31 resultados para Algorithm Analysis and Problem Complexity


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Intercontinental Ballistic Missiles are capable of placing a nuclear warhead at more than 5,000 km away from its launching base. With the lethal power of a nuclear warhead a whole city could be wiped out by a single weapon causing millions of deaths. This means that the threat posed to any country from a single ICBM captured by a terrorist group or launched by a 'rogue' state is huge. This threat is increasing as more countries are achieving nuclear and advanced launcher capabilities. In order to suppress or at least reduce this threat the United States created the National Missile Defense System which involved, among other systems, the development of long-range interceptors whose aim is to destroy incoming ballistic missiles in their midcourse phase. The Ballistic Missile Defense is a high-profile topic that has been the focus of political controversy lately when the U.S. decided to expand the Ballistic Missile system to Europe, with the opposition of Russia. However the technical characteristics of this system are mostly unknown by the general public. The Interception of an ICBM using a long range Interceptor Missile as intended within the Ground-Based Missile Defense System by the American National Missile Defense (NMD) implies a series of problems of incredible complexity: - The incoming missile has to be detected almost immediately after launch. - The incoming missile has to be tracked along its trajectory with a great accuracy. - The Interceptor Missile has to implement a fast and accurate guidance algorithm in order to reach the incoming missile as soon as possible. - The Kinetic Kill Vehicle deployed by the interceptor boost vehicle has to be able to detect the reentry vehicle once it has been deployed by ICBM, when it offers a very low infrared signature, in order to perform a final rendezvous manoeuvre. - The Kinetic Kill Vehicle has to be able to discriminate the reentry vehicle from the surrounding debris and decoys. - The Kinetic Kill Vehicle has to be able to implement an accurate guidance algorithm in order to perform a kinetic interception (direct collision) of the reentry vehicle, at relative speeds of more than 10 km/s. All these problems are being dealt simultaneously by the Ground-Based Missile Defense System that is developing very complex and expensive sensors, communications and control centers and long-range interceptors (Ground-Based Interceptor Missile) including a Kinetic Kill Vehicle. Among all the technical challenges involved in this interception scenario, this thesis focuses on the algorithms required for the guidance of the Interceptor Missile and the Kinetic Kill Vehicle in order to perform the direct collision with the ICBM. The involved guidance algorithms are deeply analysed in this thesis in part III where conventional guidance strategies are reviewed and optimal guidance algorithms are developed for this interception problem. The generation of a realistic simulation of the interception scenario between an ICBM and a Ground Based Interceptor designed to destroy it was considered as necessary in order to be able to compare different guidance strategies with meaningful results. As a consequence, a highly representative simulator for an ICBM and a Kill Vehicle has been implemented, as detailed in part II, and the generation of these simulators has also become one of the purposes of this thesis. In summary, the main purposes of this thesis are: - To develop a highly representative simulator of an interception scenario between an ICBM and a Kill Vehicle launched from a Ground Based Interceptor. -To analyse the main existing guidance algorithms both for the ascent phase and the terminal phase of the missiles. Novel conclusions of these analyses are obtained. - To develop original optimal guidance algorithms for the interception problem. - To compare the results obtained using the different guidance strategies, assess the behaviour of the optimal guidance algorithms, and analyse the feasibility of the Ballistic Missile Defense system in terms of guidance (part IV). As a secondary objective, a general overview of the state of the art in terms of ballistic missiles and anti-ballistic missile defence is provided (part I).

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The advent of new signal processing methods, such as non-linear analysis techniques, represents a new perspective which adds further value to brain signals' analysis. Particularly, Lempel–Ziv's Complexity (LZC) has proven to be useful in exploring the complexity of the brain electromagnetic activity. However, an important problem is the lack of knowledge about the physiological determinants of these measures. Although acorrelation between complexity and connectivity has been proposed, this hypothesis was never tested in vivo. Thus, the correlation between the microstructure of the anatomic connectivity and the functional complexity of the brain needs to be inspected. In this study we analyzed the correlation between LZC and fractional anisotropy (FA), a scalar quantity derived from diffusion tensors that is particularly useful as an estimate of the functional integrity of myelinated axonal fibers, in a group of sixteen healthy adults (all female, mean age 65.56 ± 6.06 years, intervals 58–82). Our results showed a positive correlation between FA and LZC scores in regions including clusters in the splenium of the corpus callosum, cingulum, parahipocampal regions and the sagittal stratum. This study supports the notion of a positive correlation between the functional complexity of the brain and the microstructure of its anatomical connectivity. Our investigation proved that a combination of neuroanatomical and neurophysiological techniques may shed some light on the underlying physiological determinants of brain's oscillations

