Optimal polygonal L1 linearization and fast interpolation of nonlinear systems

The analysis of complex nonlinear systems is often carried out using simpler piecewise linear representations of them. A principled and practical technique is proposed to linearize and evaluate arbitrary continuous nonlinear functions using polygonal (continuous piecewise linear) models under the L1 norm. A thorough error analysis is developed to guide an optimal design of two kinds of polygonal approximations in the asymptotic case of a large budget of evaluation subintervals N. The method allows the user to obtain the level of linearization (N) for a target approximation error and vice versa. It is suitable for, but not limited to, an efficient implementation in modern Graphics Processing Units (GPUs), allowing real-time performance of computationally demanding applications. The quality and efficiency of the technique has been measured in detail on two nonlinear functions that are widely used in many areas of scientific computing and are expensive to evaluate.

Global Linear Instability at the Dawn of its 4th Decade: A List of Challenges (A Practical Guide on how to Contain the Euphoria and Avoid the Oversell)

Global linear instability theory is concerned with the temporal or spatial development of small-amplitude perturbations superposed upon laminar steady or time-periodic threedimensional flows, which are inhomogeneous in two (and periodic in one) or all three spatial directions.1 The theory addresses flows developing in complex geometries, in which the parallel or weakly nonparallel basic flow approximation invoked by classic linear stability theory does not hold. As such, global linear theory is called to fill the gap in research into stability and transition in flows over or through complex geometries. Historically, global linear instability has been (and still is) concerned with solution of multi-dimensional eigenvalue problems; the maturing of non-modal linear instability ideas in simple parallel flows during the last decade of last century2–4 has given rise to investigation of transient growth scenarios in an ever increasing variety of complex flows. After a brief exposition of the theory, connections are sought with established approaches for structure identification in flows, such as the proper orthogonal decomposition and topology theory in the laminar regime and the open areas for future research, mainly concerning turbulent and three-dimensional flows, are highlighted. Recent results obtained in our group are reported in both the time-stepping and the matrix-forming approaches to global linear theory. In the first context, progress has been made in implementing a Jacobian-Free Newton Krylov method into a standard finite-volume aerodynamic code, such that global linear instability results may now be obtained in compressible flows of aeronautical interest. In the second context a new stable very high-order finite difference method is implemented for the spatial discretization of the operators describing the spatial BiGlobal EVP, PSE-3D and the TriGlobal EVP; combined with sparse matrix treatment, all these problems may now be solved on standard desktop computers.

Some past decision theory models for euro construction model codes and for road drainage in Spain, and modest hints with multi-criteria methods for agro and environmental assurance

The authors are from UPM and are relatively grouped, and all have intervened in different academic or real cases on the subject, at different times as being of different age. With precedent from E. Torroja and A. Páez in Madrid Spain Safety Probabilistic models for concrete about 1957, now in ICOSSAR conferences, author J.M. Antón involved since autumn 1967 for euro-steel construction in CECM produced a math model for independent load superposition reductions, and using it a load coefficient pattern for codes in Rome Feb. 1969, practically adopted for European constructions, giving in JCSS Lisbon Feb. 1974 suggestion of union for concrete-steel-al.. That model uses model for loads like Gumbel type I, for 50 years for one type of load, reduced to 1 year to be added to other independent loads, the sum set in Gumbel theories to 50 years return period, there are parallel models. A complete reliability system was produced, including non linear effects as from buckling, phenomena considered somehow in actual Construction Eurocodes produced from Model Codes. The system was considered by author in CEB in presence of Hydraulic effects from rivers, floods, sea, in reference with actual practice. When redacting a Road Drainage Norm in MOPU Spain an optimization model was realized by authors giving a way to determine the figure of Return Period, 10 to 50 years, for the cases of hydraulic flows to be considered in road drainage. Satisfactory examples were a stream in SE of Spain with Gumbel Type I model and a paper of Ven Te Chow with Mississippi in Keokuk using Gumbel type II, and the model can be modernized with more varied extreme laws. In fact in the MOPU drainage norm the redacting commission acted also as expert to set a table of return periods for elements of road drainage, in fact as a multi-criteria complex decision system. These precedent ideas were used e.g. in wide Codes, indicated in symposia or meetings, but not published in journals in English, and a condensate of contributions of authors is presented. The authors are somehow involved in optimization for hydraulic and agro planning, and give modest hints of intended applications in presence of agro and environment planning as a selection of the criteria and utility functions involved in bayesian, multi-criteria or mixed decision systems. Modest consideration is made of changing in climate, and on the production and commercial systems, and on others as social and financial.

