Better-quasi-order : ideals and spaces

This thesis deals with combinatorics, order theory and descriptive set theory. The first contribution is to the theory of well-quasi-orders (wqo) and better-quasi-orders (bqo). The main result is the proof of a conjecture made by Maurice Pouzet in 1978 his thèse d'état which states that any wqo whose ideal completion remainder is bqo is actually bqo. Our proof relies on new results with both a combinatorial and a topological flavour concerning maps from a front into a compact metric space. The second contribution is of a more applied nature and deals with topological spaces. We define a quasi-order on the subsets of every second countable To topological space in a way that generalises the Wadge quasi-order on the Baire space, while extending its nice properties to virtually all these topological spaces. The Wadge quasi-order of reducibility by continuous functions is wqo on Borei subsets of the Baire space, this quasi-order is however far less satisfactory for other important topological spaces such as the real line, as Hertling, Ikegami and Schlicht notably observed. Some authors have therefore studied reducibility with respect to some classes of discontinuous functions to remedy this situation. We propose instead to keep continuity but to weaken the notion of function to that of relation. Using the notion of admissible representation studied in Type-2 theory of effectivity, we define the quasi-order of reducibility by relatively continuous relations. We show that this quasi-order both refines the classical hierarchies of complexity and is wqo on the Borei subsets of virtually every second countable To space - including every (quasi-)Polish space. -- Cette thèse se situe dans les domaines de la combinatoire, de la théorie des ordres et de la théorie descriptive. La première contribution concerne la théorie des bons quasi-ordres (wqo) et des meilleurs quasi-ordres (bqo). Le résultat principal est la preuve d'une conjecture, énoncée par Pouzet en 1978 dans sa thèse d'état, qui établit que tout wqo dont l'ensemble des idéaux non principaux ordonnés par inclusion forme un bqo est alors lui-même un bqo. La preuve repose sur de nouveaux résultats, qui allient la combinatoire et la topologie, au sujet des fonctions d'un front vers un espace métrique compact. La seconde contribution de cette thèse traite de la complexité topologique dans le cadre des espaces To à base dénombrable. Dans le cas de l'espace de Baire, le quasi-ordre de Wadge est un wqo sur les sous-ensembles Boréliens qui a suscité énormément d'intérêt. Cependant cette relation de réduction par fonctions continues s'avère bien moins satisfaisante pour d'autres espaces d'importance tels que la droite réelle, comme l'ont fait notamment remarquer Hertling, Schlicht et Ikegami. Nous proposons de conserver la continuité et d'affaiblir la notion de fonction pour celle de relation. Pour ce faire, nous utilisons la notion de représentation admissible étudiée en « Type-2 theory of effectivity » initiée par Weihrauch. Nous introduisons alors le quasi-ordre de réduction par relations relativement continues et montrons que celui-ci à la fois raffine les hiérarchies classiques de complexité topologique et forme un wqo sur les sous-ensembles Boréliens de chaque espace quasi-Polonais.

Artificial evolution on network structures : how time and space influence dynamics

