Parts, places, and perspectives : a theory of spatial relations based an mereotopology and convexity

This thesis suggests to carry on the philosophical work begun in Casati's and Varzi's seminal book Parts and Places, by extending their general reflections on the basic formal structure of spatial representation beyond mereotopology and absolute location to the question of perspectives and perspective-dependent spatial relations. We show how, on the basis of a conceptual analysis of such notions as perspective and direction, a mereotopological theory with convexity can express perspectival spatial relations in a strictly qualitative framework. We start by introducing a particular mereotopological theory, AKGEMT, and argue that it constitutes an adequate core for a theory of spatial relations. Two features of AKGEMT are of particular importance: AKGEMT is an extensional mereotopology, implying that sameness of proper parts is a sufficient and necessary condition for identity, and it allows for (lower- dimensional) boundary elements in its domain of quantification. We then discuss an extension of AKGEMT, AKGEMTS, which results from the addition of a binary segment operator whose interpretation is that of a straight line segment between mereotopological points. Based on existing axiom systems in standard point-set topology, we propose an axiomatic characterisation of the segment operator and show that it is strong enough to sustain complex properties of a convexity predicate and a convex hull operator. We compare our segment-based characterisation of the convex hull to Cohn et al.'s axioms for the convex hull operator, arguing that our notion of convexity is significantly stronger. The discussion of AKGEMTS defines the background theory of spatial representation on which the developments in the second part of this thesis are built. The second part deals with perspectival spatial relations in two-dimensional space, i.e., such relations as those expressed by 'in front of, 'behind', 'to the left/right of, etc., and develops a qualitative formalism for perspectival relations within the framework of AKGEMTS. Two main claims are defended in part 2: That perspectival relations in two-dimensional space are four- place relations of the kind R(x, y, z, w), to be read as x is i?-related to y as z looks at w; and that these four-place structures can be satisfactorily expressed within the qualitative theory AKGEMTS. To defend these two claims, we start by arguing for a unified account of perspectival relations, thus rejecting the traditional distinction between 'relative' and 'intrinsic' perspectival relations. We present a formal theory of perspectival relations in the framework of AKGEMTS, deploying the idea that perspectival relations in two-dimensional space are four-place relations, having a locational and a perspectival part and show how this four-place structure leads to a unified framework of perspectival relations. Finally, we present a philosophical motivation to the idea that perspectival relations are four-place, cashing out the thesis that perspectives are vectorial properties and argue that vectorial properties are relations between spatial entities. Using Fine's notion of "qua objects" for an analysis of points of view, we show at last how our four-place approach to perspectival relations compares to more traditional understandings.

Virus infection speeds: theory versus experiment

In order to explain the speed of Vesicular Stomatitis Virus VSV infections, we develop a simple model that improves previous approaches to the propagation of virus infections. For VSV infections, we find that the delay time elapsed between the adsorption of a viral particle into a cell and the release of its progeny has a veryimportant effect. Moreover, this delay time makes the adsorption rate essentially irrelevant in order to predict VSV infection speeds. Numerical simulations are in agreement with the analytical results. Our model satisfactorily explains the experimentally measured speeds of VSV infections

Using problem-based learning for introducing producer theory and market structure in intermediate microeconomics

This paper shows how instructors can use the problem‐based learning method to introduce producer theory and market structure in intermediate microeconomics courses. The paper proposes a framework where different decision problems are presented to students, who are asked to imagine that they are the managers of a firm who need to solve a problem in a particular business setting. In this setting, the instructors’ role isto provide both guidance to facilitate student learning and content knowledge on a just‐in‐time basis

Fuzzy set Theory and Quantum Chemistry

Es discuteixen breument algunes consideracions sobre l'aplicació de la Teoria delsConjunts difusos a la Química quàntica. Es demostra aqui que molts conceptes químics associats a la teoria són adequats per ésser connectats amb l'estructura dels Conjunts difusos. També s'explica com algunes descripcions teoriques dels observables quàntics espotencien tractant-les amb les eines associades als esmentats Conjunts difusos. La funciódensitat es pren com a exemple de l'ús de distribucions de possibilitat al mateix temps queles distribucions de probabilitat quàntiques

