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Christian Senger - One of the best experts on this subject based on the ideXlab platform.
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Prefactor reduction of the guruswami sudan interpolation step
IEEE Transactions on Information Theory, 2014Co-Authors: Christian SengerAbstract:The most computationally intensive step of the Guruswami–Sudan list decoder for generalized Reed–Solomon codes is the formation of a bivariate interpolation polynomial. Complexity can be reduced if this polynomial has Prefactors, i.e., factors of its univariate constituent polynomials that are independent of the received vector, and hence known a priori . For example, the well-known re-encoding projection due to Koetter et al. leads to one class of Prefactors. This paper introduces so-called Sierpinski Prefactors that result from the property that many binomial coefficients, which arise in the multiplicity constraints defined in terms of the Hasse derivative, are zero modulo the underlying field characteristic. It is shown that re-encoding Prefactors and Sierpinski Prefactors can be combined to achieve a significantly reduced Guruswami–Sudan interpolation step. In certain practically relevant cases, the introduction of Sierpinski Prefactors reduces the number of unknown polynomial coefficients by an additional 10% or more (beyond the reduction due to re-encoding Prefactors alone), without incurring additional computational effort at the decoder.
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Prefactor Reduction of the Guruswami–Sudan Interpolation Step
IEEE Transactions on Information Theory, 2014Co-Authors: Christian SengerAbstract:The most computationally intensive step of the Guruswami-Sudan list decoder for generalized Reed-Solomon codes is the formation of a bivariate interpolation polynomial. Complexity can be reduced if this polynomial has Prefactors, i.e., factors of its univariate constituent polynomials that are independent of the received vector, and hence known a priori. For example, the well-known re-encoding projection due to Koetter et al. leads to one class of Prefactors. This paper introduces so-called Sierpínski Prefactors that result from the property that many binomial coefficients, which arise in the multiplicity constraints defined in terms of the Hasse derivative, are zero modulo the underlying field characteristic. It is shown that re-encoding Prefactors and Sierpínski Prefactors can be combined to achieve a significantly reduced Guruswami-Sudan interpolation step. In certain practically relevant cases, the introduction of Sierpínski Prefactors reduces the number of unknown polynomial coefficients by an additional 10% or more (beyond the reduction due to re-encoding Prefactors alone), without incurring additional computational effort at the decoder.
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Prefactor Reduction of the Guruswami-Sudan Interpolation Step
arXiv: Information Theory, 2013Co-Authors: Christian SengerAbstract:The concept of Prefactors is considered in order to decrease the complexity of the Guruswami-Sudan interpolation step for generalized Reed-Solomon codes. It is shown that the well-known re-encoding projection due to Koetter et al. leads to one type of such Prefactors. The new type of Sierpinski Prefactors is introduced. The latter are based on the fact that many binomial coefficients in the Hasse derivative associated with the Guruswami-Sudan interpolation step are zero modulo the base field characteristic. It is shown that both types of Prefactors can be combined and how arbitrary Prefactors can be used to derive a reduced Guruswami-Sudan interpolation step.
Victor Muñoz - One of the best experts on this subject based on the ideXlab platform.
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ultrafast folding kinetics of ww domains reveal how the amino acid sequence determines the speed limit to protein folding
Proceedings of the National Academy of Sciences of the United States of America, 2019Co-Authors: Malwina Szczepaniak, Michele Cerminara, Mourad Sadqi, Celia Sanchez De Medina, Jose C. Martinez, Irene Luque, Manuel Iglesiasbexiga, Victor MuñozAbstract:Protein (un)folding rates depend on the free-energy barrier separating the native and unfolded states and a Prefactor term, which sets the timescale for crossing such barrier or folding speed limit. Because extricating these two factors is usually unfeasible, it has been common to assume a constant Prefactor and assign all rate variability to the barrier. However, theory and simulations postulate a protein-specific Prefactor that contains key mechanistic information. Here, we exploit the special properties of fast-folding proteins to experimentally resolve the folding rate Prefactor and investigate how much it varies among structural homologs. We measure the ultrafast (un)folding kinetics of five natural WW domains using nanosecond laser-induced temperature jumps. All five WW domains fold in microseconds, but with a 10-fold difference between fastest and slowest. Interestingly, they all produce biphasic kinetics in which the slower phase corresponds to reequilibration over the small barrier (<3 RT) and the faster phase to the downhill relaxation of the minor population residing at the barrier top [transition state ensemble (TSE)]. The fast rate recapitulates the 10-fold range, demonstrating that the folding speed limit of even the simplest all-β fold strongly depends on the amino acid sequence. Given this fold's simplicity, the most plausible source for such Prefactor differences is the presence of nonnative interactions that stabilize the TSE but need to break up before folding resumes. Our results confirm long-standing theoretical predictions and bring into focus the rate Prefactor as an essential element for understanding the mechanisms of folding.
