International Institutions as Solutions to Underlying Games of Cooperation

This Working Paper was presented at the international workshop "Game Theory in International Relations at 50", organized and coordinated by Professor Jacint Jordana and Dr. Yannis Karagiannis at the Institut Barcelona d'Estudis Internacionals on May 22, 2009. The day-long Workshop was inspired by the desire to honour the ground-breaking work of Professor Thomas Schelling in 1959-1960, and to understand where the discipline International Relations lies today vis-à-vis game theory.

A numerical algorithm for finding solutions of a generalized Nash equilibrium problem

A family of nonempty closed convex sets is built by using the data of the Generalized Nash equilibrium problem (GNEP). The sets are selected iteratively such that the intersection of the selected sets contains solutions of the GNEP. The algorithm introduced by Iusem-Sosa (2003) is adapted to obtain solutions of the GNEP. Finally some numerical experiments are given to illustrate the numerical behavior of the algorithm.

Resurgence of inner solutions for perturbations of the McMillan map

A sequence of “inner equations” attached to certain perturbations of the McMillan map was considered in [MSS09], their solutions were used in that article to measure an exponentially small separatrix splitting. We prove here all the results relative to these equations which are necessary to complete the proof of the main result of [MSS09]. The present work relies on ideas from resurgence theory: we describe the formal solutions, study the analyticity of their Borel transforms and use ´Ecalle’s alien derivations to measure the discrepancy between different Borel-Laplace sums.

On Cooperative solutions of a generalized assignment game: limit theorems to the set of competitive equilibria

We study two cooperative solutions of a market with indivisible goods modeled as a generalized assignment game: Set-wise stability and Core. We first establish that the Set-wise stable set is contained in the Core and it contains the non-empty set of competitive equilibrium payoffs. We then state and prove three limit results for replicated markets. First, the sequence of Cores of replicated markets converges to the set of competitive equilibrium payoffs when the number of replicas tends to infinity. Second, the Set-wise stable set of a two-fold replicated market already coincides with the set of competitive equilibrium payoffs. Third, for any number of replicas there is a market with a Core payoff that is not a competitive equilibrium payoff.

A numerical solver for a nonlinear Fokker-Planck equation representation of neuronal network dynamics

To describe the collective behavior of large ensembles of neurons in neuronal network, a kinetic theory description was developed in [13, 12], where a macroscopic representation of the network dynamics was directly derived from the microscopic dynamics of individual neurons, which are modeled by conductance-based, linear, integrate-and-fire point neurons. A diffusion approximation then led to a nonlinear Fokker-Planck equation for the probability density function of neuronal membrane potentials and synaptic conductances. In this work, we propose a deterministic numerical scheme for a Fokker-Planck model of an excitatory-only network. Our numerical solver allows us to obtain the time evolution of probability distribution functions, and thus, the evolution of all possible macroscopic quantities that are given by suitable moments of the probability density function. We show that this deterministic scheme is capable of capturing the bistability of stationary states observed in Monte Carlo simulations. Moreover, the transient behavior of the firing rates computed from the Fokker-Planck equation is analyzed in this bistable situation, where a bifurcation scenario, of asynchronous convergence towards stationary states, periodic synchronous solutions or damped oscillatory convergence towards stationary states, can be uncovered by increasing the strength of the excitatory coupling. Finally, the computation of moments of the probability distribution allows us to validate the applicability of a moment closure assumption used in [13] to further simplify the kinetic theory.

A one-dimensional Keller-Segel equation with a drift issued from the boundary

We investigate in this note the dynamics of a one-dimensional Keller-Segel type model on the half-line. On the contrary to the classical configuration, the chemical production term is located on the boundary. We prove, under suitable assumptions, the following dichotomy which is reminiscent of the two-dimensional Keller-Segel system. Solutions are global if the mass is below the critical mass, they blow-up in finite time above the critical mass, and they converge to some equilibrium at the critical mass. Entropy techniques are presented which aim at providing quantitative convergence results for the subcritical case. This note is completed with a brief introduction to a more realistic model (still one-dimensional).

Using a NPWE model observer to assess suitable image quality for a digital mammography quality assurance programme.

