Structures spatiales dans la pensée religieuse grecque de l'époque archaïque : la représentation de quelques espaces insondables: l'éther, l'air, l'abîme marin

Cette thèse se propose d’étudier les façons dont la pensée et l’imaginaire grec de l’époque archaïque se représentaient quelques pans du réel qui ne se laissaient jamais voir ni atteindre: l’éther, l’air et l’abîme marin. Vu le caractère insondable de ces espaces, l’imagination et l’abstraction se sont ingéniées à les appréhender par un discours spécifique et à les intégrer dans le système de connaissances et de croyances propre à l’époque en leur assignant une place dans le système de l’univers, en les rattachant à une hiérarchie de l’ordre cosmologique, en leur donnant une forme, en classant leurs objets et en les rapportant aux modèles du monde connu, en les aménageant par les moyens les plus divers. Une étude des formes d’expression de la pensée grecque archaïque, autant littéraires qu’iconographiques, permet de cerner les diverses formes de représentation des domaines inaccessibles et les modèles d’organisation spatiale issus de ce type de pensée. Grâce à la dialectique particulière qui ressort du rapport entre espace et mouvement, cette thèse se propose également d’interroger le corpus des sources grecques archaïques sous des angles jusqu’ici peu explorés: comment maîtrise-t-on l’espace par les déplacements physiques en dehors des parcours terrestres? Comment les schémas du mouvement dans l’espace se sont-ils forgés? Comment les dichotomies issues de la logique spatiale archaïque (haut/bas, droite/gauche, est/ouest, en deça/au-delà, etc.) influent-elles sur la structuration spatiale? Quelles espèces d’espace révèlent les déplacements à travers les différents niveaux du monde, que ce soit ceux des dieux, ceux des mortels et d’autres entités, forces physiques et substances privilégiées dans le commerce avec le divin et le monde d’en haut? Ces analyses mettent en valeur les façons dont l’imagination et l’abstraction plutôt que l’expérience vécue ont contribué, à leur façon, à structurer l’espace et à forger l’image du monde comme κόσμος, monde mis en ordre et soumis autant aux lois physiques qu’aux lois divines.

Speech Analysis using Modern Techniques of Nonlinear Dynamics

Medical fields requires fast, simple and noninvasive methods of diagnostic techniques. Several methods are available and possible because of the growth of technology that provides the necessary means of collecting and processing signals. The present thesis details the work done in the field of voice signals. New methods of analysis have been developed to understand the complexity of voice signals, such as nonlinear dynamics aiming at the exploration of voice signals dynamic nature. The purpose of this thesis is to characterize complexities of pathological voice from healthy signals and to differentiate stuttering signals from healthy signals. Efficiency of various acoustic as well as non linear time series methods are analysed. Three groups of samples are used, one from healthy individuals, subjects with vocal pathologies and stuttering subjects. Individual vowels/ and a continuous speech data for the utterance of the sentence "iruvarum changatimaranu" the meaning in English is "Both are good friends" from Malayalam language are recorded using a microphone . The recorded audio are converted to digital signals and are subjected to analysis.Acoustic perturbation methods like fundamental frequency (FO), jitter, shimmer, Zero Crossing Rate(ZCR) were carried out and non linear measures like maximum lyapunov exponent(Lamda max), correlation dimension (D2), Kolmogorov exponent(K2), and a new measure of entropy viz., Permutation entropy (PE) are evaluated for all three groups of the subjects. Permutation Entropy is a nonlinear complexity measure which can efficiently distinguish regular and complex nature of any signal and extract information about the change in dynamics of the process by indicating sudden change in its value. The results shows that nonlinear dynamical methods seem to be a suitable technique for voice signal analysis, due to the chaotic component of the human voice. Permutation entropy is well suited due to its sensitivity to uncertainties, since the pathologies are characterized by an increase in the signal complexity and unpredictability. Pathological groups have higher entropy values compared to the normal group. The stuttering signals have lower entropy values compared to the normal signals.PE is effective in charaterising the level of improvement after two weeks of speech therapy in the case of stuttering subjects. PE is also effective in characterizing the dynamical difference between healthy and pathological subjects. This suggests that PE can improve and complement the recent voice analysis methods available for clinicians. The work establishes the application of the simple, inexpensive and fast algorithm of PE for diagnosis in vocal disorders and stuttering subjects.

