The use of non-reflecting boundary conditions in soil dynamics

In this paper some aspects of the use of non-reflecting boundaries in dynamic problems, analyzed in time domain, are considered. Current trends for treating the above mentioned problems are summarized with a particular emphasis on the use of numerical techniques, such as Boundary Element Method (BEM) or mixed and hybrid formulations, Finite Element Method (FEM) plus BEM. As an alternative to these methods, an easy time domain boundary condition, obtained from the well known consistent transmitting boundary developed by Waas for frequency domain analysis, can be applied to represent the reactions of the unbounded soil on the interest zone. The behaviour of this proposed boundary condition is studied when waves of different frequency to the one used for its obtention are acting on the physical edge of the model. As an application example,an analysis is made of the soil-structure interaction of a rigid strip foundation on a horizontal non-linear elastic layer on bed rock. The results obtained suggest the need of time domain solutions for this type of problem

Red Eléctrica de España uses integer programming for annual salary revisions

In this paper, we present a mixed-integer linear programming model for determining salary-revision matrices for an organization based on that organization?s general strategies. The solution obtained from this model consists of salary increases for each employee; these increases consider the employee?s professional performance, salary level relative to peers within the organization, and professional group. In addition to budget constraints, we modeled other elements typical of compensation systems, such as equity and justice. Red Eléctrica de España (REE), the transmission agent and operator of the Spanish electricity system, used the model to revise its 2010 and 2011 salary policies, and achieved results that were aligned with the company strategy. REE incorporated the model into the salary management module within its information system, and plans to continue to use the model in revisions of the module.

Modelo de gestión de un embalse en tiempo real durante avenidas basado en redes bayesianas entrenadas con el método de optimización PLEM

En la actualidad, la gestión de embalses para el control de avenidas se realiza, comúnmente, utilizando modelos de simulación. Esto se debe, principalmente, a su facilidad de uso en tiempo real por parte del operador de la presa. Se han desarrollado modelos de optimización de la gestión del embalse que, aunque mejoran los resultados de los modelos de simulación, su aplicación en tiempo real se hace muy difícil o simplemente inviable, pues está limitada al conocimiento de la avenida futura que entra al embalse antes de tomar la decisión de vertido. Por esta razón, se ha planteado el objetivo de desarrollar un modelo de gestión de embalses en avenidas que incorpore las ventajas de un modelo de optimización y que sea de fácil uso en tiempo real por parte del gestor de la presa. Para ello, se construyó un modelo de red Bayesiana que representa los procesos de la cuenca vertiente y del embalse y, que aprende de casos generados sintéticamente mediante un modelo hidrológico agregado y un modelo de optimización de la gestión del embalse. En una primera etapa, se generó un gran número de episodios sintéticos de avenida utilizando el método de Monte Carlo, para obtener las lluvias, y un modelo agregado compuesto de transformación lluvia- escorrentía, para obtener los hidrogramas de avenida. Posteriormente, se utilizaron las series obtenidas como señales de entrada al modelo de gestión de embalses PLEM, que optimiza una función objetivo de costes mediante programación lineal entera mixta, generando igual número de eventos óptimos de caudal vertido y de evolución de niveles en el embalse. Los episodios simulados fueron usados para entrenar y evaluar dos modelos de red Bayesiana, uno que pronostica el caudal de entrada al embalse, y otro que predice el caudal vertido, ambos en un horizonte de tiempo que va desde una a cinco horas, en intervalos de una hora. En el caso de la red Bayesiana hidrológica, el caudal de entrada que se elige es el promedio de la distribución de probabilidad de pronóstico. En el caso de la red Bayesiana hidráulica, debido al comportamiento marcadamente no lineal de este proceso y a que la red Bayesiana devuelve un rango de posibles valores de caudal vertido, se ha desarrollado una metodología para seleccionar un único valor, que facilite el trabajo del operador de la presa. Esta metodología consiste en probar diversas estrategias propuestas, que incluyen zonificaciones y alternativas de selección de un único valor de caudal vertido en cada zonificación, a un conjunto suficiente de episodios sintéticos. Los resultados de cada estrategia se compararon con el método MEV, seleccionándose las estrategias que mejoran los resultados del MEV, en cuanto al caudal máximo vertido y el nivel máximo alcanzado por el embalse, cualquiera de las cuales puede usarse por el operador de la presa en tiempo real para el embalse de estudio (Talave). La metodología propuesta podría aplicarse a cualquier embalse aislado y, de esta manera, obtener, para ese embalse particular, diversas estrategias que mejoran los resultados del MEV. Finalmente, a modo de ejemplo, se ha aplicado la metodología a una avenida sintética, obteniendo el caudal vertido y el nivel del embalse en cada intervalo de tiempo, y se ha aplicado el modelo MIGEL para obtener en cada instante la configuración de apertura de los órganos de desagüe que evacuarán el caudal. Currently, the dam operator for the management of dams uses simulation models during flood events, mainly due to its ease of use in real time. Some models have been developed to optimize the management of the reservoir to improve the results of simulation models. However, real-time application becomes very difficult or simply unworkable, because the decision to discharge depends on the unknown future avenue entering the reservoir. For this reason, the main goal is to develop a model of reservoir management at avenues that incorporates the advantages of an optimization model. At the same time, it should be easy to use in real-time by the dam manager. For this purpose, a Bayesian network model has been developed to represent the processes of the watershed and reservoir. This model learns from cases generated synthetically by a hydrological model and an optimization model for managing the reservoir. In a first stage, a large number of synthetic flood events was generated using the Monte Carlo method, for rain, and rain-added processing model composed of runoff for the flood hydrographs. Subsequently, the series obtained were used as input signals to the reservoir management model PLEM that optimizes a target cost function using mixed integer linear programming. As a result, many optimal discharge rate events and water levels in the reservoir levels were generated. The simulated events were used to train and test two models of Bayesian network. The first one predicts the flow into the reservoir, and the second predicts the discharge flow. They work in a time horizon ranging from one to five hours, in intervals of an hour. In the case of hydrological Bayesian network, the chosen inflow is the average of the probability distribution forecast. In the case of hydraulic Bayesian network the highly non-linear behavior of this process results on a range of possible values of discharge flow. A methodology to select a single value has been developed to facilitate the dam operator work. This methodology tests various strategies proposed. They include zoning and alternative selection of a single value in each discharge rate zoning from a sufficient set of synthetic episodes. The results of each strategy are compared with the MEV method. The strategies that improve the outcomes of MEV are selected and can be used by the dam operator in real time applied to the reservoir study case (Talave). The methodology could be applied to any single reservoir and, thus, obtain, for the particular reservoir, various strategies that improve results from MEV. Finally, the methodology has been applied to a synthetic flood, obtaining the discharge flow and the reservoir level in each time interval. The open configuration floodgates to evacuate the flow at each interval have been obtained applying the MIGEL model.

