11,376 research outputs found
Lyapunov-Schmidt Reduction for Unfolding Heteroclinic Networks of Equilibria and Periodic Orbits with Tangencies
This article concerns arbitrary finite heteroclinic networks in any phase
space dimension whose vertices can be a random mixture of equilibria and
periodic orbits. In addition, tangencies in the intersection of un/stable
manifolds are allowed. The main result is a reduction to algebraic equations of
the problem to find all solutions that are close to the heteroclinic network
for all time, and their parameter values. A leading order expansion is given in
terms of the time spent near vertices and, if applicable, the location on the
non-trivial tangent directions. The only difference between a periodic orbit
and an equilibrium is that the time parameter is discrete for a periodic orbit.
The essential assumptions are hyperbolicity of the vertices and transversality
of parameters. Using the result, conjugacy to shift dynamics for a generic
homoclinic orbit to a periodic orbit is proven. Finally,
equilibrium-to-periodic orbit heteroclinic cycles of various types are
considered
Canonical Interacting Quantum Fields on Two-Dimensional De Sitter Space
We present the model on de Sitter space in the
canonical formulation. We discuss the role of the Noether theorem and we
provide explicit expressions for the energy-stress tensor of the interacting
model.Comment: minor correction
Bayesian inference from photometric redshift surveys
We show how to enhance the redshift accuracy of surveys consisting of tracers
with highly uncertain positions along the line of sight. Photometric surveys
with redshift uncertainty delta_z ~ 0.03 can yield final redshift uncertainties
of delta_z_f ~ 0.003 in high density regions. This increased redshift precision
is achieved by imposing an isotropy and 2-point correlation prior in a Bayesian
analysis and is completely independent of the process that estimates the
photometric redshift. As a byproduct, the method also infers the three
dimensional density field, essentially super-resolving high density regions in
redshift space. Our method fully takes into account the survey mask and
selection function. It uses a simplified Poissonian picture of galaxy
formation, relating preferred locations of galaxies to regions of higher
density in the matter field. The method quantifies the remaining uncertainties
in the three dimensional density field and the true radial locations of
galaxies by generating samples that are constrained by the survey data. The
exploration of this high dimensional, non-Gaussian joint posterior is made
feasible using multiple-block Metropolis-Hastings sampling. We demonstrate the
performance of our implementation on a simulation containing 2.0 x 10^7
galaxies. These results bear out the promise of Bayesian analysis for upcoming
photometric large scale structure surveys with tens of millions of galaxies.Comment: 17 pages, 12 figure
Methods for Bayesian power spectrum inference with galaxy surveys
We derive and implement a full Bayesian large scale structure inference
method aiming at precision recovery of the cosmological power spectrum from
galaxy redshift surveys. Our approach improves over previous Bayesian methods
by performing a joint inference of the three dimensional density field, the
cosmological power spectrum, luminosity dependent galaxy biases and
corresponding normalizations. We account for all joint and correlated
uncertainties between all inferred quantities. Classes of galaxies with
different biases are treated as separate sub samples. The method therefore also
allows the combined analysis of more than one galaxy survey.
In particular, it solves the problem of inferring the power spectrum from
galaxy surveys with non-trivial survey geometries by exploring the joint
posterior distribution with efficient implementations of multiple block Markov
chain and Hybrid Monte Carlo methods. Our Markov sampler achieves high
statistical efficiency in low signal to noise regimes by using a deterministic
reversible jump algorithm. We test our method on an artificial mock galaxy
survey, emulating characteristic features of the Sloan Digital Sky Survey data
release 7, such as its survey geometry and luminosity dependent biases. These
tests demonstrate the numerical feasibility of our large scale Bayesian
inference frame work when the parameter space has millions of dimensions.
The method reveals and correctly treats the anti-correlation between bias
amplitudes and power spectrum, which are not taken into account in current
approaches to power spectrum estimation, a 20 percent effect across large
ranges in k-space. In addition, the method results in constrained realizations
of density fields obtained without assuming the power spectrum or bias
parameters in advance
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Representing chord sequences in OWL
Chord symbols and progressions are a common way to describe musical harmony. In this paper we present SEQ, a pattern representation using the Web Ontology Language OWL DL and its application to modelling chord sequences. SEQ provides a logical representation of order information, which is not available directly in OWL DL, together with an intuitive notation. It therefore allows the use of OWL reasoners for tasks such as classification of sequences by patterns and determining subsumption relationships between the patterns. The SEQ representation is used to express distinctive pattern obtained using data mining of multiple viewpoints of chord sequences
Patterns formation in axially symmetric Landau-Lifshitz-Gilbert-Slonczewski equations
The Landau-Lifshitz-Gilbert-Slonczewski equation describes magnetization
dynamics in the presence of an applied field and a spin polarized current. In
the case of axial symmetry and with focus on one space dimension, we
investigate the emergence of space-time patterns in the form of wavetrains and
coherent structures, whose local wavenumber varies in space. A major part of
this study concerns existence and stability of wavetrains and of front- and
domain wall-type coherent structures whose profiles asymptote to wavetrains or
the constant up-/down-magnetizations. For certain polarization the Slonczewski
term can be removed which allows for a more complete charaterization, including
soliton-type solutions. Decisive for the solution structure is the polarization
parameter as well as size of anisotropy compared with the difference of field
intensity and current intensity normalized by the damping
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