Abstract The main objective of this work is to show how the choice of the temporal dimension and of the spatial structure of the population influences an artificial evolutionary process. In the field of Artificial Evolution we can observe a common trend in synchronously evolv¬ing panmictic populations, i.e., populations in which any individual can be recombined with any other individual. Already in the '90s, the works of Spiessens and Manderick, Sarma and De Jong, and Gorges-Schleuter have pointed out that, if a population is struc¬tured according to a mono- or bi-dimensional regular lattice, the evolutionary process shows a different dynamic with respect to the panmictic case. In particular, Sarma and De Jong have studied the selection pressure (i.e., the diffusion of a best individual when the only selection operator is active) induced by a regular bi-dimensional structure of the population, proposing a logistic modeling of the selection pressure curves. This model supposes that the diffusion of a best individual in a population follows an exponential law. We show that such a model is inadequate to describe the process, since the growth speed must be quadratic or sub-quadratic in the case of a bi-dimensional regular lattice. New linear and sub-quadratic models are proposed for modeling the selection pressure curves in, respectively, mono- and bi-dimensional regu¬lar structures. These models are extended to describe the process when asynchronous evolutions are employed. Different dynamics of the populations imply different search strategies of the resulting algorithm, when the evolutionary process is used to solve optimisation problems. A benchmark of both discrete and continuous test problems is used to study the search characteristics of the different topologies and updates of the populations. In the last decade, the pioneering studies of Watts and Strogatz have shown that most real networks, both in the biological and sociological worlds as well as in man-made structures, have mathematical properties that set them apart from regular and random structures. In particular, they introduced the concepts of small-world graphs, and they showed that this new family of structures has interesting computing capabilities. Populations structured according to these new topologies are proposed, and their evolutionary dynamics are studied and modeled. We also propose asynchronous evolutions for these structures, and the resulting evolutionary behaviors are investigated. Many man-made networks have grown, and are still growing incrementally, and explanations have been proposed for their actual shape, such as Albert and Barabasi's preferential attachment growth rule. However, many actual networks seem to have undergone some kind of Darwinian variation and selection. Thus, how these networks might have come to be selected is an interesting yet unanswered question. In the last part of this work, we show how a simple evolutionary algorithm can enable the emrgence o these kinds of structures for two prototypical problems of the automata networks world, the majority classification and the synchronisation problems. Synopsis L'objectif principal de ce travail est de montrer l'influence du choix de la dimension temporelle et de la structure spatiale d'une population sur un processus évolutionnaire artificiel. Dans le domaine de l'Evolution Artificielle on peut observer une tendence à évoluer d'une façon synchrone des populations panmictiques, où chaque individu peut être récombiné avec tout autre individu dans la population. Déjà dans les année '90, Spiessens et Manderick, Sarma et De Jong, et Gorges-Schleuter ont observé que, si une population possède une structure régulière mono- ou bi-dimensionnelle, le processus évolutionnaire montre une dynamique différente de celle d'une population panmictique. En particulier, Sarma et De Jong ont étudié la pression de sélection (c-à-d la diffusion d'un individu optimal quand seul l'opérateur de sélection est actif) induite par une structure régulière bi-dimensionnelle de la population, proposant une modélisation logistique des courbes de pression de sélection. Ce modèle suppose que la diffusion d'un individu optimal suit une loi exponentielle. On montre que ce modèle est inadéquat pour décrire ce phénomène, étant donné que la vitesse de croissance doit obéir à une loi quadratique ou sous-quadratique dans le cas d'une structure régulière bi-dimensionnelle. De nouveaux modèles linéaires et sous-quadratique sont proposés pour des structures mono- et bi-dimensionnelles. Ces modèles sont étendus pour décrire des processus évolutionnaires asynchrones. Différentes dynamiques de la population impliquent strategies différentes de recherche de l'algorithme résultant lorsque le processus évolutionnaire est utilisé pour résoudre des problèmes d'optimisation. Un ensemble de problèmes discrets et continus est utilisé pour étudier les charactéristiques de recherche des différentes topologies et mises à jour des populations. Ces dernières années, les études de Watts et Strogatz ont montré que beaucoup de réseaux, aussi bien dans les mondes biologiques et sociologiques que dans les structures produites par l'homme, ont des propriétés mathématiques qui les séparent à la fois des structures régulières et des structures aléatoires. En particulier, ils ont introduit la notion de graphe sm,all-world et ont montré que cette nouvelle famille de structures possède des intéressantes propriétés dynamiques. Des populations ayant ces nouvelles topologies sont proposés, et leurs dynamiques évolutionnaires sont étudiées et modélisées. Pour des populations ayant ces structures, des méthodes d'évolution asynchrone sont proposées, et la dynamique résultante est étudiée. Beaucoup de réseaux produits par l'homme se sont formés d'une façon incrémentale, et des explications pour leur forme actuelle ont été proposées, comme le preferential attachment de Albert et Barabàsi. Toutefois, beaucoup de réseaux existants doivent être le produit d'un processus de variation et sélection darwiniennes. Ainsi, la façon dont ces structures ont pu être sélectionnées est une question intéressante restée sans réponse. Dans la dernière partie de ce travail, on montre comment un simple processus évolutif artificiel permet à ce type de topologies d'émerger dans le cas de deux problèmes prototypiques des réseaux d'automates, les tâches de densité et de synchronisation.

