Voting Power and Probability

Voting power is commonly measured using a probability. But what kind of probability is this? Is it a degree of belief or an objective chance or some other sort of probability? The aim of this paper is to answer this question. The answer depends on the use to which a measure of voting power is put. Some objectivist interpretations of probabilities are appropriate when we employ such a measure for descriptive purposes. By contrast, when voting power is used to normatively assess voting rules, the probabilities are best understood as classical probabilities, which count possibilities. This is so because, from a normative stance, voting power is most plausibly taken to concern rights and thus possibilities. The classical interpretation also underwrites the use of the Bernoulli model upon which the Penrose/Banzhaf measure is based.

Kawasaki syndrome: Cluster analysis of incident cases presenting to a pediatric tertiary care hospital in Texas from January 1, 2005 to December 31, 2009

Background: Despite almost 40 years of research into the etiology of Kawasaki Syndrome (KS), there is little research published on spatial and temporal clustering of KS cases. Previous analysis has found significant spatial and temporal clustering of cases, therefore cluster analyses were performed to substantiate these findings and provide insight into incident KS cases discharged from a pediatric tertiary care hospital. Identifying clusters from a single institution would allow for prospective analysis of risk factors and potential exposures for further insight into KS etiology. ^ Methods: A retrospective study was carried out to examine the epidemiology and distribution of patients presenting to Texas Children’s Hospital in Houston, Texas, with a diagnosis of Acute Febrile Mucocutaneous Lymph Node Syndrome (MCLS) upon discharge from January 1, 2005 to December 31, 2009. Spatial, temporal, and space-time cluster analyses were performed using the Bernoulli model with case and control event data. ^ Results: 397 of 102,761 total patients admitted to Texas Children’s Hospital had a principal or secondary diagnosis of Acute Febrile MCLS upon over the 5 year period. Demographic data for KS cases remained consistent with known disease epidemiology. Spatial, temporal, and space-time analyses of clustering using the Bernoulli model demonstrated no statistically significant clusters. ^ Discussion: Despite previous findings of spatial-temporal clustering of KS cases, there were no significant clusters of KS cases discharged from a single institution. This implicates the need for an expanded approach to conducting spatial-temporal cluster analysis and KS surveillance given the limitations of evaluating data from a single institution.^

Electrically tunable piezoelectric bimorph cantilever for energy harvesting

Con la presente tesi viene esaminato un metodo per modificare la frequenza di risonanza di trasduttori piezoelettrici mediante applicazione di carichi elettrici esterni. L'elaborato inizia con la presentazione dei cristalli utilizzati nel lavoro di tesi, concentrandosi sul processo di fabbricazione di un bimorph cantilever impiegato come convertitore elettromeccanico di energia, la cui frequenza di risonanza è modellizzata analiticamente mediante la legge di Newton e il modello di Euler-Bernoulli. Su tale struttura vengono condotte misure mediante shaker elettrodinamico e analizzatore d'impedenza, ai fini di giusticare il modello analitico presentato. Con lo scopo di sincronizzare la frequenza di risonanza del cantilever con la vibrazione dell'ambiente per massimizzare la potenza disponibile, viene proposto un algoritmo MPPT secondo l'approccio Perturba e Osserva (P&O), al quale è fornita in ingresso la tensione efficace di un layer di materiale piezoelettrico. Valutare la sua risposta in tensione, presenta dei limiti applicativi che hanno portato a prendere in considerazione un approccio totalmente diff�erente, basato sullo sfasamento tra la tensione di un trasduttore piezoelettrico e il segnale di accelerazione impiegato come eccitazione. Misure sperimentali sono state condotte con l'obiettivo di validare l'efficacia di quest'ultimo approccio qualora si voglia sincronizzare la frequenza di risonanza dei piezo con segnali di vibrazione reali.

Effect of road quality in structural health monitoring under operational conditions

The effect of unevenness in a bridge deck for the purpose of Structural Health Monitoring (SHM) under operational conditions is studied in this paper. The moving vehicle is modelled as a single degree of freedom system traversing the damaged beam at a constant speed. The bridge is modelled as an Euler-Bernoulli beam with a breathing crack, simply supported at both ends. The breathing crack is treated as a nonlinear system with bilinear stiffness characteristics related to the opening and closing of crack. The unevenness in the bridge deck considered is modelled using road classification according to ISO 8606:1995(E). Numerical simulations are conducted considering the effects of changing road surface classes from class A - very good to class E - very poor. Cumulant based statistical parameters, based on a new algorithm are computed on stochastic responses of the damaged beam due to passages of the load in order to calibrate the damage. Possibilities of damage detection and calibration under benchmarked and non-benchmarked cases are considered. The findings of this paper are important for establishing the expectations from different types of road roughness on a bridge for damage detection purposes using bridge-vehicle interaction where the bridge does not need to be closed for monitoring.