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Ultrafast folding kinetics of WW domains reveal how the amino acid sequence determines the speed limit to protein folding.
Proceedings of the National Academy of Sciences of the United States of America, 2019Co-Authors: Malwina Szczepaniak, Manuel Iglesias-bexiga, Michele Cerminara, Mourad Sadqi, Celia Sanchez De Medina, Jose C. Martinez, Irene Luque, Victor MuñozAbstract:Protein (un)folding rates depend on the free-energy barrier separating the native and unfolded states and a Prefactor term, which sets the timescale for crossing such barrier or folding speed limit. Because extricating these two factors is usually unfeasible, it has been common to assume a constant Prefactor and assign all rate variability to the barrier. However, theory and simulations postulate a protein-specific Prefactor that contains key mechanistic information. Here, we exploit the special properties of fast-folding proteins to experimentally resolve the folding rate Prefactor and investigate how much it varies among structural homologs. We measure the ultrafast (un)folding kinetics of five natural WW domains using nanosecond laser-induced temperature jumps. All five WW domains fold in microseconds, but with a 10-fold difference between fastest and slowest. Interestingly, they all produce biphasic kinetics in which the slower phase corresponds to reequilibration over the small barrier (
Ivo Klik - One of the best experts on this subject based on the ideXlab platform.
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Field-dependent Prefactor of the thermal relaxation rate in single-domain magnetic particles.
Physical review. B Condensed matter, 1993Co-Authors: Ivo Klik, Ching-ray Chang, Huei Li HuangAbstract:Within a model of the coherent rotation, we assume underdamped dynamics of magnetization in single-domain ferromagnetic particles and calculate the Prefactor f 0 (h) of the thermal decay rate as a function of the applied field h. Four different models of dissipative coupling are considered. As opposed to the previously reported temperature dependence of the Prefactor, the field dependence is remarkably independent of the chosen coupling mode. The Prefactor f 0 (h) drops off sharply as h approaches the nucleation field and significantly enhances the coercivity whose model calculation, together with that of the switching-field distribution, is carried out
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Temperature‐dependent Prefactor
Journal of Applied Physics, 1993Co-Authors: Ivo KlikAbstract:The saturationmagnetization and anisotropy constants of a ferromagnet are, below the Curie pointT C , decreasing functions of temperatureT. This effect leads to a T‐dependent barrier height for thermal activation and, also, to T‐dependent Prefactor f 0 of the thermal decay rate κ, which is here studied in the underdamped limit. For a uniaxial single domain ferromagnet f 0∼τ−1(1−τ)ρ, where τ=T/T C and ρe
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temperature dependent Prefactor
Journal of Applied Physics, 1993Co-Authors: Ivo KlikAbstract:The saturationmagnetization and anisotropy constants of a ferromagnet are, below the Curie pointT C , decreasing functions of temperatureT. This effect leads to a T‐dependent barrier height for thermal activation and, also, to T‐dependent Prefactor f 0 of the thermal decay rate κ, which is here studied in the underdamped limit. For a uniaxial single domain ferromagnet f 0∼τ−1(1−τ)ρ, where τ=T/T C and ρe<2,11/3≳ depending on the chosen model of dissipative coupling. Ohmic and superohmic couplings are considered that are either isotropic or anisotropic in space. Estimates for cubic systems are in the range ρe<13/3,32/3≳. Measurements of the function f 0(τ) may thus provide information about the dissipative mechanism in single domain particles. Its influence on measurable data is demonstrated on a model calculation of frequency‐dependent coercivity.
Roger Frech - One of the best experts on this subject based on the ideXlab platform.
