Geostatistics for constrained variables: positive data, compositions and probabilities. Applications to environmental hazard monitoring

Aquesta tesi estudia com estimar la distribució de les variables regionalitzades l'espai mostral i l'escala de les quals admeten una estructura d'espai Euclidià. Apliquem el principi del treball en coordenades: triem una base ortonormal, fem estadística sobre les coordenades de les dades, i apliquem els output a la base per tal de recuperar un resultat en el mateix espai original. Aplicant-ho a les variables regionalitzades, obtenim una aproximació única consistent, que generalitza les conegudes propietats de les tècniques de kriging a diversos espais mostrals: dades reals, positives o composicionals (vectors de components positives amb suma constant) són tractades com casos particulars. D'aquesta manera, es generalitza la geostadística lineal, i s'ofereix solucions a coneguts problemes de la no-lineal, tot adaptant la mesura i els criteris de representativitat (i.e., mitjanes) a les dades tractades. L'estimador per a dades positives coincideix amb una mitjana geomètrica ponderada, equivalent a l'estimació de la mediana, sense cap dels problemes del clàssic kriging lognormal. El cas composicional ofereix solucions equivalents, però a més permet estimar vectors de probabilitat multinomial. Amb una aproximació bayesiana preliminar, el kriging de composicions esdevé també una alternativa consistent al kriging indicador. Aquesta tècnica s'empra per estimar funcions de probabilitat de variables qualsevol, malgrat que sovint ofereix estimacions negatives, cosa que s'evita amb l'alternativa proposada. La utilitat d'aquest conjunt de tècniques es comprova estudiant la contaminació per amoníac a una estació de control automàtic de la qualitat de l'aigua de la conca de la Tordera, i es conclou que només fent servir les tècniques proposades hom pot detectar en quins instants l'amoni es transforma en amoníac en una concentració superior a la legalment permesa.