New York City: "gilt cage" or "promised land" ? : representations of urban space in Edith Wharton and Anzia Yezierska

This thesis explores the importance of literary New York City in the urban narratives of Edith Wharton and Anzia Yezierska. It specifically looks at the Empire City of the Progressive Period when the concept of the city was not only a new theme but also very much a typical American one which was as central to the American experience as had been the Western frontier. It could be argued, in fact, that the American city had become the new frontier where modern experiences like urbanization, industrialization, immigration, and also women's emancipation and suffrage, caused all kinds of sensations on the human scale from smoothly lived assimilation and acculturation to deeply felt alienation because of the constantly shifting urban landscape. The developing urban space made possible the emergence of new female literary protagonists like the working girl, the reformer, the prostitute, and the upper class lady dedicating her life to 'conspicuous consumption'. Industrialization opened up city space to female exploration: on the one hand, upper and middle class ladies ventured out of the home because of the many novel urban possibilities, and on the other, lower class and immigrant girls also left their domestic sphere to look for paid jobs outside the home. New York City at the time was not only considered the epicenter of the world at large, it was also a city of great extremes. Everything was constantly in flux: small brownstones made way for ever taller skyscrapers and huge waves of immigrants from Europe pushed native New Yorkers further uptown on the island, adding to the crowdedness and intensity of the urban experience. The city became a polarized urban space with Fifth Avenue representing one end of the spectrum and the Lower East Side the other. Questions of space and the urban home greatly mattered. It has been pointed out that the city setting functions as an ideal means for the display of human nature as well as social processes. Narrative representations of urban space, therefore, provide a similar canvas for a protagonist's journey and development. From widely diverging vantage points both Edith Wharton and Anzia Yezierska thus create a polarized city where domesticity is a primal concern. Looking at all of their New York narratives by close readings of exterior and interior city representations, this thesis shows how urban space greatly affects questions of identity, assimilation, and alienation in literary protagonists who cannot escape the influence of their respective urban settings. Edith Wharton's upper class "millionaire" heroines are framed and contained by the city interiors of "old" New York, making it impossible for them to truly participate in the urban landscape in order to develop outside of their 'Gilt Cages'. On the other side are Anzia Yezierska's struggling "immigrant" protagonists who, against all odds, never give up in their urban context of streets, rooftops, and stoops. Their New York City, while always challenging and perpetually changing, at least allows them perspectives of hope for a 'Promised Land' in the making. Central for both urban narrative approaches is the quest for a home as an architectural structure, a spiritual resting place, and a locus for identity forming. But just as the actual city embraces change, urban protagonists must embrace change also if they desire to find fulfillment and success. That this turns out to be much easier for Anzia Yezierska's driven immigrants rather than for Edith Wharton's well established native New Yorkers is a surprising conclusion to this urban theme.

A musculoskeletal shoulder model based on pseudo-inverse and null-space optimization.

The goal of the present work was assess the feasibility of using a pseudo-inverse and null-space optimization approach in the modeling of the shoulder biomechanics. The method was applied to a simplified musculoskeletal shoulder model. The mechanical system consisted in the arm, and the external forces were the arm weight, 6 scapulo-humeral muscles and the reaction at the glenohumeral joint, which was considered as a spherical joint. The muscle wrapping was considered around the humeral head assumed spherical. The dynamical equations were solved in a Lagrangian approach. The mathematical redundancy of the mechanical system was solved in two steps: a pseudo-inverse optimization to minimize the square of the muscle stress and a null-space optimization to restrict the muscle force to physiological limits. Several movements were simulated. The mathematical and numerical aspects of the constrained redundancy problem were efficiently solved by the proposed method. The prediction of muscle moment arms was consistent with cadaveric measurements and the joint reaction force was consistent with in vivo measurements. This preliminary work demonstrated that the developed algorithm has a great potential for more complex musculoskeletal modeling of the shoulder joint. In particular it could be further applied to a non-spherical joint model, allowing for the natural translation of the humeral head in the glenoid fossa.