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ion transport with charge protected and non charge protected cations using the compensated arrhenius formalism part 2 relationship between ionic conductivity and diffusion
Journal of Physical Chemistry B, 2012Co-Authors: Matt Petrowsky, Allison M Fleshman, Dharshani N Bopege, Roger FrechAbstract:Temperature-dependent ionic conductivities and cation/anion self-diffusion coefficients are measured for four electrolyte families: TbaTf-linear primary alcohols, LiTf-linear primary alcohols, TbaTf-n-alkyl acetates, and LiTf-n-alkyl acetates. The Nernst–Einstein equation does not adequately describe the data. Instead, the compensated Arrhenius formalism is applied to both conductivity and diffusion data. General trends based on temperature and alkyl chain length are observed when conductivity is plotted against cation or anion diffusion coefficient, but there is no clear pattern to the data. However, plotting conductivity exponential Prefactors against those for diffusion results in four distinct curves, one each for the alcohol and acetate families described above. Furthermore, the TbaTf-alcohol and TbaTf-acetate data are “in line” with each other. The conductivity Prefactors for the LiTf-alcohol data are smaller than those for the TbaTf data. The LiTf-acetate data have the lowest conductivity Prefactor...
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ion transport with charge protected and non charge protected cations using the compensated arrhenius formalism part 2 relationship between ionic conductivity and diffusion
The Journal of Physical Chemistry, 2012Co-Authors: Matt Petrowsky, Allison M Fleshman, Dharshani N Bopege, Roger FrechAbstract:Temperature-dependent ionic conductivities and cation/anion self-diffusion coefficients are measured for four electrolyte families: TbaTf-linear primary alcohols, LiTf-linear primary alcohols, TbaTf-n-alkyl acetates, and LiTf-n-alkyl acetates. The Nernst–Einstein equation does not adequately describe the data. Instead, the compensated Arrhenius formalism is applied to both conductivity and diffusion data. General trends based on temperature and alkyl chain length are observed when conductivity is plotted against cation or anion diffusion coefficient, but there is no clear pattern to the data. However, plotting conductivity exponential Prefactors against those for diffusion results in four distinct curves, one each for the alcohol and acetate families described above. Furthermore, the TbaTf-alcohol and TbaTf-acetate data are “in line” with each other. The conductivity Prefactors for the LiTf-alcohol data are smaller than those for the TbaTf data. The LiTf-acetate data have the lowest conductivity Prefactors. This trend in Prefactors mirrors the observed trend in degree of ionic association for these electrolytes.
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Extending the compensated Arrhenius formalism to concentrated alcohol electrolytes: Arrhenius vs. non-Arrhenius behavior
Electrochimica Acta, 2011Co-Authors: Allison M Fleshman, Matt Petrowsky, Jeremy D. Jernigen, R.s.p. Bokalawela, Matthew B. Johnson, Roger FrechAbstract:The compensated Arrhenius formalism is applied to ionic conductivities in alcohol-based electrolytes at concentrations where the salt makes a non-negligible contribution to the static dielectric constant of the solution. The temperature-dependent behavior of the conductivity depends on the amount of added salt. Non-Arrhenius behavior is observed for low to moderate salt concentrations, while Arrhenius behavior occurs at high concentrations. The compensated Arrhenius formalism provides insight into this behavior by analyzing the effect of salt concentration on the temperature dependence of the exponential Prefactor. When the compensated Arrhenius Prefactors are plotted against the solution static dielectric constants using the Ea obtained from the compensated Arrhenius equation, the Prefactors lie on a single master curve. In contrast, a similar plot based on the Ea obtained from a simple Arrhenius plot of the same conductivity data does not yield a master curve. Application of the compensated Arrhenius formalism requires the construction of a reference curve. It is essential that the range of static dielectric constant values spanned by the reference curve encompasses the range of temperature-dependent static dielectric constant values of the selected alcohol electrolyte. This will allow an accurate interpolation to obtain the appropriate reference conductivity. A detailed description is given for the method used to construct an appropriate reference conductivity curve.
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Temperature dependence of ion transport: the compensated Arrhenius equation.
