Development of Clinical Decision Support Systems based on Mathematical Models of Physiological Systems

In the last years of research, I focused my studies on different physiological problems. Together with my supervisors, I developed/improved different mathematical models in order to create valid tools useful for a better understanding of important clinical issues. The aim of all this work is to develop tools for learning and understanding cardiac and cerebrovascular physiology as well as pathology, generating research questions and developing clinical decision support systems useful for intensive care unit patients. I. ICP-model Designed for Medical Education We developed a comprehensive cerebral blood flow and intracranial pressure model to simulate and study the complex interactions in cerebrovascular dynamics caused by multiple simultaneous alterations, including normal and abnormal functional states of auto-regulation of the brain. Individual published equations (derived from prior animal and human studies) were implemented into a comprehensive simulation program. Included in the normal physiological modelling was: intracranial pressure, cerebral blood flow, blood pressure, and carbon dioxide (CO2) partial pressure. We also added external and pathological perturbations, such as head up position and intracranial haemorrhage. The model performed clinically realistically given inputs of published traumatized patients, and cases encountered by clinicians. The pulsatile nature of the output graphics was easy for clinicians to interpret. The manoeuvres simulated include changes of basic physiological inputs (e.g. blood pressure, central venous pressure, CO2 tension, head up position, and respiratory effects on vascular pressures) as well as pathological inputs (e.g. acute intracranial bleeding, and obstruction of cerebrospinal outflow). Based on the results, we believe the model would be useful to teach complex relationships of brain haemodynamics and study clinical research questions such as the optimal head-up position, the effects of intracranial haemorrhage on cerebral haemodynamics, as well as the best CO2 concentration to reach the optimal compromise between intracranial pressure and perfusion. We believe this model would be useful for both beginners and advanced learners. It could be used by practicing clinicians to model individual patients (entering the effects of needed clinical manipulations, and then running the model to test for optimal combinations of therapeutic manoeuvres). II. A Heterogeneous Cerebrovascular Mathematical Model Cerebrovascular pathologies are extremely complex, due to the multitude of factors acting simultaneously on cerebral haemodynamics. In this work, the mathematical model of cerebral haemodynamics and intracranial pressure dynamics, described in the point I, is extended to account for heterogeneity in cerebral blood flow. The model includes the Circle of Willis, six regional districts independently regulated by autoregulation and CO2 reactivity, distal cortical anastomoses, venous circulation, the cerebrospinal fluid circulation, and the intracranial pressure-volume relationship. Results agree with data in the literature and highlight the existence of a monotonic relationship between transient hyperemic response and the autoregulation gain. During unilateral internal carotid artery stenosis, local blood flow regulation is progressively lost in the ipsilateral territory with the presence of a steal phenomenon, while the anterior communicating artery plays the major role to redistribute the available blood flow. Conversely, distal collateral circulation plays a major role during unilateral occlusion of the middle cerebral artery. In conclusion, the model is able to reproduce several different pathological conditions characterized by heterogeneity in cerebrovascular haemodynamics and can not only explain generalized results in terms of physiological mechanisms involved, but also, by individualizing parameters, may represent a valuable tool to help with difficult clinical decisions. III. Effect of Cushing Response on Systemic Arterial Pressure. During cerebral hypoxic conditions, the sympathetic system causes an increase in arterial pressure (Cushing response), creating a link between the cerebral and the systemic circulation. This work investigates the complex relationships among cerebrovascular dynamics, intracranial pressure, Cushing response, and short-term systemic regulation, during plateau waves, by means of an original mathematical model. The model incorporates the pulsating heart, the pulmonary circulation and the systemic circulation, with an accurate description of the cerebral circulation and the intracranial pressure dynamics (same model as in the first paragraph). Various regulatory mechanisms are included: cerebral autoregulation, local blood flow control by oxygen (O2) and/or CO2 changes, sympathetic and vagal regulation of cardiovascular parameters by several reflex mechanisms (chemoreceptors, lung-stretch receptors, baroreceptors). The Cushing response has been described assuming a dramatic increase in sympathetic activity to vessels during a fall in brain O2 delivery. With this assumption, the model is able to simulate the cardiovascular effects experimentally observed when intracranial pressure is artificially elevated and maintained at constant level (arterial pressure increase and bradicardia). According to the model, these effects arise from the interaction between the Cushing response and the baroreflex response (secondary to arterial pressure increase). Then, patients with severe head injury have been simulated by reducing intracranial compliance and cerebrospinal fluid reabsorption. With these changes, oscillations with plateau waves developed. In these conditions, model results indicate that the Cushing response may have both positive effects, reducing the duration of the plateau phase via an increase in cerebral perfusion pressure, and negative effects, increasing the intracranial pressure plateau level, with a risk of greater compression of the cerebral vessels. This model may be of value to assist clinicians in finding the balance between clinical benefits of the Cushing response and its shortcomings. IV. Comprehensive Cardiopulmonary Simulation Model for the Analysis of Hypercapnic Respiratory Failure We developed a new comprehensive cardiopulmonary model that takes into account the mutual interactions between the cardiovascular and the respiratory systems along with their short-term regulatory mechanisms. The model includes the heart, systemic and pulmonary circulations, lung mechanics, gas exchange and transport equations, and cardio-ventilatory control. Results show good agreement with published patient data in case of normoxic and hyperoxic hypercapnia simulations. In particular, simulations predict a moderate increase in mean systemic arterial pressure and heart rate, with almost no change in cardiac output, paralleled by a relevant increase in minute ventilation, tidal volume and respiratory rate. The model can represent a valid tool for clinical practice and medical research, providing an alternative way to experience-based clinical decisions. In conclusion, models are not only capable of summarizing current knowledge, but also identifying missing knowledge. In the former case they can serve as training aids for teaching the operation of complex systems, especially if the model can be used to demonstrate the outcome of experiments. In the latter case they generate experiments to be performed to gather the missing data.

