Effects of tubers of the Jerusalem artichoke (Helianthus tuberosus) and potatoes (Solanum tuberosum) on the intestinal microbiota of pigs and evaluation of a procedure for quantification of microbial mass in pig faeces

Die Mikrobiota im Gastrointestinaltrakt (GIT) spielt eine bedeutende Rolle beim Fermentationsprozess im Bezug auf die Nährstoffversorgung sowie die Gesundheit des Darms und des gesamten Organismus. Inulin und resistente Stärke (RS) konnten als präbiotisch wirksame Substanzen identifiziert werden und sind jeweils auch in den Knollen der Topinamburpflanze (Helianthus tuberosus) und in Kartoffeln (Solanum tuberosum) enthalten. Da sie ebenfalls energiereiche Futtermittel für Schweine sind, war es das Ziel der ersten beiden Studien, die Auswirkungen der Aufnahme von Topinamburknollen und Kartoffeln auf die intestinale Mikrobiota und Parameter des Immunsystems bei Endmastschweinen zu bestimmen. In der dritten Studie wurde die mikrobielle Biomasse quantitativ mit einem Verfahren zur Isolation von Bakterien in einer Flüssigkeit durch Hochgeschwindigkeits-Zentrifugation erfasst und der bakteriell gebundene Stickstoff (MP-N) mit dem bakteriellen und endogenem Kotstickstoff (BEDN) verglichen. Im ersten Versuch wurden 72 Endmastschweine in einem Freilandhaltungssystem in eine Kontroll- (CT), die mit Kraftfutter entsprechend des Bedarfs der Tiere für ein Leistungsniveau von 700 g täglichem Lebendmassezuwachs versorgt wurde, und eine Versuchsvariante (ET) aufgeteilt. In der Versuchsvariante erhielten die Tiere nur 70% der Kraftfuttermenge der Kontrollvariante, hatten aber Zugang zu einer abgeteilten Fläche, auf der Topinamburknollen angebaut waren. Die freie Aufnahme von Topinamburknollen wurde auf 1•24 kg Trockenmasse (TM)/Tag bestimmt, entsprechend einer Inulinaufnahme von durchschnittlich 800 g/Tag. Während sich die Wachstumsleistung in der Kontrollvariante auf 0•642 ± 0•014 kg/Tag belief, war sie in der Versuchsvariante mit 0•765 ± 0•015 kg/Tag (P=0•000) höher. Die freie Verfügbarkeit von Inulin und Fructo-oligosacchariden (FOS) im GIT der Schweine erhöhte die Keimzahlen der anaeroben Bakterien (P=0•000), Laktobazillen (P=0•046) und Hefen (P=0•000) signifikant und verringerte das Vorkommen von Clostridium perfringens im Schweinekot erheblich von lg 5•24 ± 0•17 kolonie-bildende Einheiten pro g Frischmasse (KbE/ g FM) in der Kontrollvariante auf lg 0•96 ± 0•20 KbE/ g FM in der Versuchsvariante (P=0•000). C-reaktives Protein (CRP) und Antikörper gegen Lipopolysaccharide (LPS) von Escherichia coli J5 ließen keine Unterschiede zwischen den Fütterungsvarianten erkennen. In der zweiten Untersuchung wurden 58 Endmastschweine einer Kontrollvariante (CT), die bedarfsgerecht mit einer Kraftfuttermischung für ein Leistungsniveau von 700 g Tageszunahmen gefüttert wurde, und zwei Versuchsvarianten zugeteilt. Die Versuchsvarianten erhielten eine Menge von 1•2 kg TM gedämpften Kartoffeln (potato treatment, PT) oder gedämpften und einsilierten Kartoffeln (silage treatment, ST) pro Tag und nur 46% bzw. 43% der Menge des Kraftfutters der