Jensen-Steffensen type inequality for integrals with respect to bi-capacities

Bipolarni pan integral, kao novi tip integrala baziranog na fazi bi- merama je prikazan u okviru disertacije. Pored toga, u okviru ove disertacije prikazana je Jensenova nejednakost za: diskretni bipolarni pseudo-integral, novi bipolarni Šokeov g-integral, bipolarni Šilkretov i bipolarni Sugenov integral.The bipolar pan-integral as new type of integral based on bi-capacities is introduced in the thesis. The main purpose of the thesis is to establish conditions under which the Jensen type inequality is valid for: the discrete bipolar pseudo-integral, the new bipolar Choquet g-integral, the bipolar Shilkret and the bipolar Sugeno integral

Jensen-Steffensen type inequality for integrals with respect to bi-capacities

Bipolarni pan integral, kao novi tip integrala baziranog na fazi bi- merama je prikazan u okviru disertacije. Pored toga, u okviru ove disertacije prikazana je Jensenova nejednakost za: diskretni bipolarni pseudo-integral, novi bipolarni Šokeov g-integral, bipolarni Šilkretov i bipolarni Sugenov integral.The bipolar pan-integral as new type of integral based on bi-capacities is introduced in the thesis. The main purpose of the thesis is to establish conditions under which the Jensen type inequality is valid for: the discrete bipolar pseudo-integral, the new bipolar Choquet g-integral, the bipolar Shilkret and the bipolar Sugeno integral

Some well known inequalities for (h1, h2)-convex stochastic process via interval set inclusion relation

This note introduces the concept of (h1, h2)-convex stochastic processes using intervalvalued functions. First we develop Hermite-Hadmard (H.H) type inequalities, then we check the results for the product of two convex stochastic process mappings, and finally we develop Ostrowski and Jensen type inequalities for (h1, h2)-convex stochastic process. Also, we have shown that this is a more generalized and larger class of convex stochastic processes with some remark. Furthermore, we validate our main findings by providing some non-trivial examples.http://www.aimspress.com/journal/MathMathematics and Applied Mathematic

