46,691 research outputs found
Chaotic Properties of Subshifts Generated by a Non-Periodic Recurrent Orbit
The chaotic properties of some subshift maps are investigated. These
subshifts are the orbit closures of certain non-periodic recurrent points of a
shift map. We first provide a review of basic concepts for dynamics of
continuous maps in metric spaces. These concepts include nonwandering point,
recurrent point, eventually periodic point, scrambled set, sensitive dependence
on initial conditions, Robinson chaos, and topological entropy. Next we review
the notion of shift maps and subshifts. Then we show that the one-sided
subshifts generated by a non-periodic recurrent point are chaotic in the sense
of Robinson. Moreover, we show that such a subshift has an infinite scrambled
set if it has a periodic point. Finally, we give some examples and discuss the
topological entropy of these subshifts, and present two open problems on the
dynamics of subshifts
Penalized Estimation of Directed Acyclic Graphs From Discrete Data
Bayesian networks, with structure given by a directed acyclic graph (DAG),
are a popular class of graphical models. However, learning Bayesian networks
from discrete or categorical data is particularly challenging, due to the large
parameter space and the difficulty in searching for a sparse structure. In this
article, we develop a maximum penalized likelihood method to tackle this
problem. Instead of the commonly used multinomial distribution, we model the
conditional distribution of a node given its parents by multi-logit regression,
in which an edge is parameterized by a set of coefficient vectors with dummy
variables encoding the levels of a node. To obtain a sparse DAG, a group norm
penalty is employed, and a blockwise coordinate descent algorithm is developed
to maximize the penalized likelihood subject to the acyclicity constraint of a
DAG. When interventional data are available, our method constructs a causal
network, in which a directed edge represents a causal relation. We apply our
method to various simulated and real data sets. The results show that our
method is very competitive, compared to many existing methods, in DAG
estimation from both interventional and high-dimensional observational data.Comment: To appear in Statistics and Computin
High Order Momentum Modes by Resonant Superradiant Scattering
The spatial and time evolutions of superradiant scattering are studied
theoretically for a weak pump beam with different frequency components
traveling along the long axis of an elongated Bose-Einstein condensate.
Resulting from the analysis for mode competition between the different resonant
channels and the local depletion of the spatial distribution in the
superradiant Rayleigh scattering, a new method of getting a large number of
high-order forward modes by resonant frequency components of the pump beam is
provided, which is beneficial to a lager momentum transfer in atom manipulation
for the atom interferometry and atomic optics.Comment: 7 pages, 7 figure
Theory for superconductivity in alkali chromium arsenides A2Cr3As3 (A=K,Rb,Cs)
We propose an extended Hubbard model with three molecular orbitals on a
hexagonal lattice with symmetry to study recently discovered
superconductivity in ACrAs (A=K,Rb,Cs). Effective pairing
interactions from paramagnon fluctuations are derived within the random phase
approximation, and are found to be most attractive in spin triplet channels. At
small Hubbard and moderate Hund's coupling, the pairing arises from
3-dimensional (3D) band and has a spatial symmetry
, which gives line nodes in the gap function. At large
, a fully gapped -wave state, dominates at the quasi-1D
-band
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