Does Chance hide Necessity? : a reevaluation of the debate ‘determinism - indeterminism’ in the light of quantum mechanics and probability theory

Dans cette thèse l’ancienne question philosophique “tout événement a-t-il une cause ?” sera examinée à la lumière de la mécanique quantique et de la théorie des probabilités. Aussi bien en physique qu’en philosophie des sciences la position orthodoxe maintient que le monde physique est indéterministe. Au niveau fondamental de la réalité physique – au niveau quantique – les événements se passeraient sans causes, mais par chance, par hasard ‘irréductible’. Le théorème physique le plus précis qui mène à cette conclusion est le théorème de Bell. Ici les prémisses de ce théorème seront réexaminées. Il sera rappelé que d’autres solutions au théorème que l’indéterminisme sont envisageables, dont certaines sont connues mais négligées, comme le ‘superdéterminisme’. Mais il sera argué que d’autres solutions compatibles avec le déterminisme existent, notamment en étudiant des systèmes physiques modèles. Une des conclusions générales de cette thèse est que l’interprétation du théorème de Bell et de la mécanique quantique dépend crucialement des prémisses philosophiques desquelles on part. Par exemple, au sein de la vision d’un Spinoza, le monde quantique peut bien être compris comme étant déterministe. Mais il est argué qu’aussi un déterminisme nettement moins radical que celui de Spinoza n’est pas éliminé par les expériences physiques. Si cela est vrai, le débat ‘déterminisme – indéterminisme’ n’est pas décidé au laboratoire : il reste philosophique et ouvert – contrairement à ce que l’on pense souvent. Dans la deuxième partie de cette thèse un modèle pour l’interprétation de la probabilité sera proposé. Une étude conceptuelle de la notion de probabilité indique que l’hypothèse du déterminisme aide à mieux comprendre ce que c’est qu’un ‘système probabiliste’. Il semble que le déterminisme peut répondre à certaines questions pour lesquelles l’indéterminisme n’a pas de réponses. Pour cette raison nous conclurons que la conjecture de Laplace – à savoir que la théorie des probabilités présuppose une réalité déterministe sous-jacente – garde toute sa légitimité. Dans cette thèse aussi bien les méthodes de la philosophie que de la physique seront utilisées. Il apparaît que les deux domaines sont ici solidement reliés, et qu’ils offrent un vaste potentiel de fertilisation croisée – donc bidirectionnelle.

Estudio prospectivo para la facultad de odontología de la universidad cooperativa de Colombia, sede Villavicencio, 2020

Las tendencias para las Instituciones de Educación Superior, se enmarcan en ambientes cada vez menos predecibles y cambiantes. La anticipación con miras a determinar los diferentes escenarios a los que se pueda ver enfrentada este tipo de organizaciones, facilita la comprensión de los futuros posibles. Por tanto, el propósito de esta investigación se fundamenta en la realización de un estudio que permita la construcción de los escenarios de futuro para la Facultad de Odontología de la Universidad Cooperativa de Colombia, Sede Villavicencio, con un horizonte de tiempo al año 2020. Para esto se desarrolló la metodología basada en los planteamientos de la Prospectiva estratégica de Godet (1997), a través de tres (3) etapas: el Análisis estructural prospectivo, el Sistema de matrices de impacto cruzado y la propuesta del Escenario apuesta. Finalmente, el estudio presenta recomendaciones a los directivos de la Facultad de Odontología, relacionadas con la construcción del Escenario apuesta, catalogándose como herramienta para el direccionamiento estratégico y toma de decisiones.

New concepts of the power received by ideal energy storage elements: the instantaneous complex power approach

This paper presents some definitions and concepts of the Instantaneous Complex Power Theory [1] which is a new approach for the Akagi's Instantaneous Reactive Power Theory [2].The powers received by an ideal inductor are interpreted and the knowledge of the actual nature of these powers may lead to changes of the conventional electrical power concepts.

Power analysis applying the instantaneous complex power analytical expressions on a RL symmetrical three-phase system

This paper enhances some concepts of the Instantaneous Complex Power Theory by analyzing the analytical expressions for voltages, currents and powers developed on a symmetrical RL three-phase system, during the transient caused by a sinusoidal voltage excitation. The powers delivered to an ideal inductor will be interpreted, allowing a deep insight in the power phenomenon by analyzing the voltages in each element of the circuit. The results can be applied to the understanding of non-linear systems subject to sinusoidal voltage excitation and distorted currents.