Probabilistic models for human behavior learning

The problem of human behavior learning is a popular interdisciplinary research topic that has been explored from multiple perspectives, with a principal branch of study in the context of computer vision systems and activity recognition. However, the statistical methods used in these frameworks typically assume short time scales, usually of minutes or even seconds. The emergence of mobile electronic devices, such as smartphones and wearables, has changed this paradigm as long as we are now able to massively collect digital records from users. This collection of smartphone-generated data, whose attributes are obtained in an unobtrusive manner from the devices via multiple sensors and apps, shape the behavioral footprint that is unique for everyone of us. At an individual level, the data projection also di ers from person to person, as not all sensors are equal, neither the apps installed, or the devices used in the real life. This point actually reflects that learning the human behavior from the digital signature of users is an arduous task, that requires to fuse irregular data. For instance, collections of samples that are corrupted, heterogeneous, outliers or have shortterm correlations. The statistical modelling of this sort of objects is one of the principal contributions of this thesis, that we study from the perspective of Gaussian processes (gp). In the particular case of humans, as well as many other life species in our world, we are inherently conditioned to the diurnal and nocturnal cycles that everyday shape our behavior, and hence, our data. We can study these cycles in our behavioral representation to see that there exists a perpetual circadian rhytm in everyone of us. This tempo is the 24h periodic component that shapes the baseline temporal structure of our behavior, not the particular patterns that change for every person. Looking to the trajectories and variabilities that our behavior may take in the data, we can appreciate that there is not a single repetitive behavior. Instead, there are typically several patterns or routines, sampled from our own dictionary, that we choose for every special situation. At the same time, these routines are arbitrary combinations of di erents timescales, correlations, levels of mobility, social interaction, sleep quality or will for working during the same hours on weekdays. Together, the properties of human behavior already indicate to us how we shall proceed to model its structure, not as unique functions, but as a dictionary of latent behavioral profiles. To discover them, we have considered latent variable models. The main application of the statistical methods developed for human behavior learning appears as we look to medicine. Having a personalized model that is accurately fitted to the behavioral patterns of some patient of interest, sudden changes in them could be early indicators of future relapses. From a technical point of view, the traditional question use to be if newer observations conform or not to the expected behavior indicated by the already fitted model. The problem can be analyzed from two perspectives that are interrelated, one more oriented to the characterization of that single object as outlier, typically named as anomaly detection, and another focused in refreshing the learning model if no longer fits to the new sequential data. This last problem, widely known as change-point detection (cpd) is another pillar of this thesis. These methods are oriented to mental health applications, and particularly to the passive detection of crisis events. The final goal is to provide an early detection methodology based on probabilistic modeling for early intervention, e.g. prevent suicide attempts, on psychiatric outpatients with severe a ective disorders of higher prevalence, such as depression or bipolar diseases.El problema de aprendizaje del comportamiento humano es un tema de investigación interdisciplinar que ha sido explorado desde múltiples perspectivas, con una línea de estudio principal en torno a los sistemas de visión por ordenador y el reconocimiento de actividades. Sin embargo, los métodos estadísticos usados en estos casos suelen asumir escalas de tiempo cortas, generalmente de minutos o incluso segundos. La aparición de tecnologías móviles, tales como teléfonos o relojes inteligentes, ha cambiado este paradigma, dado que ahora es posible recolectar ingentes colecciones de datos a partir de los usuarios. Este conjunto de datos generados a partir de nuestro teléfono, cuyos atributos se obtienen de manera no invasiva desde múltiples sensores y apps, conforman la huella de comportamiento que es única para cada uno de nosotros. A nivel individual, la proyección sobre los datos difiere de persona a persona, dado que no todos los sensores son iguales, ni las apps instaladas así como los dispositivos utilizados en la vida real. Esto precisamente refleja que el aprendizaje del comportamiento humano a partir de la huella digital de los usuarios es una ardua tarea, que requiere principalmente fusionar datos irregulares. Por ejemplo, colecciones de muestras corruptas, heterogéneas, con outliers o poseedoras de correlaciones cortas. El modelado estadístico de este tipo de objetos es una de las contribuciones principales de esta tesis, que estudiamos desde la perspectiva de los procesos Gaussianos (gp). En el caso particular de los humanos, así como para muchas otras especies en nuestro planeta, estamos inherentemente condicionados a los ciclos diurnos y nocturnos que cada día dan forma a nuestro comportamiento, y por tanto, a nuestros datos. Podemos estudiar estos ciclos en la representación del comportamiento que obtenemos y ver que realmente existe un ritmo circadiano perpetuo en cada uno de nosotros. Este tempo es en realidad la componente periódica de 24 horas que construye la base sobre la que se asienta nuestro comportamiento, no únicamente los patrones que cambian para cada persona. Mirando a las trayectorias y variabilidades que nuestro comportamiento puede plasmar en los datos, podemos apreciar que no existe un comportamiento único y repetitivo. En su lugar, hay varios patrones o rutinas, obtenidas de nuestro propio diccionario, que elegimos para cada situación especial. Al mismo tiempo, estas rutinas son combinaciones arbitrarias de diferentes escalas de tiempo, correlaciones, niveles de movilidad, interacción social, calidad del sueño o iniciativa para trabajar durante las mismas horas cada día laborable. Juntas, estas propiedades del comportamiento humano nos indican como debemos proceder a modelar su estructura, no como funciones únicas, sino como un diccionario de perfiles ocultos de comportamiento, Para descubrirlos, hemos considerado modelos de variables latentes. La aplicación principal de los modelos estadísticos desarrollados para el aprendizaje de comportamiento humano aparece en cuanto miramos a la medicina. Teniendo un modelo personalizado que está ajustado de una manera precisa a los patrones de comportamiento de un paciente, los cambios espontáneos en ellos pueden ser indicadores de futuras recaídas. Desde un punto de vista técnico, la pregunta clásica suele ser si nuevas observaciones encajan o no con lo indicado por el modelo. Este problema se puede enfocar desde dos perspectivas que están interrelacionadas, una más orientada a la caracterización de aquellos objetos como outliers, que usualmente se conoce como detección de anomalías, y otro enfocado en refrescar el modelo de aprendizaje si este deja de ajustarse debidamente a los nuevos datos secuenciales. Este último problema, ampliamente conocido como detección de puntos de cambio (cpd) es otro de los pilares de esta tesis. Estos métodos se han orientado a aplicaciones de salud mental, y particularmente, a la detección pasiva de eventos críticos. El objetivo final es proveer de una metodología de detección temprana basada en el modelado probabilístico para intervenciones rápidas. Por ejemplo, de cara a prever intentos de suicidio en pacientes fuera de hospitales con trastornos afectivos severos de gran prevalencia, como depresión o síndrome bipolar.Programa de Doctorado en Multimedia y Comunicaciones por la Universidad Carlos III de Madrid y la Universidad Rey Juan CarlosPresidente: Pablo Martínez Olmos.- Secretario: Daniel Hernández Lobato.- Vocal: Javier González Hernánde

Measurements of Solar Vector Magnetic Fields

Various aspects of the measurement of solar magnetic fields are presented. The four major subdivisions of the study are: (1) theoretical understanding of solar vector magnetic fields; (3) techniques for interpretation of observational data; and (4) techniques for data display

Spiraling Out Of Disorder: Investigating The Behavior Of Nematic Liquid Crystalline Systems And Soft Vortex Matter Under Geometrical Confinement

