916 research outputs found
The role of the nature of the noise in the thermal conductance of mechanical systems
Focussing on a paradigmatic small system consisting of two coupled damped
oscillators, we survey the role of the L\'evy-It\^o nature of the noise in the
thermal conductance. For white noises, we prove that the L\'evy-It\^o
composition (Lebesgue measure) of the noise is irrelevant for the thermal
conductance of a non-equilibrium linearly coupled chain, which signals the
independence between mechanical and thermodynamical properties. On the other
hand, for the non-linearly coupled case, the two types of properties mix and
the explicit definition of the noise plays a central role.Comment: 9 pages, 2 figures. To be published in Physical Review
Coming of Age: Tracking the Progress and Challenges of Delivering Long-Term Services and Supports in Ohio
In a 16 year tracking of utilization trends for institutional and home and community-based services, we learned that Ohio has made considerable change in its approach to delivering and funding long-term care services. The main finding revealed that now more than four in ten older people with severe disability on Medicaid received assistance in a non-institutional setting. This research brief summarizes findings from the larger study report
Coming of Age: Tracking the Progress and Challenges of Delivering Long-Term Services and Supports in Ohio
In sixteen years of tracking utilization trends for institutional and home-and community-based services and supports, we learned that Ohio has made considerable changes in its approach to delivering and funding long-term care. For example, in 2009 more than four in ten older people on Medicaid received services in a non-institutional setting
Coming of Age: Tracking the Progress and Challenges of Delivering Long-Term Services and Supports in Ohio
16 years of tracking utilization trends for institutional and home-based services and supports shows that Ohio has made considerable changes i its approach to delivering long-term services and supports. For example, in 2009 mor than four in ten older people receiving Medicaid long-term care received assistance in a non-institutional setting
The fractional Schr\"{o}dinger operator and Toeplitz matrices
Confining a quantum particle in a compact subinterval of the real line with
Dirichlet boundary conditions, we identify the connection of the
one-dimensional fractional Schr\"odinger operator with the truncated Toeplitz
matrices. We determine the asymptotic behaviour of the product of eigenvalues
for the -stable symmetric laws by employing the Szeg\"o's strong limit
theorem. The results of the present work can be applied to a recently proposed
model for a particle hopping on a bounded interval in one dimension whose
hopping probability is given a discrete representation of the fractional
Laplacian.Comment: 10 pages, 2 figure
Harnack Inequality and Regularity for a Product of Symmetric Stable Process and Brownian Motion
In this paper, we consider a product of a symmetric stable process in
and a one-dimensional Brownian motion in . Then we
define a class of harmonic functions with respect to this product process. We
show that bounded non-negative harmonic functions in the upper-half space
satisfy Harnack inequality and prove that they are locally H\"older continuous.
We also argue a result on Littlewood-Paley functions which are obtained by the
-harmonic extension of an function.Comment: 23 page
A functional non-central limit theorem for jump-diffusions with periodic coefficients driven by stable Levy-noise
We prove a functional non-central limit theorem for jump-diffusions with
periodic coefficients driven by strictly stable Levy-processes with stability
index bigger than one. The limit process turns out to be a strictly stable Levy
process with an averaged jump-measure. Unlike in the situation where the
diffusion is driven by Brownian motion, there is no drift related enhancement
of diffusivity.Comment: Accepted to Journal of Theoretical Probabilit
Private Outsourcing of Polynomial Evaluation and Matrix Multiplication using Multilinear Maps
{\em Verifiable computation} (VC) allows a computationally weak client to
outsource the evaluation of a function on many inputs to a powerful but
untrusted server. The client invests a large amount of off-line computation and
gives an encoding of its function to the server. The server returns both an
evaluation of the function on the client's input and a proof such that the
client can verify the evaluation using substantially less effort than doing the
evaluation on its own. We consider how to privately outsource computations
using {\em privacy preserving} VC schemes whose executions reveal no
information on the client's input or function to the server. We construct VC
schemes with {\em input privacy} for univariate polynomial evaluation and
matrix multiplication and then extend them such that the {\em function privacy}
is also achieved. Our tool is the recently developed {mutilinear maps}. The
proposed VC schemes can be used in outsourcing {private information retrieval
(PIR)}.Comment: 23 pages, A preliminary version appears in the 12th International
Conference on Cryptology and Network Security (CANS 2013
One-dimensional stable probability density functions for rational index 0<α≤2
Fox’s H-function provide a unified and elegant framework to tackle several physical phenomena. We solve the space fractional diffusion equation on the real line equipped with a delta distribution initial condition and identify the corresponding H-function by studying the small x expansion of the solution. The asymptotic expansions near zero and infinity are expressed, for rational values of the index α, in terms of a finite series of generalized hypergeometric functions. In x-space, the α=1 stable law is also derived by solving the anomalous diffusion equation with an appropriately chosen infinitesimal generator for time translations. We propose a new classification scheme of stable laws according to which a stable law is now characterized by a generating probability density function. Knowing this elementary probability density function and bearing in mind the infinitely divisible property we can reconstruct the corresponding stable law. Finally, using the asymptotic behavior of H-function in terms of hypergeometric functions we can compute closed expressions for the probability density functions depending on their parameters α β c τ. Known cases are then reproduced and new probability density functions are presented
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