Applications of image-based, multi-view stereo reconstruction methods = (Aplicaciones de los métodos de reconstrucción estéreo multivista)

These slides present several 3-D reconstruction methods to obtain the geometric structure of a scene that is viewed by multiple cameras. We focus on the combination of the geometric modeling in the image formation process with the use of standard optimization tools to estimate the characteristic parameters that describe the geometry of the 3-D scene. In particular, linear, non-linear and robust methods to estimate the monocular and epipolar geometry are introduced as cornerstones to generate 3-D reconstructions with multiple cameras. Some examples of systems that use this constructive strategy are Bundler, PhotoSynth, VideoSurfing, etc., which are able to obtain 3-D reconstructions with several hundreds or thousands of cameras. En esta presentación se tratan varios métodos de reconstrucción 3-D para la obtención de la estructura geométrica de una escena que es visualizada por varias cámaras. Se enfatiza la combinación de modelado geométrico del proceso de formación de la imagen con el uso de herramientas estándar de optimización para estimar los parámetros característicos que describen la geometría de la escena 3-D. En concreto, se presentan métodos de estimación lineales, no lineales y robustos de las geometrías monocular y epipolar como punto de partida para generar reconstrucciones con tres o más cámaras. Algunos ejemplos de sistemas que utilizan este enfoque constructivo son Bundler, PhotoSynth, VideoSurfing, etc., los cuales, en la práctica pueden llegar a reconstruir una escena con varios cientos o miles de cámaras.

Continuous multi-criteria methods for crop and soil conservation planning on La Colacha (Río Cuarto, Province of Cordoba, Argentina)

Agro-areas of Arroyos Menores (La Colacha) west and south of Rand south of R?o Cuarto (Prov. of Cordoba, Argentina) basins are very fertile but have high soil loses. Extreme rain events, inundations and other severe erosions forming gullies demand urgently actions in this area to avoid soil degradation and erosion supporting good levels of agro production. The authors first improved hydrologic data on La Colacha, evaluated the systems of soil uses and actions that could be recommended considering the relevant aspects of the study area and applied decision support systems (DSS) with mathematic tools for planning of defences and uses of soils in these areas. These were conducted here using multi-criteria models, in multi-criteria decision making (MCDM); first of discrete MCDM to chose among global types of use of soils, and then of continuous MCDM to evaluate and optimize combined actions, including repartition of soil use and the necessary levels of works for soil conservation and for hydraulic management to conserve against erosion these basins. Relatively global solutions for La Colacha area have been defined and were optimised by Linear Programming in Goal Programming forms that are presented as Weighted or Lexicographic Goal Programming and as Compromise Programming. The decision methods used are described, indicating algorithms used, and examples for some representative scenarios on La Colacha area are given.

