Alternatives with stronger convergence than coordinate-descent iterative LMI algorithms

In this note we aim at putting more emphasis on the fact that trying to solve non-convex optimization problems with coordinate-descent iterative linear matrix inequality algorithms leads to suboptimal solutions, and put forward other optimization methods better equipped to deal with such problems (having theoretical convergence guarantees and/or being more efficient in practice). This fact, already outlined at several places in the literature, still appears to be disregarded by a sizable part of the systems and control community. Thus, main elements on this issue and better optimization alternatives are presented and illustrated by means of an example.Comment: 3 pages. Main experimental results reproducible from files available on http://www.mathworks.com/matlabcentral/fileexchange/33219 This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessibl

Divide and conquer in ABC: Expectation-Progagation algorithms for likelihood-free inference

ABC algorithms are notoriously expensive in computing time, as they require simulating many complete artificial datasets from the model. We advocate in this paper a "divide and conquer" approach to ABC, where we split the likelihood into n factors, and combine in some way n "local" ABC approximations of each factor. This has two advantages: (a) such an approach is typically much faster than standard ABC and (b) it makes it possible to use local summary statistics (i.e. summary statistics that depend only on the data-points that correspond to a single factor), rather than global summary statistics (that depend on the complete dataset). This greatly alleviates the bias introduced by summary statistics, and even removes it entirely in situations where local summary statistics are simply the identity function. We focus on EP (Expectation-Propagation), a convenient and powerful way to combine n local approximations into a global approximation. Compared to the EP- ABC approach of Barthelm\'e and Chopin (2014), we present two variations, one based on the parallel EP algorithm of Cseke and Heskes (2011), which has the advantage of being implementable on a parallel architecture, and one version which bridges the gap between standard EP and parallel EP. We illustrate our approach with an expensive application of ABC, namely inference on spatial extremes.Comment: To appear in the forthcoming Handbook of Approximate Bayesian Computation (ABC), edited by S. Sisson, L. Fan, and M. Beaumon

Mode-coupling theory of the glass transition for confined fluids

We present a detailed derivation of a microscopic theory for the glass transition of a liquid enclosed between two parallel walls relying on a mode-coupling approximation. This geometry lacks translational invariance perpendicular to the walls, which implies that the density profile and the density-density correlation function depends explicitly on the distances to the walls. We discuss the residual symmetry properties in slab geometry and introduce a symmetry adapted complete set of two-point correlation functions. Since the currents naturally split into components parallel and perpendicular to the walls the mathematical structure of the theory differs from the established mode-coupling equations in bulk. We prove that the equations for the nonergodicity parameters still display a covariance property similar to bulk liquids.Comment: 16 pages; to be published in PR

Forecasting using Bayesian and Information Theoretic Model Averaging: An Application to UK Inflation

In recent years there has been increasing interest in forecasting methods that utilise large datasets, driven partly by the recognition that policymaking institutions need to process large quantities of information. Factor analysis is one popular way of doing this. Forecast combination is another, and it is on this that we concentrate. Bayesian model averaging methods have been widely advocated in this area, but a neglected frequentist approach is to use information theoretic based weights. We consider the use of model averaging in forecasting UK inflation with a large dataset from this perspective. We find that an information theoretic model averaging scheme can be a powerful alternative both to the more widely used Bayesian model averaging scheme and to factor models.Forecasting, Inflation, Bayesian model averaging, Akaike criteria, Forecast combining

On Determinants of Laplacians on Compact Riemann Surfaces Equipped with Pullbacks of Conical Metrics by Meromorphic Functions

Let $\mathsf m$ be any conical (or smooth) metric of finite volume on the Riemann sphere $\Bbb CP^1$. On a compact Riemann surface $X$ of genus $g$ consider a meromorphic funciton $f: X\to {\Bbb C}P^1$ such that all poles and critical points of $f$ are simple and no critical value of $f$ coincides with a conical singularity of $\mathsf m$ or $\{\infty\}$. The pullback $f^*\mathsf m$ of $\mathsf m$ under $f$ has conical singularities of angles $4\pi$ at the critical points of $f$ and other conical singularities that are the preimages of those of $\mathsf m$. We study the $\zeta$-regularized determinant $\operatorname{Det}' \Delta_F$ of the (Friedrichs extension of) Laplace-Beltrami operator on $(X,f^*\mathsf m)$ as a functional on the moduli space of pairs $(X, f)$ and obtain an explicit formula for $\operatorname{Det}' \Delta_F$.Comment: typos. arXiv admin note: text overlap with arXiv:1612.0866

Metatranscriptomes from diverse microbial communities: assessment of data reduction techniques for rigorous annotation

Background Metatranscriptome sequence data can contain highly redundant sequences from diverse populations of microbes and so data reduction techniques are often applied before taxonomic and functional annotation. For metagenomic data, it has been observed that the variable coverage and presence of closely related organisms can lead to fragmented assemblies containing chimeric contigs that may reduce the accuracy of downstream analyses and some advocate the use of alternate data reduction techniques. However, it is unclear how such data reduction techniques impact the annotation of metatranscriptome data and thus affect the interpretation of the results. Results To investigate the effect of such techniques on the annotation of metatranscriptome data we assess two commonly employed methods: clustering and de-novo assembly. To do this, we also developed an approach to simulate 454 and Illumina metatranscriptome data sets with varying degrees of taxonomic diversity. For the Illumina simulations, we found that a two-step approach of assembly followed by clustering of contigs and unassembled sequences produced the most accurate reflection of the real protein domain content of the sample. For the 454 simulations, the combined annotation of contigs and unassembled reads produced the most accurate protein domain annotations. Conclusions Based on these data we recommend that assembly be attempted, and that unassembled reads be included in the final annotation for metatranscriptome data, even from highly diverse environments as the resulting annotations should lead to a more accurate reflection of the transcriptional behaviour of the microbial population under investigation

Orbital Circularization of Hot and Cool Kepler Eclipsing Binaries

The rate of tidal circularization is predicted to be faster for relatively cool stars with convective outer layers, compared to hotter stars with radiative outer layers. Observing this effect is challenging, because it requires large and well-characterized samples including both hot and cool stars. Here we seek evidence for the predicted dependence of circularization upon stellar type, using a sample of 945 eclipsing binaries observed by Kepler. This sample complements earlier studies of this effect, which employed smaller samples of better-characterized stars. For each Kepler binary we measure $e\cos\omega$ based on the relative timing of the primary and secondary eclipses. We examine the distribution of $e\cos\omega$ as a function of period for binaries composed of hot stars, cool stars, and mixtures of the two types. At the shortest periods, hot-hot binaries are most likely to be eccentric; for periods shorter than 4 days, significant eccentricities occur frequently for hot-hot binaries, but not for hot-cool or cool-cool binaries. This is in qualitative agreement with theoretical expectations based on the slower dissipation rates of hot stars. However, the interpretation of our results is complicated by the largely unknown ages and evolutionary states of the stars in our sample.Comment: Accepted for publication in Ap