The Experts below are selected from a list of 139656 Experts worldwide ranked by ideXlab platform
Boris Svistunov - One of the best experts on this subject based on the ideXlab platform.
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Implementation of the bin hierarchy method for restoring a Smooth Function from a sampled histogram
Computer Physics Communications, 2019Co-Authors: Olga Goulko, Nikolay Prokof'ev, Alexander Gaenko, Emanuel Gull, Boris SvistunovAbstract:Abstract We present BHM , a tool for restoring a Smooth Function from a sampled histogram using the bin hierarchy method. It is particularly useful for the analysis of data from large-scale numerical simulations of physical systems, such as diagrammatic Monte Carlo simulations of quantum many-body problems. The theoretical background of the method is presented in Goulko et al., (2018). The code automatically generates a Smooth polynomial spline with the minimal acceptable number of knots from the input data. It works universally for any sufficiently regular shaped distribution and any level of data quality (provided that the data are uncorrelated or correlations have been accounted for), requiring almost no external parameter specification. This paper explains the details of the implementation and the use of the program, including a physical example of the restoration of the Frohlich polaron Green’s Function from data sampled with diagrammatic Monte Carlo. Program summary Program Title: BHM Program Files doi: http://dx.doi.org/10.17632/dvj8gxsxpk.1 Licensing provisions: GPLv3 Programming language: C++ External routines/libraries: CMake, GSL Nature of problem: Restoring a Smooth Function from a sampled histogram. Solution method: To make use of all information contained in the sampled data, the BHM algorithm generates a hierarchy of overlapping bins of different sizes from the initially supplied fine histogram. The bin hierarchy is fitted to a polynomial spline with the minimal acceptable number of knots, the positions of which are determined automatically. The output is a Smooth Function with error band.
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Restoring a Smooth Function from its noisy integrals
Physical Review E, 2018Co-Authors: Olga Goulko, Nikolay Prokof'ev, Boris SvistunovAbstract:: Numerical (and experimental) data analysis often requires the restoration of a Smooth Function from a set of sampled integrals over finite bins. We present the bin hierarchy method that efficiently computes the maximally Smooth Function from the sampled integrals using essentially all the information contained in the data. We perform extensive tests with different classes of Functions and levels of data quality, including Monte Carlo data suffering from a severe sign problem and physical data for the Green's Function of the Frohlich polaron.
Olga Goulko - One of the best experts on this subject based on the ideXlab platform.
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Implementation of the bin hierarchy method for restoring a Smooth Function from a sampled histogram
Computer Physics Communications, 2019Co-Authors: Olga Goulko, Nikolay Prokof'ev, Alexander Gaenko, Emanuel Gull, Boris SvistunovAbstract:Abstract We present BHM , a tool for restoring a Smooth Function from a sampled histogram using the bin hierarchy method. It is particularly useful for the analysis of data from large-scale numerical simulations of physical systems, such as diagrammatic Monte Carlo simulations of quantum many-body problems. The theoretical background of the method is presented in Goulko et al., (2018). The code automatically generates a Smooth polynomial spline with the minimal acceptable number of knots from the input data. It works universally for any sufficiently regular shaped distribution and any level of data quality (provided that the data are uncorrelated or correlations have been accounted for), requiring almost no external parameter specification. This paper explains the details of the implementation and the use of the program, including a physical example of the restoration of the Frohlich polaron Green’s Function from data sampled with diagrammatic Monte Carlo. Program summary Program Title: BHM Program Files doi: http://dx.doi.org/10.17632/dvj8gxsxpk.1 Licensing provisions: GPLv3 Programming language: C++ External routines/libraries: CMake, GSL Nature of problem: Restoring a Smooth Function from a sampled histogram. Solution method: To make use of all information contained in the sampled data, the BHM algorithm generates a hierarchy of overlapping bins of different sizes from the initially supplied fine histogram. The bin hierarchy is fitted to a polynomial spline with the minimal acceptable number of knots, the positions of which are determined automatically. The output is a Smooth Function with error band.
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Restoring a Smooth Function from its noisy integrals
Physical Review E, 2018Co-Authors: Olga Goulko, Nikolay Prokof'ev, Boris SvistunovAbstract:: Numerical (and experimental) data analysis often requires the restoration of a Smooth Function from a set of sampled integrals over finite bins. We present the bin hierarchy method that efficiently computes the maximally Smooth Function from the sampled integrals using essentially all the information contained in the data. We perform extensive tests with different classes of Functions and levels of data quality, including Monte Carlo data suffering from a severe sign problem and physical data for the Green's Function of the Frohlich polaron.
Jackson Gorham - One of the best experts on this subject based on the ideXlab platform.
