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 $\xi(\theta)$ of the state $\theta$ is forced to be uniformly distributed over a given interval. From an initial sequence of distributions $(\pi_t)$ of interest, and a particular choice of $\xi(\theta)$, a free energy SMC sampler computes sequentially a sequence of biased distributions $(\tilde{\pi}_{t})$ with the following properties: (a) the marginal distribution of $\xi(\theta)$ with respect to $\tilde{\pi}_{t}$ is approximatively uniform over a specified interval, and (b) $\tilde{\pi}_{t}$ and $\pi_{t}$ have the same conditional distribution with respect to $\xi$. 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 $T_c$, 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 $G$ 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 $G/K$ of $G$. We apply this spectral sequence to the case $G = \mathrm{SO}_0(n,1)$ in Sections 8, 9, and 10 to compute the relative Lie algebra cohomology groups $H^{\bullet} \big(\mathfrak{so}(n,1), \mathrm{SO}(n); \mathcal{P}(V^k) \big)$. Here $V = \mathbb{R}^{n,1}$ is Minkowski space and $\mathcal{P}(V^k)$ is the subspace of $L^2(V^k)$ consisting of all products of polynomials with the Gaussian. In Part 2 of this paper we compute the cohomology groups $H^{\bullet}\big(\mathfrak{so}(n,1), \mathrm{SO}(n); L^2(V^k) \big)$ using spectral theory and representation theory. In Part 3 of this paper we compute the maps between the polynomial Fock and $L^2$ cohomology groups induced by the inclusions $\mathcal{P}(V^k) \subset L^2(V^k)$.Comment: 64 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 previous versio

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