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Predicting statically the running time of programs has many applications ranging from task scheduling in parallel execution to proving the ability of a program to meet strict time constraints. A starting point in order to attack this problem is to infer the computational complexity of such programs (or fragments thereof). This is one of the reasons why the development of static analysis techniques for inferring cost-related properties of programs (usually upper and/or lower bounds of actual costs) has received considerable attention.

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Alzheimer's disease (AD) is the most common cause of dementia. Over the last few years, a considerable effort has been devoted to exploring new biomarkers. Nevertheless, a better understanding of brain dynamics is still required to optimize therapeutic strategies. In this regard, the characterization of mild cognitive impairment (MCI) is crucial, due to the high conversion rate from MCI to AD. However, only a few studies have focused on the analysis of magnetoencephalographic (MEG) rhythms to characterize AD and MCI. In this study, we assess the ability of several parameters derived from information theory to describe spontaneous MEG activity from 36 AD patients, 18 MCI subjects and 26 controls. Three entropies (Shannon, Tsallis and Rényi entropies), one disequilibrium measure (based on Euclidean distance ED) and three statistical complexities (based on Lopez Ruiz–Mancini–Calbet complexity LMC) were used to estimate the irregularity and statistical complexity of MEG activity. Statistically significant differences between AD patients and controls were obtained with all parameters (p < 0.01). In addition, statistically significant differences between MCI subjects and controls were achieved by ED and LMC (p < 0.05). In order to assess the diagnostic ability of the parameters, a linear discriminant analysis with a leave-one-out cross-validation procedure was applied. The accuracies reached 83.9% and 65.9% to discriminate AD and MCI subjects from controls, respectively. Our findings suggest that MCI subjects exhibit an intermediate pattern of abnormalities between normal aging and AD. Furthermore, the proposed parameters provide a new description of brain dynamics in AD and MCI.

