the analytical predictions. The mobility of discrete solitons is studied by means of direct simulations, and semianalytically, in the framework of the Peierls-Nabarro barrier, which is introduced in terms of two different concepts, free energy and mapping analysis. It is found that persistently moving localized modes may only be of the unstaggered type.
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transition from resonances to bound states in nonlinear systems application to bose einstein condensates
arXiv: Soft Condensed Matter, 2003Co-Authors: Boris A Malomed, Nimrod Moiseyev, Lincoln D Carr, Y B BandAbstract:It is shown using the Gross-Pitaevskii equation that resonance states of Bose-Einstein condensates with attractive interactions can be stabilized into true bound states. A semiclassical Variational Approximation and an independent quantum Variational numerical method are used to calculate the energies (chemical potentials) and linewidths of resonances of the time-independent Gross-Pitaevskii equation; both methods produce similar results. Borders between the regimes of resonances, bound states, and, in two and three dimensions, collapse, are identified.
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stable 2 1 dimensional solitons in a layered medium with sign alternating kerr nonlinearity
Journal of The Optical Society of America B-optical Physics, 2002Co-Authors: I N Towers, Boris A MalomedAbstract:Transverse beam propagation is considered in a layered structure in which Kerr nonlinearity alternates between self-focusing and self-defocusing, which makes it possible to prevent collapse. A structure composed of alternating self-focusing layers with strongly different values of the Kerr coefficient is considered too. By means of both a Variational Approximation (which is implemented in a completely analytical form, including the stability analysis) and direct simulations, it is demonstrated that stable quasi-stationary (2+1)-dimensional soliton beams exist in these media (direct simulations demonstrate stable propagation over a distance exceeding 100 diffraction lengths of the beam). Quasi-stationary cylindrical solitons with intrinsic vorticity exist too, but they all are unstable, splitting into separating zero-vorticity beams.
Flaviana Iurlano - One of the best experts on this subject based on the ideXlab platform.
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Cohesive Fracture in 1D: Quasi-static Evolution and Derivation from Static Phase-Field Models
Archive for Rational Mechanics and Analysis, 2020Co-Authors: Marco Bonacini, Sergio Conti, Flaviana IurlanoAbstract:In this paper we propose a notion of irreversibility for the evolution of cracks in the presence of cohesive forces, which allows for different responses in the loading and unloading processes, motivated by a Variational Approximation with damage models, and we investigate its applicability to the construction of a quasi-static evolution in a simple one-dimensional model. The cohesive fracture model arises naturally via $$\Gamma $$ Γ -convergence from a phase-field model of the generalized Ambrosio-Tortorelli type, which may be used as regularization for numerical simulations.
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Cohesive fracture in 1D: quasi-static evolution and derivation from static phase-field models
Archive for Rational Mechanics and Analysis, 2020Co-Authors: Marco Bonacini, Sergio Conti, Flaviana IurlanoAbstract:In this paper we propose a notion of irreversibility for the evolution of cracks in presence of cohesive forces, which allows for different responses in the loading and unloading processes, motivated by a Variational Approximation with damage models. We investigate its applicability to the construction of a quasi-static evolution in a simple one-dimensional model. The cohesive fracture model arises naturally via Γ-convergence from a phase-field model of the generalized Ambrosio-Tortorelli type, which may be used as regularization for numerical simulations.
David J. Nott - One of the best experts on this subject based on the ideXlab platform.
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on a Variational Approximation based empirical likelihood abc method
arXiv: Methodology, 2020Co-Authors: Sanjay Chaudhuri, David J. Nott, Subhroshekhar Ghosh, Kim Cuc PhamAbstract:Many scientifically well-motivated statistical models in natural, engineering, and environmental sciences are specified through a generative process. However, in some cases, it may not be possible to write down the likelihood for these models analytically. Approximate Bayesian computation (ABC) methods allow Bayesian inference in such situations. The procedures are nonetheless typically computationally intensive. Recently, computationally attractive empirical likelihood-based ABC methods have been suggested in the literature. All of these methods rely on the availability of several suitable analytically tractable estimating equations, and this is sometimes problematic. We propose an easy-to-use empirical likelihood ABC method in this article. First, by using a Variational Approximation argument as a motivation, we show that the target log-posterior can be approximated as a sum of an expected joint log-likelihood and the differential entropy of the data generating density. The expected log-likelihood is then estimated by an empirical likelihood where the only inputs required are a choice of summary statistic, it's observed value, and the ability to simulate the chosen summary statistics for any parameter value under the model. The differential entropy is estimated from the simulated summaries using traditional methods. Posterior consistency is established for the method, and we discuss the bounds for the required number of simulated summaries in detail. The performance of the proposed method is explored in various examples.
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Conditionally structured Variational Gaussian Approximation with importance weights
Statistics and Computing, 2020Co-Authors: Aishwarya Bhaskaran, David J. NottAbstract:We develop flexible methods of deriving Variational inference for models with complex latent variable structure. By splitting the variables in these models into “global” parameters and “local” latent variables, we define a class of Variational Approximations that exploit this partitioning and go beyond Gaussian Variational Approximation. This Approximation is motivated by the fact that in many hierarchical models, there are global variance parameters which determine the scale of local latent variables in their posterior conditional on the global parameters. We also consider parsimonious parametrizations by using conditional independence structure and improved estimation of the log marginal likelihood and Variational density using importance weights. These methods are shown to improve significantly on Gaussian Variational Approximation methods for a similar computational cost. Application of the methodology is illustrated using generalized linear mixed models and state space models.