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Multivariate Stein Factors for Strongly Log-concave Distributions
arXiv: Probability, 2015Co-Authors: Lester Mackey, Jackson GorhamAbstract:We establish uniform bounds on the low-order derivatives of Stein equation solutions for a broad class of multivariate, strongly log-concave target distributions. These "Stein factor" bounds deliver control over Wasserstein and related Smooth Function distances and are well-suited to analyzing the computable Stein discrepancy measures of Gorham and Mackey. Our arguments of proof are probabilistic and feature the synchronous coupling of multiple overdamped Langevin diffusions.
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Multivariate Stein Factors for a Class of Strongly Log-concave Distributions
arXiv: Probability, 2015Co-Authors: Lester Mackey, Jackson GorhamAbstract:We establish uniform bounds on the low-order derivatives of Stein equation solutions for a broad class of multivariate, strongly log-concave target distributions. These "Stein factor" bounds deliver control over Wasserstein and related Smooth Function distances and are well-suited to analyzing the computable Stein discrepancy measures of Gorham and Mackey. Our arguments of proof are probabilistic and feature the synchronous coupling of multiple overdamped Langevin diffusions.
Karen E Smith - One of the best experts on this subject based on the ideXlab platform.
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uniform approximation of abhyankar valuation ideals in Smooth Function fields
American Journal of Mathematics, 2003Co-Authors: Robert Lazarsfeld, Karen E SmithAbstract:Fix a rank one valuation ν centered at a Smooth point x on an algebraic variety over a field of characteristic zero. Assume that ν is Abhyankar, that is, that its rational rank plus its transcendence degree equal the dimension of the variety. Let a m denote the ideal of elements in the local ring of x whose valuations are at least m . Our main theorem is that there exists k 0 such that a mn is contained in ( a m-k ) n for all m and n . This can be viewed as a greatly strengthened form of Izumi's Theorem for Abhyankar valuations centered on Smooth complex varieties. The proof uses the theory of asymptotic multiplier ideals.
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uniform approximation of abhyankar valuation ideals in Smooth Function fields
arXiv: Algebraic Geometry, 2002Co-Authors: Robert Lazarsfeld, Karen E SmithAbstract:In this paper we use the theory of multiplier ideals to show that the valuation ideals of a rank one Abhyankar valuation centered at a Smooth point of a complex algebraic variety are approximated, in a quite strong sense, by sequences of powers of fixed ideals. Fix a rank one valuation v centered at a Smooth point x on an algebraic variety over a field of characteristic zero. Assume that v is Abhyankar, that is, that its rational rank plus its transcendence degree equal the dimension of the variety. Let a_m denote the ideal of elements in the local ring of x whose valuations are at least m. Our main theorem is that there exists e>0 such that a_{mn} is contained in (a_{m-e})^n for all m and n. This can be viewed as a greatly strengthened form of Izumi's Theorem for Abhyankar valuations centered on Smooth complex varieties.
Nikolay Prokof'ev - One of the best experts on this subject based on the ideXlab platform.
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Implementation of the bin hierarchy method for restoring a Smooth Function from a sampled histogram
Computer Physics Communications, 2019Co-Authors: Olga Goulko, Nikolay Prokof'ev, Alexander Gaenko, Emanuel Gull, Boris SvistunovAbstract:Abstract We present BHM , a tool for restoring a Smooth Function from a sampled histogram using the bin hierarchy method. It is particularly useful for the analysis of data from large-scale numerical simulations of physical systems, such as diagrammatic Monte Carlo simulations of quantum many-body problems. The theoretical background of the method is presented in Goulko et al., (2018). The code automatically generates a Smooth polynomial spline with the minimal acceptable number of knots from the input data. It works universally for any sufficiently regular shaped distribution and any level of data quality (provided that the data are uncorrelated or correlations have been accounted for), requiring almost no external parameter specification. This paper explains the details of the implementation and the use of the program, including a physical example of the restoration of the Frohlich polaron Green’s Function from data sampled with diagrammatic Monte Carlo. Program summary Program Title: BHM Program Files doi: http://dx.doi.org/10.17632/dvj8gxsxpk.1 Licensing provisions: GPLv3 Programming language: C++ External routines/libraries: CMake, GSL Nature of problem: Restoring a Smooth Function from a sampled histogram. Solution method: To make use of all information contained in the sampled data, the BHM algorithm generates a hierarchy of overlapping bins of different sizes from the initially supplied fine histogram. The bin hierarchy is fitted to a polynomial spline with the minimal acceptable number of knots, the positions of which are determined automatically. The output is a Smooth Function with error band.
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Restoring a Smooth Function from its noisy integrals
Physical Review E, 2018Co-Authors: Olga Goulko, Nikolay Prokof'ev, Boris SvistunovAbstract:: Numerical (and experimental) data analysis often requires the restoration of a Smooth Function from a set of sampled integrals over finite bins. We present the bin hierarchy method that efficiently computes the maximally Smooth Function from the sampled integrals using essentially all the information contained in the data. We perform extensive tests with different classes of Functions and levels of data quality, including Monte Carlo data suffering from a severe sign problem and physical data for the Green's Function of the Frohlich polaron.
