51,972 research outputs found
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
How round is a protein? Exploring protein structures for globularity using conformal mapping.
We present a new algorithm that automatically computes a measure of the geometric difference between the surface of a protein and a round sphere. The algorithm takes as input two triangulated genus zero surfaces representing the protein and the round sphere, respectively, and constructs a discrete conformal map f between these surfaces. The conformal map is chosen to minimize a symmetric elastic energy E S (f) that measures the distance of f from an isometry. We illustrate our approach on a set of basic sample problems and then on a dataset of diverse protein structures. We show first that E S (f) is able to quantify the roundness of the Platonic solids and that for these surfaces it replicates well traditional measures of roundness such as the sphericity. We then demonstrate that the symmetric elastic energy E S (f) captures both global and local differences between two surfaces, showing that our method identifies the presence of protruding regions in protein structures and quantifies how these regions make the shape of a protein deviate from globularity. Based on these results, we show that E S (f) serves as a probe of the limits of the application of conformal mapping to parametrize protein shapes. We identify limitations of the method and discuss its extension to achieving automatic registration of protein structures based on their surface geometry
Exploring complete positivity in hierarchy equations of motion
We derive a purely algebraic framework for the identification of hierarchy
equations of motion that induce completely positive dynamics and demonstrate
the applicability of our approach with several examples. We find bounds on the
violation of complete positivity for microscopically derived hierarchy
equations of motion and construct well-behaved phenomenological models with
strongly non-Markovian revivals of quantum coherence
Deformations and Geometric Cosets
I review some marginal deformations of SU(2) and SL(2,R) Wess-Zumino-Witten
models, which are relevant for the investigation of the moduli space of NS5/F1
brane configurations. Particular emphasis is given to the asymmetric
deformations, triggered by electric or magnetic fluxes. These exhibit critical
values, where the target spaces become exact geometric cosets such as S2 =
SU(2)/U(1) or AdS2 = SL(2,R)/U(1)-space. I comment about further
generalizations towards the appearance of flag spaces as exact string
solutions.Comment: 10 page
Finding a needle in an exponential haystack: Discrete RRT for exploration of implicit roadmaps in multi-robot motion planning
We present a sampling-based framework for multi-robot motion planning which
combines an implicit representation of a roadmap with a novel approach for
pathfinding in geometrically embedded graphs tailored for our setting. Our
pathfinding algorithm, discrete-RRT (dRRT), is an adaptation of the celebrated
RRT algorithm for the discrete case of a graph, and it enables a rapid
exploration of the high-dimensional configuration space by carefully walking
through an implicit representation of a tensor product of roadmaps for the
individual robots. We demonstrate our approach experimentally on scenarios of
up to 60 degrees of freedom where our algorithm is faster by a factor of at
least ten when compared to existing algorithms that we are aware of.Comment: Kiril Solovey and Oren Salzman contributed equally to this pape
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