Non-evolutive pattern recognition techniques: An application in medical image diagnostics

Lo studio dell’intelligenza artificiale si pone come obiettivo la risoluzione di una classe di problemi che richiedono processi cognitivi difficilmente codificabili in un algoritmo per essere risolti. Il riconoscimento visivo di forme e figure, l’interpretazione di suoni, i giochi a conoscenza incompleta, fanno capo alla capacità umana di interpretare input parziali come se fossero completi, e di agire di conseguenza. Nel primo capitolo della presente tesi sarà costruito un semplice formalismo matematico per descrivere l’atto di compiere scelte. Il processo di “apprendimento” verrà descritto in termini della massimizzazione di una funzione di prestazione su di uno spazio di parametri per un ansatz di una funzione da uno spazio vettoriale ad un insieme finito e discreto di scelte, tramite un set di addestramento che descrive degli esempi di scelte corrette da riprodurre. Saranno analizzate, alla luce di questo formalismo, alcune delle più diffuse tecniche di artificial intelligence, e saranno evidenziate alcune problematiche derivanti dall’uso di queste tecniche. Nel secondo capitolo lo stesso formalismo verrà applicato ad una ridefinizione meno intuitiva ma più funzionale di funzione di prestazione che permetterà, per un ansatz lineare, la formulazione esplicita di un set di equazioni nelle componenti del vettore nello spazio dei parametri che individua il massimo assoluto della funzione di prestazione. La soluzione di questo set di equazioni sarà trattata grazie al teorema delle contrazioni. Una naturale generalizzazione polinomiale verrà inoltre mostrata. Nel terzo capitolo verranno studiati più nel dettaglio alcuni esempi a cui quanto ricavato nel secondo capitolo può essere applicato. Verrà introdotto il concetto di grado intrinseco di un problema. Verranno inoltre discusse alcuni accorgimenti prestazionali, quali l’eliminazione degli zeri, la precomputazione analitica, il fingerprinting e il riordino delle componenti per lo sviluppo parziale di prodotti scalari ad alta dimensionalità. Verranno infine introdotti i problemi a scelta unica, ossia quella classe di problemi per cui è possibile disporre di un set di addestramento solo per una scelta. Nel quarto capitolo verrà discusso più in dettaglio un esempio di applicazione nel campo della diagnostica medica per immagini, in particolare verrà trattato il problema della computer aided detection per il rilevamento di microcalcificazioni nelle mammografie.