Kontrollvariante. Die Wachstumsleistung und Schlachtkörperzusammensetzung ließen keine signifikanten Unterschiede zwischen den Varianten erkennen. Im PT und ST waren gegenüber dem CT im Kot der pH-Wert sowie die Gehalte von TM, Neutral-Detergenz-Faser (NDF), unverdautem Futterstickstoff (UDN) und teilweise von Säure-Detergenz-Faser (ADF) signifikant niedriger (P=0•000) und die von Ammonium (NH4) und Ammoniumstickstoff (NH4-N) signifikant höher (P=0•000). Das hohe Angebot von hitzebehandelten Kartoffeln führte zu einer erheblichen Verringerung von E. coli (P=0•000), C. perfringens (P=0•000) und Immunoglobulin A gegen LPS von E. coli J5 (P=0•001). Darüber hinaus waren in der ersten Versuchsperiode im ST die aeroben und anaeroben Gesamtkeimzahlen sowie die Laktobazillen und Hefen gegenüber dem PT signifikant erhöht. Die Unterschiede in der Mikrobiota zwischen der Kontroll- und Versuchsvarianten weisen auf die positiven Auswirkungen von Topinamburknollen und hitzebehandelten Kartoffeln auf die Mikrobiota im hinteren Darmabschnitt hin. Das Ziel der dritten Untersuchung war die Modifizierung des Verfahrens zur Isolation von Bakterien in einer Flüssigkeit mittels verschiedener Zentrifugationsschritte, um ein mikrobielles Pellet (MP) zu erhalten, welches die quantitative Abtrennung und Erfassung der Bakterien in Schweinekot ermöglicht. Zusätzlich wurde der BEDN Anteil sowie die Gehalte der Aminozucker Galactosamin, Glucosamin, Mannosamin und Muraminsäure im Kot und im MP bestimmt. Die untersuchten Kotproben stammten von Schweinen eines Phosphor (P) Stoffwechselversuch. Zehn männlich-kastrierte Schweine mit einem durchschnittlichen Lebendgewicht von 51•1 ± 8•5 kg wurden einzeln in Stoffwechselkäfigen gehalten. Die Tiere wurden fünf Fütterungsvarianten zugeteilt, die dem Bedarf der Tiere für ein Leistungsniveau von 700 g Tageszunahmen entsprachen, in den Rationen 2 bis 5 jedoch eine P-Gehalt unter dem Tagesbedarf der Tiere aufwiesen und in den Rationen 3 bis 5 mit abgestuften Gehalten von 50, 100 sowie 200 mg/kg einer experimentellen Phytase ergänz waren. Die Absenkung des P Gehaltes im Futter verringerte den Asche- (P=0•024) und Trockenmassegehalt im Kot (P=0•017) sowie die P Konzentration im MP (P=0•000) signifikant. Die mikrobielle Biomasse im Kot wurde durch die Wiegung des MP auf durchschnittlich 467 g/kg TM bestimmt. Der Stickstoffgehalt im Kot betrug im Mittel 46•1 g/kg TM und der in die Bakterienmasse eingebaute Stickstoffanteil 27•1 g/kg TM bzw. 58% vom Gesamtstickstoffgehalt im Kot. Die BEDN Fraktion wurde auf 73% am Kotstickstoff bestimmt. Der P-Gehalt im Kot sowie der N Gehalt im MP mit durchschnittlichen 10•4 und 57•9 g/kg TM lagen im Bereich von Literaturangaben. Die P Gehalte im MP schwankten in Abhängigkeit von der Zugabe von Phytase signifikant (P=0•000) von 1•8 bis 4•8 g/kg TM. Die Aminozucker wiesen keine signifikanten unterschiede zwischen Fütterungsvarianten auf und lagen im Bereich von Werten von Rinderkot. Ergebnisse weisen darauf hin, dass die angewandte Methode zur direkten Quantifizierung der mikrobiellen Biomasse geeignet ist.