The journal of physical chemistry. B, 2009Co-Authors: Matt Petrowsky, Roger FrechAbstract:The temperature-dependent conductivity originating in a thermally activated process is often described by a simple Arrhenius expression. However, this expression provides a poor description of the data for organic liquid electrolytes and amorphous polymer electrolytes. Here, we write the temperature dependence of the conductivity as an Arrhenius expression and show that the experimentally observed non-Arrhenius behavior is due to the temperature dependence of the dielectric constant contained in the exponential Prefactor. Scaling the experimentally measured conductivities to conductivities at a chosen reference temperature leads to a "compensated" Arrhenius equation that provides an excellent description of temperature-dependent conductivities. A plot of the Prefactors as a function of the solvent dielectric constant results in a single master curve for each family of solvents. These data suggest that ion transport in these and related systems is governed by a single activated process differing only in the activation energy for each family of solvents. Connection is made to the shift factor used to describe electrical and mechanical relaxation in a wide range of phenomena, suggesting that this scaling procedure might have broad applications.
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temperature dependence of ion transport the compensated arrhenius equation
Journal of Physical Chemistry B, 2009Co-Authors: Matt Petrowsky, Roger FrechAbstract:The temperature-dependent conductivity originating in a thermally activated process is often described by a simple Arrhenius expression. However, this expression provides a poor description of the data for organic liquid electrolytes and amorphous polymer electrolytes. Here, we write the temperature dependence of the conductivity as an Arrhenius expression and show that the experimentally observed non-Arrhenius behavior is due to the temperature dependence of the dielectric constant contained in the exponential Prefactor. Scaling the experimentally measured conductivities to conductivities at a chosen reference temperature leads to a “compensated” Arrhenius equation that provides an excellent description of temperature-dependent conductivities. A plot of the Prefactors as a function of the solvent dielectric constant results in a single master curve for each family of solvents. These data suggest that ion transport in these and related systems is governed by a single activated process differing only in th...
Adilet Imambekov - One of the best experts on this subject based on the ideXlab platform.
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exact Prefactors in static and dynamic correlation functions of one dimensional quantum integrable models applications to the calogore sutherland lieb liniger and xxz models
Physical Review B, 2012Co-Authors: Aditya Shashi, Jeansebastien Caux, Milosz Panfil, Adilet ImambekovAbstract:In this paper, we demonstrate a recently developed technique which addresses the problem of obtaining nonuniversal Prefactors of the correlation functions of one-dimensional (1D) systems at zero temperature. Our approach combines the effective field theory description of generic 1D quantum liquids with the finite-size scaling of form factors (matrix elements) which are obtained using microscopic techniques developed in the context of integrable models. We thus establish exact analytic forms for the Prefactors of the long-distance behavior of equal-time correlation functions as well as Prefactors of singularities of dynamic response functions. In this paper, our focus is on three specific integrable models: the Calogero-Sutherland, Lieb-Liniger, and XXZ models.
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nonuniversal Prefactors in the correlation functions of one dimensional quantum liquids
Physical Review B, 2011Co-Authors: Aditya Shashi, L I Glazman, Jeansebastien Caux, Adilet ImambekovAbstract:We develop a general approach to calculating "nonuniversal" Prefactors in static and dynamic correlation functions of 1D quantum liquids at zero temperature, by relating them to the unite size scaling of certain matrix elements (form factors). This represents a new, powerful tool for extracting data valid in the thermodynamic limit from finite-size effects. As the main application, we consider weakly interacting spinless fermions with an arbitrary pair interaction potential, for which we perturbatively calculate certain Prefactors in static and dynamic correlation functions. We also non-perturbatively evaluate Prefactors of the long-distance behavior of correlation functions for the exactly solvable Lieb-Liniger model of 1D bosons.
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Exact asymptotes of static and dynamic correlation functions of the 1D Bose gas
2010Co-Authors: Aditya Shashi, Jeansebastien Caux, Leonid I. Glazman, Adilet ImambekovAbstract:In this article we demonstrate a recently developed technique which addresses the problem of obtaining non-universal Prefactors of the correlation functions of 1D systems at zero temperature. Our approach combines the effective field theory description of generic 1D quantum liquids with the finite size scaling of form factors (matrix elements) which are obtained using microscopic techniques developed in the context of integrable models. We thus establish exact analytic forms for the Prefactors of the long-distance behavior of equal time correlation functions as well as Prefactors of singularities of dynamic response functions. In this article our focus is on three specific integrable models: the Calogero-Sutherland, Lieb-Liniger, and XXZ models.
