105 research outputs found
Tapping Thermodynamics of the One Dimensional Ising Model
We analyse the steady state regime of a one dimensional Ising model under a
tapping dynamics recently introduced by analogy with the dynamics of
mechanically perturbed granular media. The idea that the steady state regime
may be described by a flat measure over metastable states of fixed energy is
tested by comparing various steady state time averaged quantities in extensive
numerical simulations with the corresponding ensemble averages computed
analytically with this flat measure. The agreement between the two averages is
excellent in all the cases examined, showing that a static approach is capable
of predicting certain measurable properties of the steady state regime.Comment: 11 pages, 5 figure
Analytical solution of a one-dimensional Ising model with zero temperature dynamics
The one-dimensional Ising model with nearest neighbour interactions and the
zero-temperature dynamics recently considered by Lefevre and Dean -J. Phys. A:
Math. Gen. {\bf 34}, L213 (2001)- is investigated. By introducing a
particle-hole description, in which the holes are associated to the domain
walls of the Ising model, an analytical solution is obtained. The result for
the asymptotic energy agrees with that found in the mean field approximation.Comment: 6 pages, no figures; accepted in J. Phys. A: Math. Gen. (Letter to
the Editor
The statistics of critical points of Gaussian fields on large-dimensional spaces
We calculate the average number of critical points of a Gaussian field on a
high-dimensional space as a function of their energy and their index. Our
results give a complete picture of the organization of critical points and are
of relevance to glassy and disordered systems, and to landscape scenarios
coming from the anthropic approach to string theory.Comment: 5 page
Phase transitions in the steady state behavior of mechanically perturbed spin glasses and ferromagnets
We analyze the steady state regime of systems interpolating between spin
glasses and ferromagnets under a tapping dynamics recently introduced by
analogy with the dynamics of mechanically perturbed granular media. A crossover
from a second order to first order ferromagnetic transition as a function of
the spin coupling distribution is found. The flat measure over blocked states
introduced by Edwards for granular media is used to explain this scenario.
Annealed calculations of the Edwards entropy are shown to qualitatively explain
the nature of the phase transitions. A Monte-Carlo construction of the Edwards
measure confirms that this explanation is also quantitatively accurate
Steady State Behavior of Mechanically Perturbed Spin Glasses and Ferromagnets
A zero temperature dynamics of Ising spin glasses and ferromagnets on random
graphs of finite connectivity is considered, like granular media these systems
have an extensive entropy of metastable states. We consider the problem of what
energy a randomly prepared spin system falls to before becoming stuck in a
metastable state. We then introduce a tapping mechanism, analogous to that of
real experiments on granular media, this tapping, corresponding to flipping
simultaneously any spin with probability , leads to stationary regime with a
steady state energy . We explicitly solve this problem for the one
dimensional ferromagnet and spin glass and carry out extensive
numerical simulations for spin systems of higher connectivity. The link with
the density of metastable states at fixed energy and the idea of Edwards that
one may construct a thermodynamics with a flat measure over metastable states
is discussed. In addition our simulations on the ferromagnetic systems reveal a
novel first order transition, whereas the usual thermodynamic transition on
these graphs is second order.Comment: 11 pages, 7 figure
Asymptotic behavior of the density of states on a random lattice
We study the diffusion of a particle on a random lattice with fluctuating
local connectivity of average value q. This model is a basic description of
relaxation processes in random media with geometrical defects. We analyze here
the asymptotic behavior of the eigenvalue distribution for the Laplacian
operator. We found that the localized states outside the mobility band and
observed by Biroli and Monasson (1999, J. Phys. A: Math. Gen. 32 L255), in a
previous numerical analysis, are described by saddle point solutions that
breaks the rotational symmetry of the main action in the real space. The
density of states is characterized asymptotically by a series of peaks with
periodicity 1/q.Comment: 11 pages, 2 figure
Langevin dynamics of the Lebowitz-Percus model