Design, Development and Realization of Quadratic Volterra Filters for Selected Applications

The basic concepts of digital signal processing are taught to the students in engineering and science. The focus of the course is on linear, time invariant systems. The question as to what happens when the system is governed by a quadratic or cubic equation remains unanswered in the vast majority of literature on signal processing. Light has been shed on this problem when John V Mathews and Giovanni L Sicuranza published the book Polynomial Signal Processing. This book opened up an unseen vista of polynomial systems for signal and image processing. The book presented the theory and implementations of both adaptive and non-adaptive FIR and IIR quadratic systems which offer improved performance than conventional linear systems. The theory of quadratic systems presents a pristine and virgin area of research that offers computationally intensive work. Once the area of research is selected, the next issue is the choice of the software tool to carry out the work. Conventional languages like C and C++ are easily eliminated as they are not interpreted and lack good quality plotting libraries. MATLAB is proved to be very slow and so do SCILAB and Octave. The search for a language for scientific computing that was as fast as C, but with a good quality plotting library, ended up in Python, a distant relative of LISP. It proved to be ideal for scientific computing. An account of the use of Python, its scientific computing package scipy and the plotting library pylab is given in the appendix Initially, work is focused on designing predictors that exploit the polynomial nonlinearities inherent in speech generation mechanisms. Soon, the work got diverted into medical image processing which offered more potential to exploit by the use of quadratic methods. The major focus in this area is on quadratic edge detection methods for retinal images and fingerprints as well as de-noising raw MRI signals

A Distributed Model for Mobile Robot Environment-Learning and Navigation

A distributed method for mobile robot navigation, spatial learning, and path planning is presented. It is implemented on a sonar-based physical robot, Toto, consisting of three competence layers: 1) Low-level navigation: a collection of reflex-like rules resulting in emergent boundary-tracing. 2) Landmark detection: dynamically extracts landmarks from the robot's motion. 3) Map learning: constructs a distributed map of landmarks. The parallel implementation allows for localization in constant time. Spreading of activation computes both topological and physical shortest paths in linear time. The main issues addressed are: distributed, procedural, and qualitative representation and computation, emergent behaviors, dynamic landmarks, minimized communication.

Exact Solution of the Nonlinear Dynamics of Recurrent Neural Mechanisms for Direction Selectivity

Different theoretical models have tried to investigate the feasibility of recurrent neural mechanisms for achieving direction selectivity in the visual cortex. The mathematical analysis of such models has been restricted so far to the case of purely linear networks. We present an exact analytical solution of the nonlinear dynamics of a class of direction selective recurrent neural models with threshold nonlinearity. Our mathematical analysis shows that such networks have form-stable stimulus-locked traveling pulse solutions that are appropriate for modeling the responses of direction selective cortical neurons. Our analysis shows also that the stability of such solutions can break down giving raise to a different class of solutions ("lurching activity waves") that are characterized by a specific spatio-temporal periodicity. These solutions cannot arise in models for direction selectivity with purely linear spatio-temporal filtering.

Thermal Noise Behavior of the Bridge Circuit

This paper considers a connection between the deterministic and noisy behavior of nonlinear networks. Specifically, a particular bridge circuit is examined which has two possibly nonlinear energy storage elements. By proper choice of the constitutive relations for the network elements, the deterministic terminal behavior reduces to that of a single linear resistor. This reduction of the deterministic terminal behavior, in which a natural frequency of a linear circuit does not appear in the driving-point impedance, has been shown in classical circuit theory books (e.g. [1, 2]). The paper shows that, in addition to the reduction of the deterministic behavior, the thermal noise at the terminals of the network, arising from the usual Nyquist-Johnson noise model associated with each resistor in the network, is also exactly that of a single linear resistor. While this result for the linear time-invariant (LTI) case is a direct consequence of a well-known result for RLC circuits, the nonlinear result is novel. We show that the terminal noise current is precisely that predicted by the Nyquist-Johnson model for R if the driving voltage is zero or constant, but not if the driving voltage is time-dependent or the inductor and capacitor are time-varying

Modeling of hybrid systems by piecewise decomposition

Piecewise linear models systems arise as mathematical models of systems in many practical applications, often from linearization for nonlinear systems. There are two main approaches of dealing with these systems according to their continuous or discrete-time aspects. We propose an approach which is based on the state transformation, more particularly the partition of the phase portrait in different regions where each subregion is modeled as a two-dimensional linear time invariant system. Then the Takagi-Sugeno model, which is a combination of local model is calculated. The simulation results show that the Alpha partition is well-suited for dealing with such a system

Option pricing in market models driven by telegraph processes with jumps

Esta tesis está dividida en dos partes: en la primera parte se presentan y estudian los procesos telegráficos, los procesos de Poisson con compensador telegráfico y los procesos telegráficos con saltos. El estudio presentado en esta primera parte incluye el cálculo de las distribuciones de cada proceso, las medias y varianzas, así como las funciones generadoras de momentos entre otras propiedades. Utilizando estas propiedades en la segunda parte se estudian los modelos de valoración de opciones basados en procesos telegráficos con saltos. En esta parte se da una descripción de cómo calcular las medidas neutrales al riesgo, se encuentra la condición de no arbitraje en este tipo de modelos y por último se calcula el precio de las opciones Europeas de compra y venta.

A compositional framework for hardware/software co-design

We describe a compositional framework, together with its supporting toolset, for hardware/software co-design. Our framework is an integration of a formal approach within a traditional design flow. The formal approach is based on Interval Temporal Logic and its executable subset, Tempura. Refinement is the key element in our framework because it will derive from a single formal specification of the system the software and hardware parts of the implementation, while preserving all properties of the system specification. During refinement simulation is used to choose the appropriate refinement rules, which are applied automatically in the HOL system. The framework is illustrated with two case studies. The work presented is part of a UK collaborative research project between the Software Technology Research Laboratory at the De Montfort University and the Oxford University Computing Laboratory.

