Dynamic interfacial trapping of flexural waves in structured plates

The paper presents new results on the localization and transmission of flexural waves in a structured plate containing a semi-infinite two-dimensional array of rigid pins. In particular, localized waves are identified and studied at the interface boundary between the homogeneous part of the flexural plate and the part occupied by rigid pins. A formal connection has been made with the dispersion properties of flexural Bloch waves in an infinite doubly periodic array of rigid pins. Special attention is given to regimes corresponding to standing waves of different types as well as Dirac-like points that may occur on the dispersion surfaces. A single half-grating problem, hitherto unreported in the literature, is also shown to bring interesting solutions

Some Variations on Maxwell's Equations

In the first sections of this article, we discuss two variations on Maxwell's equations that have been introduced in earlier work--a class of nonlinear Maxwell theories with well-defined Galilean limits (and correspondingly generalized Yang-Mills equations), and a linear modification motivated by the coupling of the electromagnetic potential with a certain nonlinear Schroedinger equation. In the final section, revisiting an old idea of Lorentz, we write Maxwell's equations for a theory in which the electrostatic force of repulsion between like charges differs fundamentally in magnitude from the electrostatic force of attraction between unlike charges. We elaborate on Lorentz' description by means of electric and magnetic field strengths, whose governing equations separate into two fully relativistic Maxwell systems--one describing ordinary electromagnetism, and the other describing a universally attractive or repulsive long-range force. If such a force cannot be ruled out {\it a priori} by known physical principles, its magnitude should be determined or bounded experimentally. Were it to exist, interesting possibilities go beyond Lorentz' early conjecture of a relation to (Newtonian) gravity.Comment: 26 pages, submitted to a volume in preparation to honor Gerard Emch v. 2: discussion revised, factors of 4\pi corrected in some equation

Underwriting Apophenia and Cryptids: Are Cycles Statistical Figments of our Imagination?

This paper re-examines the evidence in favour of the existence of underwriting cycles in property and casualty insurance and their economical significance. Using a meta-analysis of published papers in the area of insurance economics, we show that the evidence supporting the existence of underwriting cycles is misleading. There is, in fact, little evidence in favour of insurance cycles with a linear autoregressive character. This means that any cyclicality in firm profitability in the property and casualty insurance industry is not predictable in a classical econometric framework. It follows that pricing in the property and casualty insurance industry is not incompatible with that of a competitive market

Comparison of the Full Outline of UnResponsiveness and Glasgow Liege Scale/Glasgow Coma Scale in an Intensive Care Unit Population.

peer reviewedBACKGROUND: The Full Outline of UnResponsiveness (FOUR) has been proposed as an alternative for the Glasgow Coma Scale (GCS)/Glasgow Liege Scale (GLS) in the evaluation of consciousness in severely brain-damaged patients. We compared the FOUR and GLS/GCS in intensive care unit patients who were admitted in a comatose state. METHODS: FOUR and GLS evaluations were performed in randomized order in 176 acutely (<1 month) brain-damaged patients. GLS scores were transformed in GCS scores by removing the GLS brainstem component. Inter-rater agreement was assessed in 20% of the studied population (N = 35). A logistic regression analysis adjusted for age, and etiology was performed to assess the link between the studied scores and the outcome 3 months after injury (N = 136). RESULTS: GLS/GCS verbal component was scored 1 in 146 patients, among these 131 were intubated. We found that the inter-rater reliability was good for the FOUR score, the GLS/GCS. FOUR, GLS/GCS total scores predicted functional outcome with and without adjustment for age and etiology. 71 patients were considered as being in a vegetative/unresponsive state based on the GLS/GCS. The FOUR score identified 8 of these 71 patients as being minimally conscious given that these patients showed visual pursuit. CONCLUSIONS: The FOUR score is a valid tool with good inter-rater reliability that is comparable to the GLS/GCS in predicting outcome. It offers the advantage to be performable in intubated patients and to identify non-verbal signs of consciousness by assessing visual pursuit, and hence minimal signs of consciousness (11% in this study), not assessed by GLS/GCS scales

Formalization of Transform Methods using HOL Light

Transform methods, like Laplace and Fourier, are frequently used for analyzing the dynamical behaviour of engineering and physical systems, based on their transfer function, and frequency response or the solutions of their corresponding differential equations. In this paper, we present an ongoing project, which focuses on the higher-order logic formalization of transform methods using HOL Light theorem prover. In particular, we present the motivation of the formalization, which is followed by the related work. Next, we present the task completed so far while highlighting some of the challenges faced during the formalization. Finally, we present a roadmap to achieve our objectives, the current status and the future goals for this project.Comment: 15 Pages, CICM 201

Thermodynamic analysis of black hole solutions in gravitating nonlinear electrodynamics