El mètode APT (Auto Adjusting Perturbation Theory) de diagonalització de matrius

Es presenta un nou algorisme per a la diagonalització de matrius amb diagonal dominant. Es mostra la seva eficàcia en el tractament de matrius no simètriques, amb elements definits sobre el cos complex i, fins i tot, de grans dimensions. Es posa de manifest la senzillesa del mètode així com la facilitat d'implementació en forma de codi de programació. Es comentenels seus avantatges i característiques limitants, així com algunes de les millores que es poden implementar. Finalment, es mostren alguns exemples numèrics

Conditional compositional biplots: theory and application

The biplot has proved to be a powerful descriptive and analytical tool in many areasof applications of statistics. For compositional data the necessary theoreticaladaptation has been provided, with illustrative applications, by Aitchison (1990) andAitchison and Greenacre (2002). These papers were restricted to the interpretation ofsimple compositional data sets. In many situations the problem has to be described insome form of conditional modelling. For example, in a clinical trial where interest isin how patients’ steroid metabolite compositions may change as a result of differenttreatment regimes, interest is in relating the compositions after treatment to thecompositions before treatment and the nature of the treatments applied. To study thisthrough a biplot technique requires the development of some form of conditionalcompositional biplot. This is the purpose of this paper. We choose as a motivatingapplication an analysis of the 1992 US President ial Election, where interest may be inhow the three-part composition, the percentage division among the three candidates -Bush, Clinton and Perot - of the presidential vote in each state, depends on the ethniccomposition and on the urban-rural composition of the state. The methodology ofconditional compositional biplots is first developed and a detailed interpretation of the1992 US Presidential Election provided. We use a second application involving theconditional variability of tektite mineral compositions with respect to major oxidecompositions to demonstrate some hazards of simplistic interpretation of biplots.Finally we conjecture on further possible applications of conditional compositionalbiplots

Reactive rise in blood pressure upon cuff inflation : cuff inflation at the arm causes a greater rise in pressure than at the wrist in hypertensive patients

Résumé en français: Il est admis que l'inflation d'une manchette à pression au niveau du bras engendre une augmentation réactionnelle de la tension artérielle qui peut être le résultat d'une gêne lors de l'inflation et peut diminuer la précision de la mesure. Dans cette étude, nous comparons séquentiellement l'augmentation de la tension artérielle lorsque la manchette à pression est positionnée au niveau du bras et au niveau du poignet. Nous avons étudié un collectif de 34 participants normotendus et 34 patients hypertendus. Chacun d'eux était équipé de deux manchettes à pression, l'une au niveau du bras et l'autre au niveau du poignet. Nous avons randomisé l'ordre d'inflation des manchettes ainsi que la pression d'inflation maximale (180mmHg versus 240mmHg). Trois mesures étaient effectuées pour chaque pression d'inflation maximale, ceci au bras comme poignet, et leur séquence était également randomisée. En parallèle, un enregistrement continu de la tension artérielle avait lieu au niveau du majeur de la main opposée à l'aide d'un photoplethysmographe. Cette valeur était considérée comme la valeur de tension artérielle au repos. Pour les participants normotendus, aucune différence statistiquement significative n'a pu être mise en évidence en lien avec la position de la manchette à pression, ceci indépendamment de la pression d'inflation maximale. Variation de la pression systolique à 180 mmHg: 4.3+/-3.0 mmHg au bras et 3.7+/-2.9 mmHg au poignet (p=ns), à 240 mmHg: 5.5+/-3.9 au bras et 4.2+/-2.7 mmHg au poignet (p=0.052). En revanche, concernant les patients hypertendus, une augmentation significative de la tension artérielle a été mise en évidence entre le bras et le poignet. Ceci pour les valeurs de tension artérielle systolique et diastolique et quelle que soit la pression d'inflation maximale utilisée. Augmentation de la pression artérielle systolique 6.513.5 mmHg au bras et 3.812.1mmHg au poignet pour une pression d'inflation maximale de 180 mmHg (p<0.01) et respectivement 6.413.5 mmHg et 4.713.0 mmHg pour 240 mmHg (p=0.01). L'augmentation des valeurs de tension artérielle était indépendante de la valeur tensionnelle de base. Ces résultats montrent que les patients hypertendus réagissent significativement moins à l'inflation d'une manchette ä pression lorsque celle-ci est positionnée au niveau du poignet par rapport au bras, ceci indépendamment des valeurs de tension artérielle de base des patients. Nous pouvons donc suggérer que l'inflation d'une manchette à pression cause moins de désagrément lorsqu'elle est placée au niveau du poignet, notamment chez les patients hypertendus et qu'elle peut être une alternative à la mesure standard au niveau du bras.

