Information and Questionnaires in Statistical Inference

1 online resource (PDF, 118 pages

Useful information and questionnaires

A questionnaire is an inquiry process, using a probabilistic latticoïd. We suppose that a positive valuation, called an utility, characterizes every terminal vertex. The useful information and the useful routing length of a questionnaire have been introduced in a particular case. We propose, in this article, to define and to study these quantities in the general case, and to exhibit some properties relative to a product of questionnaires, corresponding to dependent or independent processes

Disentangling complexity from randomness and chaos

During the last ten years complexity research has received a large amount of attention by both the scientific community and the general public. One of the greatest draws of complexity as a field of research is the possibility of recognizing it in virtually every branch of science and he social sciences. However, despite the labelling of an increasingly large number of models and natural systems as ‘complex', the definition of the term has remained vague. In particular, attempts at such a definition have failed to fully emancipate the notion of a complex system from those of a stochastically random and deterministically chaotic one. In this paper we will try to disentangle the definition of complexity from randomness and chaos. We will also examine the power of some existing entropy and complexity measures to distinguish a complex system from the other two. Our analysis indicates that the affinity of complexity to chaos has been overstated in the existing literature and that a careful distinction between phenomenological (perceived) and dynamical complexity will be needed to achieve a successful definition

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

Applications of Visibility Graphs for the representation of Time Series

[EN] In this thesis, we consider two problems: we first explore the application of visibility graphs for describing the orbits of a discrete dynamical system that is governed by a fractional version of the logistic equation. We also study how to use this type of graphs to study response time series from the perspective of psychology. The preliminaries and introduction of these visibility graphs are presented in Chapter 1, where we revisit some basic facts from network science related to them. In the first part of this thesis, we analyze a phenomenon of mathematical nature. Wu and Baleanu introduced a fractional discrete dynamical system inspired by the fractional difference logistic equation. In order to study the trajectories of this model under this perspective of network science, in Chapter 2, we first review the most used fractional derivatives (Riemann-Liouville, Caputo, and Gründwald-Letnikov). Later, we show how to consider discrete fractional derivatives. Within our work, we present an alternative way of deducing the governing equation with respect to the one shown by Wu and Baleanu. We revisit the Wu-Baleanu equation in Chapter 3, focused on the visibility graphs of trajectories generated under different values of the scaling factor and the fractional exponent. We also study the existing connections between these parameters and the fitting with the degree distribution of the corresponding visibility graphs. When chaos is present, we link them with the exponent obtained when fitting the degree distribution to a power-law of the form x^(¿¿). With this approach, we provide an integrated vision of the dynamics of a family of fractional discrete dynamical systems that cannot be obtained from single Feigenbaum diagrams computed for each scaling factor and fractional exponent. We also connect the power-law exponent of the degree distribution fitting with the Shannon entropy of the visibility graphs degree distribution. In the second part, we analyze the response times of students to a binary decision task from the perspective of network science. We analyze the properties of the natural visibility graphs associated with their reaction time series. We observe that the degree distribution of these graphs usually fits a power-law distribution p(x) = x^(¿¿). We study the range in which parameter ¿ occurs and the changes of this exponent with respect to the age and gender of the students. Besides, we also study the links between the parameter ¿ and the ex-Gaussian distribution parameters that best fits each subject's response times. Finally, we outline some conclusions and perspectives of future research in both parts in Chapter 6.