Increasing respiratory dead space improves sleep disordered breathing and hypoxemia in patients with chronic mountain sickness

Background: Chronic mountain sickness (CMS), which is characterised by hypoxemia, erythrocytosis and pulmonary hypertension, is a major public health problem in high-altitude dwellers. The only existing treatment is descent to low altitude, an option that for social reasons almost never exists. Sleep disordered breathing may represent an underlying mechanism. We recently found that in mountaineers increasing the respiratory dead space markedly improves sleep disordered breathing. The aim of the present study was to assess the effects of this procedure on sleep disordered breathing in patients with CMS. Methods: In 10 male Bolivian high-altitude dwellers (mean ± SD age, 59 ± 9 y) suffering from CMS (haemoglobin >20 g/L) full night sleep recordings (Embletta, RespMed) were obtained in La Paz (3600 m). In random order, one night was spent with a 500 ml increase in dead space through a custom designed full face mask and the other night without it. Exclusion criteria were: secondary erythrocytosis, smoking, drug intake, acute infection, cardio- pulmonary or neurologic disease and travelling to low altitude in the preceding 6 months. Results: The major new finding was that added dead space dramatically improved sleep disordered breathing in patients suffering from CMS. The apnea/hypopnea index decreased by >50% (from 34.5 ± 25.0 to 16.8 ± 14.9, P = 0.003), the oxygen desaturation index decreased from 46.2 ± 23.0 to 27.2 ± 20.0 (P = 0.0004) and hypopnea index from 28.8 ± 20.9 to 16.3 ± 14.0 (P = 0.01), whereas nocturnal oxygen saturation increased from 79.8 ± 3.6 to 80.9 ± 3.0% (P = 0.009). The procedure was easily accepted and well tolerated. Conclusion: Here, we show for the very first time that an increase in respiratory dead space through a fitted mask dramatically improves nocturnal breathing in high-altitude dwellers suffering from CMS. We speculate that when used in the long-term, this procedure will improve erythrocytosis and pulmonary hypertension and offer an inexpensive and easily implementable treatment for this major public health problem.

Learning-induced plasticity in human audition: Objects, time, and space.

The human auditory system is comprised of specialized but interacting anatomic and functional pathways encoding object, spatial, and temporal information. We review how learning-induced plasticity manifests along these pathways and to what extent there are common mechanisms subserving such plasticity. A first series of experiments establishes a temporal hierarchy along which sounds of objects are discriminated along basic to fine-grained categorical boundaries and learned representations. A widespread network of temporal and (pre)frontal brain regions contributes to object discrimination via recursive processing. Learning-induced plasticity typically manifested as repetition suppression within a common set of brain regions. A second series considered how the temporal sequence of sound sources is represented. We show that lateralized responsiveness during the initial encoding phase of pairs of auditory spatial stimuli is critical for their accurate ordered perception. Finally, we consider how spatial representations are formed and modified through training-induced learning. A population-based model of spatial processing is supported wherein temporal and parietal structures interact in the encoding of relative and absolute spatial information over the initial ∼300ms post-stimulus onset. Collectively, these data provide insights into the functional organization of human audition and open directions for new developments in targeted diagnostic and neurorehabilitation strategies.

Pore space analysis of beech wood: The vessel network

Water transport in wood is vital for the survival of trees. With synchrotron radiation X-ray tomographic microscopy (SRXTM), it has become possible to characterize and quantify the three-dimensional (3D) network formed by vessels that are responsible for longitudinal transport. In the present study, the spatial size dependence of vessels and the organization inside single growth rings in terms of vessel-induced porosity was studied by SRXTM. Network characteristics, such as connectivity, were deduced by digital image analysis from the processed tomographic data and related to known complex network topologies.

Binding under Conflict Conditions: State-Space Analysis of Multivariate EEG Synchronization.