A Monte Carlo-Based Fiber Tracking Algorithm using Diffusion Tensor MRI

Diffusion tensor magnetic resonance imaging, which measures directional information of water diffusion in the brain, has emerged as a powerful tool for human brain studies. In this paper, we introduce a new Monte Carlo-based fiber tracking approach to estimate brain connectivity. One of the main characteristics of this approach is that all parameters of the algorithm are automatically determined at each point using the entropy of the eigenvalues of the diffusion tensor. Experimental results show the good performance of the proposed approach

Ultra-fast recovery from right neglect after 'awake surgery' for slow-growing tumor invading the left parietal area

It is now possible to perform resections of slow-growing tumors in awake patients. Using direct electrical stimulation, real-time functional mapping of the brain can be used to prevent the resection of essential areas near the tumor. Simple clinical observations of patients with a resection of slow-growing tumors have demonstrated substantial recovery within a few days of such 'awake surgery'. The aim of this study was to investigate the kinetics of recovery following the resection of slow-growing tumors invading the left parietal area and to focus mainly on its rapidity. Two patients were assessed by standard line bisection tests and compared with eight healthy individuals. Independently of the pure nature of the symptoms, we report that the patients rapidly and substantially recovered from pronounced right neglect. They were tested 48 hours after the surgery and the recovery was significant for both patients after less than 4 hours. Strikingly, for one patient, recovery was ultra fast and substantial in the first practice session within less than 7 minutes: it occurred without verbal feedback and was substantially retained during the following testing session. Its rapidity suggests a process of unmasking redundant networks. With the slow growth of the lesion, the contralesional hemisphere is probably progressively prepared for rapid unmasking of homologue networks. These results have major clinical implications. For patients with an invading left-side tumor, it is now clear that line bisections are required before, during, and after awake surgery to: plan the surgery, control the quality of the resection, and also optimize the rehabilitation of the patient

KAM theory for conformally symplectic systems

We present a KAM theory for some dissipative systems (geometrically, these are conformally symplectic systems, i.e. systems that transform a symplectic form into a multiple of itself). For systems with n degrees of freedom depending on n parameters we show that it is possible to find solutions with n-dimensional (Diophantine) frequencies by adjusting the parameters. We do not assume that the system is close to integrable, but we use an a-posteriori format. Our unknowns are a parameterization of the solution and a parameter. We show that if there is a sufficiently approximate solution of the invariance equation, which also satisfies some explicit non–degeneracy conditions, then there is a true solution nearby. We present results both in Sobolev norms and in analytic norms. The a–posteriori format has several consequences: A) smooth dependence on the parameters, including the singular limit of zero dissipation; B) estimates on the measure of parameters covered by quasi–periodic solutions; C) convergence of perturbative expansions in analytic systems; D) bootstrap of regularity (i.e., that all tori which are smooth enough are analytic if the map is analytic); E) a numerically efficient criterion for the break–down of the quasi–periodic solutions. The proof is based on an iterative quadratically convergent method and on suitable estimates on the (analytical and Sobolev) norms of the approximate solution. The iterative step takes advantage of some geometric identities, which give a very useful coordinate system in the neighborhood of invariant (or approximately invariant) tori. This system of coordinates has several other uses: A) it shows that for dissipative conformally symplectic systems the quasi–periodic solutions are attractors, B) it leads to efficient algorithms, which have been implemented elsewhere. Details of the proof are given mainly for maps, but we also explain the slight modifications needed for flows and we devote the appendix to present explicit algorithms for flows.