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This thesis contributes to the analysis and design of printed reflectarray antennas. The main part of the work is focused on the analysis of dual offset antennas comprising two reflectarray surfaces, one of them acts as sub-reflector and the second one acts as mainreflector. These configurations introduce additional complexity in several aspects respect to conventional dual offset reflectors, however they present a lot of degrees of freedom that can be used to improve the electrical performance of the antenna. The thesis is organized in four parts: the development of an analysis technique for dualreflectarray antennas, a preliminary validation of such methodology using equivalent reflector systems as reference antennas, a more rigorous validation of the software tool by manufacturing and testing a dual-reflectarray antenna demonstrator and the practical design of dual-reflectarray systems for some applications that show the potential of these kind of configurations to scan the beam and to generate contoured beams. In the first part, a general tool has been implemented to analyze high gain antennas which are constructed of two flat reflectarray structures. The classic reflectarray analysis based on MoM under local periodicity assumption is used for both sub and main reflectarrays, taking into account the incident angle on each reflectarray element. The incident field on the main reflectarray is computed taking into account the field radiated by all the elements on the sub-reflectarray.. Two approaches have been developed, one which employs a simple approximation to reduce the computer run time, and the other which does not, but offers in many cases, improved accuracy. The approximation is based on computing the reflected field on each element on the main reflectarray only once for all the fields radiated by the sub-reflectarray elements, assuming that the response will be the same because the only difference is a small variation on the angle of incidence. This approximation is very accurate when the reflectarray elements on the main reflectarray show a relatively small sensitivity to the angle of incidence. An extension of the analysis technique has been implemented to study dual-reflectarray antennas comprising a main reflectarray printed on a parabolic surface, or in general in a curved surface. In many applications of dual-reflectarray configurations, the reflectarray elements are in the near field of the feed-horn. To consider the near field radiated by the horn, the incident field on each reflectarray element is computed using a spherical mode expansion. In this region, the angles of incidence are moderately wide, and they are considered in the analysis of the reflectarray to better calculate the actual incident field on the sub-reflectarray elements. This technique increases the accuracy for the prediction of co- and cross-polar patterns and antenna gain respect to the case of using ideal feed models. In the second part, as a preliminary validation, the proposed analysis method has been used to design a dual-reflectarray antenna that emulates previous dual-reflector antennas in Ku and W-bands including a reflectarray as subreflector. The results for the dualreflectarray antenna compare very well with those of the parabolic reflector and reflectarray subreflector; radiation patterns, antenna gain and efficiency are practically the same when the main parabolic reflector is substituted by a flat reflectarray. The results show that the gain is only reduced by a few tenths of a dB as a result of the ohmic losses in the reflectarray. The phase adjustment on two surfaces provided by the dual-reflectarray configuration can be used to improve the antenna performance in some applications requiring multiple beams, beam scanning or shaped beams. Third, a very challenging dual-reflectarray antenna demonstrator has been designed, manufactured and tested for a more rigorous validation of the analysis technique presented. The proposed antenna configuration has the feed, the sub-reflectarray and the main-reflectarray in the near field one to each other, so that the conventional far field approximations are not suitable for the analysis of such antenna. This geometry is used as benchmarking for the proposed analysis tool in very stringent conditions. Some aspects of the proposed analysis technique that allow improving the accuracy of the analysis are also discussed. These improvements include a novel method to reduce the inherent cross polarization which is introduced mainly from grounded patch arrays. It has been checked that cross polarization in offset reflectarrays can be significantly reduced by properly adjusting the patch dimensions in the reflectarray in order to produce an overall cancellation of the cross-polarization. The dimensions of the patches are adjusted in order not only to provide the required phase-distribution to shape the beam, but also to exploit the crosses by zero of the cross-polarization components. The last part of the thesis deals with direct applications of the technique described. The technique presented is directly applicable to the design of contoured beam antennas for DBS applications, where the requirements of cross-polarisation are very stringent. The beam shaping is achieved by synthesithing the phase distribution on the main reflectarray while the sub-reflectarray emulates an equivalent hyperbolic subreflector. Dual-reflectarray antennas present also the ability to scan the beam over small angles about boresight. Two possible architectures for a Ku-band antenna are also described based on a dual planar reflectarray configuration that provides electronic beam scanning in a limited angular range. In the first architecture, the beam scanning is achieved by introducing a phase-control in the elements of the sub-reflectarray and the mainreflectarray is passive. A second alternative is also studied, in which the beam scanning is produced using 1-bit control on the main reflectarray, while a passive subreflectarray is designed to provide a large focal distance within a compact configuration. The system aims to develop a solution for bi-directional satellite links for emergency communications. In both proposed architectures, the objective is to provide a compact optics and simplicity to be folded and deployed.

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This paper presents an analysis of the fault tolerance achieved by an autonomous, fully embedded evolvable hardware system, which uses a combination of partial dynamic reconfiguration and an evolutionary algorithm (EA). It demonstrates that the system may self-recover from both transient and cumulative permanent faults. This self-adaptive system, based on a 2D array of 16 (4×4) Processing Elements (PEs), is tested with an image filtering application. Results show that it may properly recover from faults in up to 3 PEs, that is, more than 18% cumulative permanent faults. Two fault models are used for testing purposes, at PE and CLB levels. Two self-healing strategies are also introduced, depending on whether fault diagnosis is available or not. They are based on scrubbing, fitness evaluation, dynamic partial reconfiguration and in-system evolutionary adaptation. Since most of these adaptability features are already available on the system for its normal operation, resource cost for self-healing is very low (only some code additions in the internal microprocessor core)

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This paper proposes a method for the identification of different partial discharges (PDs) sources through the analysis of a collection of PD signals acquired with a PD measurement system. This method, robust and sensitive enough to cope with noisy data and external interferences, combines the characterization of each signal from the collection, with a clustering procedure, the CLARA algorithm. Several features are proposed for the characterization of the signals, being the wavelet variances, the frequency estimated with the Prony method, and the energy, the most relevant for the performance of the clustering procedure. The result of the unsupervised classification is a set of clusters each containing those signals which are more similar to each other than to those in other clusters. The analysis of the classification results permits both the identification of different PD sources and the discrimination between original PD signals, reflections, noise and external interferences. The methods and graphical tools detailed in this paper have been coded and published as a contributed package of the R environment under a GNU/GPL license.

