Estructura Combinatoria de Politopos asociados a Medidas Difusas

Tesis inédita de la Universidad Complutense de Madrid, Facultad de Ciencias Matemáticas, leída el 23-11-2020This PhD thesis is devoted to the study of geometric and combinatorial aspects of polytopes associated to fuzzy measures. Fuzzy measures are an essential tool, since they generalize the concept of probability. This greater generality allows applications to be developed in various elds, from the Decision Theory to the Game Theory. The set formed by all fuzzy measures on a referential set is a polytope. In the same way, many of the most relevant subfamilies of fuzzy measures are also polytopes. Studying the combinatorial structure of these polytopes arises as a natural problem that allows us to better understand the properties of the associated fuzzy measures. Knowing the combinatorial structure of these polytopes helps us to develop algorithms to generate points uniformly at random inside these polytopes. Generating points uniformly inside a polytope is a complex problem from both a theoretical and a computational point of view. Having algorithms that allow us to sample uniformly in polytopes associated to fuzzy measures allows us to solve many problems, among them the identi cation problem, i.e. estimate the fuzzy measure that underlies an observed data set...La presente tesis doctoral esta dedicada al estudio de distintas propiedades geometricas y combinatorias de politopos de medidas difusas. Las medidas difusas son una herramienta esencial puesto que generalizan el concepto de probabilidad. Esta mayor generalidad permite desarrollar aplicaciones en diversos campos, desde la Teoría de la Decision a laTeoría de Juegos. El conjunto formado por todas las medidas difusas sobre un referencial tiene estructura de politopo. De la misma forma, la mayora de las subfamilias mas relevantes de medidas difusas son tambien politopos. Estudiar la estructura combinatoria de estos politopos surge como un problema natural que nos permite comprender mejor las propiedades delas medidas difusas asociadas. Conocer la estructura combinatoria de estos politopos tambien nos ayuda a desarrollar algoritmos para generar aleatoria y uniformemente puntos dentro de estos politopos. Generar puntos de forma uniforme dentro de un politopo es un problema complejo desde el punto de vista tanto teorico como computacional. Disponer de algoritmos que nos permitan generar uniformemente en politopos asociados a medidas difusas nos permite resolver muchos problemas, entre ellos el problema de identificacion que trata de estimarla medida difusa que subyace a un conjunto de datos observado...Fac. de Ciencias MatemáticasTRUEunpu

Bottom-Up: a New Algorithm to Generate Random Linear Extensions of a Poset

In this paper we present a new method for deriving a random linear extension of a poset. This new strategy combines Probability with Combinatorics and obtains a procedure where each minimal element of a sequence of subposets is selected via a probability distribution. The method consists in obtaining a weight vector on the elements of P, so that an element is selected with a probability proportional to its weight. From some properties on the graph of adjacent linear extensions, it is shown that the probability distribution can be obtained by solving a linear system. The number of equations involved in this system relies on the number of what we have called positioned antichains, that allows a reduced number of equations. Finally, we give some examples of the applicability of the algorithm. This procedure cannot be applied to every poset, but it is exact when it can be used. Moreover, the method is quick and easy to implement. Besides, it allows a simple way to derive the number of linear extensions of a given poset

Convexity analysis in financial instruments

Depto. de Estadística e Investigación OperativaFac. de Ciencias MatemáticasTRUEunpu

Applying Young diagrams to 2-symmetric fuzzy measures with an application to general fuzzy measures

In this paper we apply Young diagrams, a well-known object appearing in Combinatorics and Group Representation Theory, to study some properties of the polytope of 2-symmetric fuzzy measures with respect to a given partition, a subpolytope of the set of fuzzy measures. The main result in the paper allows to build a simple and fast algorithm for generating points on this polytope in a random fashion. Besides, we also study some other properties of this polytope, as for example its volume. In the last section, we give an application of this result to the problem of identification of general fuzzy measures

The autologous chondrocyte implantation in the public health system of Andalusia. Results after 6 years of care circuits