Design and control of multi-finger haptic devices for dexterous manipulation

En la interacción con el entorno que nos rodea durante nuestra vida diaria (utilizar un cepillo de dientes, abrir puertas, utilizar el teléfono móvil, etc.) y en situaciones profesionales (intervenciones médicas, procesos de producción, etc.), típicamente realizamos manipulaciones avanzadas que incluyen la utilización de los dedos de ambas manos. De esta forma el desarrollo de métodos de interacción háptica multi-dedo dan lugar a interfaces hombre-máquina más naturales y realistas. No obstante, la mayoría de interfaces hápticas disponibles en el mercado están basadas en interacciones con un solo punto de contacto; esto puede ser suficiente para la exploración o palpación del entorno pero no permite la realización de tareas más avanzadas como agarres. En esta tesis, se investiga el diseño mecánico, control y aplicaciones de dispositivos hápticos modulares con capacidad de reflexión de fuerzas en los dedos índice, corazón y pulgar del usuario. El diseño mecánico de la interfaz diseñada, ha sido optimizado con funciones multi-objetivo para conseguir una baja inercia, un amplio espacio de trabajo, alta manipulabilidad y reflexión de fuerzas superiores a 3 N en el espacio de trabajo. El ancho de banda y la rigidez del dispositivo se han evaluado mediante simulación y experimentación real. Una de las áreas más importantes en el diseño de estos dispositivos es el efector final, ya que es la parte que está en contacto con el usuario. Durante este trabajo se ha diseñado un dedal de bajo peso, adaptable a diferentes usuarios que, mediante la incorporación de sensores de contacto, permite estimar fuerzas normales y tangenciales durante la interacción con entornos reales y virtuales. Para el diseño de la arquitectura de control, se estudiaron los principales requisitos para estos dispositivos. Entre estos, cabe destacar la adquisición, procesado e intercambio a través de internet de numerosas señales de control e instrumentación; la computación de equaciones matemáticas incluyendo la cinemática directa e inversa, jacobiana, algoritmos de detección de agarres, etc. Todos estos componentes deben calcularse en tiempo real garantizando una frecuencia mínima de 1 KHz. Además, se describen sistemas para manipulación de precisión virtual y remota; así como el diseño de un método denominado "desacoplo cinemático iterativo" para computar la cinemática inversa de robots y la comparación con otros métodos actuales. Para entender la importancia de la interacción multimodal, se ha llevado a cabo un estudio para comprobar qué estímulos sensoriales se correlacionan con tiempos de respuesta más rápidos y de mayor precisión. Estos experimentos se desarrollaron en colaboración con neurocientíficos del instituto Technion Israel Institute of Technology. Comparando los tiempos de respuesta en la interacción unimodal (auditiva, visual y háptica) con combinaciones bimodales y trimodales de los mismos, se demuestra que el movimiento sincronizado de los dedos para generar respuestas de agarre se basa principalmente en la percepción háptica. La ventaja en el tiempo de procesamiento de los estímulos hápticos, sugiere que los entornos virtuales que incluyen esta componente sensorial generan mejores contingencias motoras y mejoran la credibilidad de los eventos. Se concluye que, los sistemas que incluyen percepción háptica dotan a los usuarios de más tiempo en las etapas cognitivas para rellenar información de forma creativa y formar una experiencia más rica. Una aplicación interesante de los dispositivos hápticos es el diseño de nuevos simuladores que permitan entrenar habilidades manuales en el sector médico. En colaboración con fisioterapeutas de Griffith University en Australia, se desarrolló un simulador que permite realizar ejercicios de rehabilitación de la mano. Las propiedades de rigidez no lineales de la articulación metacarpofalange del dedo índice se estimaron mediante la utilización del efector final diseñado. Estos parámetros, se han implementado en un escenario que simula el comportamiento de la mano humana y que permite la interacción háptica a través de esta interfaz. Las aplicaciones potenciales de este simulador están relacionadas con entrenamiento y educación de estudiantes de fisioterapia. En esta tesis, se han desarrollado nuevos métodos que permiten el control simultáneo de robots y manos robóticas en la interacción con entornos reales. El espacio de trabajo alcanzable por el dispositivo háptico, se extiende mediante el cambio de modo de control automático entre posición y velocidad. Además, estos métodos permiten reconocer el gesto del usuario durante las primeras etapas de aproximación al objeto para su agarre. Mediante experimentos de manipulación avanzada de objetos con un manipulador y diferentes manos robóticas, se muestra que el tiempo en realizar una tarea se reduce y que el sistema permite la realización de la tarea con precisión. Este trabajo, es el resultado de una colaboración con investigadores de Harvard BioRobotics Laboratory. ABSTRACT When we interact with the environment in our daily life (using a