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The relationship between abstract interpretation and partial deduction has received considerable attention and (partial) integrations have been proposed starting from both the partial deduction and abstract interpretation perspectives. In this work we present what we argüe is the first fully described generic algorithm for efñcient and precise integration of abstract interpretation and partial deduction. Taking as starting point state-of-the-art algorithms for context-sensitive, polyvariant abstract interpretation and (abstract) partial deduction, we present an algorithm which combines the best of both worlds. Key ingredients include the accurate success propagation inherent to abstract interpretation and the powerful program transformations achievable by partial deduction. In our algorithm, the calis which appear in the analysis graph are not analyzed w.r.t. the original definition of the procedure but w.r.t. specialized definitions of these procedures. Such specialized definitions are obtained by applying both unfolding and abstract executability. Our framework is parametric w.r.t. different control strategies and abstract domains. Different combinations of such parameters correspond to existing algorithms for program analysis and specialization. Simultaneously, our approach opens the door to the efñcient computation of strictly more precise results than those achievable by each of the individual techniques. The algorithm is now one of the key components of the CiaoPP analysis and specialization system.

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Pragmatism is the leading motivation of regularization. We can understand regularization as a modification of the maximum-likelihood estimator so that a reasonable answer could be given in an unstable or ill-posed situation. To mention some typical examples, this happens when fitting parametric or non-parametric models with more parameters than data or when estimating large covariance matrices. Regularization is usually used, in addition, to improve the bias-variance tradeoff of an estimation. Then, the definition of regularization is quite general, and, although the introduction of a penalty is probably the most popular type, it is just one out of multiple forms of regularization. In this dissertation, we focus on the applications of regularization for obtaining sparse or parsimonious representations, where only a subset of the inputs is used. A particular form of regularization, L1-regularization, plays a key role for reaching sparsity. Most of the contributions presented here revolve around L1-regularization, although other forms of regularization are explored (also pursuing sparsity in some sense). In addition to present a compact review of L1-regularization and its applications in statistical and machine learning, we devise methodology for regression, supervised classification and structure induction of graphical models. Within the regression paradigm, we focus on kernel smoothing learning, proposing techniques for kernel design that are suitable for high dimensional settings and sparse regression functions. We also present an application of regularized regression techniques for modeling the response of biological neurons. Supervised classification advances deal, on the one hand, with the application of regularization for obtaining a na¨ıve Bayes classifier and, on the other hand, with a novel algorithm for brain-computer interface design that uses group regularization in an efficient manner. Finally, we present a heuristic for inducing structures of Gaussian Bayesian networks using L1-regularization as a filter. El pragmatismo es la principal motivación de la regularización. Podemos entender la regularización como una modificación del estimador de máxima verosimilitud, de tal manera que se pueda dar una respuesta cuando la configuración del problema es inestable. A modo de ejemplo, podemos mencionar el ajuste de modelos paramétricos o no paramétricos cuando hay más parámetros que casos en el conjunto de datos, o la estimación de grandes matrices de covarianzas. Se suele recurrir a la regularización, además, para mejorar el compromiso sesgo-varianza en una estimación. Por tanto, la definición de regularización es muy general y, aunque la introducción de una función de penalización es probablemente el método más popular, éste es sólo uno de entre varias posibilidades. En esta tesis se ha trabajado en aplicaciones de regularización para obtener representaciones dispersas, donde sólo se usa un subconjunto de las entradas. En particular, la regularización L1 juega un papel clave en la búsqueda de dicha dispersión. La mayor parte de las contribuciones presentadas en la tesis giran alrededor de la regularización L1, aunque también se exploran otras formas de regularización (que igualmente persiguen un modelo disperso). Además de presentar una revisión de la regularización L1 y sus aplicaciones en estadística y aprendizaje de máquina, se ha desarrollado metodología para regresión, clasificación supervisada y aprendizaje de estructura en modelos gráficos. Dentro de la regresión, se ha trabajado principalmente en métodos de regresión local, proponiendo técnicas de diseño del kernel que sean adecuadas a configuraciones de alta dimensionalidad y funciones de regresión dispersas. También se presenta una aplicación de las técnicas de regresión regularizada para modelar la respuesta de neuronas reales. Los avances en clasificación supervisada tratan, por una parte, con el uso de regularización para obtener un clasificador naive Bayes y, por otra parte, con el desarrollo de un algoritmo que usa regularización por grupos de una manera eficiente y que se ha aplicado al diseño de interfaces cerebromáquina. Finalmente, se presenta una heurística para inducir la estructura de redes Bayesianas Gaussianas usando regularización L1 a modo de filtro.

