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Boris Ryabko - One of the best experts on this subject based on the ideXlab platform.
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compression based methods for nonparametric density estimation on line prediction regression and classification for time series
Information Theory Workshop, 2008Co-Authors: Boris RyabkoAbstract:We address the problem of nonparametric estimation of characteristics for stationary and ergodic time series. We consider finite-alphabet time series and the real-valued ones and the following problems: estimation of the (Limiting) Probability P(u0 hellip us) for every s and each sequence u0 hellip us of letters from the process alphabet (or estimation of the density p(x0, hellip , xs) for real-valued time series), so-called on-line prediction, where the conditional Probability P(xt+1/x1x2 hellip xt) (or the conditional density p(xt+1/x1x2 hellip xt)) should be estimated (in the case where x1x2 hellip xt is known), regression and classification (or so-called problems with side information). We show that any universal code (or a universal data compressor) can be used as a basis for constructing asymptotically optimal methods for the above problems.
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compression based methods for nonparametric density estimation on line prediction regression and classification for time series
arXiv: Information Theory, 2007Co-Authors: Boris RyabkoAbstract:We address the problem of nonparametric estimation of characteristics for stationary and ergodic time series. We consider finite-alphabet time series and real-valued ones and the following four problems: i) estimation of the (Limiting) Probability (or estimation of the density for real-valued time series), ii) on-line prediction, iii) regression and iv) classification (or so-called problems with side information). We show that so-called archivers (or data compressors) can be used as a tool for solving these problems. In particular, firstly, it is proven that any so-called universal code (or universal data compressor) can be used as a basis for constructing asymptotically optimal methods for the above problems. (By definition, a universal code can "compress" any sequence generated by a stationary and ergodic source asymptotically till the Shannon entropy of the source.) And, secondly, we show experimentally that estimates, which are based on practically used methods of data compression, have a reasonable precision.
S Teitel - One of the best experts on this subject based on the ideXlab platform.
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shear driven flow of athermal frictionless spherocylinder suspensions in two dimensions stress jamming and contacts
Physical Review E, 2019Co-Authors: Theodore Marschall, S TeitelAbstract:: We use numerical simulations to study the flow of a bidisperse mixture of athermal, frictionless, soft-core two-dimensional spherocylinders driven by a uniform steady-state shear strain applied at a fixed finite rate. Energy dissipation occurs via a viscous drag with respect to a uniformly sheared host fluid, giving a simple model for flow in a non-Brownian suspension and resulting in a Newtonian rheology. We study the resulting pressure p and deviatoric shear stress σ of the interacting spherocylinders as a function of packing fraction ϕ, strain rate γ[over ], and a parameter α that measures the asphericity of the particles; α is varied to consider the range from nearly circular disks to elongated rods. We consider the direction of anisotropy of the stress tensor, the macroscopic friction μ=σ/p, and the divergence of the transport coefficient η_{p}=p/γ[over ] as ϕ is increased to the jamming transition ϕ_{J}. From a phenomenological analysis of Herschel-Bulkley rheology above jamming, we estimate ϕ_{J} as a function of asphericity α and show that the variation of ϕ_{J} with α is the main cause for differences in rheology as α is varied; when plotted as ϕ/ϕ_{J}, rheological curves for different α qualitatively agree. However, a detailed scaling analysis of the divergence of η_{p} for our most elongated particles suggests that the jamming transition of spherocylinders may be in a different universality class than that of circular disks. We also compute the number of contacts per particle Z in the system and show that the value at jamming Z_{J} is a nonmonotonic function of α that is always smaller than the isostatic value. We measure the Probability distribution of contacts per unit surface length P(ϑ) at polar angle ϑ with respect to the spherocylinder spine and find that as α→0 this distribution seems to diverge at ϑ=π/2, giving a finite Limiting Probability for contacts on the vanishingly small flat sides of the spherocylinder. Finally, we consider the variation of the average contact force as a function of location on the particle surface.
Theodore Marschall - One of the best experts on this subject based on the ideXlab platform.