toothbrush, opening doors, using cell-phones, etc.), or in professional situations (medical interventions, manufacturing processes, etc.) we typically perform dexterous manipulations that involve multiple fingers and palm for both hands. Therefore, multi-Finger haptic methods can provide a realistic and natural human-machine interface to enhance immersion when interacting with simulated or remote environments. Most commercial devices allow haptic interaction with only one contact point, which may be sufficient for some exploration or palpation tasks but are not enough to perform advanced object manipulations such as grasping. In this thesis, I investigate the mechanical design, control and applications of a modular haptic device that can provide force feedback to the index, thumb and middle fingers of the user. The designed mechanical device is optimized with a multi-objective design function to achieve a low inertia, a large workspace, manipulability, and force-feedback of up to 3 N within the workspace; the bandwidth and rigidity for the device is assessed through simulation and real experimentation. One of the most important areas when designing haptic devices is the end-effector, since it is in contact with the user. In this thesis the design and evaluation of a thimble-like, lightweight, user-adaptable, and cost-effective device that incorporates four contact force sensors is described. This design allows estimation of the forces applied by a user during manipulation of virtual and real objects. The design of a real-time, modular control architecture for multi-finger haptic interaction is described. Requirements for control of multi-finger haptic devices are explored. Moreover, a large number of signals have to be acquired, processed, sent over the network and mathematical computations such as device direct and inverse kinematics, jacobian, grasp detection algorithms, etc. have to be calculated in Real Time to assure the required high fidelity for the haptic interaction. The Hardware control architecture has different modules and consists of an FPGA for the low-level controller and a RT controller for managing all the complex calculations (jacobian, kinematics, etc.); this provides a compact and scalable solution for the required high computation capabilities assuring a correct frequency rate for the control loop of 1 kHz. A set-up for dexterous virtual and real manipulation is described. Moreover, a new algorithm named the iterative kinematic decoupling method was implemented to solve the inverse kinematics of a robotic manipulator. In order to understand the importance of multi-modal interaction including haptics, a subject study was carried out to look for sensory stimuli that correlate with fast response time and enhanced accuracy. This experiment was carried out in collaboration with neuro-scientists from Technion Israel Institute of Technology. By comparing the grasping response times in unimodal (auditory, visual, and haptic) events with the response times in events with bimodal and trimodal combinations. It is concluded that in grasping tasks the synchronized motion of the fingers to generate the grasping response relies on haptic cues. This processing-speed advantage of haptic cues suggests that multimodalhaptic virtual environments are superior in generating motor contingencies, enhancing the plausibility of events. Applications that include haptics provide users with more time at the cognitive stages to fill in missing information creatively and form a richer experience. A major application of haptic devices is the design of new simulators to train manual skills for the medical sector. In collaboration with physical therapists from Griffith University in Australia, we developed a simulator to allow hand rehabilitation manipulations. First, the non-linear stiffness properties of the metacarpophalangeal joint of the index finger were estimated by using the designed end-effector; these parameters are implemented in a scenario that simulates the behavior of the human hand and that allows haptic interaction through the designed haptic device. The potential application of this work is related to educational and medical training purposes. In this thesis, new methods to simultaneously control the position and orientation of a robotic manipulator and the grasp of a robotic hand when interacting with large real environments are studied. The reachable workspace is extended by automatically switching between rate and position control modes. Moreover, the human hand gesture is recognized by reading the relative movements of the index, thumb and middle fingers of the user during the early stages of the approximation-to-the-object phase and then mapped to the robotic hand actuators. These methods are validated to perform dexterous manipulation of objects with a robotic manipulator, and different robotic hands. This work is the result of a research collaboration with researchers from the Harvard BioRobotics Laboratory. The developed experiments show that the overall task time is reduced and that the developed methods allow for full dexterity and correct completion of dexterous manipulations.