Contact Sensing: A Sequential Decision Approach to Sensing Manipulation Contact

This paper describes a new statistical, model-based approach to building a contact state observer. The observer uses measurements of the contact force and position, and prior information about the task encoded in a graph, to determine the current location of the robot in the task configuration space. Each node represents what the measurements will look like in a small region of configuration space by storing a predictive, statistical, measurement model. This approach assumes that the measurements are statistically block independent conditioned on knowledge of the model, which is a fairly good model of the actual process. Arcs in the graph represent possible transitions between models. Beam Viterbi search is used to match measurement history against possible paths through the model graph in order to estimate the most likely path for the robot. The resulting approach provides a new decision process that can be use as an observer for event driven manipulation programming. The decision procedure is significantly more robust than simple threshold decisions because the measurement history is used to make decisions. The approach can be used to enhance the capabilities of autonomous assembly machines and in quality control applications.

Scientific production on the Mantel-Haenszel procedure as a way of detecting DIF

Resumen tomado de la publicaci??n

Unusual voltage sag event detection in power systems

Three multivariate statistical tools (principal component analysis, factor analysis, analysis discriminant) have been tested to characterize and model the sags registered in distribution substations. Those models use several features to represent the magnitude, duration and unbalanced grade of sags. They have been obtained from voltage and current waveforms. The techniques are tested and compared using 69 registers of sags. The advantages and drawbacks of each technique are listed

Foreign perception of sovereign risk : an event study of the colombian armed conflict

Este paper estudia la relación entre algunos de los eventos más importantes del conflicto colombiano con la percepción extranjera de riesgo soberano, medido por los Credit Default Swaps (CDS) de los bonos del Gobierno Colombiano. Usando dos metodologías relativamente recientes, yo estimo el efecto causal de los eventos de conflicto ampliamente cubierto por los medios internacionales. En primer lugar construyo un grupo de control sintético que funciona como contra factual de la serie real de los CDS colombianos pero en ausencia de eventos de conflicto. Segundo, estimo el efecto acumulado del evento bajo la metodología de retornos anormales acumulados. Los resultados sugieren que los efectos de los eventos de conflicto sobre la percepción extranjera de riesgo soberano dependen de las especificaciones de cada evento.

Eficacia de la n-acetilcisteína en nefropatía inducida por contraste en pacientes con alteración renal previa: meta-análisis. (METACIAKI)

INTRODUCCIÓN: Se define lesión renal aguda inducida por contraste (CIAKI), al deterioro de la función renal en las 48 horas posteriores a la administración de radiofármacos. Para prevenir este evento se han estudiado diversas intervenciones clínicas, como la administración de N-Acetilcisteina (NAC), previa al procedimiento diagnóstico. Meta-análisis anteriores comparan diferentes intervenciones clínicas para prevenir CIAKI sin resultados concluyentes. El presente meta-análisis analiza la evidencia de la eficacia la administración de NAC previa al procedimiento diagnóstico para prevenir CIAKI en pacientes con nefropatía previa. METODOLOGÍA: Se analizaron por 3 revisores independientes estudios ECCA, en población con nefropatía, en inglés, español, portugués, italiano, alemán y francés tanto publicados como de literatura gris, en donde se comparara NAC versus hidratación o placebo. RESULTADOS: Los estudios encontrados fueron publicados entre el año 2000 y 2010. Se analizaron 37 reportes con 6.022 pacientes. La correlación intraclase para tres observadores fue kappa r=0.97 [IC95% 0.93-0.99]). Los pacientes con nefropatía a quienes se les administró NAC previo al procedimiento tuvieron un 34% menos de probabilidad de hacer falla renal aguda, con OR ajustado por sesgo de publicación de 0.66 [IC95% 0.50-0.88] con un p de 0.002. Al realizar análisis de sensibilidad por la escala de Jadad, se encuentra que los resultados en los estudios con baja calidad no son significativos (p=0.202). CONCLUSION: Los resultados soportan la asociación entre el tratamiento preventivo con N-Acetilcisteina y una menor frecuencia de lesión renal aguda inducida por medio de contraste en pacientes nefrópatas.

Event Driven Programming in Java

Event driven programming is a way of writing a program that works by responding to things happening (rather than executing a preplanned series of tasks). It is most often used to manage more advanced user interactions, such as GUI programs. In this session we look at how event driven programming works in Java GUIs, as both an introduction to events (using MouseListeners), and also to the way that GUI programs are constructed.

Faculty Good Practice - Event

Slides and link to Panopto recording about 'good practice' within from across the Faculty Adam Procter - Winchester School of Art. Liz Williams - Southampton Law School. Jean Leah - School of Management.