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high dimensional copula Variational Approximation through transformation
Journal of Computational and Graphical Statistics, 2020Co-Authors: Michael S Smith, Ruben Loaizamaya, David J. NottAbstract:Variational methods are attractive for computing Bayesian inference when exact inference is impractical. They approximate a target distribution—either the posterior or an augmented posterior—using ...
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high dimensional copula Variational Approximation through transformation
arXiv: Computation, 2019Co-Authors: Michael S Smith, Ruben Loaizamaya, David J. NottAbstract:Variational methods are attractive for computing Bayesian inference for highly parametrized models and large datasets where exact inference is impractical. They approximate a target distribution - either the posterior or an augmented posterior - using a simpler distribution that is selected to balance accuracy with computational feasibility. Here we approximate an element-wise parametric transformation of the target distribution as multivariate Gaussian or skew-normal. Approximations of this kind are implicit copula models for the original parameters, with a Gaussian or skew-normal copula function and flexible parametric margins. A key observation is that their adoption can improve the accuracy of Variational inference in high dimensions at limited or no additional computational cost. We consider the Yeo-Johnson and G&H transformations, along with sparse factor structures for the scale matrix of the Gaussian or skew-normal. We also show how to implement efficient reparametrization gradient methods for these copula-based Approximations. The efficacy of the approach is illustrated by computing posterior inference for three different models using six real datasets. In each case, we show that our proposed copula model distributions are more accurate Variational Approximations than Gaussian or skew-normal distributions, but at only a minor or no increase in computational cost.
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gaussian Variational Approximation with a factor covariance structure
Journal of Computational and Graphical Statistics, 2018Co-Authors: Victor M H Ong, David J. Nott, Michael S SmithAbstract:Variational Approximations have the potential to scale Bayesian computations to large datasets and highly parameterized models. Gaussian Approximations are popular, but can be computationally burde...
Raz Kupferman - One of the best experts on this subject based on the ideXlab platform.
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mean field Variational Approximation for continuous time bayesian networks
Journal of Machine Learning Research, 2010Co-Authors: Ido Cohn, Nir Friedman, Tal Elhay, Raz KupfermanAbstract:Continuous-time Bayesian networks is a natural structured representation language for multi-component stochastic processes that evolve continuously over time. Despite the compact representation provided by this language, inference in such models is intractable even in relatively simple structured networks. We introduce a mean field Variational Approximation in which we use a product of inhomogeneous Markov processes to approximate a joint distribution over trajectories. This Variational approach leads to a globally consistent distribution, which can be efficiently queried. Additionally, it provides a lower bound on the probability of observations, thus making it attractive for learning tasks. Here we describe the theoretical foundations for the Approximation, an efficient implementation that exploits the wide range of highly optimized ordinary differential equations (ODE) solvers, experimentally explore characterizations of processes for which this Approximation is suitable, and show applications to a large-scale real-world inference problem.
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mean field Variational Approximation for continuous time bayesian networks
Uncertainty in Artificial Intelligence, 2009Co-Authors: Ido Cohn, Nir Friedman, Tal Elhay, Raz KupfermanAbstract:Continuous-time Bayesian networks is a natural structured representation language for multi-component stochastic processes that evolve continuously over time. Despite the compact representation, inference in such models is intractable even in relatively simple structured networks. Here we introduce a mean field Variational Approximation in which we use a product of inhomogeneous Markov processes to approximate a distribution over trajectories. This Variational approach leads to a globally consistent distribution, which can be efficiently queried. Additionally, it provides a lower bound on the probability of observations, thus making it attractive for learning tasks. We provide the theoretical foundations for the Approximation, an efficient implementation that exploits the wide range of highly optimized ordinary differential equations (ODE) solvers, experimentally explore characterizations of processes for which this Approximation is suitable, and show applications to a large-scale real-world inference problem.
Tokiro Numasawa - One of the best experts on this subject based on the ideXlab platform.
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quantum chaos thermodynamics and black hole microstates in the mass deformed syk model
Journal of High Energy Physics, 2020Co-Authors: Tomoki Nosaka, Tokiro NumasawaAbstract:We study various aspects of the mass deformed SYK model which can escape the interiors of pure boundary state black holes. SYK boundary states are given by a simple local boundary condition on the Majorana fermions and then evolved in Euclidean time in the SYK Hamiltonian. We study the ground state of this mass deformed SYK model in detail. We also use SYK boundary states as a Variational Approximation to the ground state of the mass deformed SYK model. We compare Variational Approximation with the exact ground state results and they showed a good agreement. We also study the time evolution of the mass deformed ground state under the SYK Hamiltonian. We give a gravity interpretation of the mass deformed ground state and its time evolutions. In gravity side, mass deformation gives a way to prepare black hole microstates that are similar to pure boundary state black holes. Escaping protocol on these ground states simply gives a global AdS2 with an IR end of the world brane. We also study the thermodynamics and quantum chaotic properties of this mass deformed SYK model. Interestingly, we do not observe the Hawking Page like phase transition in this model in spite of similarity of the Hamiltonian with eternal traversable wormhole model where we have the phase transition.