A multi-criteria optimization and decision-making approach for improvement of food engineering processes.

The objective of this study was to propose a multi-criteria optimization and decision-making technique to solve food engineering problems. This technique was demostrated using experimental data obtained on osmotic dehydratation of carrot cubes in a sodium chloride solution. The Aggregating Functions Approach, the Adaptive Random Search Algorithm, and the Penalty Functions Approach were used in this study to compute the initial set of non-dominated or Pareto-optimal solutions. Multiple non-linear regression analysis was performed on a set of experimental data in order to obtain particular multi-objective functions (responses), namely water loss, solute gain, rehydration ratio, three different colour criteria of rehydrated product, and sensory evaluation (organoleptic quality). Two multi-criteria decision-making approaches, the Analytic Hierarchy Process (AHP) and the Tabular Method (TM), were used simultaneously to choose the best alternative among the set of non-dominated solutions. The multi-criteria optimization and decision-making technique proposed in this study can facilitate the assessment of criteria weights, giving rise to a fairer, more consistent, and adequate final compromised solution or food process. This technique can be useful to food scientists in research and education, as well as to engineers involved in the improvement of a variety of food engineering processes.

Linear Bayes policy for learning in contextual-bandits

Machine and Statistical Learning techniques are used in almost all online advertisement systems. The problem of discovering which content is more demanded (e.g. receive more clicks) can be modeled as a multi-armed bandit problem. Contextual bandits (i.e., bandits with covariates, side information or associative reinforcement learning) associate, to each specific content, several features that define the “context” in which it appears (e.g. user, web page, time, region). This problem can be studied in the stochastic/statistical setting by means of the conditional probability paradigm using the Bayes’ theorem. However, for very large contextual information and/or real-time constraints, the exact calculation of the Bayes’ rule is computationally infeasible. In this article, we present a method that is able to handle large contextual information for learning in contextual-bandits problems. This method was tested in the Challenge on Yahoo! dataset at ICML2012’s Workshop “new Challenges for Exploration & Exploitation 3”, obtaining the second place. Its basic exploration policy is deterministic in the sense that for the same input data (as a time-series) the same results are obtained. We address the deterministic exploration vs. exploitation issue, explaining the way in which the proposed method deterministically finds an effective dynamic trade-off based solely in the input-data, in contrast to other methods that use a random number generator.

Optimal Piecewise Linear Function Approximation for GPU-based Applications

Many computer vision and human-computer interaction applications developed in recent years need evaluating complex and continuous mathematical functions as an essential step toward proper operation. However, rigorous evaluation of this kind of functions often implies a very high computational cost, unacceptable in real-time applications. To alleviate this problem, functions are commonly approximated by simpler piecewise-polynomial representations. Following this idea, we propose a novel, efficient, and practical technique to evaluate complex and continuous functions using a nearly optimal design of two types of piecewise linear approximations in the case of a large budget of evaluation subintervals. To this end, we develop a thorough error analysis that yields asymptotically tight bounds to accurately quantify the approximation performance of both representations. It provides an improvement upon previous error estimates and allows the user to control the trade-off between the approximation error and the number of evaluation subintervals. To guarantee real-time operation, the method is suitable for, but not limited to, an efficient implementation in modern Graphics Processing Units (GPUs), where it outperforms previous alternative approaches by exploiting the fixed-function interpolation routines present in their texture units. The proposed technique is a perfect match for any application requiring the evaluation of continuous functions, we have measured in detail its quality and efficiency on several functions, and, in particular, the Gaussian function because it is extensively used in many areas of computer vision and cybernetics, and it is expensive to evaluate.