A note on the hypercomplex riemann-cauchy like relations for quaternions and laplace equations

In this Note it is worked out a new set of Laplace-Like equations for quaternions through Riemann-Cauchy hypercomplex relations otained earlier [1]. As in the theory of functions of a complex variable, it is expected that this new set of Laplace-Like equations might be applied to a large number of Physical problems, providing new insights in the Classical Fields Theory.

A complex networks approach for data clustering

This work proposes a method for data clustering based on complex networks theory. A data set is represented as a network by considering different metrics to establish the connection between each pair of objects. The clusters are obtained by taking into account five community detection algorithms. The network-based clustering approach is applied in two real-world databases and two sets of artificially generated data. The obtained results suggest that the exponential of the Minkowski distance is the most suitable metric to quantify the similarities between pairs of objects. In addition, the community identification method based on the greedy optimization provides the best cluster solution. We compare the network-based clustering approach with some traditional clustering algorithms and verify that it provides the lowest classification error rate. (C) 2012 Elsevier B.V. All rights reserved.

Topics in geometry, analysis and inverse problems

The thesis consists of three independent parts. Part I: Polynomial amoebas We study the amoeba of a polynomial, as de ned by Gelfand, Kapranov and Zelevinsky. A central role in the treatment is played by a certain convex function which is linear in each complement component of the amoeba, which we call the Ronkin function. This function is used in two di erent ways. First, we use it to construct a polyhedral complex, which we call a spine, approximating the amoeba. Second, the Monge-Ampere measure of the Ronkin function has interesting properties which we explore. This measure can be used to derive an upper bound on the area of an amoeba in two dimensions. We also obtain results on the number of complement components of an amoeba, and consider possible extensions of the theory to varieties of codimension higher than 1. Part II: Differential equations in the complex plane We consider polynomials in one complex variable arising as eigenfunctions of certain differential operators, and obtain results on the distribution of their zeros. We show that in the limit when the degree of the polynomial approaches innity, its zeros are distributed according to a certain probability measure. This measure has its support on the union of nitely many curve segments, and can be characterized by a simple condition on its Cauchy transform. Part III: Radon transforms and tomography This part is concerned with different weighted Radon transforms in two dimensions, in particular the problem of inverting such transforms. We obtain stability results of this inverse problem for rather general classes of weights, including weights of attenuation type with data acquisition limited to a 180 degrees range of angles. We also derive an inversion formula for the exponential Radon transform, with the same restriction on the angle.

Mixed Mode Fracture Behaviour of Piezoelectric Materials

Piezoelectrics present an interactive electromechanical behaviour that, especially in recent years, has generated much interest since it renders these materials adapt for use in a variety of electronic and industrial applications like sensors, actuators, transducers, smart structures. Both mechanical and electric loads are generally applied on these devices and can cause high concentrations of stress, particularly in proximity of defects or inhomogeneities, such as flaws, cavities or included particles. A thorough understanding of their fracture behaviour is crucial in order to improve their performances and avoid unexpected failures. Therefore, a considerable number of research works have addressed this topic in the last decades. Most of the theoretical studies on this subject find their analytical background in the complex variable formulation of plane anisotropic elasticity. This theoretical approach bases its main origins in the pioneering works of Muskelishvili and Lekhnitskii who obtained the solution of the elastic problem in terms of independent analytic functions of complex variables. In the present work, the expressions of stresses and elastic and electric displacements are obtained as functions of complex potentials through an analytical formulation which is the application to the piezoelectric static case of an approach introduced for orthotropic materials to solve elastodynamics problems. This method can be considered an alternative to other formalisms currently used, like the Stroh’s formalism. The equilibrium equations are reduced to a first order system involving a six-dimensional vector field. After that, a similarity transformation is induced to reach three independent Cauchy-Riemann systems, so justifying the introduction of the complex variable notation. Closed form expressions of near tip stress and displacement fields are therefore obtained. In the theoretical study of cracked piezoelectric bodies, the issue of assigning consistent electric boundary conditions on the crack faces is of central importance and has been addressed by many researchers. Three different boundary conditions are commonly accepted in literature: the permeable, the impermeable and the semipermeable (“exact”) crack model. This thesis takes into considerations all the three models, comparing the results obtained and analysing the effects of the boundary condition choice on the solution. The influence of load biaxiality and of the application of a remote electric field has been studied, pointing out that both can affect to a various extent the stress fields and the angle of initial crack extension, especially when non-singular terms are retained in the expressions of the electro-elastic solution. Furthermore, two different fracture criteria are applied to the piezoelectric case, and their outcomes are compared and discussed. The work is organized as follows: Chapter 1 briefly introduces the fundamental concepts of Fracture Mechanics. Chapter 2 describes plane elasticity formalisms for an anisotropic continuum (Eshelby-Read-Shockley and Stroh) and introduces for the simplified orthotropic case the alternative formalism we want to propose. Chapter 3 outlines the Linear Theory of Piezoelectricity, its basic relations and electro-elastic equations. Chapter 4 introduces the proposed method for obtaining the expressions of stresses and elastic and electric displacements, given as functions of complex potentials. The solution is obtained in close form and non-singular terms are retained as well. Chapter 5 presents several numerical applications aimed at estimating the effect of load biaxiality, electric field, considered permittivity of the crack. Through the application of fracture criteria the influence of the above listed conditions on the response of the system and in particular on the direction of crack branching is thoroughly discussed.