Factores asociados a la aparición de mediastinitis en revascularizacion miocárdica

Objetivos: La mediastinitis se presenta hasta en el 4% de los pacientes sometidos a revascularización miocárdica, con un mortalidad hospitalaria reportada del 14 al 47%, generando aumento en los costos de atención, deterioro de la calidad de vida y la sobrevida a largo plazo del enfermo; su etiología es multifactorial. El objetivo de este estudio fue determinar cuáles antecedentes clínicos del paciente y factores relacionados con el procedimiento quirúrgico se asocian con la aparición mediastinitis. Métodos: Diseño de casos y controles anidado en una cohorte histórica de pacientes sometidos a revascularización miocárdica en el periodo de enero de 2005 a julio de 2011. Los pacientes con mediastinitis se compararon con un grupo control sin mediastinitis tomados del mismo grupo de riesgo en una relación 1:4, y pareados por fecha de cirugía. El diagnóstico de mediastinitis se hizo con criterios clínicos, de laboratorio y hallazgos quirúrgicos. Resultados: Se identificaron 30 casos en ese periodo. Los factores asociados a la aparición del evento fueron: Diabetes Mellitus OR 2,3 (1.1- 4,9), uso de circulación extracorpórea OR 2,4 (1,1 -5.5), tiempo de perfusión OR 1,1 (1,1 – 1.3) y pacientes mayores de 70 años OR 1.1 (1,2-1-4). Conclusiones: La mediastinitis sigue siendo una complicación de baja prevalencia con consecuencias devastadoras. El impacto clínico y económico de esta complicación debe obligar a los grupos quirúrgicos a crear estrategias de prevención con base en el conocimiento de los factores de riesgo de su población.

The mutual agreement procedure and arbitration of double taxation disputes

It is in the interest of most states to eliminate double taxation (i.e. the payment of the same tax in two jurisdictions) of transnational commercial enterprises. Because such disputes involve, on the one hand, the state imposition of taxes, a right universally asserted by all states, and private entities on the other, taxation disputes between such parties are not, on their face, easily susceptible to arbitration. This article analyzes two dispute settlement procedures-the OECD First Model Tax Convention and a similar EU Convention-with the exclusive focus on disputes relating to the imposition of double taxation. It will look at the ways in which state roles may vary under these procedures from assisting in the negotiation process to taking a part similar to, but with important differences from, diplomatic protection on behalf of an affected enterprise. The article will examine the situations under which the settlement procedure is required and/or available, how the procedures are triggered, the obligations and parts played by the parties, the means by which the disputes are resolved (from negotiations to tribunals) and the limitations of the procedures. Are they “taxpayer friendly”? As a result the reader may draw comparisons between the two procedures. Finally, the article will look at the proposed OECD Arbitration Clause which is intended to be incorporated into Article 25 of the OECD Model Tax Convention as well as how these mechanisms relate and/or conflict with bilateral tax treaties and the GATS.

Normalization procedure for the Baptista Depression Scale - Adult Version (EBADEP-A): transferring of norms

Regarding the standardization of psychological assessment instruments, that is, the construction of referential interpretations of a test, we can find different procedures performed both by Classical Test Theory (CTT) and the Theory of Item Response (IRT). Especially in this case (IRT), we can admit one test as a default, so to use its standardization and transfer the cut-off point to another instrument. Based on this information, the present study aimed to provide a cutoff score for the Baptista Depression Scale - Adult Version (EBADEP-A) through procedures of norms-transfer based on the Center for Epidemiologic Studies – Depression Scale (CES-D). The EBADEP-A presented good distribution and ability to discriminate depressive symptoms, and the sample, consisting of Brazilian College students, received a cutoff score of 32 points. It is emphasized that this is an exploratory and preliminary study, and it is suggested further analyzes to be performed with clinical samples for which results can be corroborated or confronted.