Applied Graph Theory in Computer Vision and Pattern Recognition

This book will serve as a foundation for a variety of useful applications of graph theory to computer vision, pattern recognition, and related areas. It covers a representative set of novel graph-theoretic methods for complex computer vision and pattern recognition tasks. The first part of the book presents the application of graph theory to low-level processing of digital images such as a new method for partitioning a given image into a hierarchy of homogeneous areas using graph pyramids, or a study of the relationship between graph theory and digital topology. Part II presents graph-theoretic learning algorithms for high-level computer vision and pattern recognition applications, including a survey of graph based methodologies for pattern recognition and computer vision, a presentation of a series of computationally efficient algorithms for testing graph isomorphism and related graph matching tasks in pattern recognition and a new graph distance measure to be used for solving graph matching problems. Finally, Part III provides detailed descriptions of several applications of graph-based methods to real-world pattern recognition tasks. It includes a critical review of the main graph-based and structural methods for fingerprint classification, a new method to visualize time series of graphs, and potential applications in computer network monitoring and abnormal event detection.

Cost-effectiveness of different strategies to monitor adults on antiretroviral treatment: a combined analysis of three mathematical models

Background: WHO's 2013 revisions to its Consolidated Guidelines on antiretroviral drugs recommend routine viral load monitoring, rather than clinical or immunological monitoring, as the preferred monitoring approach on the basis of clinical evidence. However, HIV programmes in resource-limited settings require guidance on the most cost-effective use of resources in view of other competing priorities such as expansion of antiretroviral therapy coverage. We assessed the cost-effectiveness of alternative patient monitoring strategies. Methods: We evaluated a range of monitoring strategies, including clinical, CD4 cell count, and viral load monitoring, alone and together, at different frequencies and with different criteria for switching to second-line therapies. We used three independently constructed and validated models simultaneously. We estimated costs on the basis of resource use projected in the models and associated unit costs; we quantified impact as disability-adjusted life years (DALYs) averted. We compared alternatives using incremental cost-effectiveness analysis. Findings: All models show that clinical monitoring delivers significant benefit compared with a hypothetical baseline scenario with no monitoring or switching. Regular CD4 cell count monitoring confers a benefit over clinical monitoring alone, at an incremental cost that makes it affordable in more settings than viral load monitoring, which is currently more expensive. Viral load monitoring without CD4 cell count every 6—12 months provides the greatest reductions in morbidity and mortality, but incurs a high cost per DALY averted, resulting in lost opportunities to generate health gains if implemented instead of increasing antiretroviral therapy coverage or expanding antiretroviral therapy eligibility. Interpretation: The priority for HIV programmes should be to expand antiretroviral therapy coverage, firstly at CD4 cell count lower than 350 cells per μL, and then at a CD4 cell count lower than 500 cells per μL, using lower-cost clinical or CD4 monitoring. At current costs, viral load monitoring should be considered only after high antiretroviral therapy coverage has been achieved. Point-of-care technologies and other factors reducing costs might make viral load monitoring more affordable in future. Funding: Bill & Melinda Gates Foundation, WHO.

Sample size considerations using mathematical models: an example with Chlamydia trachomatis infection and its sequelae pelvic inflammatory disease.

BACKGROUND The success of an intervention to prevent the complications of an infection is influenced by the natural history of the infection. Assumptions about the temporal relationship between infection and the development of sequelae can affect the predicted effect size of an intervention and the sample size calculation. This study investigates how a mathematical model can be used to inform sample size calculations for a randomised controlled trial (RCT) using the example of Chlamydia trachomatis infection and pelvic inflammatory disease (PID). METHODS We used a compartmental model to imitate the structure of a published RCT. We considered three different processes for the timing of PID development, in relation to the initial C. trachomatis infection: immediate, constant throughout, or at the end of the infectious period. For each process we assumed that, of all women infected, the same fraction would develop PID in the absence of an intervention. We examined two sets of assumptions used to calculate the sample size in a published RCT that investigated the effect of chlamydia screening on PID incidence. We also investigated the influence of the natural history parameters of chlamydia on the required sample size. RESULTS The assumed event rates and effect sizes used for the sample size calculation implicitly determined the temporal relationship between chlamydia infection and PID in the model. Even small changes in the assumed PID incidence and relative risk (RR) led to considerable differences in the hypothesised mechanism of PID development. The RR and the sample size needed per group also depend on the natural history parameters of chlamydia. CONCLUSIONS Mathematical modelling helps to understand the temporal relationship between an infection and its sequelae and can show how uncertainties about natural history parameters affect sample size calculations when planning a RCT.