Real-Time Dynamic PGD Calculation of Non-Linear Soil Behavior

El estudio sísmico en los últimos 50 años y el análisis del comportamiento dinámico del suelo revelan que el comportamiento del suelo es altamente no lineal e histéretico incluso para pequeñas deformaciones. El comportamiento no lineal del suelo durante un evento sísmico tiene un papel predominante en el análisis de la respuesta de sitio. Los análisis unidimensionales de la respuesta sísmica del suelo son a menudo realizados utilizando procedimientos lineales equivalentes, que requieren generalmente pocos parámetros conocidos. Los análisis de respuesta de sitio no lineal tienen el potencial para simular con mayor precisión el comportamiento del suelo, pero su aplicación en la práctica se ha visto limitada debido a la selección de parámetros poco documentadas y poco claras, así como una inadecuada documentación de los beneficios del modelado no lineal en relación al modelado lineal equivalente. En el análisis del suelo, el comportamiento del suelo es aproximado como un sólido Kelvin-Voigt con un módulo de corte elástico y amortiguamiento viscoso. En el análisis lineal y no lineal del suelo se están considerando geometrías y modelos reológicos más complejos. El primero está siendo dirigido por considerar parametrizaciones más ricas del comportamiento linealizado y el segundo mediante el uso de multi-modo de los elementos de resorte-amortiguador con un eventual amortiguador fraccional. El uso del cálculo fraccional está motivado en gran parte por el hecho de que se requieren menos parámetros para lograr la aproximación exacta a los datos experimentales. Basándose en el modelo de Kelvin-Voigt, la viscoelasticidad es revisada desde su formulación más estándar a algunas descripciones más avanzada que implica la amortiguación dependiente de la frecuencia (o viscosidad), analizando los efectos de considerar derivados fraccionarios para representar esas contribuciones viscosas. Vamos a demostrar que tal elección se traduce en modelos más ricos que pueden adaptarse a diferentes limitaciones relacionadas con la potencia disipada, amplitud de la respuesta y el ángulo de fase. Por otra parte, el uso de derivados fraccionarios permite acomodar en paralelo, dentro de un análogo de Kelvin-Voigt generalizado, muchos amortiguadores que contribuyen a aumentar la flexibilidad del modelado para la descripción de los resultados experimentales. Obviamente estos modelos ricos implican muchos parámetros, los asociados con el comportamiento y los relacionados con los derivados fraccionarios. El análisis paramétrico de estos modelos requiere técnicas numéricas eficientemente capaces de simular comportamientos complejos. El método de la Descomposición Propia Generalizada (PGD) es el candidato perfecto para la construcción de este tipo de soluciones paramétricas. Podemos calcular off-line la solución paramétrica para el depósito de suelo, para todos los parámetros del modelo, tan pronto como tales soluciones paramétricas están disponibles, el problema puede ser resuelto en tiempo real, porque no se necesita ningún nuevo cálculo, el solucionador sólo necesita particularizar on-line la solución paramétrica calculada off-line, que aliviará significativamente el procedimiento de solución. En el marco de la PGD, parámetros de los materiales y los diferentes poderes de derivación podrían introducirse como extra-coordenadas en el procedimiento de solución. El cálculo fraccional y el nuevo método de reducción modelo llamado Descomposición Propia Generalizada han sido aplicado en esta tesis tanto al análisis lineal como al análisis no lineal de la respuesta del suelo utilizando un método lineal equivalente. ABSTRACT Studies of earthquakes over the last 50 years and the examination of dynamic soil behavior reveal that soil behavior is highly nonlinear and hysteretic even at small strains. Nonlinear behavior of soils during a seismic event has a predominant role in current site response analysis. One-dimensional seismic ground response analysis are often performed using equivalent-linear procedures, which require few, generally well-known parameters. Nonlinear analyses have the potential to more accurately simulate soil behavior, but their implementation in practice has been limited because of poorly documented and unclear parameter selection, as well as inadequate documentation of the benefits of nonlinear modeling relative to equivalent linear modeling. In soil analysis, soil behaviour is approximated as a Kelvin-Voigt solid with a elastic shear modulus and viscous damping. In linear and nonlinear analysis more complex geometries and more complex rheological models are being considered. The first is being addressed by considering richer parametrizations of the linearized behavior and the second by using multi-mode spring-dashpot elements with eventual fractional damping. The use of fractional calculus is motivated in large part by the fact that fewer parameters are required to achieve accurate approximation of experimental data. Based in Kelvin-Voigt model the viscoelastodynamics is revisited from its most standard formulation to some more advanced description involving frequency-dependent damping (or viscosity), analyzing the effects of considering fractional derivatives for representing such viscous contributions. We will prove that such a choice results in richer models that can accommodate different constraints related to the dissipated power, response amplitude and phase angle. Moreover, the use of fractional derivatives allows to accommodate in parallel, within a generalized Kelvin-Voigt analog, many dashpots that contribute to increase the modeling flexibility for describing experimental findings. Obviously these rich models involve many parameters, the ones associated with the behavior and the ones related to the fractional derivatives. The parametric analysis of all these models require efficient numerical techniques able to simulate complex behaviors. The Proper Generalized Decomposition (PGD) is the perfect candidate for producing such kind of parametric solutions. We can compute off-line the parametric solution for the soil deposit, for all parameter of the model, as soon as such parametric solutions are available, the problem can be solved in real time because no new calculation is needed, the solver only needs particularize on-line the parametric solution calculated off-line, which will alleviate significantly the solution procedure. Within the PGD framework material parameters and the different derivation powers could be introduced as extra-coordinates in the solution procedure. Fractional calculus and the new model reduction method called Proper Generalized Decomposition has been applied in this thesis to the linear analysis and nonlinear soil response analysis using a equivalent linear method.