Modelling, control and supervision for a class of hybrid systems

The aim of this thesis is to narrow the gap between two different control techniques: the continuous control and the discrete event control techniques DES. This gap can be reduced by the study of Hybrid systems, and by interpreting as Hybrid systems the majority of large-scale systems. In particular, when looking deeply into a process, it is often possible to identify interaction between discrete and continuous signals. Hybrid systems are systems that have both continuous, and discrete signals. Continuous signals are generally supposed continuous and differentiable in time, since discrete signals are neither continuous nor differentiable in time due to their abrupt changes in time. Continuous signals often represent the measure of natural physical magnitudes such as temperature, pressure etc. The discrete signals are normally artificial signals, operated by human artefacts as current, voltage, light etc. Typical processes modelled as Hybrid systems are production systems, chemical process, or continuos production when time and continuous measures interacts with the transport, and stock inventory system. Complex systems as manufacturing lines are hybrid in a global sense. They can be decomposed into several subsystems, and their links. Another motivation for the study of Hybrid systems is the tools developed by other research domains. These tools benefit from the use of temporal logic for the analysis of several properties of Hybrid systems model, and use it to design systems and controllers, which satisfies physical or imposed restrictions. This thesis is focused in particular types of systems with discrete and continuous signals in interaction. That can be modelled hard non-linealities, such as hysteresis, jumps in the state, limit cycles, etc. and their possible non-deterministic future behaviour expressed by an interpretable model description. The Hybrid systems treated in this work are systems with several discrete states, always less than thirty states (it can arrive to NP hard problem), and continuous dynamics evolving with expression: with Ki ¡ Rn constant vectors or matrices for X components vector. In several states the continuous evolution can be several of them Ki = 0. In this formulation, the mathematics can express Time invariant linear system. By the use of this expression for a local part, the combination of several local linear models is possible to represent non-linear systems. And with the interaction with discrete events of the system the model can compose non-linear Hybrid systems. Especially multistage processes with high continuous dynamics are well represented by the proposed methodology. Sate vectors with more than two components, as third order models or higher is well approximated by the proposed approximation. Flexible belt transmission, chemical reactions with initial start-up and mobile robots with important friction are several physical systems, which profits from the benefits of proposed methodology (accuracy). The motivation of this thesis is to obtain a solution that can control and drive the Hybrid systems from the origin or starting point to the goal. How to obtain this solution, and which is the best solution in terms of one cost function subject to the physical restrictions and control actions is analysed. Hybrid systems that have several possible states, different ways to drive the system to the goal and different continuous control signals are problems that motivate this research. The requirements of the system on which we work is: a model that can represent the behaviour of the non-linear systems, and that possibilities the prediction of possible future behaviour for the model, in order to apply an supervisor which decides the optimal and secure action to drive the system toward the goal. Specific problems can be determined by the use of this kind of hybrid models are: - The unity of order. - Control the system along a reachable path. - Control the system in a safe path. - Optimise the cost function. - Modularity of control The proposed model solves the specified problems in the switching models problem, the initial condition calculus and the unity of the order models. Continuous and discrete phenomena are represented in Linear hybrid models, defined with defined eighth-tuple parameters to model different types of hybrid phenomena. Applying a transformation over the state vector : for LTI system we obtain from a two-dimensional SS a single parameter, alpha, which still maintains the dynamical information. Combining this parameter with the system output, a complete description of the system is obtained in a form of a graph in polar representation. Using Tagaki-Sugeno type III is a fuzzy model which include linear time invariant LTI models for each local model, the fuzzyfication of different LTI local model gives as a result a non-linear time invariant model. In our case the output and the alpha measure govern the membership function. Hybrid systems control is a huge task, the processes need to be guided from the Starting point to the desired End point, passing a through of different specific states and points in the trajectory. The system can be structured in different levels of abstraction and the control in three layers for the Hybrid systems from planning the process to produce the actions, these are the planning, the process and control layer. In this case the algorithms will be applied to robotics ¡V a domain where improvements are well accepted ¡V it is expected to find a simple repetitive processes for which the extra effort in complexity can be compensated by some cost reductions. It may be also interesting to implement some control optimisation to processes such as fuel injection, DC-DC converters etc. In order to apply the RW theory of discrete event systems on a Hybrid system, we must abstract the continuous signals and to project the events generated for these signals, to obtain new sets of observable and controllable events. Ramadge & Wonham¡¦s theory along with the TCT software give a Controllable Sublanguage of the legal language generated for a Discrete Event System (DES). Continuous abstraction transforms predicates over continuous variables into controllable or uncontrollable events, and modifies the set of uncontrollable, controllable observable and unobservable events. Continuous signals produce into the system virtual events, when this crosses the bound limits. If this event is deterministic, they can be projected. It is necessary to determine the controllability of this event, in order to assign this to the corresponding set, , controllable, uncontrollable, observable and unobservable set of events. Find optimal trajectories in order to minimise some cost function is the goal of the modelling procedure. Mathematical model for the system allows the user to apply mathematical techniques over this expression. These possibilities are, to minimise a specific cost function, to obtain optimal controllers and to approximate a specific trajectory. The combination of the Dynamic Programming with Bellman Principle of optimality, give us the procedure to solve the minimum time trajectory for Hybrid systems. The problem is greater when there exists interaction between adjacent states. In Hybrid systems the problem is to determine the partial set points to be applied at the local models. Optimal controller can be implemented in each local model in order to assure the minimisation of the local costs. The solution of this problem needs to give us the trajectory to follow the system. Trajectory marked by a set of set points to force the system to passing over them. Several ways are possible to drive the system from the Starting point Xi to the End point Xf. Different ways are interesting in: dynamic sense, minimum states, approximation at set points, etc. These ways need to be safe and viable and RchW. And only one of them must to be applied, normally the best, which minimises the proposed cost function. A Reachable Way, this means the controllable way and safe, will be evaluated in order to obtain which one minimises the cost function. Contribution of this work is a complete framework to work with the majority Hybrid systems, the procedures to model, control and supervise are defined and explained and its use is demonstrated. Also explained is the procedure to model the systems to be analysed for automatic verification. Great improvements were obtained by using this methodology in comparison to using other piecewise linear approximations. It is demonstrated in particular cases this methodology can provide best approximation. The most important contribution of this work, is the Alpha approximation for non-linear systems with high dynamics While this kind of process is not typical, but in this case the Alpha approximation is the best linear approximation to use, and give a compact representation.

A study of variables that may influence continued placement in schools for the deaf

This paper reviews variables that influence placement of a hearing impaired child into a special education program instead of being mainstreamed into a public school.

A study of variables influencing placement in schools for hearing

This paper reviews mainstreaming of former students of CID, 1965-1975.

Variables that influence the real-ear response of the TDH-49 earphone

This paper discusses a study performed to determine whether anatomical features of the outer ear affect the sound stimulus delivered by earphone to the tympanic membrane.