We revisit the hard-spheres lattice gas model in the spherical approximation
proposed by Lebowitz and Percus (J. L. Lebowitz, J. K. Percus, Phys. Rev.{\
144} (1966) 251). Although no disorder is present in the model, we find that
the short-range dynamical restrictions in the model induce glassy behavior. We
examine the off-equilibrium Langevin dynamics of this model and study the
relaxation of the density as well as the correlation, response and overlap
two-time functions. We find that the relaxation proceeds in two steps as well
as absence of anomaly in the response function. By studying the violation of
the fluctuation-dissipation ratio we conclude that the glassy scenario of this
model corresponds to the dynamics of domain growth in phase ordering kinetics.Comment: 21 pages, RevTeX, 14 PS figure
Exact Occupation Time Distribution in a Non-Markovian Sequence and Its Relation to Spin Glass Models
We compute exactly the distribution of the occupation time in a discrete {\em
non-Markovian} toy sequence which appears in various physical contexts such as
the diffusion processes and Ising spin glass chains. The non-Markovian property
makes the results nontrivial even for this toy sequence. The distribution is
shown to have non-Gaussian tails characterized by a nontrivial large deviation
function which is computed explicitly. An exact mapping of this sequence to an
Ising spin glass chain via a gauge transformation raises an interesting new
question for a generic finite sized spin glass model: at a given temperature,
what is the distribution (over disorder) of the thermally averaged number of
spins that are aligned to their local fields? We show that this distribution
remains nontrivial even at infinite temperature and can be computed explicitly
in few cases such as in the Sherrington-Kirkpatrick model with Gaussian
disorder.Comment: 10 pages Revtex (two-column), 1 eps figure (included
Large Deviations of the Maximum Eigenvalue in Wishart Random Matrices
We compute analytically the probability of large fluctuations to the left of
the mean of the largest eigenvalue in the Wishart (Laguerre) ensemble of
positive definite random matrices. We show that the probability that all the
eigenvalues of a (N x N) Wishart matrix W=X^T X (where X is a rectangular M x N
matrix with independent Gaussian entries) are smaller than the mean value
=N/c decreases for large N as , where \beta=1,2 correspond respectively to
real and complex Wishart matrices, c=N/M < 1 and \Phi_{-}(x;c) is a large
deviation function that we compute explicitly. The result for the Anti-Wishart
case (M < N) simply follows by exchanging M and N. We also analytically
determine the average spectral density of an ensemble of constrained Wishart
matrices whose eigenvalues are forced to be smaller than a fixed barrier. The
numerical simulations are in excellent agreement with the analytical
predictions.Comment: Published version. References and appendix adde
HSRA: Hadoop-based spliced read aligner for RNA sequencing data
[Abstract] Nowadays, the analysis of transcriptome sequencing (RNA-seq) data has become the standard method for quantifying the levels of gene expression. In RNA-seq experiments, the mapping of short reads to a reference genome or transcriptome is considered a crucial step that remains as one of the most time-consuming. With the steady development of Next Generation Sequencing (NGS) technologies, unprecedented amounts of genomic data introduce significant challenges in terms of storage, processing and downstream analysis. As cost and throughput continue to improve, there is a growing need for new software solutions that minimize the impact of increasing data volume on RNA read alignment. In this work we introduce HSRA, a Big Data tool that takes advantage of the MapReduce programming model to extend the multithreading capabilities of a state-of-the-art spliced read aligner for RNA-seq data (HISAT2) to distributed memory systems such as multi-core clusters or cloud platforms. HSRA has been built upon the Hadoop MapReduce framework and supports both single- and paired-end reads from FASTQ/FASTA datasets, providing output alignments in SAM format. The design of HSRA has been carefully optimized to avoid the main limitations and major causes of inefficiency found in previous Big Data mapping tools, which cannot fully exploit the raw performance of the underlying aligner. On a 16-node multi-core cluster, HSRA is on average 2.3 times faster than previous Hadoop-based tools. Source code in Java as well as a user’s guide are publicly available for download at http://hsra.dec.udc.es.Ministerio de Economía, Industria y Competitividad; TIN2016-75845-PXunta de Galicia; ED431G/0
- …