Automated wordlength optimization framework for multi-source statistical interval-based analysis of nonlinear systems with control-flow structures

El uso de aritmética de punto fijo es una opción de diseño muy extendida en sistemas con fuertes restricciones de área, consumo o rendimiento. Para producir implementaciones donde los costes se minimicen sin impactar negativamente en la precisión de los resultados debemos llevar a cabo una asignación cuidadosa de anchuras de palabra. Encontrar la combinación óptima de anchuras de palabra en coma fija para un sistema dado es un problema combinatorio NP-hard al que los diseñadores dedican entre el 25 y el 50 % del ciclo de diseño. Las plataformas hardware reconfigurables, como son las FPGAs, también se benefician de las ventajas que ofrece la aritmética de coma fija, ya que éstas compensan las frecuencias de reloj más bajas y el uso más ineficiente del hardware que hacen estas plataformas respecto a los ASICs. A medida que las FPGAs se popularizan para su uso en computación científica los diseños aumentan de tamaño y complejidad hasta llegar al punto en que no pueden ser manejados eficientemente por las técnicas actuales de modelado de señal y ruido de cuantificación y de optimización de anchura de palabra. En esta Tesis Doctoral exploramos distintos aspectos del problema de la cuantificación y presentamos nuevas metodologías para cada uno de ellos: Las técnicas basadas en extensiones de intervalos han permitido obtener modelos de propagación de señal y ruido de cuantificación muy precisos en sistemas con operaciones no lineales. Nosotros llevamos esta aproximación un paso más allá introduciendo elementos de Multi-Element Generalized Polynomial Chaos (ME-gPC) y combinándolos con una técnica moderna basada en Modified Affine Arithmetic (MAA) estadístico para así modelar sistemas que contienen estructuras de control de flujo. Nuestra metodología genera los distintos caminos de ejecución automáticamente, determina las regiones del dominio de entrada que ejercitarán cada uno de ellos y extrae los momentos estadísticos del sistema a partir de dichas soluciones parciales. Utilizamos esta técnica para estimar tanto el rango dinámico como el ruido de redondeo en sistemas con las ya mencionadas estructuras de control de flujo y mostramos la precisión de nuestra aproximación, que en determinados casos de uso con operadores no lineales llega a tener tan solo una desviación del 0.04% con respecto a los valores de referencia obtenidos mediante simulación. Un inconveniente conocido de las técnicas basadas en extensiones de intervalos es la explosión combinacional de términos a medida que el tamaño de los sistemas a estudiar crece, lo cual conlleva problemas de escalabilidad. Para afrontar este problema presen tamos una técnica de inyección de ruidos agrupados que hace grupos con las señales del sistema, introduce las fuentes de ruido para cada uno de los grupos por separado y finalmente combina los resultados de cada uno de ellos. De esta forma, el número de fuentes de ruido queda controlado en cada momento y, debido a ello, la explosión combinatoria se minimiza. También presentamos un algoritmo de particionado multi-vía destinado a minimizar la desviación de los resultados a causa de la pérdida de correlación entre términos de ruido con el objetivo de mantener los resultados tan precisos como sea posible. La presente Tesis Doctoral también aborda el desarrollo de metodologías de optimización de anchura de palabra basadas en simulaciones de Monte-Cario que se ejecuten en tiempos razonables. Para ello presentamos dos nuevas técnicas que exploran la reducción del tiempo de ejecución desde distintos ángulos: En primer lugar, el método interpolativo aplica un interpolador sencillo pero preciso para estimar la sensibilidad de cada señal, y que es usado después durante la etapa de optimización. En segundo lugar, el método incremental gira en torno al hecho de que, aunque es estrictamente necesario mantener un intervalo de confianza dado para los resultados finales de nuestra búsqueda, podemos emplear niveles de confianza más relajados, lo cual deriva en un menor número de pruebas por simulación, en las etapas iniciales de la búsqueda, cuando todavía estamos lejos de las soluciones optimizadas. Mediante estas dos aproximaciones demostramos que podemos acelerar el tiempo de ejecución de los algoritmos clásicos de búsqueda voraz en factores de hasta x240 para problemas de tamaño pequeño/mediano. Finalmente, este libro presenta HOPLITE, una infraestructura de cuantificación automatizada, flexible y modular que incluye la implementación de las técnicas anteriores y se proporciona de forma pública. Su objetivo es ofrecer a desabolladores e investigadores un entorno común para prototipar y verificar nuevas metodologías de cuantificación de forma sencilla. Describimos el flujo de trabajo, justificamos las