Quantum metric spaces as a model for pregeometry

A new arena for the dynamics of spacetime is proposed, in which the basic quantum variable is the two-point distance on a metric space. The scaling dimension (that is, the Kolmogorov capacity) in the neighborhood of each point then defines in a natural way a local concept of dimension. We study our model in the region of parameter space in which the resulting spacetime is not too different from a smooth manifold.

Affaires de patrons, usages de la frontière : géographie des réseaux marchands entre Niger, Bénin et Nigéria

Résumé L'objectif de la thèse est de comprendre le mode d'organisation économique spécifique aux petits centres urbains qui composent les espaces frontaliers sahéliens, en s'interrogeant sur leur concurrence ou leur complémentarité éventuelle à l'intérieur d'un régime de spatialité particulier. En s'appuyant sur l'exemple du carrefour économique de Gaya-Malanville-Kamba situé à la frontière entre le Niger, le Bénin et le Nigeria, il questionne le rôle de la ville-frontière ainsi que le jeu des acteurs marchands localement dominants, à partir de quatre grandes interrogations : Quelles sont les spécificités de l'Afrique sahélienne qui obligent à renouveler les approches géographiques de l'espace marchand? Quels sont les facteurs déterminants de l'activité économique frontalière? Les formes d'organisation de l'espace qui concourent à la structuration de l'économie sont-elles concurrentes ou coopératives? Les logiques économiques frontalières sont-elles compatibles avec l'orientation des programmes de développement adoptés par les pays sahéliens et leurs partenaires bi- ou multilatéraux? Dans une première partie, un modèle territorial de l'Afrique sahélienne permet de rendre compte de la prédominance des logiques circulatoires sur les logiques productives, une propriété essentielle de toute organisation économique confrontée à l'instabilité climatique. Dans une seconde partie, l'étude considère les facteurs déterminants de l'activité économique frontalière que sont le degré d'enclavement des territoires, la libre circulation des biens et des personnes, les relations concurrentielles ou coopératives qui lient les marchés ainsi que les liens clientélistes qui unissent patron et obligés. Une troisième partie est consacrée aux productions agricoles de tente organisées sous forme de coopératives paysannes ou d'initiatives privées. Une quatrième partie s'intéresse aux réseaux de l'import-export et du commerce de détail qui bénéficient de l'augmentation des besoins engendrée par l'urbanisation sahélienne. L'économie spatiale qui résulte de ces flux est organisée selon deux logiques distinctes : d'une part, les opportunités relatives à la production agricole conduisent certains investisseurs à intensifier l'irrigation pour satisfaire la demande des marchés urbains, d'autre part, les acteurs du capitalisme marchand, actifs dans l'import-export et la vente de détail, développent des réseaux informels et mobiles qui se jouent des différentiels nationaux. Les activités commerciales des villes-marchés connaissent alors des fluctuations liées aux entreprises productives et circulatoires de ces patrons, lesquelles concourent à l'organisation territoriale générale de l>Afrique sahélienne. Ces logiques évoluent dans un contexte fortement marqué par les politiques des institutions financières internationales, des agences bilatérales de coopération et des ONGs. Celles-ci se donnent pour ambition de transformer les économies, les systèmes politiques et les organisations sociales sahéliennes, en faisant la promotion du libéralisme, de la bonne gouvernance et de la société civile. Ces axes directeurs, qui constituent le champ de bataille contemporain du développement, forment un ensemble dans lequel la spécificité sahélienne notamment frontalière est rarement prise en compte. C'est pourquoi l'étude conclut en faveur d'un renouvellement des politiques de développement appliquées aux espaces frontaliers. Trois grands axes d'intervention peuvent alors être dégagés, lesquels permettent de réconcilier des acteurs et des logiques longtemps dissociés: ceux des espaces séparés par une limite administrative, ceux de la sphère urbaine et rurale et ceux du capitalisme marchand et de l'investissement agricole, en renforçant la coopération économique transfrontalière, en prenant en considération les interactions croissantes entre villes et campagnes et en appuyant les activités marchandes. Abstract: Urbanisation in West Africa is recent and fast. If only 10 % of the total population was living in urban areas in 1950, this proportion reached 40 % in 2000 and will be estimated to 60 % in 2025. Small and intermediate cities, located between the countryside and large metropolis, are particularly concerned with this process. They are nowadays considered as efficient vectors of local economic development because of fiscal or monetary disparities between states, which enable businessmen to develop particular skills based on local urban networks. The majority of theses networks are informal and extremely flexible, like in the Gaya - Malanville - Kamba region, located between Niger, Benin and Nigeria. Evidence show that this economic space is characterised by high potentialities (climatic and hydrological conditions, location on main economic West African axis) and few constraints (remoteness of some potentially high productive areas). In this context, this PhD deals with the economic relationships between the three market cities. Focusing on the links that unite the businessmen of the local markets - called patron; - it reveals the extreme flexibility of their strategies as well as the deeply informal nature of their activities. Through the analysis of examples taken from the commerce of agricultural products, import and export flows and detail activities, it studies the changes that have taken place in the city centres of Gaya, Malanville and Kamba. Meanwhile, this research shows how these cities represent a border economical area based on rival and complementary connections. In the first Part, it was necessary to reconsider the usual spatial analysis devoted to the question of economic centrality. As a matter of fact, the organisation of West African economic spaces is very flexible and mobile. Centrality is always precarious because of seasonal or temporary reasons. This is why the first chapters are devoted to the study of the specificity of the Sahelian territoriality. Two main elements are relevant: first the population diversity and second, the urban-rural linkages. In the second part, the study considers three main factors on which the cross-border economic networks are dependent: enclosure that prevents goods to reach the markets, administrative constraints that limit free trade between states and cities and the concurrent or complementary relationships between markets. A third part deals with the clientelist ties engaged between the patrons and their clients with the hypothesis that these relationships are based on reciprocity and inequality. A fourth part is devoted to' the study of the spatial organisation of commercial goods across the borders, as far as the agriculture commercial products, the import-export merchandises and the retail products are concerned. This leads to the conclusion that the economic activity is directly linked to urban growth. However, the study notices that there is a lack of efficient policies dealing with strengthening the business sector and improving the cross-border cooperation. This particularity allows us to favour new local development approaches, which would take into account the important potential of private economical actors. In the same time, the commercial flows should be regulated with the help of public policies, as long as they are specifically adapted to the problems that these areas have to deal with.