Operations on Risk Variables

In the article the author considers and analyzes operations and functions on risk variables. She takes into account the following variables: the sum of risk variables, its product, multiplication by a constant, division, maximum, minimum and median of a sum of random variables. She receives the formulas for probability distribution and basic distribution parameters. She conducts the analysis for dependent and independent random variables. She propose the examples of the situations in the economy and production management of risk modelled by this operations. The analysis is conducted with the way of mathematical proving. Some of the formulas presented are taken from the literature but others are the permanent results of the author.

Análisis y preparación estadística de variables para el diseño de un modelo credit score de gestión de riesgo de crédito

El presente estudio busca enfatizar la labor previa a la construcción de cualquier modelo de gestión de riesgo crediticio basado en un sistema tipo scoring. Esta importante fase inicial involucra la identificación de las fuentes de información, la verificación de la cantidad y calidad de los datos, la determinación y tipificación de variables cualitativas, cuantitativas, demográficas, así como la verificación y cuantificación del poder discriminante de dichas variables respecto el objetivo planteado. Con este fin se profundiza en el análisis estadístico a nivel descriptivo, en forma individual y conjunta de los datos, además de bosquejar los pasos esenciales en la arquitectura de un modelo credit score de gestión de riesgo crediticio.

Gestión de riesgo de crédito de la Cooperativa de Ahorro y Crédito Maquita Cushunchic: análisis y preparación estadística de variables para el diseño de un modelo Credit Score de cartera de consumo

El presente estudio busca analizar y preparar estadísticamente un conjunto de variables para el diseño de un modelo de aprobación CREDIT SCORE de cartera de consumo, tipo probabilístico, que apoye al oficial de crédito en la toma de la decisión antes de conceder o no un crédito de consumo; para que la decisión no sea subjetiva sino objetiva, medible (probabilística) apoyada en una ecuación que contenga sustento teórico y empírico dado por la base de datos histórica de la Cooperativa de ahorro y crédito Maquita Cushunchic. En la presente tesis partimos con fundamentación teórica que sustenta nuestro trabajo de investigación. En el segundo capítulo se realiza un diagnostico situacional de la empresa, donde se define la visión, la misión y definición de temas estratégicos. En el tercer capítulo realizaremos un análisis y preparación estadística de variables para el diseño de un modelo de aprobación CREDIT SCORE de cartera de consumo, esta fase involucra “la identificación de las fuentes de información, la verificación de cantidad y calidad de los datos, la determinación y tipificación de variables cualitativas, cuantitativas y demográficas, así como la verificación y cuantificación del poder discriminante de dichas variables respecto al objetivo planteado” 1, todo esto se lo realiza con el objetivo de aplicar un concepto de sistemas de calificación de crédito que se define de la siguiente manera: “la calificación supone que el desempeño de los prestamos futuros con características dadas, será parecido al desempeño de los prestamos pasados con características similares"2. Lo que se busca finalmente es que el modelo sea una herramienta de apoyo empírico que ayude a la toma de decisiones antes de conceder o no un credito. Finalmente termina este trabajo formulando conclusiones y recomendaciones.

Desarrollo de un Score de crédito para el financiamiento automotríz, con base en el análisis estadístico de variables

El mercado automotriz en el Ecuador es uno de los sectores que dinamiza la economía; a través de la producción e importación de vehículos y la comercialización de estos. El crecimiento de este sector en los últimos años ha sido constante y sostenido, al igual que el incremento de financiamientos otorgados a los consumidores o sujetos de crédito para la compra de un vehículo. El presente trabajo tiene como propósito el desarrollo de un score de crédito para el financiamiento automotriz que permita identificar a los buenos y malos solicitantes y así decidir entre otorgar o no el crédito. Para ello se han desarrollado cuatro capítulos. En el primer capítulo se realiza una introducción sobre el mercado automotriz su producción, niveles de importación, cadena de distribución, y otros; además de la composición del parque automotor y problemas de movilidad y el comportamiento de compra y los niveles de crédito automotriz. En el segundo capítulo se trata sobre la base de datos de las organizaciones y los tipos de variables que pueden contener y se explica los tipos de modelos de regresiones que se pueden realizar. En el tercer capítulo se define al modelo de score de crédito y los pasos a seguir para la construcción de este. En el cuarto capítulo se desarrollan todos los pasos para la construcción del score de crédito y en quinto capítulo se encuentran las conclusiones y recomendaciones del presente trabajo.