Effects of vehicle speed in structural health monitoring from operational conditions of bridges

The effects of vehicle speed for Structural Health Monitoring (SHM) of bridges under operational conditions are studied in this paper. The moving vehicle is modelled as a single degree oscillator traversing a damaged beam at a constant speed. The bridge is modelled as simply supported Euler-Bernoulli beam with a breathing crack. The breathing crack is treated as a nonlinear system with bilinear stiffness characteristics related to the opening and closing of crack. The unevenness of the bridge deck is modelled using road classification according to ISO 8606:1995(E). The stochastic description of the unevenness of the road surface is used as an aid to monitor the health of the structure in its operational condition. Numerical simulations are conducted considering the effects of changing vehicle speed with regards to cumulant based statistical damage detection parameters. The detection and calibration of damage at different levels is based on an algorithm dependent on responses of the damaged beam due to passages of the load. Possibilities of damage detection and calibration under benchmarked and non-benchmarked cases are considered. Sensitivity of calibration values is studied. The findings of this paper are important for establishing the expectations from different vehicle speeds on a bridge for damage detection purposes using bridge-vehicle interaction where the bridge does not need to be closed for monitoring. The identification of bunching of these speed ranges provides guidelines for using the methodology developed in the paper.

Elastically restrained Bernoulli-Euler beams applied to rotary machinery modelling

Facing the lateral vibration problem of a machine rotor as a beam on elastic supports in bending, the authors deal with the free vibration of elastically restrained Bernoulli-Euler beams carrying a finite number of concentrated elements along their length. Based on Rayleigh's quotient, an iterative strategy is developed to find the approximated torsional stiffness coefficients, which allows the reconciliation between the theoretical model results and the experimental ones, obtained through impact tests. The mentioned algorithm treats the vibration of continuous beams under a determined set of boundary and continuity conditions, including different torsional stiffness coefficients and the effect of attached concentrated masses and rotational inertias, not only in the energetic terms of the Rayleigh's quotient but also on the mode shapes, considering the shape functions defined in branches. Several loading cases are examined and examples are given to illustrate the validity of the model and accuracy of the obtained natural frequencies.

Modelling a Rotating Shaft as an Elastically Restrained Bernoulli-Euler Beam

Industrial rotating machines may be exposed to severe dynamic excitations due to resonant working regimes. Dealing with the bending vibration, problem of a machine rotor, the shaft - and attached discs - can be simply modelled using the Bernoulli-Euler beam theory, as a continuous beam subjected to a specific set of boundary conditions. In this study, the authors recall Rayleigh's method to propose an iterative strategy, which allows for the determination of natural frequencies and mode shapes of continuous beams taking into account the effect of attached concentrated masses and rotational inertias, including different stiffness coefficients at the right and the left end sides. The algorithm starts with the exact solutions from Bernoulli-Euler's beam theory, which are then updated through Rayleigh's quotient parameters. Several loading cases are examined in comparison with the experimental data and examples are presented to illustrate the validity of the model and the accuracy of the obtained values.

BORN-INFELD ELECTRODYNAMICS and EULER-HEISENBERG-LIKE MODEL: OUTSTANDING EXAMPLES of THE LACK of COMMUTATIVITY AMONG QUANTIZED TRUNCATED ACTIONS and TRUNCATED QUANTIZED ACTIONS

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Elementos finitos con acciones repartidas equivalentes de cualquier orden. Aplicación a los modelos de vigas de Timoshenko y Bernoulli-Euler

En este trabajo se introducen, en el contexto del Método de Elementos Finitos, dos alternativas posibles en relación con el concepto de acción repartida equivalente. La primera consiste en emplear pocos elementos, elevando el orden de dicha acción, mientras que la segunda se basa en emplear un mayor número de elementos dejando la acción en el orden más bajo posible. Se ilustran ambas situaciones mediante aplicaciones a los modelos de vigas de Timoshenko y Bernoulli-Euler, empleando estas acciones con diferentes órdenes, las cuales aproximan a la acción original, mediante polinomios ortogonales de Legendre en cada elemento. Como conclusión destacable, se indica que cuando se considera el menor número posible de elementos, es decir uno, para los casos de carga poco regular, ha bastado con utilizar acciones repartidas equivalentes de orden ligeramente superior al mínimo (orden cuatro), para obtener una excelente aproximación en los desplazamientos, giros y esfuerzos en el interior de los elementos.