decisiones de diseño tomadas, explicamos su API pública y hacemos una demostración paso a paso de su funcionamiento. Además mostramos, a través de un ejemplo sencillo, la forma en que conectar nuevas extensiones a la herramienta con las interfaces ya existentes para poder así expandir y mejorar las capacidades de HOPLITE. ABSTRACT Using fixed-point arithmetic is one of the most common design choices for systems where area, power or throughput are heavily constrained. In order to produce implementations where the cost is minimized without negatively impacting the accuracy of the results, a careful assignment of word-lengths is required. The problem of finding the optimal combination of fixed-point word-lengths for a given system is a combinatorial NP-hard problem to which developers devote between 25 and 50% of the design-cycle time. Reconfigurable hardware platforms such as FPGAs also benefit of the advantages of fixed-point arithmetic, as it compensates for the slower clock frequencies and less efficient area utilization of the hardware platform with respect to ASICs. As FPGAs become commonly used for scientific computation, designs constantly grow larger and more complex, up to the point where they cannot be handled efficiently by current signal and quantization noise modelling and word-length optimization methodologies. In this Ph.D. Thesis we explore different aspects of the quantization problem and we present new methodologies for each of them: The techniques based on extensions of intervals have allowed to obtain accurate models of the signal and quantization noise propagation in systems with non-linear operations. We take this approach a step further by introducing elements of MultiElement Generalized Polynomial Chaos (ME-gPC) and combining them with an stateof- the-art Statistical Modified Affine Arithmetic (MAA) based methodology in order to model systems that contain control-flow structures. Our methodology produces the different execution paths automatically, determines the regions of the input domain that will exercise them, and extracts the system statistical moments from the partial results. We use this technique to estimate both the dynamic range and the round-off noise in systems with the aforementioned control-flow structures. We show the good accuracy of our approach, which in some case studies with non-linear operators shows a 0.04 % deviation respect to the simulation-based reference values. A known drawback of the techniques based on extensions of intervals is the combinatorial explosion of terms as the size of the targeted systems grows, which leads to scalability problems. To address this issue we present a clustered noise injection technique that groups the signals in the system, introduces the noise terms in each group independently and then combines the results at the end. In this way, the number of noise sources in the system at a given time is controlled and, because of this, the combinato rial explosion is minimized. We also present a multi-way partitioning algorithm aimed at minimizing the deviation of the results due to the loss of correlation between noise terms, in order to keep the results as accurate as possible. This Ph.D. Thesis also covers the development of methodologies for word-length optimization based on Monte-Carlo simulations in reasonable times. We do so by presenting two novel techniques that explore the reduction of the execution times approaching the problem in two different ways: First, the interpolative method applies a simple but precise interpolator to estimate the sensitivity of each signal, which is later used to guide the optimization effort. Second, the incremental method revolves on the fact that, although we strictly need to guarantee a certain confidence level in the simulations for the final results of the optimization process, we can do it with more relaxed levels, which in turn implies using a considerably smaller amount of samples, in the initial stages of the process, when we are still far from the optimized solution. Through these two approaches we demonstrate that the execution time of classical greedy techniques can be accelerated by factors of up to ×240 for small/medium sized problems. Finally, this book introduces HOPLITE, an automated, flexible and modular framework for quantization that includes the implementation of the previous techniques and is provided for public access. The aim is to offer a common ground for developers and researches for prototyping and verifying new techniques for system modelling and word-length optimization easily. We describe its work flow, justifying the taken design decisions, explain its public API and we do a step-by-step demonstration of its execution. We also show, through an example, the way new extensions to the flow should be connected to the existing interfaces in order to expand and improve the capabilities of HOPLITE.