Artículo publicadoObjective: To asses the results of Autologous Chondrocyte Implantation (ACI) whith periosteal patch and To propagate the care circuits existing about in Andalusia. Material and Methods: From its of ficial licence in 2005, the tissue bank and the Virgen de la Victoria Hospital from Málaga, performed the ACI in the Andalusian public health system. 16 patients has been operated between 2006-2013, whith medium follow-up 47,6 months (6 months-6 years), from public hos- pitals throughout Andalucia, managed by hospital admission source and destination. Physiologically younger patients were selected ( 2cm2 symptomatics chondral lesions, in stables and well aligned knees. ACI was used as res- cue procedure after microfracture ́s failure except osteochondritis dissecans. To assess the results the Concinnati score and the Short Form 36 (SF-36) score were used. A descriptive analysis was performed and non-parametric tests were used to establish correlations and compare results. Results: In 15 patients with more than one year of follow-up: 14 men(87.5%) and 2women (14.5%), medium age 28.2 years old (min 17 max 43), the lesion was located into de femoral condyle, mostly in the internal one (81,2%) with medium size 2,7cm2(2-4,2). We founded significant improvement (p<0,001), both daily activities ( 89,3% preop. limitatión - 9% postop), as in the sports (90,2% preop limitatión - 38% postop) and the exploration of the knee (67,7% hpatological findings preop- 13,3%postop). The SF-36 score improved in all categories, over all in mental health (p> 0,01). The patient satisfaction was high or very high in 12 of the 15 patients ( 80%), and low in 3 patients. Conclusions: ACI improve quality of life and knee function in femoral condyle chondral lesions. The case ́s selection and the collaboration with Tissue Bank, allows us to create care circuits for treatment of patients from other provinces in the Public Sanitary Health System in Andalucia. It is necessary to increase the experience with this type of therapy, consolidating multicenter workgroups that provide strength to the conclusions.YesObjetivo: Evaluar los resultados del Implante de Condrocitos Autólogos (ICA) con parche de periostio y difundir los circuitos asistenciales existentes al respecto en Andalucía. Material y método: Desde su autorización oficial en 2005, el Banco de Tejidos y el Hospital Virgen dla Victoria de Málaga, llevan a cabo los ICA del sistema sanitario público andaluz. Se han operado 16 pacientes entre 2006-2013 con seguimiento medio 47,6 meses (6 meses-6 años), de hospitales públicos de toda Andalucía, gestionados por los servicios de admisión de los hospitales origen y destino. Se seleccionaron pacientes fisiológicamente jóvenes (2cm 2, en rodillas estables y sin desalineación. El ICA fue utilizado como procedimiento de rescate de fracaso de microfracturas, salvo en osteocondritis disecante. Para valorar los resultados se utilizaron la escala de Cincinnati y la Short Form 36 (SF-36). Se realizó un análisis descriptivo y test no paramétricos para buscar correlaciones y comparar resultados. Resultados: En los 15 pacientes con más de un año de seguimiento: 14 hombres (87,5%) y 2 mujeres (14,5%), de edad media 28,2 años (min 17 max 43), la lesión asentó en los cóndilos femorales, más en el interno (81,2%) y tamaño 2,7cm 2 (2-4,2). Encontramos mejoría significativa (p<0,001), tanto en actividades de la vida diaria (89,3% limitación preoperatoria -preop- y 9% postoperatoria -postop-), como en las deportivas (90,2% preop - 38% postop) y en la exploración de la rodilla (67,7% hallazgos patológicos preop y 13,3% postop). La escala de calidad de vida SF-36 mejoró en todas las dimensiones sobre todo la salud mental (p> 0,01). El grado de satisfacción de los pacientes fue alto o muy alto en 12 de los 15 casos (80%) y bajo en los 3 restantes. Conclusiones: El ICA mejora la calidad de vida y la funcionalidad de la rodilla con lesiones condrales en cóndilo femoral. La selección de casos y la colaboración con el Banco de Tejidos, permite crear circuitos asistenciales para tratar pacientes de otras provincias del Sistema Sanitario Público de Andalucía. Es necesario ampliar la experiencia en este tipo de terapia, consolidando grupos de trabajo multicén- tricos que aporten solidez a las conclusiones