Self-similarity of complex networks and hidden metric spaces

We demonstrate that the self-similarity of some scale-free networks with respect to a simple degree-thresholding renormalization scheme finds a natural interpretation in the assumption that network nodes exist in hidden metric spaces. Clustering, i.e., cycles of length three, plays a crucial role in this framework as a topological reflection of the triangle inequality in the hidden geometry. We prove that a class of hidden variable models with underlying metric spaces are able to accurately reproduce the self-similarity properties that we measured in the real networks. Our findings indicate that hidden geometries underlying these real networks are a plausible explanation for their observed topologies and, in particular, for their self-similarity with respect to the degree-based renormalization.

Determinacy and Weakly Ramsey sets in Banach spaces

We give a sufficient condition for a set of block subspaces in an infinite-dimensional Banach space to be weakly Ramsey. Using this condition we prove that in the Levy-collapse of a Mahlo cardinal, every projective set is weakly Ramsey. This, together with a construction of W. H. Woodin, is used to show that the Axiom of Projective Determinacy implies that every projective set is weakly Ramsey. In the case of co we prove similar results for a stronger Ramsey property. And for hereditarily indecomposable spaces we show that the Axiom of Determinacy plus the Axiom of Dependent Choices imply that every set is weakly Ramsey. These results are the generalizations to the class of projective sets of some theorems from W. T. Gowers, and our paper "Weakly Ramsey sets in Banach spaces."

Best approach regions for potential spaces

We characterize the approach regions so that the non-tangential maximal function is of weak-type on potential spaces, for which we use a simple argument involving Carleson measure estimates.

Real interpolation for families of Banach spaces (II)

In this paper, we study the dual space and reiteration theorems for the real method of interpolation for infinite families of Banach spaces introduced in [2]. We also give examples of interpolation spaces constructed with this method.

Some spectral properties of the canonical solution operator to $\bar\partial$ on weighted Fock spaces

We characterize the Schatten class membership of the canonical solution operator to $\overline{\partial}$ acting on $L^2(e^{-2\phi})$, where $\phi$ is a subharmonic function with $\Delta\phi$ a doubling measure. The obtained characterization is in terms of $\Delta\phi$. As part of our approach, we study Hankel operators with anti-analytic symbols acting on the corresponding Fock space of entire functions in $L^2(e^{-2\phi})$

European integration, FDI and the internal geography of trade : evidence from Western European border regions

In this paper we use a gravity model to study the trade performance of French and Spanishborder regions relatively to non-border regions, over the past two decades. We find that,controlling for their size, proximity and location characteristics, border regions trade onaverage between 62% and 193% more with their neighbouring country than other regions,and twice as much if they are endowed with good cross border transport infrastructures.Despite European integration, however, this trade outperformance has fallen for the mostperipheral regions within the EU. We show that this trend was linked in part to a shift in the propensity of foreign investors to move their affiliates from the regions near their home market to the regions bordering the EU core.

Chemodiversity and molecular plasticity: recognition processes as explored by property spaces.

In the last few years, a need to account for molecular flexibility in drug-design methodologies has emerged, even if the dynamic behavior of molecular properties is seldom made explicit. For a flexible molecule, it is indeed possible to compute different values for a given conformation-dependent property and the ensemble of such values defines a property space that can be used to describe its molecular variability; a most representative case is the lipophilicity space. In this review, a number of applications of lipophilicity space and other property spaces are presented, showing that this concept can be fruitfully exploited: to investigate the constraints exerted by media of different levels of structural organization, to examine processes of molecular recognition and binding at an atomic level, to derive informative descriptors to be included in quantitative structure--activity relationships and to analyze protein simulations extracting the relevant information. Much molecular information is neglected in the descriptors used by medicinal chemists, while the concept of property space can fill this gap by accounting for the often-disregarded dynamic behavior of both small ligands and biomacromolecules. Property space also introduces some innovative concepts such as molecular sensitivity and plasticity, which appear best suited to explore the ability of a molecule to adapt itself to the environment variously modulating its property and conformational profiles. Globally, such concepts can enhance our understanding of biological phenomena providing fruitful descriptors in drug-design and pharmaceutical sciences.

Traces of functions in Fock spaces on lattices of critical density

Following a scheme of Levin we describe the values that functions in Fock spaces take on lattices of critical density in terms of both the size of the values and a cancelation condition that involves discrete versions of the Cauchy and Beurling-Ahlfors transforms.