We perform a general study of the thermodynamic properties of static electrically charged black hole solutions of nonlinear electrodynamics minimally coupled to gravitation in three space dimensions. The Lagrangian densities governing the dynamics of these models in flat space are defined as arbitrary functions of the gauge field invariants, constrained by some requirements for physical admissibility. The exhaustive classification of these theories in flat space, in terms of the behaviour of the Lagrangian densities in vacuum and on the boundary of their domain of definition, defines twelve families of admissible models. When these models are coupled to gravity, the flat space classification leads to a complete characterization of the associated sets of gravitating electrostatic spherically symmetric solutions by their central and asymptotic behaviours. We focus on nine of these families, which support asymptotically Schwarzschild-like black hole configurations, for which the thermodynamic analysis is possible and pertinent. In this way, the thermodynamic laws are extended to the sets of black hole solutions of these families, for which the generic behaviours of the relevant state variables are classified and thoroughly analyzed in terms of the aforementioned boundary properties of the Lagrangians. Moreover, we find universal scaling laws (which hold and are the same for all the black hole solutions of models belonging to any of the nine families) running the thermodynamic variables with the electric charge and the horizon radius. These scale transformations form a one-parameter multiplicative group, leading to universal "renormalization group"-like first-order differential equations. The beams of characteristics of these equations generate the full set of black hole states associated to any of these gravitating nonlinear electrodynamics...Comment: 51 single column pages, 19 postscript figures, 2 tables, GRG tex style; minor corrections added; final version appearing in General Relativity and Gravitatio

Liquid-infiltrated photonic crystals - enhanced light-matter interactions for lab-on-a-chip applications

Optical techniques are finding widespread use in analytical chemistry for chemical and bio-chemical analysis. During the past decade, there has been an increasing emphasis on miniaturization of chemical analysis systems and naturally this has stimulated a large effort in integrating microfluidics and optics in lab-on-a-chip microsystems. This development is partly defining the emerging field of optofluidics. Scaling analysis and experiments have demonstrated the advantage of micro-scale devices over their macroscopic counterparts for a number of chemical applications. However, from an optical point of view, miniaturized devices suffer dramatically from the reduced optical path compared to macroscale experiments, e.g. in a cuvette. Obviously, the reduced optical path complicates the application of optical techniques in lab-on-a-chip systems. In this paper we theoretically discuss how a strongly dispersive photonic crystal environment may be used to enhance the light-matter interactions, thus potentially compensating for the reduced optical path in lab-on-a-chip systems. Combining electromagnetic perturbation theory with full-wave electromagnetic simulations we address the prospects for achieving slow-light enhancement of Beer-Lambert-Bouguer absorption, photonic band-gap based refractometry, and high-Q cavity sensing.Comment: Invited paper accepted for the "Optofluidics" special issue to appear in Microfluidics and Nanofluidics (ed. Prof. David Erickson). 11 pages including 8 figure

A mathematical and computational review of Hartree-Fock SCF methods in Quantum Chemistry

We present here a review of the fundamental topics of Hartree-Fock theory in Quantum Chemistry. From the molecular Hamiltonian, using and discussing the Born-Oppenheimer approximation, we arrive to the Hartree and Hartree-Fock equations for the electronic problem. Special emphasis is placed in the most relevant mathematical aspects of the theoretical derivation of the final equations, as well as in the results regarding the existence and uniqueness of their solutions. All Hartree-Fock versions with different spin restrictions are systematically extracted from the general case, thus providing a unifying framework. Then, the discretization of the one-electron orbitals space is reviewed and the Roothaan-Hall formalism introduced. This leads to a exposition of the basic underlying concepts related to the construction and selection of Gaussian basis sets, focusing in algorithmic efficiency issues. Finally, we close the review with a section in which the most relevant modern developments (specially those related to the design of linear-scaling methods) are commented and linked to the issues discussed. The whole work is intentionally introductory and rather self-contained, so that it may be useful for non experts that aim to use quantum chemical methods in interdisciplinary applications. Moreover, much material that is found scattered in the literature has been put together here to facilitate comprehension and to serve as a handy reference.Comment: 64 pages, 3 figures, tMPH2e.cls style file, doublesp, mathbbol and subeqn package

Combining Feature Selection and Integration—A Neural Model for MT Motion Selectivity

Background: The computation of pattern motion in visual area MT based on motion input from area V1 has been investigated in many experiments and models attempting to replicate the main mechanisms. Two different core conceptual approaches were developed to explain the findings. In integrationist models the key mechanism to achieve pattern selectivity is the nonlinear integration of V1 motion activity. In contrast, selectionist models focus on the motion computation at positions with 2D features. Methodology/Principal Findings: Recent experiments revealed that neither of the two concepts alone is sufficient to explain all experimental data and that most of the existing models cannot account for the complex behaviour found. MT pattern selectivity changes over time for stimuli like type II plaids from vector average to the direction computed with an intersection of constraint rule or by feature tracking. Also, the spatial arrangement of the stimulus within the receptive field of a MT cell plays a crucial role. We propose a recurrent neural model showing how feature integration and selection can be combined into one common architecture to explain these findings. The key features of the model are the computation of 1D and 2D motion in model area V1 subpopulations that are integrated in model MT cells using feedforward and feedback processing. Our results are also in line with findings concerning the solution of the aperture problem. Conclusions/Significance: We propose a new neural model for MT pattern computation and motion disambiguation that i