Blind equalization of nonminimum phase channels: higher order cumulant based algorithm

Higher order cumulant analysis is applied to the blind equalization of linear time-invariant (LTI) nonminimum-phase channels. The channel model is moving-average based. To identify the moving average parameters of channels, a higher-order cumulant fitting approach is adopted in which a novel relay algorithm is proposed to obtain the global solution. In addition, the technique incorporates model order determination. The transmitted data are considered as independently identically distributed random variables over some discrete finite set (e.g., set {±1, ±3}). A transformation scheme is suggested so that third-order cumulant analysis can be applied to this type of data. Simulation examples verify the feasibility and potential of the algorithm. Performance is compared with that of the noncumulant-based Sato scheme in terms of the steady state MSE and convergence rate.

Blind equalisation of multilevel PAM data for nonminimum phase channels via second- and fourth-order cumulants

This paper introduces a new blind equalisation algorithm for the pulse amplitude modulation (PAM) data transmitted through nonminimum phase (NMP) channels. The algorithm itself is based on a noncausal AR model of communication channels and the second- and fourth-order cumulants of the received data series, where only the diagonal slices of cumulants are used. The AR parameters are adjusted at each sample by using a successive over-relaxation (SOR) scheme, a variety of the ordinary LMS scheme, but with a faster convergence rate and a greater robustness to the selection of the ‘step-size’ in iterations. Computer simulations are implemented for both linear time-invariant (LTI) and linear time-variant (LTV) NMP channels, and the results show that the algorithm proposed in this paper has a fast convergence rate and a potential capability to track the LTV NMP channels.

Utopia Ltd

Utopia Ltd. explores the relationship between utopian ideas and commodification, bringing together artwork by Blaise Drummond, Brendan Earley, Pil and Galia Kollectiv, David Mabb, Lizi Sanchez and Mary-Ruth Walsh. The seven artists’ work opens up a debate on the utopian within painting, sculpture, architecture, design and video.The works in Utopia Ltd. represent modernist architecture and design in its various mutations within a spectacularised, commodified 20th century consumer society. In these works, the utopian dream seems to burst through again and again, despite rather than because of the permutations of commodity culture. By picturing the past, present and possible future, the works destabilize fixed linear time. By rescuing, reclaiming and re-picturing, Utopia Ltd. suggests that utopian ideas persist in contemporary art, making a provocative demand on the viewer’s capacity to produce utopian dreams of their own. The exhibition’s title Utopia Ltd. is a satirical echo of an operetta by Gilbert and Sullivan, Utopia (Limited) or, The Flowers of Progress (1893), in which a utopian colony is turned into a joint stock company.

Regularization of descriptor systems

Implicit dynamic-algebraic equations, known in control theory as descriptor systems, arise naturally in many applications. Such systems may not be regular (often referred to as singular). In that case the equations may not have unique solutions for consistent initial conditions and arbitrary inputs and the system may not be controllable or observable. Many control systems can be regularized by proportional and/or derivative feedback.We present an overview of mathematical theory and numerical techniques for regularizing descriptor systems using feedback controls. The aim is to provide stable numerical techniques for analyzing and constructing regular control and state estimation systems and for ensuring that these systems are robust. State and output feedback designs for regularizing linear time-invariant systems are described, including methods for disturbance decoupling and mixed output problems. Extensions of these techniques to time-varying linear and nonlinear systems are discussed in the final section.

A general Trotter-Kato formula for a class of evolution operators

In this article we prove new results concerning the existence and various properties of an evolution system U(A+B)(t, s)0 <= s <= t <= T generated by the sum -(A(t) + B(t)) of two linear, time-dependent, and generally unbounded operators defined on time-dependent domains in a complex and separable Banach space B. In particular, writing L(B) for the algebra of all linear bounded operators on B, we can express U(A+B)(t, s)0 <= s <= t <= T as the strong limit in C(8) of a product of the holomorphic contraction semigroups generated by -A (t) and - B(t), respectively, thereby proving a product formula of the Trotter-Kato type under very general conditions which allow the domain D(A(t) + B(t)) to evolve with time provided there exists a fixed set D subset of boolean AND(t is an element of)[0,T] D(A(t) + B(t)) everywhere dense in B. We obtain a special case of our formula when B(t) = 0, which, in effect, allows us to reconstruct U(A)(t, s)0 <=(s)<=(t)<=(T) very simply in terms of the semigroup generated by -A(t). We then illustrate our results by considering various examples of nonautonomous parabolic initial-boundary value problems, including one related to the theory of timedependent singular perturbations of self-adjoint operators. We finally mention what we think remains an open problem for the corresponding equations of Schrodinger type in quantum mechanics.