4,825 research outputs found
Free energy Sequential Monte Carlo, application to mixture modelling
We introduce a new class of Sequential Monte Carlo (SMC) methods, which we
call free energy SMC. This class is inspired by free energy methods, which
originate from Physics, and where one samples from a biased distribution such
that a given function of the state is forced to be
uniformly distributed over a given interval. From an initial sequence of
distributions of interest, and a particular choice of ,
a free energy SMC sampler computes sequentially a sequence of biased
distributions with the following properties: (a) the
marginal distribution of with respect to is
approximatively uniform over a specified interval, and (b)
and have the same conditional distribution with respect to . We
apply our methodology to mixture posterior distributions, which are highly
multimodal. In the mixture context, forcing certain hyper-parameters to higher
values greatly faciliates mode swapping, and makes it possible to recover a
symetric output. We illustrate our approach with univariate and bivariate
Gaussian mixtures and two real-world datasets.Comment: presented at "Bayesian Statistics 9" (Valencia meetings, 4-8 June
2010, Benidorm
Study of the skin effect in superconducting materials
The skin effect is analyzed to provide the numerous measurements of the
penetration depth of the electromagnetic field in superconducting materials
with a theoretical basis. Both the normal and anomalous skin effects are
accounted for within a single framework. The emphasis is laid on the conditions
required for the penetration depth to be equal to London's length, which
enables us to validate an assumption widely used in the interpretation of all
current experimental results.Comment: 4 pages, 2 figures. arXiv admin note: text overlap with
arXiv:1507.0333
An observable prerequisite for the existence of persistent currents
A classical model is presented for persistent currents in superconductors.
Their existence is argued to be warranted because their decay would violate the
second law of thermodynamics. This conclusion is achieved by analyzing
comparatively Ohm's law and the Joule effect in normal metals and
superconducting materials. Whereas Ohm's law applies in identical terms in both
cases, the Joule effect is shown to cause the temperature of a superconducting
sample to \textit{decrease}. An experiment is proposed to check the validity of
this work in superconductors of both types I and II.Comment: 11 pages, 4 figure
Revisiting low-frequency susceptibility data in superconducting materials
Old susceptibility data, measured in superconducting materials at
low-frequency, are shown to be accounted for consistently within the framework
of a recently published\cite{sz1} analysis of the skin effect. Their main merit
is to emphasize the significance of the skin-depth measurements, performed
\textit{just beneath} the critical temperature , in order to disprove an
assumption, which thwarted any understanding of the skin-depth data, achieved
so far by conventional high-frequency methods, so that those data might, from
now on, give access to the temperature dependence of the concentration of
superconducting electrons.Comment: 7 pages, 4 figure
The Relative Lie Algebra Cohomology of the Weil Representation of SO(n,1)
In Part 1 of this paper we construct a spectral sequence converging to the
relative Lie algebra cohomology associated to the action of any subgroup of
the symplectic group on the polynomial Fock model of the Weil representation,
see Section 7. These relative Lie algebra cohomology groups are of interest
because they map to the cohomology of suitable arithmetic quotients of the
symmetric space of . We apply this spectral sequence to the case in Sections 8, 9, and 10 to compute the relative Lie
algebra cohomology groups . Here is Minkowski space and
is the subspace of consisting of all products of
polynomials with the Gaussian. In Part 2 of this paper we compute the
cohomology groups using spectral theory and representation theory. In Part 3 of this paper
we compute the maps between the polynomial Fock and cohomology groups
induced by the inclusions .Comment: 64 pages, 5 figure
Organized Behavior Classification of Tweet Sets using Supervised Learning Methods
During the 2016 US elections Twitter experienced unprecedented levels of
propaganda and fake news through the collaboration of bots and hired persons,
the ramifications of which are still being debated. This work proposes an
approach to identify the presence of organized behavior in tweets. The Random
Forest, Support Vector Machine, and Logistic Regression algorithms are each
used to train a model with a data set of 850 records consisting of 299 features
extracted from tweets gathered during the 2016 US presidential election. The
features represent user and temporal synchronization characteristics to capture
coordinated behavior. These models are trained to classify tweet sets among the
categories: organic vs organized, political vs non-political, and pro-Trump vs
pro-Hillary vs neither. The random forest algorithm performs better with
greater than 95% average accuracy and f-measure scores for each category. The
most valuable features for classification are identified as user based
features, with media use and marking tweets as favorite to be the most
dominant.Comment: 51 pages, 5 figure
Rotational Spectral Unmixing of Exoplanets: Degeneracies between Surface Colors and Geography
Unmixing the disk-integrated spectra of exoplanets provides hints about
heterogeneous surfaces that we cannot directly resolve in the foreseeable
future. It is particularly important for terrestrial planets with diverse
surface compositions like Earth. Although previous work on unmixing the spectra
of Earth from disk-integrated multi-band light curves appeared successful, we
point out a mathematical degeneracy between the surface colors and their
spatial distributions. Nevertheless, useful constraints on the spectral shape
of individual surface types may be obtained from the premise that albedo is
everywhere between 0 and 1. We demonstrate the degeneracy and the possible
constraints using both mock data based on a toy model of Earth, as well as real
observations of Earth. Despite the severe degeneracy, we are still able to
recover an approximate albedo spectrum for an ocean. In general, we find that
surfaces are easier to identify when they cover a large fraction of the planet
and when their spectra approach zero or unity in certain bands.Comment: 11 pages, 7 figures, published in AJ. Minor text updates from
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