1,274 research outputs found
Weyl Expansion for Symmetric Potentials
We present a semiclassical expansion of the smooth part of the density of
states in potentials with some form of symmetry. The density of states of each
irreducible representation is separately evaluated using the Wigner transforms
of the projection operators. For discrete symmetries the expansion yields a
formally exact but asymptotic series in , while for the rotational
symmetries the expansion requires averaging over angular momentum as
well as energy. A numerical example is given in two dimensions, in which we
calculate the leading terms of the Weyl expansion as well as the leading
periodic orbit contributions to the symmetry reduced level density.Comment: Four of the five figures are appended as a postscript file. The fifth
figure is available by snail mail
Atomic frequency comb memory with spin wave storage in 153Eu3+:Y2SiO5
153Eu3+:Y2SiO5 is a very attractive candidate for a long lived, multimode
quantum memory due to the long spin coherence time (~15 ms), the relatively
large hyperfine splitting (100 MHz) and the narrow optical homogeneous
linewidth (~100 Hz). Here we show an atomic frequency comb memory with spin
wave storage in a promising material 153Eu3+:Y2SiO5, reaching storage times
slightly beyond 10 {\mu}s. We analyze the efficiency of the storage process and
discuss ways of improving it. We also measure the inhomogeneous spin linewidth
of 153Eu3+:Y2SiO5, which we find to be 69 \pm 3 kHz. These results represent a
further step towards realising a long lived multi mode solid state quantum
memory.Comment: 7 pages and 7 figure
Divergence functions in Information Geometry
A recently introduced canonical divergence for a dual structure
is discussed in connection to other divergence
functions. Finally, open problems concerning symmetry properties are outlined.Comment: 10 page
Maximum Likelihood Estimation in Gaussian Chain Graph Models under the Alternative Markov Property
The AMP Markov property is a recently proposed alternative Markov property
for chain graphs. In the case of continuous variables with a joint multivariate
Gaussian distribution, it is the AMP rather than the earlier introduced LWF
Markov property that is coherent with data-generation by natural
block-recursive regressions. In this paper, we show that maximum likelihood
estimates in Gaussian AMP chain graph models can be obtained by combining
generalized least squares and iterative proportional fitting to an iterative
algorithm. In an appendix, we give useful convergence results for iterative
partial maximization algorithms that apply in particular to the described
algorithm.Comment: 15 pages, article will appear in Scandinavian Journal of Statistic
Practical Bayesian Modeling and Inference for Massive Spatial Datasets On Modest Computing Environments
With continued advances in Geographic Information Systems and related
computational technologies, statisticians are often required to analyze very
large spatial datasets. This has generated substantial interest over the last
decade, already too vast to be summarized here, in scalable methodologies for
analyzing large spatial datasets. Scalable spatial process models have been
found especially attractive due to their richness and flexibility and,
particularly so in the Bayesian paradigm, due to their presence in hierarchical
model settings. However, the vast majority of research articles present in this
domain have been geared toward innovative theory or more complex model
development. Very limited attention has been accorded to approaches for easily
implementable scalable hierarchical models for the practicing scientist or
spatial analyst. This article is submitted to the Practice section of the
journal with the aim of developing massively scalable Bayesian approaches that
can rapidly deliver Bayesian inference on spatial process that are practically
indistinguishable from inference obtained using more expensive alternatives. A
key emphasis is on implementation within very standard (modest) computing
environments (e.g., a standard desktop or laptop) using easily available
statistical software packages without requiring message-parsing interfaces or
parallel programming paradigms. Key insights are offered regarding assumptions
and approximations concerning practical efficiency.Comment: 20 pages, 4 figures, 2 table
Transfer Entropy as a Log-likelihood Ratio
Transfer entropy, an information-theoretic measure of time-directed
information transfer between joint processes, has steadily gained popularity in
the analysis of complex stochastic dynamics in diverse fields, including the
neurosciences, ecology, climatology and econometrics. We show that for a broad
class of predictive models, the log-likelihood ratio test statistic for the
null hypothesis of zero transfer entropy is a consistent estimator for the
transfer entropy itself. For finite Markov chains, furthermore, no explicit
model is required. In the general case, an asymptotic chi-squared distribution
is established for the transfer entropy estimator. The result generalises the
equivalence in the Gaussian case of transfer entropy and Granger causality, a
statistical notion of causal influence based on prediction via vector
autoregression, and establishes a fundamental connection between directed
information transfer and causality in the Wiener-Granger sense
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