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The aim of this thesis is to study the mechanisms of instability that occur in swept wings when the angle of attack increases. For this, a simplified model for the a simplified model for the non-orthogonal swept leading edge boundary layer has been used as well as different numerical techniques in order to solve the linear stability problem that describes the behavior of perturbations superposed upon this base flow. Two different approaches, matrix-free and matrix forming methods, have been validated using direct numerical simulations with spectral resolution. In this way, flow instability in the non-orthogonal swept attachment-line boundary layer is addressed in a linear analysis framework via the solution of the pertinent global (Bi-Global) PDE-based eigenvalue problem. Subsequently, a simple extension of the extended G¨ortler-H¨ammerlin ODEbased polynomial model proposed by Theofilis, Fedorov, Obrist & Dallmann (2003) for orthogonal flow, which includes previous models as particular cases and recovers global instability analysis results, is presented for non-orthogonal flow. Direct numerical simulations have been used to verify the stability results and unravel the limits of validity of the basic flow model analyzed. The effect of the angle of attack, AoA, on the critical conditions of the non-orthogonal problem has been documented; an increase of the angle of attack, from AoA = 0 (orthogonal flow) up to values close to _/2 which make the assumptions under which the basic flow is derived questionable, is found to systematically destabilize the flow. The critical conditions of non-orthogonal flows at 0 _ AoA _ _/2 are shown to be recoverable from those of orthogonal flow, via a simple analytical transformation involving AoA. These results can help to understand the mechanisms of destabilization that occurs in the attachment line of wings at finite angles of attack. Studies taking into account variations of the pressure field in the basic flow or the extension to compressible flows are issues that remain open. El objetivo de esta tesis es estudiar los mecanismos de la inestabilidad que se producen en ciertos dispositivos aerodinámicos cuando se aumenta el ángulo de ataque. Para ello se ha utilizado un modelo simplificado del flujo de base, así como diferentes técnicas numéricas, con el fin de resolver el problema de estabilidad lineal asociado que describe el comportamiento de las perturbaciones. Estos métodos; sin y con formación de matriz, se han validado utilizando simulaciones numéricas directas con resolución espectral. De esta manera, la inestabilidad del flujo de capa límite laminar oblicuo entorno a la línea de estancamiento se aborda en un marco de análisis lineal por medio del método Bi-Global de resolución del problema de valores propios en derivadas parciales. Posteriormente se propone una extensión simple para el flujo no-ortogonal del modelo polinomial de ecuaciones diferenciales ordinarias, G¨ortler-H¨ammerlin extendido, propuesto por Theofilis et al. (2003) para el flujo ortogonal, que incluye los modelos previos como casos particulares y recupera los resultados del analisis global de estabilidad lineal. Se han realizado simulaciones directas con el fin de verificar los resultados del análisis de estabilidad así como para investigar los límites de validez del modelo de flujo base utilizado. En este trabajo se ha documentado el efecto del ángulo de ataque AoA en las condiciones críticas del problema no ortogonal obteniendo que el incremento del ángulo de ataque, de AoA = 0 (flujo ortogonal) hasta valores próximos a _/2, en el cual las hipótesis sobre las que se basa el flujo base dejan de ser válidas, tiende sistemáticamente a desestabilizar el flujo. Las condiciones críticas del caso no ortogonal 0 _ AoA _ _/2 pueden recuperarse a partir del caso ortogonal mediante el uso de una transformación analítica simple que implica el ángulo de ataque AoA. Estos resultados pueden ayudar a comprender los mecanismos de desestabilización que se producen en el borde de ataque de las alas de los aviones a ángulos de ataque finitos. Como tareas pendientes quedaría realizar estudios que tengan en cuenta variaciones del campo de presión en el flujo base así como la extensión de éste al caso de flujos compresibles.