The Devil’s Calculus: Mathematical Models of Civil War

In spite of the movement to turn political science into a real science, various mathematical methods that are now the staples of physics, biology, and even economics are thoroughly uncommon in political science, especially the study of civil war. This study seeks to apply such methods - specifically, ordinary differential equations (ODEs) - to model civil war based on what one might dub the capabilities school of thought, which roughly states that civil wars end only when one side’s ability to make war falls far enough to make peace truly attractive. I construct several different ODE-based models and then test them all to see which best predicts the instantaneous capabilities of both sides of the Sri Lankan civil war in the period from 1990 to 1994 given parameters and initial conditions. The model that the tests declare most accurate gives very accurate predictions of state military capabilities and reasonable short term predictions of cumulative deaths. Analysis of the model reveals the scale of the importance of rebel finances to the sustainability of insurgency, most notably that the number of troops required to put down the Tamil Tigers is reduced by nearly a full order of magnitude when Tiger foreign funding is stopped. The study thus demonstrates that accurate foresight may come of relatively simple dynamical models, and implies the great potential of advanced and currently unconventional non-statistical mathematical methods in political science.

Analysis of The Key Parameters in Pedestrian Safety Assessment for the European Vehicle Fleet Using Multibody and Finite Element Mathematical Models

Esta tesis investiga cuales son los parámetros más críticos que condicionan los resultados que obtienen en los ensayos de protección de peatones la flota Europea de vehículos, según la reglamentación europea de protección de peatones de 2003 (Directiva CE 2003/102) y el posterior Reglamento de 2009 (Reglamento CE 2009/78). En primer lugar se ha analizado el contexto de la protección de peatones en Europa, viendo la historia de las diferentes propuestas de procedimientos de ensayo así como los cambios (y las razones de los mismos) que han sufrido a lo largo del proceso de definición de la normativa Europea. Con la información disponible de más de 400 de estos ensayos se han desarrollado corredores de rigidez para los frontales de los diferentes segmentos de la flota de vehículos europea, siendo este uno de los resultados más relevantes de esta tesis. Posteriormente, esta tesis ha realizado un estudio accidentológico en detalle de los escenarios de atropello de peatones, identificando sus características más relevantes, los grupos de población con mayor riesgo y los tipos de lesiones más importantes que aparecen (en frecuencia y severidad), que han sentado las bases para analizar con modelos matemáticos hasta qué punto los métodos de ensayo propuestos realmente tienen estos factores en cuenta. Estos análisis no habrían sido posibles sin el desarrollo de las nuevas herramientas que se presentan en esta tesis, que permiten construir instantáneamente el modelo matemático de cualquier vehículo y cualquier peatón adulto para analizar su iteración. Así, esta tesis ha desarrollado una metodología rápida para desarrollar modelos matemáticos de vehículos a demanda, de cualquier marca y modelo y con las características geométricas y de rigidez deseados que permitan representarlo matemáticamente y del mismo modo, ha investigado cómo evoluciona el comportamiento del cuerpo humano durante el envejecimiento y ha implementado una funcionalidad de escalado en edad al modelo de peatón en multicuerpo de MADYMO (ya escalable en tamaño) para permitir modelar ad hoc cualquier peatón adulto (en género y edad). Finalmente, esta tesis también ha realizado, utilizando modelos de elementos finitos del cuerpo humano, diferentes estudios sobre la biomecánica de las lesiones más frecuentes de este tipo de accidentes, (en piernas y cabeza) con el objetivo de mejorar los procedimientos de ensayo para que predigan mejor el tipo de lesiones que se quieren evitar. Con el marco temporal y las condiciones de contorno de esta tesis se han centrado los esfuerzos en reforzar algunos aspectos críticos pero puntuales sobre cómo mejorar el ensayo de cabeza y, sobretodo, en proponer soluciones viables y con un valor añadido real al ensayo de pierna contra parachoques, sin cambiar la esencia del mismo pero proponiendo un nuevo impactador mejorado que incorpore una masa extra que representa a la parte superior del cuerpo y sea válido para toda la flota europea de vehículos independiente de la geometría de su frontal.