Impact of artifact correction methods on R-R interbeat signals to quantifying heart rate variability (HRV) according to linear and nonlinear methods.

In the analysis of heart rate variability (HRV) are used temporal series that contains the distances between successive heartbeats in order to assess autonomic regulation of the cardiovascular system. These series are obtained from the electrocardiogram (ECG) signal analysis, which can be affected by different types of artifacts leading to incorrect interpretations in the analysis of the HRV signals. Classic approach to deal with these artifacts implies the use of correction methods, some of them based on interpolation, substitution or statistical techniques. However, there are few studies that shows the accuracy and performance of these correction methods on real HRV signals. This study aims to determine the performance of some linear and non-linear correction methods on HRV signals with induced artefacts by quantification of its linear and nonlinear HRV parameters. As part of the methodology, ECG signals of rats measured using the technique of telemetry were used to generate real heart rate variability signals without any error. In these series were simulated missing points (beats) in different quantities in order to emulate a real experimental situation as accurately as possible. In order to compare recovering efficiency, deletion (DEL), linear interpolation (LI), cubic spline interpolation (CI), moving average window (MAW) and nonlinear predictive interpolation (NPI) were used as correction methods for the series with induced artifacts. The accuracy of each correction method was known through the results obtained after the measurement of the mean value of the series (AVNN), standard deviation (SDNN), root mean square error of the differences between successive heartbeats (RMSSD), Lomb\'s periodogram (LSP), Detrended Fluctuation Analysis (DFA), multiscale entropy (MSE) and symbolic dynamics (SD) on each HRV signal with and without artifacts. The results show that, at low levels of missing points the performance of all correction techniques are very similar with very close values for each HRV parameter. However, at higher levels of losses only the NPI method allows to obtain HRV parameters with low error values and low quantity of significant differences in comparison to the values calculated for the same signals without the presence of missing points.