[ES] En esta tesis, hemos considerado dos problemas: primero exploramos la aplicación de los grafos de visibilidad para describir las órbitas de un sistema dinámico discreto que está gobernado por una versión fraccionaria de la ecuación logística. Además, también estudiamos cómo usar este tipo de grafos para estudiar series temporales de tiempos de respuesta desde una perspectiva psicológica. Los preliminares, así como una introducción a estos grafos de visibilidad, se presentan en el Capítulo 1, donde revisitamos algunos hechos básicos de la ciencia de redes relacionados con dichos grafos. En la primera parte de esta tesis, analizamos un fenómeno de naturaleza matemática. Wu y Baleanu introdujeron un sistema dinámico discreto fraccionario inspirado en la ecuación logística con derivadas fraccionarias. Con el propósito de estudiar las trayectorias de este modelo desde la perspectiva de la ciencia de redes, en el Capítulo 2, primero revisamos las derivadas fraccionarias más utilizadas (Riemann-Liouville, Caputo y Gründwald-Letnikov). Posteriormente, mostramos cómo considerar derivadas fraccionarias discretas. En nuestro trabajo, presentamos una forma alternativa de deducir la ecuación gobernante con respecto a la presentada por Wu y Baleanu. Revisitamos la ecuación de Wu-Baleanu en el Capítulo 3, centrado en los grafos de visibilidad de trayectorias generadas a partir de distintos valores del factor de escala y del exponente fraccionario. También estudiamos la existencia de conexiones entre estos parámetros y el ajuste de la distribución de los grados de los correspondientes grafos de visibilidad. Cuando el caos está presente, los enlazamos con el exponente obtenido al ajustar la distribución de los grados a una ley de potencias de la forma x^(¿¿). A través de este enfoque, proporcionamos una visión integrada de la dinámica de una familia de sistemas dinámicos discretos fraccionarios que no se pueden obtener a partir de diagramas de Feigenbaum individuales calculados para cada factor de escala y exponente fraccionario. Además, relacionamos el exponente de la ley de potencias del ajuste de la distribución de grados con la entropía de Shannon de la distribución de grados de los grafos de visibilidad. En la segunda parte, analizamos el tiempo de respuesta de un grupo de estudiantes que realizaron una tarea de decisión binaria desde la perspectiva de la ciencia de redes. Estudiamos las propiedades de los grafos de visibilidad natural asociados con sus correspondientes series de tiempos de respuesta. Observamos que la distribución de los grados de estos grafos normalmente sigue una distribución ley de potencias p(x) = x^(¿¿). Analizamos el rango en el cual el parámetro ¿ se mueve y los cambios de este exponente con respecto a la edad y el sexo de los estudiantes. Por otro lado, también estudiamos la relación entre el parámetro ¿ y los parámetros de la distribución ex-Gaussiana que mejor se ajusta al tiempo de respuesta de cada sujeto. Finalmente, destacamos algunas conclusiones y perspectivas de investigación futura en ambas líneas de trabajo en el Capítulo 6.[CAT] En aquesta tesi, hem considerat dos problemes: primer explorem l'aplicació dels grafs de visibilitat per a descriure les òrbites d'un sistema dinàmic discret que està governat per una versió fraccionària de l'equació logística. A més a més, també estudiem com emprar aquest tipus de grafs per a analitzar sèries temporals de temps de resposta des d'una perspectiva psicològica. Els preliminars, així com una introducció a aquests grafs de visibilitat, es presenten al Capítol 1, on revisitem alguns fets bàsics de la ciència de xarxes relacionats amb ells. En la primera part d'aquesta tesi, analitzem un fenomen de naturalesa matemàtica. Wu i Baleanu van introduir un sistema dinàmic discret fraccionari inspirat en l'equació logística amb derivades fraccionàries. Amb el fi d'estudiar les trajectòries d'aquest model des d'una perspectiva de la ciència de xarxes, en el Capítol 2, primer revisem les derivades fraccionàries més utilitzades (Riemann-Liouville, Caputo i Gründwald-Letnikov). Posteriorment, mostrem com considerar derivades fraccionàries discretes. Al nostre treball, presentem una forma alternativa de deduir l'equació governant respecte a la presentada per Wu i Baleanu. Revisitem l'equació de Wu-Baleanu al Capítol 3, focalitzat en els grafs de visibilitat de trajectòries generades a partir de valors diferents del factor d'escala i de l'exponent fraccionari. També estudiem l'existència de connexions entre aquests paràmetres i l'ajust de la distribució dels graus dels corresponents grafs de visibilitat. Quan el caos hi és, els enllacem amb l'exponent que hem obtés en ajustar la distribució dels graus a una llei de potències de la forma x^(¿¿). Des d'aquesta perspectiva, proporcionem una visió integrada de la dinàmica d'una família de sistemes dinàmics discrets fraccionaris que no es poden obtenir a partir de diagrames de Feigenbaum individuals calculats per a cada factor d'escala i exponent fraccionari. A més a més, relacionem l'exponent de la llei de potències de l'ajust de la distribució de graus amb l'entropia de Shannon de la distribució de graus dels grafs de visibilitat. A la segona part, analitzem el temps de resposta d'un grup d'estudiants que realitzaren una tasca de decisió binària des del punt de vista de la ciència de xarxes. Estudiem les propietats dels grafs de visibilitat natural associats amb les seues corresponents sèries temporals de temps de resposta. Observem que la distribució dels graus d'aquests grafs normalment segueix una distribució llei de potències p(x) = x^(¿¿). Analitzem el rang en què el paràmetre ¿ es mou i els canvis d'aquest exponent respecte a l'edat i el sexe dels estudiants. D'altra banda, també estudiem la relació entre el paràmetre ¿ i els paràmetres de la distribució ex-Gaussiana que millor fita el temps de resposta de cada subjecte. Finalment, destaquem algunes conclusions i perspectives d'investigació futura en ambdues línies de treball en el Capítol 6.Mira Iglesias, A. (2021). Applications of Visibility Graphs for the representation of Time Series [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/176012TESI

