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72
Cluster Expansions And Iterative Scaling For Maximum Entropy Language Models
 Maximum Entropy and Bayesian Methods
, 1995
"... . The maximum entropy method has recently been successfully introduced to a variety of natural language applications. In each of these applications, however, the power of the maximum entropy method is achieved at the cost of a considerable increase in computational requirements. In this paper we pre ..."
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Cited by 20 (1 self)
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. The maximum entropy method has recently been successfully introduced to a variety of natural language applications. In each of these applications, however, the power of the maximum entropy method is achieved at the cost of a considerable increase in computational requirements. In this paper we present a technique, closely related to the classical cluster expansion from statistical mechanics, for reducing the computational demands necessary to calculate conditional maximum entropy language models. 1. Introduction In this paper we present a computational technique that can enable faster calculation of maximum entropy models. The starting point for our method is an algorithm [1] for constructing maximum entropy distributions that is an extension of the generalized iterative scaling algorithm of Darroch and Ratcliff [2,3]. The extended algorithm relaxes the assumption of [2,3] that the constraint functions sum to a constant, and results in a set of decoupled polynomial equations, one fo...
A review of dispersive limits of (non)linear Schrödingertype equations
 501–529. OPTICS FOR NLS 29
"... Abstract. In this review paper we present the most important mathematical properties of dispersive limits of (non)linear Schrödinger type equations. Different formulations are used to study these singular limits, e.g., the kinetic formulation of the linear Schrödinger equation based on the Wigner tr ..."
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Cited by 16 (1 self)
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Abstract. In this review paper we present the most important mathematical properties of dispersive limits of (non)linear Schrödinger type equations. Different formulations are used to study these singular limits, e.g., the kinetic formulation of the linear Schrödinger equation based on the Wigner transform is well suited for globalintime analysis without using WKB(expansion) techniques, while the modified Madelung transformation reformulating Schrödinger equations in terms of a dispersive perturbation of a quasilinear symmetric hyperbolic system usually only gives localintime results due to the hyperbolic nature of the limit equations. Deterministic analogues of turbulence are also discussed. There, turbulent diffusion appears naturally in the zero dispersion limit. 1.
Positive Solutions To Singular Second And Third Order Differential Equations For Quantum Fluids
, 1999
"... A steadystate hydrodynamic model for quantum fluids is analyzed. The momentum equation can be written as a dispersive thirdorder equation for the particle density where viscous effects can be incorporated. The phenomena that admit positivity of the solutions are studied. The cases: dispersive or n ..."
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Cited by 13 (6 self)
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A steadystate hydrodynamic model for quantum fluids is analyzed. The momentum equation can be written as a dispersive thirdorder equation for the particle density where viscous effects can be incorporated. The phenomena that admit positivity of the solutions are studied. The cases: dispersive or nondispersive, viscous or nonviscous are thoroughly analyzed with respect to positivity and existence or nonexistence of solutions. It is proven that in the dispersive, nonviscous model, a classical positive solution only exists for "small" data and no weak solution can exist for "large" data, whereas the dispersive, viscous problem admits a classical positive solution for all data. The viscous term is shown to correspond to hyperviscosity or ultradiffusion. The proofs are based on a reformulation of the equations as a singular elliptic secondorder problem and on a variant of the Stampacchia truncation technique. The results are extended to general thirdorder equations in any space dim...
EUROPHYSICS LETTERS
, 1999
"... Longrange Casimir interactions between impurities in nematic liquid crystals and the collapse of polymer chains in such solvents ..."
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Cited by 5 (0 self)
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Longrange Casimir interactions between impurities in nematic liquid crystals and the collapse of polymer chains in such solvents
On the Time Evolution of the MeanField Polaron
"... In this paper a meanfield theory for the evolution of an electron in a crystal is proposed in the framework of the Schrodinger formalism. The wellposedness of the problem as well as the conservation laws associated to the invariances of the Action Functional of the problem and the stability of the ..."
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Cited by 3 (2 self)
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In this paper a meanfield theory for the evolution of an electron in a crystal is proposed in the framework of the Schrodinger formalism. The wellposedness of the problem as well as the conservation laws associated to the invariances of the Action Functional of the problem and the stability of the minimal energy solution are studied. 1 Introduction and main results The analysis of transport phenomena in solids (specially in semiconductors), has attracted much attention from a physical, engineering and mathematical point of view due to the increasing miniaturization of electronic devices. The relevant scales are of the order of nanometers and quantum effects are shown to become relevant. Under these circumstances the charge carriers (for example electrons) must be handled from a quantummechanical perspective. The general problem is rather complicated to be described from first principles in the general case, hence simplified models provide useful insight into this problem. An outsta...
A nonperturbative RealSpace Renormalization Group scheme I
"... In this article we present a first application of our recently invented realspace RG formulation [1]. We work out a rigorous nonperturbative RG approach for the spin 1 2 XXX Heisenberg model. This allows us to determine accurately the flow behaviour in the effective coupling constant for the non ..."
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In this article we present a first application of our recently invented realspace RG formulation [1]. We work out a rigorous nonperturbative RG approach for the spin 1 2 XXX Heisenberg model. This allows us to determine accurately the flow behaviour in the effective coupling constant for the non trivial fixed point region, which is still an open problem. We examine both, the ferromagnetic and the antiferromagnetic regime and explain the details of the implementation of our new idea in both cases. PACS: 75.10.Jm
Density Matrix Renormalization
 CRM Proceedings
, 1999
"... The Density Matrix Renormalization Group (DMRG) has become a powerful numerical method that can be applied to lowdimensional strongly correlated fermionic and bosonic systems. It allows for a very precise calculation of static, dynamic and thermodynamic properties as well as calculations in classic ..."
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The Density Matrix Renormalization Group (DMRG) has become a powerful numerical method that can be applied to lowdimensional strongly correlated fermionic and bosonic systems. It allows for a very precise calculation of static, dynamic and thermodynamic properties as well as calculations in classical systems. In this article, we briefly review the main aspects of the method. We also comment on some of the most relevant applications so as to give an overview on the scope and possibilities of DMRG and mention the most important extensions of the method such as the calculation of dynamical properties, the application to classical systems, inclusion of temperature, phonons and disorder and a recent modification for the ab initio calculation of electronic states in molecules. 1
New Trends in Density Matrix Renormalization
, 2006
"... (April 2006) The Density Matrix Renormalization Group (DMRG) has become a powerful numerical method that can be applied to lowdimensional strongly correlated fermionic and bosonic systems. It allows for a very precise calculation of static, dynamic and thermodynamic properties. Its field of applica ..."
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(April 2006) The Density Matrix Renormalization Group (DMRG) has become a powerful numerical method that can be applied to lowdimensional strongly correlated fermionic and bosonic systems. It allows for a very precise calculation of static, dynamic and thermodynamic properties. Its field of applicability has now extended beyond Condensed Matter, and is successfully used in Quantum Chemistry, Statistical Mechanics, Quantum Information Theory, Nuclear and High Energy Physics as well. In this article, we briefly review the main aspects of the method and present some of the most relevant applications so as to give an overview on the scope and possibilities of DMRG. We focus on the most important extensions of the method such as the calculation of dynamical properties, the application to classical systems, finite temperature simulations, phonons and disorder, field theory, timedependent properties and the ab initio calculation of electronic states in molecules. The recent quantum information interpretation, the development of highly accurate timedependent algorithms and the possibility of using the DMRG as the impuritysolver of the Dynamical Mean Field Method (DMFT) give new insights into its present and potential uses. We review the numerous very recent applications of these techniques where the DMRG has shown to be one of the most reliable and