4,975 research outputs found
Center vortex model for the infrared sector of SU(3) Yang-Mills theory: Topological susceptibility
The topological susceptibility of the SU(3) random vortex world-surface
ensemble, an effective model of infrared Yang-Mills dynamics, is investigated.
The model is implemented by composing vortex world-surfaces of elementary
squares on a hypercubic lattice, supplemented by an appropriate specification
of vortex color structure on the world-surfaces. Topological charge is
generated in this picture by writhe and self-intersection of the vortex
world-surfaces. Systematic uncertainties in the evaluation of the topological
charge, engendered by the hypercubic construction, are discussed. Results for
the topological susceptibility are reported as a function of temperature and
compared to corresponding measurements in SU(3) lattice Yang-Mills theory. In
the confined phase, the topological susceptibility of the random vortex
world-surface ensemble appears quantitatively consistent with Yang-Mills
theory. As the temperature is raised into the deconfined regime, the
topological susceptibility falls off rapidly, but significantly less so than in
SU(3) lattice Yang-Mills theory. Possible causes of this deviation, ranging
from artefacts of the hypercubic description to more physical sources, such as
the adopted vortex dynamics, are discussed.Comment: 30 pages, 6 figure
Hierarchical Compound Poisson Factorization
Non-negative matrix factorization models based on a hierarchical
Gamma-Poisson structure capture user and item behavior effectively in extremely
sparse data sets, making them the ideal choice for collaborative filtering
applications. Hierarchical Poisson factorization (HPF) in particular has proved
successful for scalable recommendation systems with extreme sparsity. HPF,
however, suffers from a tight coupling of sparsity model (absence of a rating)
and response model (the value of the rating), which limits the expressiveness
of the latter. Here, we introduce hierarchical compound Poisson factorization
(HCPF) that has the favorable Gamma-Poisson structure and scalability of HPF to
high-dimensional extremely sparse matrices. More importantly, HCPF decouples
the sparsity model from the response model, allowing us to choose the most
suitable distribution for the response. HCPF can capture binary, non-negative
discrete, non-negative continuous, and zero-inflated continuous responses. We
compare HCPF with HPF on nine discrete and three continuous data sets and
conclude that HCPF captures the relationship between sparsity and response
better than HPF.Comment: Will appear on Proceedings of the 33 rd International Conference on
Machine Learning, New York, NY, USA, 2016. JMLR: W&CP volume 4
Effects of neutral selection on the evolution of molecular species
We introduce a new model of evolution on a fitness landscape possessing a
tunable degree of neutrality. The model allows us to study the general
properties of molecular species undergoing neutral evolution. We find that a
number of phenomena seen in RNA sequence-structure maps are present also in our
general model. Examples are the occurrence of "common" structures which occupy
a fraction of the genotype space which tends to unity as the length of the
genotype increases, and the formation of percolating neutral networks which
cover the genotype space in such a way that a member of such a network can be
found within a small radius of any point in the space. We also describe a
number of new phenomena which appear to be general properties of neutrally
evolving systems. In particular, we show that the maximum fitness attained
during the adaptive walk of a population evolving on such a fitness landscape
increases with increasing degree of neutrality, and is directly related to the
fitness of the most fit percolating network.Comment: 16 pages including 4 postscript figures, typeset in LaTeX2e using the
Elsevier macro package elsart.cl
Expandable Factor Analysis
Bayesian sparse factor models have proven useful for characterizing
dependence in multivariate data, but scaling computation to large numbers of
samples and dimensions is problematic. We propose expandable factor analysis
for scalable inference in factor models when the number of factors is unknown.
The method relies on a continuous shrinkage prior for efficient maximum a
posteriori estimation of a low-rank and sparse loadings matrix. The structure
of the prior leads to an estimation algorithm that accommodates uncertainty in
the number of factors. We propose an information criterion to select the
hyperparameters of the prior. Expandable factor analysis has better false
discovery rates and true positive rates than its competitors across diverse
simulations. We apply the proposed approach to a gene expression study of aging
in mice, illustrating superior results relative to four competing methods.Comment: 28 pages, 4 figure
- …