On Random Matrix Averages Involving Half-Integer Powers of GOE Characteristic Polynomials

Correlation functions involving products and ratios of half-integer powers of characteristic polynomials of random matrices from the Gaussian Orthogonal Ensemble (GOE) frequently arise in applications of Random Matrix Theory (RMT) to physics of quantum chaotic systems, and beyond. We provide an explicit evaluation of the large-$N$ limits of a few non-trivial objects of that sort within a variant of the supersymmetry formalism, and via a related but different method. As one of the applications we derive the distribution of an off-diagonal entry $K_{ab}$ of the resolvent (or Wigner $K$-matrix) of GOE matrices which, among other things, is of relevance for experiments on chaotic wave scattering in electromagnetic resonators.Comment: 25 pages (2 figures); published version (conclusion added, minor changes

Slug Self-Propulsion in a Capillary Tube Mathematical Modeling and Numerical Simulation

A composite droplet made of two miscible fluids in a narrow tube generally moves under the action of capillarity until complete mixture is attained. This physical situation is analysed here on a combined theoretical and numerical analysis. The mathematical framework consists of the two-phase flow phase-field equation set, an advection-diffusion chemical concentration equation, and closure relationships relating the surface tensions to the chemical concentration. The numerical framework is composed of the COMSOL Laminar two-phase flow phase-field method coupled with an advection-diffusion chemical concentration equation. Through transient studies, we show that the penetrating length of the bidroplet system into the capillary tube is linear at early-time regime and exponential at late-time regime. Through parametric studies, we show that the rate of penetration of the bidroplet system into the capillary tube is proportional to a time-dependent exponential function. We also show that this speed obeys the Poiseuille law at the early-time regime. A series of position, speed-versus-property graphs are included to support the analysis. Finally, the overall results are contrasted with available experimental data, grouped together to settle a general mathematical description of the phenomenon, and explained and concluded on this basis

Elastomeric micropillar arrays for the study of protrusive forces in hyphal invasion

Fungi and Oomycetes are microorganisms that can be pathogenic and grow invasively causing significant economic losses and diseases1. • These organisms grow by extending the cell at the tip. This involves turgor pressure, cell wall yielding and a dynamic cytoskeleton, giving rise to a protrusive force2,3. •A Lab-on-a-Chip platform, with integrated force sensor based on elastomeric micro-pillars, is allowing us to study the molecular mechanisms which enable the generation of protrusive force at the tip of invasively-growing hyphae. •A maximum force of 16 μN was measured for the oomycete Achlya bisexualis cultured on the chip

Universal K-matrix distribution in beta=2 ensembles of random matrices

11 pages; published version (added proportionality constants, minor changes)YVF and AN were supported by EPSRC grant EP/J002763/1 'Insights into Disordered Landscapes via Random Matrix Theory and Statistical Mechanics'

Bregman Voronoi Diagrams: Properties, Algorithms and Applications

The Voronoi diagram of a finite set of objects is a fundamental geometric structure that subdivides the embedding space into regions, each region consisting of the points that are closer to a given object than to the others. We may define many variants of Voronoi diagrams depending on the class of objects, the distance functions and the embedding space. In this paper, we investigate a framework for defining and building Voronoi diagrams for a broad class of distance functions called Bregman divergences. Bregman divergences include not only the traditional (squared) Euclidean distance but also various divergence measures based on entropic functions. Accordingly, Bregman Voronoi diagrams allow to define information-theoretic Voronoi diagrams in statistical parametric spaces based on the relative entropy of distributions. We define several types of Bregman diagrams, establish correspondences between those diagrams (using the Legendre transformation), and show how to compute them efficiently. We also introduce extensions of these diagrams, e.g. k-order and k-bag Bregman Voronoi diagrams, and introduce Bregman triangulations of a set of points and their connexion with Bregman Voronoi diagrams. We show that these triangulations capture many of the properties of the celebrated Delaunay triangulation. Finally, we give some applications of Bregman Voronoi diagrams which are of interest in the context of computational geometry and machine learning.Comment: Extend the proceedings abstract of SODA 2007 (46 pages, 15 figures

Exploring strategies used following a group-based fatigue management programme for people with multiple sclerosis (FACETS) via the Fatigue Management Strategies Questionnaire (FMSQ)

