39,217 research outputs found
Intrinsic data depth for Hermitian positive definite matrices
Nondegenerate covariance, correlation and spectral density matrices are
necessarily symmetric or Hermitian and positive definite. The main contribution
of this paper is the development of statistical data depths for collections of
Hermitian positive definite matrices by exploiting the geometric structure of
the space as a Riemannian manifold. The depth functions allow one to naturally
characterize most central or outlying matrices, but also provide a practical
framework for inference in the context of samples of positive definite
matrices. First, the desired properties of an intrinsic data depth function
acting on the space of Hermitian positive definite matrices are presented.
Second, we propose two computationally fast pointwise and integrated data depth
functions that satisfy each of these requirements and investigate several
robustness and efficiency aspects. As an application, we construct depth-based
confidence regions for the intrinsic mean of a sample of positive definite
matrices, which is applied to the exploratory analysis of a collection of
covariance matrices associated to a multicenter research trial
CosmoHammer: Cosmological parameter estimation with the MCMC Hammer
We study the benefits and limits of parallelised Markov chain Monte Carlo
(MCMC) sampling in cosmology. MCMC methods are widely used for the estimation
of cosmological parameters from a given set of observations and are typically
based on the Metropolis-Hastings algorithm. Some of the required calculations
can however be computationally intensive, meaning that a single long chain can
take several hours or days to calculate. In practice, this can be limiting,
since the MCMC process needs to be performed many times to test the impact of
possible systematics and to understand the robustness of the measurements being
made. To achieve greater speed through parallelisation, MCMC algorithms need to
have short auto-correlation times and minimal overheads caused by tuning and
burn-in. The resulting scalability is hence influenced by two factors, the MCMC
overheads and the parallelisation costs. In order to efficiently distribute the
MCMC sampling over thousands of cores on modern cloud computing infrastructure,
we developed a Python framework called CosmoHammer which embeds emcee, an
implementation by Foreman-Mackey et al. (2012) of the affine invariant ensemble
sampler by Goodman and Weare (2010). We test the performance of CosmoHammer for
cosmological parameter estimation from cosmic microwave background data. While
Metropolis-Hastings is dominated by overheads, CosmoHammer is able to
accelerate the sampling process from a wall time of 30 hours on a dual core
notebook to 16 minutes by scaling out to 2048 cores. Such short wall times for
complex data sets opens possibilities for extensive model testing and control
of systematics.Comment: Published version. 17 pages, 6 figures. The code is available at
http://www.astro.ethz.ch/refregier/research/Software/cosmohamme
Multi-Architecture Monte-Carlo (MC) Simulation of Soft Coarse-Grained Polymeric Materials: SOft coarse grained Monte-carlo Acceleration (SOMA)
Multi-component polymer systems are important for the development of new
materials because of their ability to phase-separate or self-assemble into
nano-structures. The Single-Chain-in-Mean-Field (SCMF) algorithm in conjunction
with a soft, coarse-grained polymer model is an established technique to
investigate these soft-matter systems. Here we present an im- plementation of
this method: SOft coarse grained Monte-carlo Accelera- tion (SOMA). It is
suitable to simulate large system sizes with up to billions of particles, yet
versatile enough to study properties of different kinds of molecular
architectures and interactions. We achieve efficiency of the simulations
commissioning accelerators like GPUs on both workstations as well as
supercomputers. The implementa- tion remains flexible and maintainable because
of the implementation of the scientific programming language enhanced by
OpenACC pragmas for the accelerators. We present implementation details and
features of the program package, investigate the scalability of our
implementation SOMA, and discuss two applications, which cover system sizes
that are difficult to reach with other, common particle-based simulation
methods
Alternative fidelity measure for quantum states
We propose an alternative fidelity measure (namely, a measure of the degree
of similarity) between quantum states and benchmark it against a number of
properties of the standard Uhlmann-Jozsa fidelity. This measure is a simple
function of the linear entropy and the Hilbert-Schmidt inner product between
the given states and is thus, in comparison, not as computationally demanding.
It also features several remarkable properties such as being jointly concave
and satisfying all of "Jozsa's axioms". The trade-off, however, is that it is
supermultiplicative and does not behave monotonically under quantum operations.
In addition, new metrics for the space of density matrices are identified and
the joint concavity of the Uhlmann-Jozsa fidelity for qubit states is
established.Comment: 12 pages, 3 figures. v2 includes minor changes, new references and
new numerical results (Sec. IV
A Brief History of Web Crawlers
Web crawlers visit internet applications, collect data, and learn about new
web pages from visited pages. Web crawlers have a long and interesting history.
Early web crawlers collected statistics about the web. In addition to
collecting statistics about the web and indexing the applications for search
engines, modern crawlers can be used to perform accessibility and vulnerability
checks on the application. Quick expansion of the web, and the complexity added
to web applications have made the process of crawling a very challenging one.
Throughout the history of web crawling many researchers and industrial groups
addressed different issues and challenges that web crawlers face. Different
solutions have been proposed to reduce the time and cost of crawling.
Performing an exhaustive crawl is a challenging question. Additionally
capturing the model of a modern web application and extracting data from it
automatically is another open question. What follows is a brief history of
different technique and algorithms used from the early days of crawling up to
the recent days. We introduce criteria to evaluate the relative performance of
web crawlers. Based on these criteria we plot the evolution of web crawlers and
compare their performanc
An Optimized and Scalable Eigensolver for Sequences of Eigenvalue Problems
In many scientific applications the solution of non-linear differential
equations are obtained through the set-up and solution of a number of
successive eigenproblems. These eigenproblems can be regarded as a sequence
whenever the solution of one problem fosters the initialization of the next. In
addition, in some eigenproblem sequences there is a connection between the
solutions of adjacent eigenproblems. Whenever it is possible to unravel the
existence of such a connection, the eigenproblem sequence is said to be
correlated. When facing with a sequence of correlated eigenproblems the current
strategy amounts to solving each eigenproblem in isolation. We propose a
alternative approach which exploits such correlation through the use of an
eigensolver based on subspace iteration and accelerated with Chebyshev
polynomials (ChFSI). The resulting eigensolver is optimized by minimizing the
number of matrix-vector multiplications and parallelized using the Elemental
library framework. Numerical results show that ChFSI achieves excellent
scalability and is competitive with current dense linear algebra parallel
eigensolvers.Comment: 23 Pages, 6 figures. First revision of an invited submission to
special issue of Concurrency and Computation: Practice and Experienc
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