96,478 research outputs found
Identifying dynamical systems with bifurcations from noisy partial observation
Dynamical systems are used to model a variety of phenomena in which the
bifurcation structure is a fundamental characteristic. Here we propose a
statistical machine-learning approach to derive lowdimensional models that
automatically integrate information in noisy time-series data from partial
observations. The method is tested using artificial data generated from two
cell-cycle control system models that exhibit different bifurcations, and the
learned systems are shown to robustly inherit the bifurcation structure.Comment: 16 pages, 6 figure
Properties making a chaotic system a good Pseudo Random Number Generator
We discuss two properties making a deterministic algorithm suitable to
generate a pseudo random sequence of numbers: high value of Kolmogorov-Sinai
entropy and high-dimensionality. We propose the multi dimensional Anosov
symplectic (cat) map as a Pseudo Random Number Generator. We show what chaotic
features of this map are useful for generating Pseudo Random Numbers and
investigate numerically which of them survive in the discrete version of the
map. Testing and comparisons with other generators are performed.Comment: 10 pages, 3 figures, new version, title changed and minor correction
Conformally Coupled General Relativity
Gravity model developed in the series of papers
\cite{Arbuzov:2009zza,Arbuzov:2010fz,Pervushin:2011gz} is revisited. Model is
based on Ogievetsky theorem that specifies structure of general coordinate
transformation group. The theorem is implemented in the context of Noether
theorem with the use of nonlinear representation technique. Canonical
quantization is performed with the use of reparametrization-invariant time and
ADM foliation techniques. Basic quantum features of the models are discussed.
Mistakes occurred in the previous papers are corrected.Comment: 20 page
Goal-oriented sensitivity analysis for lattice kinetic Monte Carlo simulations
In this paper we propose a new class of coupling methods for the sensitivity
analysis of high dimensional stochastic systems and in particular for lattice
Kinetic Monte Carlo. Sensitivity analysis for stochastic systems is typically
based on approximating continuous derivatives with respect to model parameters
by the mean value of samples from a finite difference scheme. Instead of using
independent samples the proposed algorithm reduces the variance of the
estimator by developing a strongly correlated-"coupled"- stochastic process for
both the perturbed and unperturbed stochastic processes, defined in a common
state space. The novelty of our construction is that the new coupled process
depends on the targeted observables, e.g. coverage, Hamiltonian, spatial
correlations, surface roughness, etc., hence we refer to the proposed method as
em goal-oriented sensitivity analysis. In particular, the rates of the coupled
Continuous Time Markov Chain are obtained as solutions to a goal-oriented
optimization problem, depending on the observable of interest, by considering
the minimization functional of the corresponding variance. We show that this
functional can be used as a diagnostic tool for the design and evaluation of
different classes of couplings. Furthermore the resulting KMC sensitivity
algorithm has an easy implementation that is based on the Bortz-Kalos-Lebowitz
algorithm's philosophy, where here events are divided in classes depending on
level sets of the observable of interest. Finally, we demonstrate in several
examples including adsorption, desorption and diffusion Kinetic Monte Carlo
that for the same confidence interval and observable, the proposed
goal-oriented algorithm can be two orders of magnitude faster than existing
coupling algorithms for spatial KMC such as the Common Random Number approach
q-Deformed de Sitter/Conformal Field Theory Correspondence
Unitary principal series representations of the conformal group appear in the
dS/CFT correspondence. These are infinite dimensional irreducible
representations, without highest weights. In earlier work of Guijosa and the
author it was shown for the case of two-dimensional de Sitter, there was a
natural q-deformation of the conformal group, with q a root of unity, where the
unitary principal series representations become finite-dimensional cyclic
unitary representations. Formulating a version of the dS/CFT correspondence
using these representations can lead to a description with a finite-dimensional
Hilbert space and unitary evolution. In the present work, we generalize to the
case of quantum-deformed three-dimensional de Sitter spacetime and compute the
entanglement entropy of a quantum field across the cosmological horizon.Comment: 18 pages, 2 figures, revtex, (v2 reference added
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