LSD-induced increase of Ising temperature and algorithmic complexity of brain dynamics

A topic of growing interest in computational neuroscience is the discovery of fundamental principles underlying global dynamics and the self-organization of the brain. In particular, the notion that the brain operates near criticality has gained considerable support, and recent work has shown that the dynamics of different brain states may be modeled by pairwise maximum entropy Ising models at various distances from a phase transition, i.e., from criticality. Here we aim to characterize two brain states (psychedelics-induced and placebo) as captured by functional magnetic resonance imaging (fMRI), with features derived from the Ising spin model formalism (system temperature, critical point, susceptibility) and from algorithmic complexity. We hypothesized, along the lines of the entropic brain hypothesis, that psychedelics drive brain dynamics into a more disordered state at a higher Ising temperature and increased complexity. We analyze resting state blood-oxygen-level-dependent (BOLD) fMRI data collected in an earlier study from fifteen subjects in a control condition (placebo) and during ingestion of lysergic acid diethylamide (LSD). Working with the automated anatomical labeling (AAL) brain parcellation, we first create “archetype” Ising models representative of the entire dataset (global) and of the data in each condition. Remarkably, we find that such archetypes exhibit a strong correlation with an average structural connectome template obtained from dMRI (r = 0.6). We compare the archetypes from the two conditions and find that the Ising connectivity in the LSD condition is lower than in the placebo one, especially in homotopic links (interhemispheric connectivity), reflecting a significant decrease of homotopic functional connectivity in the LSD condition. The global archetype is then personalized for each individual and condition by adjusting the system temperature. The resulting temperatures are all near but above the critical point of the model in the paramagnetic (disordered) phase. The individualized Ising temperatures are higher in the LSD condition than in the placebo condition (p = 9 × 10−5). Next, we estimate the Lempel-Ziv-Welch (LZW) complexity of the binarized BOLD data and the synthetic data generated with the individualized model using the Metropolis algorithm for each participant and condition. The LZW complexity computed from experimental data reveals a weak statistical relationship with condition (p = 0.04 one-tailed Wilcoxon test) and none with Ising temperature (r(13) = 0.13, p = 0.65), presumably because of the limited length of the BOLD time series. Similarly, we explore complexity using the block decomposition method (BDM), a more advanced method for estimating algorithmic complexity. The BDM complexity of the experimental data displays a significant correlation with Ising temperature (r(13) = 0.56, p = 0.03) and a weak but significant correlation with condition (p = 0.04, one-tailed Wilcoxon test). This study suggests that the effects of LSD increase the complexity of brain dynamics by loosening interhemispheric connectivity—especially homotopic links. In agreement with earlier work using the Ising formalism with BOLD data, we find the brain state in the placebo condition is already above the critical point, with LSD resulting in a shift further away from criticality into a more disordered state