Búsqueda de selección en el polimorfismo 677C>T (c.665C>T) del gen de la metilentetrahidrofolato reductasa (MTHFR) en una población Colombiana

Se realizó un estudio genético – poblacional en dos grupos etarios de población colombiana con la finalidad de evaluar las diferencias genéticas relacionadas con el polimorfismo MTHFR 677CT en busca de eventos genéticos que soporten la persistencia de este polimorfismo en la especie humana debido que este ha sido asociado con múltiples enfermedades. De esta manera se genotipificaron los individuos, se analizaron los genotipos, frecuencias alélicas y se realizaron diferentes pruebas genéticas-poblacionales. Contrario a lo observado en poblaciones Colombianas revisadas se identificó la ausencia del Equilibrio Hardy-Weinberg en el grupo de los niños y estructuras poblacionales entre los adultos lo que sugiere diferentes historias demográficas y culturales entre estos dos grupos poblacionales al tiempo, lo que soporta la hipótesis de un evento de selección sobre el polimorfismo en nuestra población. De igual manera nuestros datos fueron analizados junto con estudios previos a nivel nacional y mundial lo cual sustenta que el posible evento selectivo es debido a que el aporte de ácido fólico se ha incrementado durante las últimas dos décadas como consecuencia de las campañas de fortificación de las harinas y suplementación a las embarazadas con ácido fólico, por lo tanto aquí se propone un modelo de selección que se ajusta a los datos encontrados en este trabajo se establece una relación entre los patrones nutricionales de la especie humana a través de la historia que explica las diferencias en frecuencias de este polimorfismo a nivel espacial y temporal.  

Factores asociados a insuficiencia renal postoperatoria en cirugía de revascularización miocárdica

Introducción: La insuficiencia renal postoperatoria (IRP) es una complicación de alta prevalencia y de importancia en la cirugía cardiaca. Se estima que más del 30% de los pacientes sometidos a cirugía cardiaca desarrollan IRP clínicamente importante. Una estrategia razonable a realizar es la identificación de factores de riesgo modificables para intervenir sobre ellos. Objetivos: Determinar cuáles de los antecedentes clínicos del paciente y factores relacionados con el procedimiento quirúrgico se asocian a la aparición de IRP en pacientes sometidos a cirugía de –revascularización miocárdica (RVM). Métodos: Estudio de casos y controles. Casos fueron pacientes sometidos a cirugía de revascularización miocárdica electiva que presentaron insuficiencia renal postoperatoria durante el postoperatorio inmediato hasta el egreso. Controles pacientes sometidos a cirugía de revascularización miocárdica electiva que no presentaron insuficiencia renal postoperatoria durante el postoperatorio inmediato hasta el egreso. Estudio realizado entre enero de 2005 y diciembre de 2013. Se realizó un modelo de regresión logística para determinar los factores asociados a insuficiencia renal posoperatoria. Las asociaciones se expresan en OR con sus respectivos intervalos de confianza. Resultados: Edad avanzada OR 1.03 IC 95% (1.01-1.04), presencia preoperatoria de diabetes mellitus OR 1.8 IC 95% (1.9-3.4), enfermedad pulmonar OR 1.3 IC 95% (1.1-1.6), dislipidemia OR 3.5 IC 95% (1.7-7.1), insuficiencia cardiaca OR 2.7 IC 95% (1.1-6.7) y mayor tiempo de perfusión OR 1.02 IC 95% (1.01-1.03) se asociaron a mayor riesgo de IRP. Mayor hematocrito OR 0.86 IC95% (0.82-0.91) y mayor fracción de eyección OR 0.94 IC 95% (0.92-0.96) se asociaron disminuyendo el riesgo de IRP. Conclusiones: En pacientes sometidos a RVM los factores asociados a la presentación de IRP fueron comorbilidades que se asocian a daño renal progresivo dentro y fuera del contexto de la cirugía. Esto implica que las estrategias para minimizar este evento estarán enfocadas a identificar tempranamente los pacientes y realizar una adecuada nefroprotección.

Children born preterm have high risk for central auditory processing deficits, as indexed by the auditory brain event-related potentials (ERPs). 'Los niños prematuros tienen un alto riesgo de dificultades en el procesamiento auditivo central, evidenciadas mediante los potenciales evocados auditivos'.

Resumen basado en el de la publicación. Resumen en español

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.