6,852 research outputs found
Complexity and phase transitions in a holographic QCD model
Applying the "Complexity=Action" conjecture, we study the holographic
complexity close to crossover/phase transition in a holographic QCD model
proposed by Gubser et al. This model can realize three types of phase
transition, crossover or first and second order, depending on the parameters of
the dilaton potential. The re-scaled late-time growth rate of holographic
complexity density for the three cases is calculated. Our results show that it
experiences a fast drop/jump close to the critical point while approaching
constants far beyond the critical temperature. Moreover, close to the critical
temperature, it shows a behavior characterizing the type of the transition.
These features suggest that the growth rate of the holographic complexity may
be used as a good parameter to characterize the phase transition. The Lloyd's
bound is always satisfied for the cases we considered but only saturated for
the conformal case.Comment: v1: 14 pages, 2 figures; v2: refs added, minor modifications. arXiv
admin note: substantial text overlap with arXiv:1608.03072; v3: More details
on the Lloyd's bound, matching the published versio
Holographic entanglement entropy close to crossover/phase transition in strongly coupled systems
We investigate the behavior of entanglement entropy in the holographic QCD
model proposed by Gubser et al. By choosing suitable parameters of the scalar
self-interaction potential, this model can exhibit various types of phase
structures: crossover, first order and second order phase transitions. We use
entanglement entropy to probe the crossover/phase transition, and find that it
drops quickly/suddenly when the temperature approaches the critical point which
can be seen as a signal of confinement. Moreover, the critical behavior of the
entanglement entropy suggests that we may use it to characterize the
corresponding phase structures.Comment: v1:19 pages, 5 figures; v2: refs added; v3: 20 pages,
high-temperature behaviors of holographic entanglement entropy are given,
accecpted for publication by NP
Estimation in high-dimensional linear models with deterministic design matrices
Because of the advance in technologies, modern statistical studies often
encounter linear models with the number of explanatory variables much larger
than the sample size. Estimation and variable selection in these
high-dimensional problems with deterministic design points is very different
from those in the case of random covariates, due to the identifiability of the
high-dimensional regression parameter vector. We show that a reasonable
approach is to focus on the projection of the regression parameter vector onto
the linear space generated by the design matrix. In this work, we consider the
ridge regression estimator of the projection vector and propose to threshold
the ridge regression estimator when the projection vector is sparse in the
sense that many of its components are small. The proposed estimator has an
explicit form and is easy to use in application. Asymptotic properties such as
the consistency of variable selection and estimation and the convergence rate
of the prediction mean squared error are established under some sparsity
conditions on the projection vector. A simulation study is also conducted to
examine the performance of the proposed estimator.Comment: Published in at http://dx.doi.org/10.1214/12-AOS982 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Holographic Thermalization in Charged Dilaton Anti-de Sitter Spacetime
We study holographic thermalization in spacetimes with a chemical potential
and a non-trivial dilaton field. Three non-local observables are used to probe
the whole process and investigate the effect of the ratio of the chemical
potential over temperature and the dilaton-Maxwell coupling constant
. It is found that the saturation time is not always a monotonically
increasing function of , the situation depends on . When , larger yields longer saturation time, while for
, the situation becomes more complex. More interesting, we found that
although indeed has influence on the whole thermalization process, it
nearly does not affect the saturation time, which indicates the universality of
the saturation time for the dual one-parameter field theories.Comment: 22 pages, 5 figure
Solving the undirected feedback vertex set problem by local search
An undirected graph consists of a set of vertices and a set of undirected
edges between vertices. Such a graph may contain an abundant number of cycles,
then a feedback vertex set (FVS) is a set of vertices intersecting with each of
these cycles. Constructing a FVS of cardinality approaching the global minimum
value is a optimization problem in the nondeterministic polynomial-complete
complexity class, therefore it might be extremely difficult for some large
graph instances. In this paper we develop a simulated annealing local search
algorithm for the undirected FVS problem. By defining an order for the vertices
outside the FVS, we replace the global cycle constraints by a set of local
vertex constraints on this order. Under these local constraints the cardinality
of the focal FVS is then gradually reduced by the simulated annealing dynamical
process. We test this heuristic algorithm on large instances of Er\"odos-Renyi
random graph and regular random graph, and find that this algorithm is
comparable in performance to the belief propagation-guided decimation
algorithm.Comment: 6 page
A pseudo empirical likelihood approach for stratified samples with nonresponse
Nonresponse is common in surveys. When the response probability of a survey
variable depends on through an observed auxiliary categorical variable
(i.e., the response probability of is conditionally independent of
given ), a simple method often used in practice is to use categories as
imputation cells and construct estimators by imputing nonrespondents or
reweighting respondents within each imputation cell. This simple method,
however, is inefficient when some categories have small sizes and ad hoc
methods are often applied to collapse small imputation cells. Assuming a
parametric model on the conditional probability of given and a
nonparametric model on the distribution of , we develop a pseudo empirical
likelihood method to provide more efficient survey estimators. Our method
avoids any ad hoc collapsing small categories, since reweighting or
imputation is done across categories. Asymptotic distributions for
estimators of population means based on the pseudo empirical likelihood method
are derived. For variance estimation, we consider a bootstrap procedure and its
consistency is established. Some simulation results are provided to assess the
finite sample performance of the proposed estimators.Comment: Published in at http://dx.doi.org/10.1214/07-AOS578 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
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