A Probabilistic Evaluation Framework for Preference Aggregation Reflecting Group Homogeneity

Groups differ in the homogeneity of their members' preferences. Reflecting this, we propose a probabilistic criterion for evaluating and comparing the adequateness of preference aggregation procedures that takes into account information on the considered group's homogeneity structure. Further, we discuss two approaches for approximating our criterion if information is only imperfectly given and show how to estimate these approximations from data. As a preparation, we elaborate some general minimal requirements for measuring homogeneity and discuss a specific proposal for a homogeneity measure. Finally, we investigate our framework by comparing aggregation rules in a simulation study

Anomaly Detection, Rule Adaptation and Rule Induction Methodologies in the Context of Automated Sports Video Annotation.

Automated video annotation is a topic of considerable interest in computer vision due to its applications in video search, object based video encoding and enhanced broadcast content. The domain of sport broadcasting is, in particular, the subject of current research attention due to its fixed, rule governed, content. This research work aims to develop, analyze and demonstrate novel methodologies that can be useful in the context of adaptive and automated video annotation systems. In this thesis, we present methodologies for addressing the problems of anomaly detection, rule adaptation and rule induction for court based sports such as tennis and badminton. We first introduce an HMM induction strategy for a court-model based method that uses the court structure in the form of a lattice for two related modalities of singles and doubles tennis to tackle the problems of anomaly detection and rectification. We also introduce another anomaly detection methodology that is based on the disparity between the low-level vision based classifiers and the high-level contextual classifier. Another approach to address the problem of rule adaptation is also proposed that employs Convex hulling of the anomalous states. We also investigate a number of novel hierarchical HMM generating methods for stochastic induction of game rules. These methodologies include, Cartesian product Label-based Hierarchical Bottom-up Clustering (CLHBC) that employs prior information within the label structures. A new constrained variant of the classical Chinese Restaurant Process (CRP) is also introduced that is relevant to sports games. We also propose two hybrid methodologies in this context and a comparative analysis is made against the flat Markov model. We also show that these methods are also generalizable to other rule based environments

Unveiling human interactions : approaches and techniques toward the discovery and representation of interactions in networks

L'abstract è presente nell'allegato / the abstract is in the attachmen

New Trends in Neutrosophic Theory and Applications Volume II

Neutrosophic set has been derived from a new branch of philosophy, namely Neutrosophy. Neutrosophic set is capable of dealing with uncertainty, indeterminacy and inconsistent information. Neutrosophic set approaches are suitable to modeling problems with uncertainty, indeterminacy and inconsistent information in which human knowledge is necessary, and human evaluation is needed. Neutrosophic set theory was proposed in 1998 by Florentin Smarandache, who also developed the concept of single valued neutrosophic set, oriented towards real world scientific and engineering applications. Since then, the single valued neutrosophic set theory has been extensively studied in books and monographs introducing neutrosophic sets and its applications, by many authors around the world. Also, an international journal - Neutrosophic Sets and Systems started its journey in 2013. Single valued neutrosophic sets have found their way into several hybrid systems, such as neutrosophic soft set, rough neutrosophic set, neutrosophic bipolar set, neutrosophic expert set, rough bipolar neutrosophic set, neutrosophic hesitant fuzzy set, etc. Successful applications of single valued neutrosophic sets have been developed in multiple criteria and multiple attribute decision making. This second volume collects original research and application papers from different perspectives covering different areas of neutrosophic studies, such as decision making, graph theory, image processing, probability theory, topology, and some theoretical papers. This volume contains four sections: DECISION MAKING, NEUTROSOPHIC GRAPH THEORY, IMAGE PROCESSING, ALGEBRA AND OTHER PAPERS. First paper (Pu Ji, Peng-fei Cheng, Hongyu Zhang, Jianqiang Wang. Interval valued neutrosophic Bonferroni mean operators and the application in the selection of renewable energy) aims to construct selection approaches for renewable energy considering the interrelationships among criteria. To do that, Bonferroni mean (BM) and geometric BM (GBM) are employed