Langevin dynamics, large deviations and instantons for the quasi-geostrophic model and two-dimensional Euler equations

We investigate a class of simple models for Langevin dynamics of turbulent flows, including the one-layer quasi-geostrophic equation and the two-dimensional Euler equations. Starting from a path integral representation of the transition probability, we compute the most probable fluctuation paths from one attractor to any state within its basin of attraction. We prove that such fluctuation paths are the time reversed trajectories of the relaxation paths for a corresponding dual dynamics, which are also within the framework of quasi-geostrophic Langevin dynamics. Cases with or without detailed balance are studied. We discuss a specific example for which the stationary measure displays either a second order (continuous) or a first order (discontinuous) phase transition and a tricritical point. In situations where a first order phase transition is observed, the dynamics are bistable. Then, the transition paths between two coexisting attractors are instantons (fluctuation paths from an attractor to a saddle), which are related to the relaxation paths of the corresponding dual dynamics. For this example, we show how one can analytically determine the instantons and compute the transition probabilities for rare transitions between two attractors.

Distributed power control algorithm for multiple access systems based on Verhulst model

In this paper the continuous Verhulst dynamic model is used to synthesize a new distributed power control algorithm (DPCA) for use in direct sequence code division multiple access (DS-CDMA) systems. The Verhulst model was initially designed to describe the population growth of biological species under food and physical space restrictions. The discretization of the corresponding differential equation is accomplished via the Euler numeric integration (ENI) method. Analytical convergence conditions for the proposed DPCA are also established. Several properties of the proposed recursive algorithm, such as Euclidean distance from optimum vector after convergence, convergence speed, normalized mean squared error (NSE), average power consumption per user, performance under dynamics channels, and implementation complexity aspects, are analyzed through simulations. The simulation results are compared with two other DPCAs: the classic algorithm derived by Foschini and Miljanic and the sigmoidal of Uykan and Koivo. Under estimated errors conditions, the proposed DPCA exhibits smaller discrepancy from the optimum power vector solution and better convergence (under fixed and adaptive convergence factor) than the classic and sigmoidal DPCAs. (C) 2010 Elsevier GmbH. All rights reserved.

Analytical solution and numerical model for the interface in a stratified long wave system

For a two layered long wave propagation, linearized governing equations, which were derived earlier from the Euler equations of mass and momentum assuming negligible friction and interfacial mixing are solved analytically using Fourier transform. For the solution, variations of upper layer water level is assumed to be sinosoidal having known amplitude and variations of interface level is solved. As the governing equations are too complex to solve it analytically, density of upper layer fluid is assumed as very close to the density of lower layer fluid to simplify the lower layer equation. A numerical model is developed using the staggered leap-forg scheme for computation of water level and discharge in one dimensional propagation having known amplitude for the variations of upper layer water level and interface level to be solved. For the numerical model, water levels (upper layer and interface) at both the boundaries are assumed to be known from analytical solution. Results of numerical model are verified by comparing with the analytical solutions for different time period. Good agreements between analytical solution and numerical model are found for the stated boundary condition. The reliability of the developed numerical model is discussed, using it for different a (ratio of density of fluid in the upper layer to that in the lower layer) and p (ratio of water depth in the lower layer to that in the upper layer) values. It is found that as ‘CX’ increases amplification of interface also increases for same upper layer amplitude. Again for a constant lower layer depth, as ‘p’ increases amplification of interface. also increases for same upper layer amplitude.

A hybrid procedure to identify the optimal stiffness coefficients of elastically restrained beams

The formulation of a bending vibration problem of an elastically restrained Bernoulli-Euler beam carrying a finite number of concentrated elements along its length is presented. In this study, the authors exploit the application of the differential evolution optimization technique to identify the torsional stiffness properties of the elastic supports of a Bernoulli-Euler beam. This hybrid strategy allows the determination of the natural frequencies and mode shapes of continuous beams, taking into account the effect of attached concentrated masses and rotational inertias, followed by a reconciliation step between the theoretical model results and the experimental ones. The proposed optimal identification of the elastic support parameters is computationally demanding if the exact eigenproblem solving is considered. Hence, the use of a Gaussian process regression as a meta-model is addressed. An experimental application is used in order to assess the accuracy of the estimated parameters throughout the comparison of the experimentally obtained natural frequency, from impact tests, and the correspondent computed eigenfrequency.

Stability and asymptotic analysis of a fluid-particle interaction model

We are interested in coupled microscopic/macroscopic models describing the evolution of particles dispersed in a fluid. The system consists in a Vlasov-Fokker-Planck equation to describe the microscopic motion of the particles coupled to the Euler equations for a compressible fluid. We investigate dissipative quantities, equilibria and their stability properties and the role of external forces. We also study some asymptotic problems, their equilibria and stability and the derivation of macroscopic two-phase models.