1,053 research outputs found
Anomalous Processes with General Waiting Times: Functionals and Multipoint Structure
Many transport processes in nature exhibit anomalous diffusive properties
with non-trivial scaling of the mean square displacement, e.g., diffusion of
cells or of biomolecules inside the cell nucleus, where typically a crossover
between different scaling regimes appears over time. Here, we investigate a
class of anomalous diffusion processes that is able to capture such complex
dynamics by virtue of a general waiting time distribution. We obtain a complete
characterization of such generalized anomalous processes, including their
functionals and multi-point structure, using a representation in terms of a
normal diffusive process plus a stochastic time change. In particular, we
derive analytical closed form expressions for the two-point correlation
functions, which can be readily compared with experimental data.Comment: Accepted in Phys. Rev. Let
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
Coupled oscillators and Feynman's three papers
According to Richard Feynman, the adventure of our science of physics is a
perpetual attempt to recognize that the different aspects of nature are really
different aspects of the same thing. It is therefore interesting to combine
some, if not all, of Feynman's papers into one. The first of his three papers
is on the ``rest of the universe'' contained in his 1972 book on statistical
mechanics. The second idea is Feynman's parton picture which he presented in
1969 at the Stony Brook conference on high-energy physics. The third idea is
contained in the 1971 paper he published with his students, where they show
that the hadronic spectra on Regge trajectories are manifestations of
harmonic-oscillator degeneracies. In this report, we formulate these three
ideas using the mathematics of two coupled oscillators. It is shown that the
idea of entanglement is contained in his rest of the universe, and can be
extended to a space-time entanglement. It is shown also that his parton model
and the static quark model can be combined into one Lorentz-covariant entity.
Furthermore, Einstein's special relativity, based on the Lorentz group, can
also be formulated within the mathematical framework of two coupled
oscillators.Comment: 31 pages, 6 figures, based on the concluding talk at the 3rd Feynman
Festival (Collage Park, Maryland, U.S.A., August 2006), minor correction
Transition Densities and Traces for Invariant Feller Processes on Compact Symmetric Spaces
We find necessary and sufficient conditions for a finite K–bi–invariant
measure on a compact Gelfand pair (G, K) to have a square–integrable
density. For convolution semigroups, this is equivalent to having a
continuous density in positive time. When (G, K) is a compact Riemannian
symmetric pair, we study the induced transition density for
G–invariant Feller processes on the symmetric space X = G/K. These
are obtained as projections of K–bi–invariant L´evy processes on G,
whose laws form a convolution semigroup. We obtain a Fourier series
expansion for the density, in terms of spherical functions, where the
spectrum is described by Gangolli’s L´evy–Khintchine formula. The
density of returns to any given point on X is given by the trace of
the transition semigroup, and for subordinated Brownian motion, we
can calculate the short time asymptotics of this quantity using recent
work of Ba˜nuelos and Baudoin. In the case of the sphere, there is an
interesting connection with the Funk–Hecke theorem
First exit times of solutions of stochastic differential equations driven by multiplicative Levy noise with heavy tails
In this paper we study first exit times from a bounded domain of a gradient
dynamical system perturbed by a small multiplicative
L\'evy noise with heavy tails. A special attention is paid to the way the
multiplicative noise is introduced. In particular we determine the asymptotics
of the first exit time of solutions of It\^o, Stratonovich and Marcus canonical
SDEs.Comment: 19 pages, 2 figure
The weakly coupled fractional one-dimensional Schr\"{o}dinger operator with index
We study fundamental properties of the fractional, one-dimensional Weyl
operator densely defined on the Hilbert space
and determine the asymptotic behaviour of
both the free Green's function and its variation with respect to energy for
bound states. In the sequel we specify the Birman-Schwinger representation for
the Schr\"{o}dinger operator
and extract the finite-rank portion which is essential for the asymptotic
expansion of the ground state. Finally, we determine necessary and sufficient
conditions for there to be a bound state for small coupling constant .Comment: 16 pages, 1 figur
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
L\'evy-Schr\"odinger wave packets
We analyze the time--dependent solutions of the pseudo--differential
L\'evy--Schr\"odinger wave equation in the free case, and we compare them with
the associated L\'evy processes. We list the principal laws used to describe
the time evolutions of both the L\'evy process densities, and the
L\'evy--Schr\"odinger wave packets. To have self--adjoint generators and
unitary evolutions we will consider only absolutely continuous, infinitely
divisible L\'evy noises with laws symmetric under change of sign of the
independent variable. We then show several examples of the characteristic
behavior of the L\'evy--Schr\"odinger wave packets, and in particular of the
bi-modality arising in their evolutions: a feature at variance with the typical
diffusive uni--modality of both the L\'evy process densities, and the usual
Schr\"odinger wave functions.Comment: 41 pages, 13 figures; paper substantially shortened, while keeping
intact examples and results; changed format from "report" to "article";
eliminated Appendices B, C, F (old names); shifted Chapters 4 and 5 (old
numbers) from text to Appendices C, D (new names); introduced connection
between Relativistic q.m. laws and Generalized Hyperbolic law
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