Self-assembly of ordered phases can be exploited to design new functional materials. Such structures can be heavily influenced by the confining geometry, which may be incommensurate with the ordering of the phase. In this thesis, I investigate two soft matter systems in which the interplay between the preferred ordering and confining geometry leads to emergent behaviors. I demonstrate that loxodromes, spirals that form a fixed angle relative to the principal directions on a surface of revolution, are key to understanding the behavior of both systems. In the first project, I theoretically investigate the twisting behavior of a highly ordered spindle-shaped polymer system that has nematic orientational ordering. Using geometric arguments, I develop a model that describes the twisting structure as loxodromes with fixed length. I show that the model captures the observed relationship between the spindle aspect ratio and surface twist angle as well as the observed transition from achiral to chiral. Next, I investigate the energetics of twisted spindles and show that loxodromes minimize the free energy on a spindle surface if a length constraint is included. I then show that in the bulk the twisting solution is well approximated by loxodromes. Extending ideas from the geometric model to the bulk, I show that including the length constraint makes twisted structures favorable over a larger parameter range than the bulk Frank free energy alone. In the second project, I use molecular dynamics simulations to determine the lattice ground states of vortices in a type-II superconductor confined to the surface of a conical frustum. I demonstrate that the confining geometry is incommensurate with an ideal lattice, resulting in structural lattice transitions. I show that the topological defect patterns at the transitions depend on properties of the two adjacent lattice structures. Using properties of the ground states, I demonstrate that inducing a density gradient in the lattice allows the creation of defect-free structures. I show that the idealized defect-free state is a conformal crystal, the construction of which involves loxodromes. This construction therefore provides a natural example of a configuration in which loxodromes appear

Fuzzy Sets, Fuzzy Logic and Their Applications 2020

The present book contains the 24 total articles accepted and published in the Special Issue “Fuzzy Sets, Fuzzy Logic and Their Applications, 2020” of the MDPI Mathematics journal, which covers a wide range of topics connected to the theory and applications of fuzzy sets and systems of fuzzy logic and their extensions/generalizations. These topics include, among others, elements from fuzzy graphs; fuzzy numbers; fuzzy equations; fuzzy linear spaces; intuitionistic fuzzy sets; soft sets; type-2 fuzzy sets, bipolar fuzzy sets, plithogenic sets, fuzzy decision making, fuzzy governance, fuzzy models in mathematics of finance, a philosophical treatise on the connection of the scientific reasoning with fuzzy logic, etc. It is hoped that the book will be interesting and useful for those working in the area of fuzzy sets, fuzzy systems and fuzzy logic, as well as for those with the proper mathematical background and willing to become familiar with recent advances in fuzzy mathematics, which has become prevalent in almost all sectors of the human life and activity

Physics of Ionic Conduction in Narrow Biological and Artificial Channels

The book reprints a set of important scientific papers applying physics and mathematics to address the problem of selective ionic conduction in narrow water-filled channels and pores. It is a long-standing problem, and an extremely important one. Life in all its forms depends on ion channels and, furthermore, the technological applications of artificial ion channels are already widespread and growing rapidly. They include desalination, DNA sequencing, energy harvesting, molecular sensors, fuel cells, batteries, personalised medicine, and drug design. Further applications are to be anticipated.The book will be helpful to researchers and technologists already working in the area, or planning to enter it. It gives detailed descriptions of a diversity of modern approaches, and shows how they can be particularly effective and mutually reinforcing when used together. It not only provides a snapshot of current cutting-edge scientific activity in the area, but also offers indications of how the subject is likely to evolve in the future

Fuzzy Sets, Fuzzy Logic and Their Applications

The present book contains 20 articles collected from amongst the 53 total submitted manuscripts for the Special Issue “Fuzzy Sets, Fuzzy Loigic and Their Applications” of the MDPI journal Mathematics. The articles, which appear in the book in the series in which they were accepted, published in Volumes 7 (2019) and 8 (2020) of the journal, cover a wide range of topics connected to the theory and applications of fuzzy systems and their extensions and generalizations. This range includes, among others, management of the uncertainty in a fuzzy environment; fuzzy assessment methods of human-machine performance; fuzzy graphs; fuzzy topological and convergence spaces; bipolar fuzzy relations; type-2 fuzzy; and intuitionistic, interval-valued, complex, picture, and Pythagorean fuzzy sets, soft sets and algebras, etc. The applications presented are oriented to finance, fuzzy analytic hierarchy, green supply chain industries, smart health practice, and hotel selection. This wide range of topics makes the book interesting for all those working in the wider area of Fuzzy sets and systems and of fuzzy logic and for those who have the proper mathematical background who wish to become familiar with recent advances in fuzzy mathematics, which has entered to almost all sectors of human life and activity