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shear driven flow of athermal frictionless spherocylinder suspensions in two dimensions stress jamming and contacts
Physical Review E, 2019Co-Authors: Theodore Marschall, S TeitelAbstract:: We use numerical simulations to study the flow of a bidisperse mixture of athermal, frictionless, soft-core two-dimensional spherocylinders driven by a uniform steady-state shear strain applied at a fixed finite rate. Energy dissipation occurs via a viscous drag with respect to a uniformly sheared host fluid, giving a simple model for flow in a non-Brownian suspension and resulting in a Newtonian rheology. We study the resulting pressure p and deviatoric shear stress σ of the interacting spherocylinders as a function of packing fraction ϕ, strain rate γ[over ], and a parameter α that measures the asphericity of the particles; α is varied to consider the range from nearly circular disks to elongated rods. We consider the direction of anisotropy of the stress tensor, the macroscopic friction μ=σ/p, and the divergence of the transport coefficient η_{p}=p/γ[over ] as ϕ is increased to the jamming transition ϕ_{J}. From a phenomenological analysis of Herschel-Bulkley rheology above jamming, we estimate ϕ_{J} as a function of asphericity α and show that the variation of ϕ_{J} with α is the main cause for differences in rheology as α is varied; when plotted as ϕ/ϕ_{J}, rheological curves for different α qualitatively agree. However, a detailed scaling analysis of the divergence of η_{p} for our most elongated particles suggests that the jamming transition of spherocylinders may be in a different universality class than that of circular disks. We also compute the number of contacts per particle Z in the system and show that the value at jamming Z_{J} is a nonmonotonic function of α that is always smaller than the isostatic value. We measure the Probability distribution of contacts per unit surface length P(ϑ) at polar angle ϑ with respect to the spherocylinder spine and find that as α→0 this distribution seems to diverge at ϑ=π/2, giving a finite Limiting Probability for contacts on the vanishingly small flat sides of the spherocylinder. Finally, we consider the variation of the average contact force as a function of location on the particle surface.
Miklos Z Racz - One of the best experts on this subject based on the ideXlab platform.
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a smooth transition from powerlessness to absolute power
Journal of Artificial Intelligence Research, 2013Co-Authors: Elchanan Mossel, Ariel D Procaccia, Miklos Z RaczAbstract:We study the phase transition of the coalitional manipulation problem for generalized scoring rules. Previously it has been shown that, under some conditions on the distribution of votes, if the number of manipulators is o (√n), where n is the number of voters, then the Probability that a random profile is manipulable by the coalition goes to zero as the number of voters goes to infinity, whereas if the number of manipulators is ω(√n), then the Probability that a random profile is manipulable goes to one. Here we consider the critical window, where a coalition has size c√n, and we show that as c goes from zero to infinity, the Limiting Probability that a random profile is manipulable goes from zero to one in a smooth fashion, i.e., there is a smooth phase transition between the two regimes. This result analytically validates recent empirical results, and suggests that deciding the coalitional manipulation problem may be of limited computational hardness in practice.
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a smooth transition from powerlessness to absolute power
arXiv: Computer Science and Game Theory, 2012Co-Authors: Elchanan Mossel, Ariel D Procaccia, Miklos Z RaczAbstract:We study the phase transition of the coalitional manipulation problem for generalized scoring rules. Previously it has been shown that, under some conditions on the distribution of votes, if the number of manipulators is $o(\sqrt{n})$, where $n$ is the number of voters, then the Probability that a random profile is manipulable by the coalition goes to zero as the number of voters goes to infinity, whereas if the number of manipulators is $\omega(\sqrt{n})$, then the Probability that a random profile is manipulable goes to one. Here we consider the critical window, where a coalition has size $c\sqrt{n}$, and we show that as $c$ goes from zero to infinity, the Limiting Probability that a random profile is manipulable goes from zero to one in a smooth fashion, i.e., there is a smooth phase transition between the two regimes. This result analytically validates recent empirical results, and suggests that deciding the coalitional manipulation problem may be of limited computational hardness in practice.
Andrew J Majda - One of the best experts on this subject based on the ideXlab platform.
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the random uniform shear layer an explicit example of turbulent diffusion with broad tail Probability distributions
Physics of Fluids, 1993Co-Authors: Andrew J MajdaAbstract:Recent experimental and computational observations demonstrate the occurrence of large‐scale intermittency for diffusing passive scalars, as manifested by broader than Gaussian Probability distribution functions. Here, a family of explicit exactly solvable examples is developed which demonstrates these effects of large‐scale intermittency at any positive time through simple formulas for the higher flatness factors without any phenomenological approximations. The exact solutions involve advection–diffusion with velocity fields involving a uniform shear flow perturbed by a random fluctuating uniform shear flow. Through an exact quantum mechanical analogy, the higher‐order statistics for the scalar in these models are solved exactly by formulas for the quantum‐harmonic oscillator. These explicit formulas also demonstrate that the large time asymptotic Limiting Probability distribution function for the normalized scalar can be either broader than Gaussian or Gaussian depending on the relative strength of the mean flow and the fluctuating velocity field.