Mathematical models for the arrangement and the cleaning of the river basin and surroundings of the river sandy grounds to its passage by the city of Salta (Argentina)

The province of Salta is located the Northwest of Argentina in the border with Bolivia, Chile and Paraguay. Its Capital is the city of Salta that concentrates half of the inhabitants of the province and has grown to 600000 hab., from a small active Spanish town well founded in 1583. The city is crossed by the Arenales River descending from close mountains at North, source of water and end of sewers. But with actual growing it has become a focus of infection and of remarkable unhealthiness. It is necessary to undertake a plan for the recovery of the river, directed to the attainment of the well-being and to improve the life?s quality of the Community. The fundamental idea of the plan is to obtain an ordering of the river basin and an integral management of the channel and its surroundings, including the cleaning out. The improvement of the water?s quality, the healthiness of the surroundings and the improvement of the environment, must go hand by hand with the development of sport activities, of relaxation, tourism, establishment of breeding grounds, kitchen gardens, micro enterprises with clean production and other actions that contribute to their benefit by the society, that being a basic factor for their care and sustainable use. The present pollution is organic, chemical, industrial, domestic, due to the disposition of sweepings and sewer effluents that affects not only the flora and small fauna, destroying the biodiversity, but also to the health of people living in their margins. Within the plan it will be necessary to consider, besides hydric and environmental cleaning and the prevention of floods, the planning of the extraction of aggregates, the infrastructure and consolidation of margins works and the arrangement of all the river basin. It will be necessary to consider the public intervention at state, provincial and local level, and the private intervention. In the model it has been necessary to include the sub-model corresponding to the election of the entity to be the optimal instrument to reach the proposed objectives, giving an answer to the social, environmental and economic requirements. For that the authors have used multi-criteria decision methods to qualify and select alternatives, and for the programming of their implementation. In the model the authors have contemplated the short, average and long term actions. They conform a Paretooptimal alternative which secures the ordering, integral and suitable management of the basin of the Arenales River, focusing on its passage by the city of Salta.

