Contractive metrics for a Boltzmann equation for granular gases: diffusive equilibriaThe Patterson-Sullivan embedding and minimal volume entropy for outer space

We quantify the long-time behavior of a system of (partially) inelastic particles in a stochastic thermostat by means of the contractivity of a suitable metric in the set of probability measures. Existence, uniqueness, boundedness of moments and regularity of a steady state are derived from this basic property. The solutions of the kinetic model are proved to converge exponentially as t→ ∞ to this diffusive equilibrium in this distance metrizing the weak convergence of measures. Then, we prove a uniform bound in time on Sobolev norms of the solution, provided the initial data has a finite norm in the corresponding Sobolev space. These results are then combined, using interpolation inequalities, to obtain exponential convergence to the diffusive equilibrium in the strong L¹-norm, as well as various Sobolev norms.

The Patterson-Sullivan embedding and minimal volume entropy for outer space

"Vegeu el resum a l'inici del document del fitxer adjunt."

Metrics on diagram groups and uniform embeddings in a Hilbert space

"Vegeu el resum a l'inici del document del fitxer adjunt".

An ordinal shapley value for economic environments

We propose a new solution concept to address the problem of sharing a surplus among the agents generating it. The sharing problem is formulated in the preferences-endowments space. The solution is defined in a recursive manner incorporating notions of consistency and fairness and relying on properties satisfied by the Shapley value for Transferable Utility (TU) games. We show a solution exists, and refer to it as an Ordinal Shapley value (OSV). The OSV associates with each problem an allocation as well as a matrix of concessions ``measuring'' the gains each agent foregoes in favor of the other agents. We analyze the structure of the concessions, and show they are unique and symmetric. Next we characterize the OSV using the notion of coalitional dividends, and furthermore show it is monotone in an agent's initial endowments and satisfies anonymity. Finally, similarly to the weighted Shapley value for TU games, we construct a weighted OSV as well.

Infinite time aggregation for the critical Patlak-Keller-Segel model in R2

We analyze the two-dimensional parabolic-elliptic Patlak-Keller-Segel model in the whole Euclidean space R2. Under the hypotheses of integrable initial data with finite second moment and entropy, we first show local in time existence for any mass of "free-energy solutions", namely weak solutions with some free energy estimates. We also prove that the solution exists as long as the entropy is controlled from above. The main result of the paper is to show the global existence of free-energy solutions with initial data as before for the critical mass 8 Π/Χ. Actually, we prove that solutions blow-up as a delta dirac at the center of mass when t→∞ keeping constant their second moment at any time. Furthermore, all moments larger than 2 blow-up as t→∞ if initially bounded.

Data size sufficiency analyses of haplotype inference algortihms

We present experimental and theoretical analyses of data requirements for haplotype inference algorithms. Our experiments include a broad range of problem sizes under two standard models of tree distribution and were designed to yield statistically robust results despite the size of the sample space. Our results validate Gusfield's conjecture that a population size of n log n is required to give (with high probability) sufficient information to deduce the n haplotypes and their complete evolutionary history. The experimental results inspired our experimental finding with theoretical bounds on the population size. We also analyze the population size required to deduce some fixed fraction of the evolutionary history of a set of n haplotypes and establish linear bounds on the required sample size. These linear bounds are also shown theoretically.

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.

Label Space Reduction in All-Optical Label Switchiing Networks

Report for the scientific sojourn at the Department of Information Technology (INTEC) at the Ghent University, Belgium, from january to june 2007. All-Optical Label Swapping (AOLS) forms a key technology towards the implementation of All-Optical Packet Switching nodes (AOPS) for the future optical Internet. The capital expenditures of the deployment of AOLS increases with the size of the label spaces (i.e. the number of used labels), since a special optical device is needed for each recognized label on every node. Label space sizes are affected by the wayin which demands are routed. For instance, while shortest-path routing leads to the usage of fewer labels but high link utilization, minimum interference routing leads to the opposite. This project studies and proposes All-Optical Label Stacking (AOLStack), which is an extension of the AOLS architecture. AOLStack aims at reducing label spaces while easing the compromise with link utilization. In this project, an Integer Lineal Program is proposed with the objective of analyzing the softening of the aforementioned trade-off due to AOLStack. Furthermore, a heuristic aiming at finding good solutions in polynomial-time is proposed as well. Simulation results show that AOLStack either a) reduces the label spaces with a low increase in the link utilization or, similarly, b) uses better the residual bandwidth to decrease the number of labels even more.

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.

Agglomeration and inequality across space: what can we learn from the European experience?

The purpose of this contribution is to draw a picture of the (uneven) distribution of economic activities across the states of the European Union (EU) and the consequences entailed by it. We will briefly summarize the most salient and recent contributions. Then, in the light of the economic geography theory, we will discuss the economic and social advantages and disadvantages associated with a core- periphery structure. In this sense, particular attention will be addressed to the EU financial system of Structural Funds and the effects they produced. Finally, we will formulate some suggestions, relying on the EU experience, that could be of interest to the current Brazilian regional policy.

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.

Social capital formation across space: proximity and trust in European regions

An extensive economics and regional science literature has discussed the importance of social capital for economic growth and development. Yet, what social capital is and how it is formed are elusive issues, which require further investigation. Here, we refer to social capital in terms of civic capital and good culture , as rephrased by Guiso, Sapienza and Zingales (2010) and Tabellini (2010). The accumulation of this kind of capital allows the emerging of regional informal institutions, which may help explaining diff erences in regional development. In this paper, we take a regional perspective and use exploratory space and space-time methods to assess whether geography, via proximity, contributes to the formation of social capital across European regions. In particular, we ask whether generalized trust, a fundamental constituent of social capital and an ingredient of economic development, tends to be clustered across space and over time. From the policy standpoint, the spatial hysteresis of regional trust may contribute to the formation of spatial traps of social capital and act as a further barrier to regional economic development and convergence.

Noncooperative Oligopoly in Markets with a Continuum of Traders: A Limit Theorem µa la Cournot

In this paper, we consider an exchange economy µa la Shitovitz (1973), with atoms and an atomless set. We associate with it a strategic market game of the kind first proposed by Lloyd S. Shapley and known as the Shapley window model. We analyze the relationship between the set of the Cournot-Nash equilibrium allocations of the strategic market game and the Walras equilibrium allocations of the exchange economy with which it is associated. We show, with an example, that even when atoms are countably in¯nite, any Cournot-Nash equilibrium allocation of the game is not a Walras equilibrium of the underlying exchange economy. Accordingly, in the original spirit of Cournot (1838), we par- tially replicate the mixed exchange economy by increasing the number of atoms, without a®ecting the atomless part, and ensuring that the measure space of agents remains finite. We show that any sequence of Cournot-Nash equilibrium allocations of the strategic market games associated with the partially replicated exchange economies approximates a Walras equilibrium allocation of the original exchange economy.