Toeplitz operators on finite and infinite dimensional spaces with associated psi *-Fréchet algebras

The present thesis is a contribution to the multi-variable theory of Bergman and Hardy Toeplitz operators on spaces of holomorphic functions over finite and infinite dimensional domains. In particular, we focus on certain spectral invariant Frechet operator algebras F closely related to the local symbol behavior of Toeplitz operators in F. We summarize results due to B. Gramsch et.al. on the construction of Psi_0- and Psi^*-algebras in operator algebras and corresponding scales of generalized Sobolev spaces using commutator methods, generalized Laplacians and strongly continuous group actions. In the case of the Segal-Bargmann space H^2(C^n,m) of Gaussian square integrable entire functions on C^n we determine a class of vector-fields Y(C^n) supported in complex cones K. Further, we require that for any finite subset V of Y(C^n) the Toeplitz projection P is a smooth element in the Psi_0-algebra constructed by commutator methods with respect to V. As a result we obtain Psi_0- and Psi^*-operator algebras F localized in cones K. It is an immediate consequence that F contains all Toeplitz operators T_f with a symbol f of certain regularity in an open neighborhood of K. There is a natural unitary group action on H^2(C^n,m) which is induced by weighted shifts and unitary groups on C^n. We examine the corresponding Psi^*-algebra A of smooth elements in Toeplitz-C^*-algebras. Among other results sufficient conditions on the symbol f for T_f to belong to A are given in terms of estimates on its Berezin-transform. Local aspects of the Szegö projection P_s on the Heisenbeg group and the corresponding Toeplitz operators T_f with symbol f are studied. In this connection we apply a result due to Nagel and Stein which states that for any strictly pseudo-convex domain U the projection P_s is a pseudodifferential operator of exotic type (1/2, 1/2). The second part of this thesis is devoted to the infinite dimensional theory of Bergman and Hardy spaces and the corresponding Toeplitz operators. We give a new proof of a result observed by Boland and Waelbroeck. Namely, that the space of all holomorphic functions H(U) on an open subset U of a DFN-space (dual Frechet nuclear space) is a FN-space (Frechet nuclear space) equipped with the compact open topology. Using the nuclearity of H(U) we obtain Cauchy-Weil-type integral formulas for closed subalgebras A in H_b(U), the space of all bounded holomorphic functions on U, where A separates points. Further, we prove the existence of Hardy spaces of holomorphic functions on U corresponding to the abstract Shilov boundary S_A of A and with respect to a suitable boundary measure on S_A. Finally, for a domain U in a DFN-space or a polish spaces we consider the symmetrizations m_s of measures m on U by suitable representations of a group G in the group of homeomorphisms on U. In particular,in the case where m leads to Bergman spaces of holomorphic functions on U, the group G is compact and the representation is continuous we show that m_s defines a Bergman space of holomorphic functions on U as well. This leads to unitary group representations of G on L^p- and Bergman spaces inducing operator algebras of smooth elements related to the symmetries of U.

Preprocessing and analyzing genetic data with complex networks: An application to Obstructive Nephropathy

Many diseases have a genetic origin, and a great effort is being made to detect the genes that are responsible for their insurgence. One of the most promising techniques is the analysis of genetic information through the use of complex networks theory. Yet, a practical problem of this approach is its computational cost, which scales as the square of the number of features included in the initial dataset. In this paper, we propose the use of an iterative feature selection strategy to identify reduced subsets of relevant features, and show an application to the analysis of congenital Obstructive Nephropathy. Results demonstrate that, besides achieving a drastic reduction of the computational cost, the topologies of the obtained networks still hold all the relevant information, and are thus able to fully characterize the severity of the disease.