Oscillatory genetic circuits: new designs and mathematical models

Introduction and motivation: A wide variety of organisms have developed in-ternal biomolecular clocks in order to adapt to cyclic changes of the environment. Clock operation involves genetic networks. These genetic networks have to be mod¬eled in order to understand the underlying mechanism of oscillations and to design new synthetic cellular clocks. This doctoral thesis has resulted in two contributions to the fields of genetic clocks and systems and synthetic biology, generally. The first contribution is a new genetic circuit model that exhibits an oscillatory behav¬ior through catalytic RNA molecules. The second and major contribution is a new genetic circuit model demonstrating that a repressor molecule acting on the positive feedback of a self-activating gene produces reliable oscillations. First contribution: A new model of a synthetic genetic oscillator based on a typical two-gene motif with one positive and one negative feedback loop is pre¬sented. The originality is that the repressor is a catalytic RNA molecule rather than a protein or a non-catalytic RNA molecule. This catalytic RNA is a ribozyme that acts post-transcriptionally by binding to and cleaving target mRNA molecules. This genetic clock involves just two genes, a mRNA and an activator protein, apart from the ribozyme. Parameter values that produce a circadian period in both determin¬istic and stochastic simulations have been chosen as an example of clock operation. The effects of the stochastic fluctuations are quantified by a period histogram and autocorrelation function. The conclusion is that catalytic RNA molecules can act as repressor proteins and simplify the design of genetic oscillators. Second and major contribution: It is demonstrated that a self-activating gene in conjunction with a simple negative interaction can easily produce robust matically validated. This model is comprised of two clearly distinct parts. The first is a positive feedback created by a protein that binds to the promoter of its own gene and activates the transcription. The second is a negative interaction in which a repressor molecule prevents this protein from binding to its promoter. A stochastic study shows that the system is robust to noise. A deterministic study identifies that the oscillator dynamics are mainly driven by two types of biomolecules: the protein, and the complex formed by the repressor and this protein. The main conclusion of this study is that a simple and usual negative interaction, such as degradation, se¬questration or inhibition, acting on the positive transcriptional feedback of a single gene is a sufficient condition to produce reliable oscillations. One gene is enough and the positive transcriptional feedback signal does not need to activate a second repressor gene. At the genetic level, this means that an explicit negative feedback loop is not necessary. Unlike many genetic oscillators, this model needs neither cooperative binding reactions nor the formation of protein multimers. Applications and future research directions: Recently, RNA molecules have been found to play many new catalytic roles. The first oscillatory genetic model proposed in this thesis uses ribozymes as repressor molecules. This could provide new synthetic biology design principles and a better understanding of cel¬lular clocks regulated by RNA molecules. The second genetic model proposed here involves only a repression acting on a self-activating gene and produces robust oscil¬lations. Unlike current two-gene oscillators, this model surprisingly does not require a second repressor gene. This result could help to clarify the design principles of cellular clocks and constitute a new efficient tool for engineering synthetic genetic oscillators. Possible follow-on research directions are: validate models in vivo and in vitro, research the potential of second model as a genetic memory, investigate new genetic oscillators regulated by non-coding RNAs and design a biosensor of positive feedbacks in genetic networks based on the operation of the second model Resumen Introduccion y motivacion: Una amplia variedad de organismos han desarro-llado relojes biomoleculares internos con el fin de adaptarse a los cambios ciclicos del entorno. El funcionamiento de estos relojes involucra redes geneticas. El mo delado de estas redes geneticas es esencial tanto para entender los mecanismos que producen las oscilaciones como para diseiiar nuevos circuitos sinteticos en celulas. Esta tesis doctoral ha dado lugar a dos contribuciones dentro de los campos de los circuitos geneticos en particular, y biologia de sistemas y sintetica en general. La primera contribucion es un nuevo modelo de circuito genetico que muestra un comportamiento oscilatorio usando moleculas de ARN cataliticas. La segunda y principal contribucion es un nuevo modelo de circuito genetico que demuestra que una molecula represora actuando sobre el lazo de un gen auto-activado produce oscilaciones robustas. Primera contribucion: Es un nuevo modelo de oscilador genetico sintetico basado en una tipica red genetica compuesta por dos genes con dos lazos de retroa-limentacion, uno positivo y otro negativo. La novedad de este modelo es que el represor es una molecula de ARN catalftica, en lugar de una protefna o una molecula de ARN no-catalitica. Este ARN catalitico es una ribozima que actua despues de la transcription genetica uniendose y cortando moleculas de ARN mensajero (ARNm). Este reloj genetico involucra solo dos genes, un ARNm y una proteina activadora, aparte de la ribozima. Como ejemplo de funcionamiento, se han escogido valores de los parametros que producen oscilaciones con periodo circadiano (24 horas) tanto en simulaciones deterministas como estocasticas. El efecto de las fluctuaciones es-tocasticas ha sido cuantificado mediante un histograma del periodo y la función de auto-correlacion. La conclusion es que las moleculas de ARN con propiedades cataliticas pueden jugar el misnio papel que las protemas represoras, y por lo tanto, simplificar el diseno de los osciladores geneticos. Segunda y principal contribucion: Es un nuevo modelo de oscilador genetico que demuestra que un gen auto-activado junto con una simple interaction negativa puede producir oscilaciones robustas. Este modelo ha sido estudiado y validado matematicamente. El modelo esta compuesto de dos partes bien diferenciadas. La primera parte es un lazo de retroalimentacion positiva creado por una proteina que se une al promotor de su propio gen activando la transcription. La segunda parte es una interaction negativa en la que una molecula represora evita la union de la proteina con el promotor. Un estudio estocastico muestra que el sistema es robusto al ruido. Un estudio determinista muestra que la dinamica del sistema es debida principalmente a dos tipos de biomoleculas: la proteina, y el complejo formado por el represor y esta proteina. La conclusion principal de este estudio es que una simple y usual interaction negativa, tal como una degradation, un secuestro o una inhibition, actuando sobre el lazo de retroalimentacion positiva de un solo gen es una condition suficiente para producir oscilaciones robustas. Un gen es suficiente y el lazo de retroalimentacion positiva no necesita activar a un segundo gen represor, tal y como ocurre en los relojes actuales con dos genes. Esto significa que a nivel genetico un lazo de retroalimentacion negativa no es necesario de forma explicita. Ademas, este modelo no necesita reacciones cooperativas ni la formation de multimeros proteicos, al contrario que en muchos osciladores geneticos. Aplicaciones y futuras lineas de investigacion: En los liltimos anos, se han descubierto muchas moleculas de ARN con capacidad catalitica. El primer modelo de oscilador genetico propuesto en esta tesis usa ribozimas como moleculas repre¬soras. Esto podria proporcionar nuevos principios de diseno en biologia sintetica y una mejor comprension de los relojes celulares regulados por moleculas de ARN. El segundo modelo de oscilador genetico propuesto aqui involucra solo una represion actuando sobre un gen auto-activado y produce oscilaciones robustas. Sorprendente-mente, un segundo gen represor no es necesario al contrario que en los bien conocidos osciladores con dos genes. Este resultado podria ayudar a clarificar los principios de diseno de los relojes celulares naturales y constituir una nueva y eficiente he-rramienta para crear osciladores geneticos sinteticos. Algunas de las futuras lineas de investigation abiertas tras esta tesis son: (1) la validation in vivo e in vitro de ambos modelos, (2) el estudio del potential del segundo modelo como circuito base para la construction de una memoria genetica, (3) el estudio de nuevos osciladores geneticos regulados por ARN no codificante y, por ultimo, (4) el rediseno del se¬gundo modelo de oscilador genetico para su uso como biosensor capaz de detectar genes auto-activados en redes geneticas.