Linear chaos for the Quick-Thinking-Driver model.

In recent years, the topic of car-following has experimented an increased importance in traffic engineering and safety research. This has become a very interesting topic because of the development of driverless cars (Google driverless cars, http://en.wikipedia.org/wiki/Google_driverless_car). Driving models which describe the interaction between adjacent vehicles in the same lane have a big interest in simulation modeling, such as the Quick-Thinking-Driver model. A non-linear version of it can be given using the logistic map, and then chaos appears. We show that an infinite-dimensional version of the linear model presents a chaotic behaviour using the same approach as for studying chaos of death models of cell growth.

Modelagem e controle de posição e orientação de uma Plataforma de Stewart

Este trabalho apresenta o controle de posição e orientação de um modelo não linear de Plataforma de Stewart com seis graus de liberdade construído no ambiente de sistemas multicorpos ADAMS® desenvolvido pela Mechanical Dynamics, Inc. O modelo não linear é exportado para o ambiente SIMULINK® desenvolvido pela MathWorks, Inc., onde o controle de posição e orientação é realizado a partir da linearização do modelo e a aplicação de um sistema seguidor com realimentação de estados. Utililiza-se, também o SIMULINK® para implementar a dinâmica de um sistema servoválvula e cilindro hidráulico com um servocontrole de pressão e assim simular o comportamento dinâmico de um simulador de vôo com acionamento hidráulico. A utilização destes pacotes comerciais visa obter uma economia de tempo e esforço na modelagem de sistemas mecânicos complexos e na programação para obtenção da resposta do sistema no tempo, além de facilitar a análise de várias configurações de Plataformas de Stewart

Análise do aproveitamento múltiplo do reservatório de Barra Bonita - SP, através da aplicação de técnica de programação linear associada a modelo de rede de fluxo

O objeto deste trabalho é a análise do aproveitamento múltiplo do reservatório de Barra Bonita, localizado na confluência entre os rios Piracicaba e Tietê, no estado de São Paulo e pertencente ao chamado sistema Tietê-Paraná. Será realizada a otimização da operação do reservatório, através de programação linear, com o objetivo de aumentar a geração de energia elétrica, através da maximização da vazão turbinada. Em seguida, a partir dos resultados da otimização da geração de energia, serão utilizadas técnicas de simulação computacional, para se obter índices de desempenho conhecidos como confiabilidade, resiliência e vulnerabilidade, além de outros fornecidos pelo próprio modelo de simulação a ser utilizado. Estes índices auxiliam a avaliação da freqüência, magnitude e duração dos possíveis conflitos existentes. Serão analisados os possíveis conflitos entre a navegação, o armazenamento no reservatório, a geração de energia e a ocorrência de enchentes na cidade de Barra Bonita, localizada a jusante da barragem.

Mathematical approach for predicting non-negative tristimulus values using the CAT02 chromatic adaptation transform

It has been reported that for certain colour samples, the chromatic adaptation transform CAT02 imbedded in the CIECAM02 colour appearance model predicts corresponding colours with negative tristimulus values (TSVs), which can cause problems in certain applications. To overcome this problem, a mathematical approach is proposed for modifying CAT02. This approach combines a non-negativity constraint for the TSVs of corresponding colours with the minimization of the colour differences between those values for the corresponding colours obtained by visual observations and the TSVs of the corresponding colours predicted by the model, which is a constrained non-linear optimization problem. By solving the non-linear optimization problem, a new matrix is found. The performance of the CAT02 transform with various matrices including the original CAT02 matrix, and the new matrix are tested using visual datasets and the optimum colours. Test results show that the CAT02 with the new matrix predicted corresponding colours without negative TSVs for all optimum colours and the colour matching functions of the two CIE standard observers under the test illuminants considered. However, the accuracy with the new matrix for predicting the visual data is approximately 1 CIELAB colour difference unit worse compared with the original CAT02. This indicates that accuracy has to be sacrificed to achieve the non-negativity constraint for the TSVs of the corresponding colours.