Anomalous Consistency in Mild Cognitive Impairment: A Complex Networks Approach

Increased variability in performance has been associated with the emergence of several neurological and psychiatric pathologies. However, whether and how consistency of neuronal activity may also be indicative of an underlying pathology is still poorly understood. Here we propose a novel method for evaluating consistency from non-invasive brain recordings. We evaluate the consistency of the cortical activity recorded with magnetoencephalography in a group of subjects diagnosed with Mild Cognitive Impairment (MCI), a condition sometimes prodromal of dementia, during the execution of a memory task. We use metrics coming from nonlinear dynamics to evaluate the consistency of cortical regions. A representation known as parenclitic networks is constructed, where atypical features are endowed with a network structure, the topological properties of which can be studied at various scales. Pathological conditions correspond to strongly heterogeneous networks, whereas typical or normative conditions are characterized by sparsely connected networks with homogeneous nodes. The analysis of this kind of networks allows identifying the extent to which consistency is affected in the MCI group and the focal points where MCI is especially severe. To the best of our knowledge, these results represent the first attempt at evaluating the consistency of brain functional activity using complex networks theory.

Higher mathematics. A text-book for classical and engineering colleges.

"Bibliography ... general works on the history of mathematics in the nineteenth century": p. 568-570.

Dissolution of a spatially variable DNAPL (dense non aqueous phase liquid) source

Dissolution of non-aqueous phase liquids (NAPLs) or gases into groundwater is a key process, both for contamination problems originating from organic liquid sources, and for dissolution trapping in geological storage of CO2. Dissolution in natural systems typically will involve both high and low NAPL saturations and a wide range of pore water flow velocities within the same source zone for dissolution to groundwater. To correctly predict dissolution in such complex systems and as the NAPL saturations change over time, models must be capable of predicting dissolution under a range of saturations and flow conditions. To provide data to test and validate such models, an experiment was conducted in a two-dimensional sand tank, where the dissolution of a spatially variable, 5x5 cm**2 DNAPL tetrachloroethene source was carefully measured using x-ray attenuation techniques at a resolution of 0.2x0.2 cm**2. By continuously measuring the NAPL saturations, the temporal evolution of DNAPL mass loss by dissolution to groundwater could be measured at each pixel. Next, a general dissolution and solute transport code was written and several published rate-limited (RL) dissolution models and a local equilibrium (LE) approach were tested against the experimental data. It was found that none of the models could adequately predict the observed dissolution pattern, particularly in the zones of higher NAPL saturation. Combining these models with a model for NAPL pool dissolution produced qualitatively better agreement with experimental data, but the total matching error was not significantly improved. A sensitivity study of commonly used fitting parameters further showed that several combinations of these parameters could produce equally good fits to the experimental observations. The results indicate that common empirical model formulations for RL dissolution may be inadequate in complex, variable saturation NAPL source zones, and that further model developments and testing is desirable.

Monogenic polynomials of four variables with binomial expansion

In the recent past one of the main concern of research in the field of Hypercomplex Function Theory in Clifford Algebras was the development of a variety of new tools for a deeper understanding about its true elementary roots in the Function Theory of one Complex Variable. Therefore the study of the space of monogenic (Clifford holomorphic) functions by its stratification via homogeneous monogenic polynomials is a useful tool. In this paper we consider the structure of those polynomials of four real variables with binomial expansion. This allows a complete characterization of sequences of 4D generalized monogenic Appell polynomials by three different types of polynomials. A particularly important case is that of monogenic polynomials which are simply isomorphic to the integer powers of one complex variable and therefore also called pseudo-complex powers.

Using GeoGebra to study complex functions

The aim of this workshop to present some of the strategies studied to use GeoGebra in the analysis of complex functions. The proposed tasks focus on complex analysis topics target for students of the 1st year of higher education, which can be easily adapted to pre-university students. In the first part of this workshop we will illustrate how to use the two graphical windows of GeoGebra to represent complex functions of complex variable. The second part will present the use of the dynamic color Geogebra in order to obtain Coloring domains that correspond to the graphic representation of complex functions. Finally, we will use the threedimensional graphics window in GeoGebra to study the component functions of a complex function. During the workshop will be provided scripts orientation of the different tasks proposed to be held on computers with Geogebra version 5.0 or high.