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Quantitative descriptive analysis (QDA) is used to describe the nature and the intensity of sensory properties from a single evaluation of a product, whereas temporal dominance of sensation (TDS) is primarily used to identify dominant sensory properties over time. Previous studies with TDS have focused on model systems, but this is the first study to use a sequential approach, i.e. QDA then TDS in measuring sensory properties of a commercial product category, using the same set of trained assessors (n = 11). The main objectives of this study were to: (1) investigate the benefits of using a sequential approach of QDA and TDS and (2) to explore the impact of the sample composition on taste and flavour perceptions in blackcurrant squashes. The present study has proposed an alternative way of determining the choice of attributes for TDS measurement based on data obtained from previous QDA studies, where available. Both methods indicated that the flavour profile was primarily influenced by the level of dilution and complexity of sample composition combined with blackcurrant juice content. In addition, artificial sweeteners were found to modify the quality of sweetness and could also contribute to bitter notes. Using QDA and TDS in tandem was shown to be more beneficial than each just on its own enabling a more complete sensory profile of the products.

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We consider the problem of developing efficient sampling schemes for multiband sparse signals. Previous results on multicoset sampling implementations that lead to universal sampling patterns (which guarantee perfect reconstruction), are based on a set of appropriate interleaved analog to digital converters, all of them operating at the same sampling frequency. In this paper we propose an alternative multirate synchronous implementation of multicoset codes, that is, all the analog to digital converters in the sampling scheme operate at different sampling frequencies, without need of introducing any delay. The interleaving is achieved through the usage of different rates, whose sum is significantly lower than the Nyquist rate of the multiband signal. To obtain universal patterns the sampling matrix is formulated and analyzed. Appropriate choices of the parameters, that is the block length and the sampling rates, are also proposed.

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The combination of minimum time control and multiphase converter is a favorable option for dc-dc converters in applications where output voltage variation is required, such as RF amplifiers and dynamic voltage scaling in microprocessors, due to their advantage of fast dynamic response. In this paper, an improved minimum time control approach for multiphase buck converter that is based on charge balance technique, aiming at fast output voltage transition is presented. Compared with the traditional method, the proposed control takes into account the phase delay and current ripple in each phase. Therefore, by investigating the behavior of multiphase converter during voltage transition, it resolves the problem of current unbalance after the transient, which can lead to long settling time of the output voltage. The restriction of this control is that the output voltage that the converter can provide is related to the number of the phases, because only the duty cycles at which the multiphase converter has total ripple cancellation are used in this approach. The model of the proposed control is introduced, and the design constraints of the buck converters filter for this control are discussed. In order to prove the concept, a four-phase buck converter is implemented and the experimental results that validate the proposed control method are presented. The application of this control to RF envelope tracking is also presented in this paper.

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We present a novel framework for the analysis and optimization of encoding latency for multiview video. Firstly, we characterize the elements that have an influence in the encoding latency performance: (i) the multiview prediction structure and (ii) the hardware encoder model. Then, we provide algorithms to find the encoding latency of any arbitrary multiview prediction structure. The proposed framework relies on the directed acyclic graph encoder latency (DAGEL) model, which provides an abstraction of the processing capacity of the encoder by considering an unbounded number of processors. Using graph theoretic algorithms, the DAGEL model allows us to compute the encoding latency of a given prediction structure, and determine the contribution of the prediction dependencies to it. As an example of DAGEL application, we propose an algorithm to reduce the encoding latency of a given multiview prediction structure up to a target value. In our approach, a minimum number of frame dependencies are pruned, until the latency target value is achieved, thus minimizing the degradation of the rate-distortion performance due to the removal of the prediction dependencies. Finally, we analyze the latency performance of the DAGEL derived prediction structures in multiview encoders with limited processing capacity.

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This paper proposes a method for the identification of different partial discharges (PDs) sources through the analysis of a collection of PD signals acquired with a PD measurement system. This method, robust and sensitive enough to cope with noisy data and external interferences, combines the characterization of each signal from the collection, with a clustering procedure, the CLARA algorithm. Several features are proposed for the characterization of the signals, being the wavelet variances, the frequency estimated with the Prony method, and the energy, the most relevant for the performance of the clustering procedure. The result of the unsupervised classification is a set of clusters each containing those signals which are more similar to each other than to those in other clusters. The analysis of the classification results permits both the identification of different PD sources and the discrimination between original PD signals, reflections, noise and external interferences. The methods and graphical tools detailed in this paper have been coded and published as a contributed package of the R environment under a GNU/GPL license.