Real-world objects are often endowed with features that violate Gestalt principles. In our experiment, we examined the neural correlates of binding under conflict conditions in terms of the binding-by-synchronization hypothesis. We presented an ambiguous stimulus ("diamond illusion") to 12 observers. The display consisted of four oblique gratings drifting within circular apertures. Its interpretation fluctuates between bound ("diamond") and unbound (component gratings) percepts. To model a situation in which Gestalt-driven analysis contradicts the perceptually explicit bound interpretation, we modified the original diamond (OD) stimulus by speeding up one grating. Using OD and modified diamond (MD) stimuli, we managed to dissociate the neural correlates of Gestalt-related (OD vs. MD) and perception-related (bound vs. unbound) factors. Their interaction was expected to reveal the neural networks synchronized specifically in the conflict situation. The synchronization topography of EEG was analyzed with the multivariate S-estimator technique. We found that good Gestalt (OD vs. MD) was associated with a higher posterior synchronization in the beta-gamma band. The effect of perception manifested itself as reciprocal modulations over the posterior and anterior regions (theta/beta-gamma bands). Specifically, higher posterior and lower anterior synchronization supported the bound percept, and the opposite was true for the unbound percept. The interaction showed that binding under challenging perceptual conditions is sustained by enhanced parietal synchronization. We argue that this distributed pattern of synchronization relates to the processes of multistage integration ranging from early grouping operations in the visual areas to maintaining representations in the frontal networks of sensory memory.

Segmentation of brain structures in presence of a space-occupying lesion.

Brain deformations induced by space-occupying lesions may result in unpredictable position and shape of functionally important brain structures. The aim of this study is to propose a method for segmentation of brain structures by deformation of a segmented brain atlas in presence of a space-occupying lesion. Our approach is based on an a priori model of lesion growth (MLG) that assumes radial expansion from a seeding point and involves three steps: first, an affine registration bringing the atlas and the patient into global correspondence; then, the seeding of a synthetic tumor into the brain atlas providing a template for the lesion; finally, the deformation of the seeded atlas, combining a method derived from optical flow principles and a model of lesion growth. The method was applied on two meningiomas inducing a pure displacement of the underlying brain structures, and segmentation accuracy of ventricles and basal ganglia was assessed. Results show that the segmented structures were consistent with the patient's anatomy and that the deformation accuracy of surrounding brain structures was highly dependent on the accurate placement of the tumor seeding point. Further improvements of the method will optimize the segmentation accuracy. Visualization of brain structures provides useful information for therapeutic consideration of space-occupying lesions, including surgical, radiosurgical, and radiotherapeutic planning, in order to increase treatment efficiency and prevent neurological damage.

Fission yeast: in shape to divide.

How are cell morphogenesis and cell cycle coordinated? The fission yeast is a rod-shaped unicellular organism widely used to study how a cell self-organizes in space and time. Here, we discuss recent advances in understanding how the cell acquires and maintains its regular rod shape and uses it to control cell division. The cellular body plan is established by microtubules, which mark antipodal growth zones and medial division. In turn, cellular dimensions are defined by the small GTPase Cdc42 and downstream regulators of vesicle trafficking. Yeast cells then repetitively use their simple rod shape to orchestrate the position and timing of cell division.

Spin-labeling coronary MR angiography with steady-state free precession and radial k-space sampling: initial results in healthy volunteers.

The purpose of this study was to prospectively compare free-breathing navigator-gated cardiac-triggered three-dimensional steady-state free precession (SSFP) spin-labeling coronary magnetic resonance (MR) angiography performed by using Cartesian k-space sampling with that performed by using radial k-space sampling. A new dedicated placement of the two-dimensional selective labeling pulse and an individually adjusted labeling delay time approved by the institutional review board were used. In 14 volunteers (eight men, six women; mean age, 28.8 years) who gave informed consent, signal-to-noise ratio (SNR), contrast-to-noise ratio (CNR), vessel sharpness, vessel length, and subjective image quality were investigated. Differences between groups were analyzed with nonparametric tests (Wilcoxon, Pearson chi2). Radial imaging, as compared with Cartesian imaging, resulted in a significant reduction in the severity of motion artifacts, as well as an increase in SNR (26.9 vs 12.0, P < .05) in the coronary arteries and CNR (23.1 vs 8.8, P < .05) between the coronary arteries and the myocardium. A tendency toward improved vessel sharpness and vessel length was also found with radial imaging. Radial SSFP imaging is a promising technique for spin-labeling coronary MR angiography.