The Learning of the Mathematical Models to Aid Decision Making in the High Level Engineering Schools?

At present, in the University curricula in most countries, the decision theory and the mathematical models to aid decision making is not included, as in the graduate program like in Doctored and Master´s programs. In the Technical School of High Level Agronomic Engineers of the Technical University of Madrid (ETSIA-UPM), the need to offer to the future engineers training in a subject that could help them to take decisions in their profession was felt. Along the life, they will have to take a lot of decisions. Ones, will be important and others no. In the personal level, they will have to take several very important decisions, like the election of a career, professional work, or a couple, but in the professional field, the decision making is the main role of the Managers, Politicians and Leaders. They should be decision makers and will be paid for it. Therefore, nobody can understand that such a professional that is called to practice management responsibilities in the companies, does not take training in such an important matter. For it, in the year 2000, it was requested to the University Board to introduce in the curricula an optional qualified subject of the second cycle with 4,5 credits titled " Mathematical Methods for Making Decisions ". A program was elaborated, the didactic material prepared and programs as Maple, Lingo, Math Cad, etc. installed in several IT classrooms, where the course will be taught. In the course 2000-2001 this subject was offered with a great acceptance that exceeded the forecasts of capacity and had to be prepared more classrooms. This course in graduate program took place in the Department of Applied Mathematics to the Agronomic Engineering, as an extension of the credits dedicated to Mathematics in the career of Engineering.

Development of mathematical models to elaborate strategies, select alternatives and development of plans for adaptation of communities to climate change in different geographical areas including costs to implement it.

There is evidence that the climate changes and that now, the change is influenced and accelerated by the CO2 augmentation in atmosphere due to combustion by humans. Such ?Climate change? is on the policy agenda at the global level, with the aim of understanding and reducing its causes and to mitigate its consequences. In most countries and international organisms UNO (e.g. Rio de Janeiro 1992), OECD, EC, etc . . . the efforts and debates have been directed to know the possible causes, to predict the future evolution of some variable conditioners, and trying to make studies to fight against the effects or to delay the negative evolution of such. The Protocol of Kyoto 1997 set international efforts about CO2 emissions, but it was partial and not followed e.g. by USA and China . . . , and in Durban 2011 the ineffectiveness of humanity on such global real challenges was set as evident. Among all that, the elaboration of a global model was not boarded that can help to choose the best alternative between the feasible ones, to elaborate the strategies and to evaluate the costs, and the authors propose to enter in that frame for study. As in all natural, technological and social changes, the best-prepared countries will have the best bear and the more rapid recover. In all the geographic areas the alternative will not be the same one, but the model must help us to make the appropriated decision. It is essential to know those areas that are more sensitive to the negative effects of climate change, the parameters to take into account for its evaluation, and comprehensive plans to deal with it. The objective of this paper is to elaborate a mathematical model support of decisions, which will allow to develop and to evaluate alternatives of adaptation to the climatic change of different communities in Europe and Latin-America, mainly in especially vulnerable areas to the climatic change, considering in them all the intervening factors. The models will consider criteria of physical type (meteorological, edaphic, water resources), of use of the ground (agriculturist, forest, mining, industrial, urban, tourist, cattle dealer), economic (income, costs, benefits, infrastructures), social (population), politician (implementation, legislation), educative (Educational programs, diffusion) and environmental, at the present moment and the future. The intention is to obtain tools for aiding to get a realistic position for these challenges, which are an important part of the future problems of humanity in next decades.