Objectives: To explore cross-sectional patterns of use of fatigue management strategies in people with multiple sclerosis (MS) who had attended a groupbased fatigue management programme, Fatigue: Applying Cognitive behavioural and Energy effectiveness Techniques to lifeStyle ('FACETS'). In a multicentre randomised controlled trial (RCT) the FACETS programme was shown to reduce fatigue severity and improve self-efficacy and quality of life. Design: A questionnaire substudy within a RCT involving the self-completed Fatigue Management Strategies Questionnaire (FMSQ). The FMSQ includes: (1) closed questions about the use and helpfulness of fatigue management strategies taught in FACETS and (2) open items about changes to lifestyle, attitudes or expectations, barriers or difficulties encountered and helpful strategies not covered in FACETS. Participants: All had a clinical diagnosis of MS, significant fatigue, were ambulatory and had attended at least 4 of 6 scheduled FACETS sessions. Methods: Participants (n=72) were posted the FMSQ with a prepaid return envelope 4 months after the end of the FACETS programme. Results: 82% (59/72) of participants returned the FMSQ. The fatigue management strategies most frequently used since attending FACETS were prioritisation (80%), pacing (78%), saying no to others (78%), grading tasks (75%) and challenging unhelpful thoughts (71%). Adding in those participants who were already using the respective strategies prior to FACETS, the three most used strategies at 4 months were prioritisation (55/59), grading (54/59) and pacing (53/58). Free-text comments illustrated the complex interplay between attitudes/expectations, behaviours, emotions and the environment. Issues related to expectations featured strongly in participants' comments. Expectations (from self and others) were both facilitators and barriers to effective fatigue management. Conclusions: Individuals' comments highlighted the complex, multifaceted nature of fatigue management. Revising expectations and a greater acceptance of fatigue were important shifts following the programme. Findings support the relevance of a cognitive behavioural approach for fatigue management. Booster sessions might be a useful addition to the FACETS programme

Droplet actuation induced by coalescence: experimental evidences and phenomenological modeling

This paper considers the interaction between two droplets placed on a substrate in immediate vicinity. We show here that when the two droplets are of different fluids and especially when one of the droplet is highly volatile, a wealth of fascinating phenomena can be observed. In particular, the interaction may result in the actuation of the droplet system, i.e. its displacement over a finite length. In order to control this displacement, we consider droplets confined on a hydrophilic stripe created by plasma-treating a PDMS substrate. This controlled actuation opens up unexplored opportunities in the field of microfluidics. In order to explain the observed actuation phenomenon, we propose a simple phenomenological model based on Newton's second law and a simple balance between the driving force arising from surface energy gradients and the viscous resistive force. This simple model is able to reproduce qualitatively and quantitatively the observed droplet dynamics

The Bregman chord divergence

Distances are fundamental primitives whose choice significantly impacts the performances of algorithms in machine learning and signal processing. However selecting the most appropriate distance for a given task is an endeavor. Instead of testing one by one the entries of an ever-expanding dictionary of {\em ad hoc} distances, one rather prefers to consider parametric classes of distances that are exhaustively characterized by axioms derived from first principles. Bregman divergences are such a class. However fine-tuning a Bregman divergence is delicate since it requires to smoothly adjust a functional generator. In this work, we propose an extension of Bregman divergences called the Bregman chord divergences. This new class of distances does not require gradient calculations, uses two scalar parameters that can be easily tailored in applications, and generalizes asymptotically Bregman divergences.Comment: 10 page

Creating a FACETS digital toolkit to promote quality of life of people with multiple sclerosis through Participatory Design

In this paper, we report on the first stages of creating a stand-alone digital toolkit focusing on the homework elements of FACETS (Fatigue: Applying Cognitive behavioural and Energy effectiveness Techniques to lifeStyle). FACETS is an evidence-based face-to-face fatigue management group programme for people with multiple sclerosis. This paper details the participatory design process from requirements elicitation to initial prototyping and how offline activities linked to each session have been mapped in the digitised solution (mobile app)

Survey of highly non-Keplerian orbits with low-thrust propulsion

Celestial mechanics has traditionally been concerned with orbital motion under the action of a conservative gravitational potential. In particular, the inverse square gravitational force due to the potential of a uniform, spherical mass leads to a family of conic section orbits, as determined by Isaac Newton, who showed that Kepler‟s laws were derivable from his theory of gravitation. While orbital motion under the action of a conservative gravitational potential leads to an array of problems with often complex and interesting solutions, the addition of non-conservative forces offers new avenues of investigation. In particular, non-conservative forces lead to a rich diversity of problems associated with the existence, stability and control of families of highly non-Keplerian orbits generated by a gravitational potential and a non-conservative force. Highly non-Keplerian orbits can potentially have a broad range of practical applications across a number of different disciplines. This review aims to summarize the combined wealth of literature concerned with the dynamics, stability and control of highly non-Keplerian orbits for various low thrust propulsion devices, and to demonstrate some of these potential applications