Calmness modulus of linear semi-infinite programs

Our main goal is to compute or estimate the calmness modulus of the argmin mapping of linear semi-infinite optimization problems under canonical perturbations, i.e., perturbations of the objective function together with continuous perturbations of the right-hand side of the constraint system (with respect to an index ranging in a compact Hausdorff space). Specifically, we provide a lower bound on the calmness modulus for semi-infinite programs with unique optimal solution which turns out to be the exact modulus when the problem is finitely constrained. The relationship between the calmness of the argmin mapping and the same property for the (sub)level set mapping (with respect to the objective function), for semi-infinite programs and without requiring the uniqueness of the nominal solution, is explored, too, providing an upper bound on the calmness modulus of the argmin mapping. When confined to finitely constrained problems, we also provide a computable upper bound as it only relies on the nominal data and parameters, not involving elements in a neighborhood. Illustrative examples are provided.

Calmness of the Feasible Set Mapping for Linear Inequality Systems

In this paper we deal with parameterized linear inequality systems in the n-dimensional Euclidean space, whose coefficients depend continuosly on an index ranging in a compact Hausdorff space. The paper is developed in two different parametric settings: the one of only right-hand-side perturbations of the linear system, and that in which both sides of the system can be perturbed. Appealing to the backgrounds on the calmness property, and exploiting the specifics of the current linear structure, we derive different characterizations of the calmness of the feasible set mapping, and provide an operative expresion for the calmness modulus when confined to finite systems. In the paper, the role played by the Abadie constraint qualification in relation to calmness is clarified, and illustrated by different examples. We point out that this approach has the virtue of tackling the calmness property exclusively in terms of the system’s data.

Robust solutions to multi-objective linear programs with uncertain data

In this paper we examine multi-objective linear programming problems in the face of data uncertainty both in the objective function and the constraints. First, we derive a formula for the radius of robust feasibility guaranteeing constraint feasibility for all possible scenarios within a specified uncertainty set under affine data parametrization. We then present numerically tractable optimality conditions for minmax robust weakly efficient solutions, i.e., the weakly efficient solutions of the robust counterpart. We also consider highly robust weakly efficient solutions, i.e., robust feasible solutions which are weakly efficient for any possible instance of the objective matrix within a specified uncertainty set, providing lower bounds for the radius of highly robust efficiency guaranteeing the existence of this type of solutions under affine and rank-1 objective data uncertainty. Finally, we provide numerically tractable optimality conditions for highly robust weakly efficient solutions.

Game theory and programming; National Science Foundation summer mathematics institute notes.

Bibliography: leaves [87]-[88]

Adaptive phase measurements in linear optical quantum computation

Photon counting induces an effective non-linear optical phase shift in certain states derived by linear optics from single photons. Although this non-linearity is non-deterministic, it is sufficient in principle to allow scalable linear optics quantum computation (LOQC). The most obvious way to encode a qubit optically is as a superposition of the vacuum and a single photon in one mode-so-called 'single-rail' logic. Until now this approach was thought to be prohibitively expensive (in resources) compared to 'dual-rail' logic where a qubit is stored by a photon across two modes. Here we attack this problem with real-time feedback control, which can realize a quantum-limited phase measurement on a single mode, as has been recently demonstrated experimentally. We show that with this added measurement resource, the resource requirements for single-rail LOQC are not substantially different from those of dual-rail LOQC. In particular, with adaptive phase measurements an arbitrary qubit state a alpha/0 > + beta/1 > can be prepared deterministically.

Analytical solutions of linear finite- and small-strain one-dimensional consolidation

Analytical solutions are presented for linear finite-strain one-dimensional consolidation of initially unconsolidated soil layers with surcharge loading for both one- and two-way drainage. These solutions complement earlier solutions for initially unconsolidated soil layers without surcharge and initially normally consolidated soil layers with surcharge. Small-strain solutions for the consolidation of initially unconsolidated soil layers with surcharge loading are also presented, and the relationship between the earlier solutions for initially unconsolidated soil without surcharge and the corresponding small-strain solutions, which was not addressed in the earlier work, is clarified. The new solutions for initially unconsolidated soil with surcharge loading can be applied to the analysis of low stress consolidation tests and to the partial validation of numerical solutions of non-linear finite-strain consolidation. They also clarify a formerly perplexing aspect of finite-strain solution charts first noted in numerical solutions. Copyright (C) 2004 John Wiley Sons, Ltd.

Bifurcations in the non-dissipative dynamics of ultra cold atoms

We present the first experimental observation of several bifurcations in a controllable non-linear Hamiltonian system. Dynamics of cold atoms are used to test predictions of non-linear, non-dissipative Hamiltonian dynamics.