Variables associated with nest survival of Golden-winged Warblers (Vermivora chrysoptera) among vegetation communities commonly used for nesting

Among shrubland- and young forest-nesting bird species in North America, Golden-winged Warblers (Vermivora chrysoptera) are one of the most rapidly declining partly because of limited nesting habitat. Creation and management of high quality vegetation communities used for nesting are needed to reduce declines. Thus, we examined whether common characteristics could be managed across much of the Golden-winged Warbler’s breeding range to increase daily survival rate (DSR) of nests. We monitored 388 nests on 62 sites throughout Minnesota, Wisconsin, New York, North Carolina, Pennsylvania, Tennessee, and West Virginia. We evaluated competing DSR models in spatial-temporal (dominant vegetation type, population segment, state, and year), intraseasonal (nest stage and time-within-season), and vegetation model suites. The best-supported DSR models among the three model suites suggested potential associations between daily survival rate of nests and state, time-within-season, percent grass and Rubus cover within 1 m of the nest, and distance to later successional forest edge. Overall, grass cover (negative association with DSR above 50%) and Rubus cover (DSR lowest at about 30%) within 1 m of the nest and distance to later successional forest edge (negative association with DSR) may represent common management targets across our states for increasing Golden-winged Warbler DSR, particularly in the Appalachian Mountains population segment. Context-specific adjustments to management strategies, such as in wetlands or areas of overlap with Blue-winged Warblers (Vermivora cyanoptera), may be necessary to increase DSR for Golden-winged Warblers.

Solar influences on dynamical coupling between the stratosphere and troposphere

We use a simplified atmospheric general circulation model (AGCM) to investigate the response of the lower atmosphere to thermal perturbations in the lower stratosphere. The results show that generic heating of the lower stratosphere tends to weaken the sub-tropical jets and the tropospheric mean meridional circulations. The positions of the jets, and the extent of the Hadley cells, respond to the distribution of the stratospheric heating, with low latitude heating displacing them poleward, and uniform heating displacing them equatorward. The patterns of response to the low latitude heating are similar to those found to be associated with solar variability in previous observational data analysis, and to the effects of varying solar UV radiation in sophisticated AGCMs. In order to investigate the chain of causality involved in converting the stratospheric thermal forcing to a tropospheric climate signal we conduct an experiment which uses an ensemble of model spin-ups to analyse the time development of the response to an applied stratospheric perturbation. We find that the initial effect of the change in static stability at the tropopause is to reduce the eddy momentum flux convergence in this region. This is followed by a vertical transfer of the momentum forcing anomaly by an anomalous mean circulation to the surface, where it is partly balanced by surface stress anomalies. The unbalanced part drives the evolution of the vertically integrated zonal flow. We conclude that solar heating of the stratosphere may produce changes in the circulation of the troposphere even without any direct forcing below the tropopause. We suggest that the impact of the stratospheric changes on wave propagation is key to the mechanisms involved.

Classifying dynamical forcing mechanisms using a climatology of extratropical cyclones

A climatology of almost 700 extratropical cyclones is compiled by applying an automated feature tracking algorithm to a database of objectively identified cyclonic features. Cyclones are classified according to the relative contributions to the midlevel vertical motion of the forcing from upper and lower levels averaged over the cyclone intensification period (average U/L ratio) and also by the horizontal separation between their upper-level trough and low-level cyclone (tilt). The frequency distribution of the average U/L ratio of the cyclones contains two significant peaks and a long tail at high U/L ratio. Although discrete categories of cyclones have not been identified, the cyclones comprising the peaks and tail have characteristics that have been shown to be consistent with the type A, B, and C cyclones of the threefold classification scheme. Using the thresholds in average U/L ratio determined from the frequency distribution, type A, B, and C cyclones account for 30\%, 38\%, and 32\% of the total number of cyclones respectively. Cyclones with small average U/L ratio are more likely to be developing cyclones (attain a relative vorticity $\ge 1.2 \times 10^{-4} \mbox{s}^{-1}$) whereas cyclones with large average U/L ratio are more likely to be nondeveloping cyclones (60\% of type A cyclones develop whereas 31\% of type C cyclones develop). Type A cyclogenesis dominates in the development region East of the Rockies and over the gulf stream, type B cyclogenesis dominates in the region off the East coast of the USA, and type C cyclogenesis is more common over the oceans in regions of weaker low-level baroclinicity.