9,525 research outputs found
Analysis of stochastic time series in the presence of strong measurement noise
A new approach for the analysis of Langevin-type stochastic processes in the
presence of strong measurement noise is presented. For the case of Gaussian
distributed, exponentially correlated, measurement noise it is possible to
extract the strength and the correlation time of the noise as well as
polynomial approximations of the drift and diffusion functions from the
underlying Langevin equation.Comment: 12 pages, 10 figures; corrected typos and reference
Numerical treatment of the hyperboloidal initial value problem for the vacuum Einstein equations. I. The conformal field equations
This is the first in a series of articles on the numerical solution of
Friedrich's conformal field equations for Einstein's theory of gravity. We will
discuss in this paper why one should be interested in applying the conformal
method to physical problems and why there is good hope that this might even be
a good idea from the numerical point of view. We describe in detail the
derivation of the conformal field equations in the spinor formalism which we
use for the implementation of the equations, and present all the equations as a
reference for future work. Finally, we discuss the implications of the
assumptions of a continuous symmetry.Comment: 19 pages, LaTeX2
Nonstationary Increments, Scaling Distributions, and Variable Diffusion Processes in Financial Markets
Arguably the most important problem in quantitative finance is to understand
the nature of stochastic processes that underlie market dynamics. One aspect of
the solution to this problem involves determining characteristics of the
distribution of fluctuations in returns. Empirical studies conducted over the
last decade have reported that they arenon-Gaussian, scale in time, and have
power-law(or fat) tails. However, because they use sliding interval methods of
analysis, these studies implicitly assume that the underlying process has
stationary increments. We explicitly show that this assumption is not valid for
the Euro-Dollar exchange rate between 1999-2004. In addition, we find that
fluctuations in returns of the exchange rate are uncorrelated and scale as
power-laws for certain time intervals during each day. This behavior is
consistent with a diffusive process with a diffusion coefficient that depends
both on the time and the price change. Within scaling regions, we find that
sliding interval methods can generate fat-tailed distributions as an artifact,
and that the type of scaling reported in many previous studies does not exist.Comment: 12 pages, 4 figure
Effect of Local Electron-Electron Correlation in Hydrogen-like Impurities in Ge
We have studied the electronic and local magnetic structure of the hydrogen
interstitial impurity at the tetrahedral site in diamond-structure Ge, using an
empirical tight binding + dynamical mean field theory approach because within
the local density approximation (LDA) Ge has no gap. We first establish that
within LDA the 1s spectral density bifurcates due to entanglement with the four
neighboring sp3 antibonding orbitals, providing an unanticipated richness of
behavior in determining under what conditions a local moment hyperdeep donor or
Anderson impurity will result, or on the other hand a gap state might appear.
Using a supercell approach, we show that the spectrum, the occupation, and the
local moment of the impurity state displays a strong dependence on the strength
of the local on-site Coulomb interaction U, the H-Ge hopping amplitude, the
depth of the bare 1s energy level epsilon_H, and we address to some extent the
impurity concentration dependence. In the isolated impurity, strong interaction
regime a local moment emerges over most of the parameter ranges indicating
magnetic activity, and spectral density structure very near (or in) the gap
suggests possible electrical activity in this regime.Comment: 9 pages, 5 figure
First-order symmetrizable hyperbolic formulations of Einstein's equations including lapse and shift as dynamical fields
First-order hyperbolic systems are promising as a basis for numerical
integration of Einstein's equations. In previous work, the lapse and shift have
typically not been considered part of the hyperbolic system and have been
prescribed independently. This can be expensive computationally, especially if
the prescription involves solving elliptic equations. Therefore, including the
lapse and shift in the hyperbolic system could be advantageous for numerical
work. In this paper, two first-order symmetrizable hyperbolic systems are
presented that include the lapse and shift as dynamical fields and have only
physical characteristic speeds.Comment: 11 page
Exponential Decay for Small Non-Linear Perturbations of Expanding Flat Homogeneous Cosmologies
It is shown that during expanding phases of flat homogeneous cosmologies all
small enough non-linear perturbations decay exponentially. This result holds
for a large class of perfect fluid equations of state, but notably not for very
``stiff'' fluids as the pure radiation case
Revised Huang-Yang multipolar pseudopotential
A number of authors have recently pointed out inconsistencies of results
obtained with the Huang-Yang multipolar pseudo-potential for low-energy
scattering [K. Huang and K. C. Yang, Phys. Rev. A, v 105, 767 (1957); later
revised in K. Huang, ``Statistical Mechanics'', (Wiley, New York, 1963)]. The
conceptual validity of their original derivation has been questioned. Here I
show that these inconsistencies are rather due to an {\em algebraic} mistake
made by Huang and Yang. With the corrected error, I present the revised version
of the multipolar pseudo-potential
Theoretical investigation into the possibility of very large moments in Fe16N2
We examine the mystery of the disputed high-magnetization \alpha"-Fe16N2
phase, employing the Heyd-Scuseria-Ernzerhof screened hybrid functional method,
perturbative many-body corrections through the GW approximation, and onsite
Coulomb correlations through the GGA+U method. We present a first-principles
computation of the effective on-site Coulomb interaction (Hubbard U) between
localized 3d electrons employing the constrained random-phase approximation
(cRPA), finding only somewhat stronger on-site correlations than in bcc Fe. We
find that the hybrid functional method, the GW approximation, and the GGA+U
method (using parameters computed from cRPA) yield an average spin moment of
2.9, 2.6 - 2.7, and 2.7 \mu_B per Fe, respectively.Comment: 8 pages, 3 figure
3D simulations of Einstein's equations: symmetric hyperbolicity, live gauges and dynamic control of the constraints
We present three-dimensional simulations of Einstein equations implementing a
symmetric hyperbolic system of equations with dynamical lapse. The numerical
implementation makes use of techniques that guarantee linear numerical
stability for the associated initial-boundary value problem. The code is first
tested with a gauge wave solution, where rather larger amplitudes and for
significantly longer times are obtained with respect to other state of the art
implementations. Additionally, by minimizing a suitably defined energy for the
constraints in terms of free constraint-functions in the formulation one can
dynamically single out preferred values of these functions for the problem at
hand. We apply the technique to fully three-dimensional simulations of a
stationary black hole spacetime with excision of the singularity, considerably
extending the lifetime of the simulations.Comment: 21 pages. To appear in PR
Estimation of drift and diffusion functions from time series data: A maximum likelihood framework
Complex systems are characterized by a huge number of degrees of freedom
often interacting in a non-linear manner. In many cases macroscopic states,
however, can be characterized by a small number of order parameters that obey
stochastic dynamics in time. Recently techniques for the estimation of the
corresponding stochastic differential equations from measured data have been
introduced. This contribution develops a framework for the estimation of the
functions and their respective (Bayesian posterior) confidence regions based on
likelihood estimators. In succession approximations are introduced that
significantly improve the efficiency of the estimation procedure. While being
consistent with standard approaches to the problem this contribution solves
important problems concerning the applicability and the accuracy of estimated
parameters.Comment: 18 pages, 2 figure
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