A method of objectively determining imaging performance for a mammography quality assurance programme for digital systems was developed. The method is based on the assessment of the visibility of a spherical microcalcification of 0.2 mm using a quasi-ideal observer model. It requires the assessment of the spatial resolution (modulation transfer function) and the noise power spectra of the systems. The contrast is measured using a 0.2-mm thick Al sheet and Polymethylmethacrylate (PMMA) blocks. The minimal image quality was defined as that giving a target contrast-to-noise ratio (CNR) of 5.4. Several evaluations of this objective method for evaluating image quality in mammography quality assurance programmes have been considered on computed radiography (CR) and digital radiography (DR) mammography systems. The measurement gives a threshold CNR necessary to reach the minimum standard image quality required with regards to the visibility of a 0.2-mm microcalcification. This method may replace the CDMAM image evaluation and simplify the threshold contrast visibility test used in mammography quality.

Paclitaxel-eluting biodegradable synthetic vascular prostheses: a step towards reduction of neointima formation?

BACKGROUND: Clinical small-caliber vascular prostheses are unsatisfactory. Reasons for failure are early thrombosis and late intimal hyperplasia. We thus prepared biodegradable small-caliber vascular prostheses using electrospun polycaprolactone (PCL) with slow-releasing paclitaxel (PTX), an antiproliferative drug. METHODS AND RESULTS: PCL solutions containing PTX were used to prepare nonwoven nanofibre-based 2-mm ID prostheses. Mechanical morphological properties and drug loading, distribution, and release were studied in vitro. Infrarenal abdominal aortic replacement was carried out with nondrug-loaded and drug-loaded prostheses in 18 rats and followed for 6 months. Patency, stenosis, tissue reaction, and drug effect on endothelialization, vascular remodeling, and neointima formation were studied in vivo. In vitro prostheses showed controlled morphology mimicking extracellular matrix with mechanical properties similar to those of native vessels. PTX-loaded grafts with suitable mechanical properties and controlled drug-release were obtained by factorial design. In vivo, both groups showed 100% patency, no stenosis, and no aneurysmal dilatation. Endothelial coverage and cell ingrowth were significantly reduced at 3 weeks and delayed at 12 and 24 weeks in PTX grafts, but as envisioned, neointima formation was significantly reduced in these grafts at 12 weeks and delayed at 6 months. CONCLUSIONS: Biodegradable, electrospun, nanofibre, polycaprolactone prostheses are promising because in vitro they maintain their mechanical properties (regardless of PTX loading), and in vivo show good patency, reendothelialize, and remodel with autologous cells. PTX loading delays endothelialization and cellular ingrowth. Conversely, it reduces neointima formation until the end point of our study and thus may be an interesting option for small caliber vascular grafts.

On stability of solutions to systems of convex inequalities

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

Some solutions to obtain very efficient separations in isocratic and gradient modes using small particles size and ultra-high pressure.

The UHPLC strategy which combines sub-2 microm porous particles and ultra-high pressure (>1000 bar) was investigated considering very high resolution criteria in both isocratic and gradient modes, with mobile phase temperatures between 30 and 90 degrees C. In isocratic mode, experimental conditions to reach the maximal efficiency were determined using the kinetic plot representation for DeltaP(max)=1000 bar. It has been first confirmed that the molecular weight of the compounds (MW) was a critical parameter which should be considered in the construction of such curves. With a MW around 1000 g mol(-1), efficiencies as high as 300,000 plates could be theoretically attained using UHPLC at 30 degrees C. By limiting the column length to 450 mm, the maximal plate count was around 100,000. In gradient mode, the longest column does not provide the maximal peak capacity for a given analysis time in UHPLC. This was attributed to the fact that peak capacity is not only related to the plate number but also to column dead time. Therefore, a compromise should be found and a 150 mm column should be preferentially selected for gradient lengths up to 60 min at 30 degrees C, while the columns coupled in series (3x 150 mm) were attractive only for t(grad)>250 min. Compared to 30 degrees C, peak capacities were increased by about 20-30% for a constant gradient length at 90 degrees C and gradient time decreased by 2-fold for an identical peak capacity.

Extensional flow of nematic liquid crystal under electric field gradient

Systematic asymptotic methods are used to formulate a model for the extensional flow of a thin sheet of nematic liquid crystal. With no external body forces applied, the model is found to be equivalent to the so-called Trouton model for Newtonian sheets (and fi bers), albeit with a modi fied "Trouton ratio". However, with a symmetry-breaking electric field gradient applied, behavior deviates from the Newtonian case, and the sheet can undergo fi nite-time breakup if a suitable destabilizing field is applied. Some simple exact solutions are presented to illustrate the results in certain idealized limits, as well as sample numerical results to the full model equations.

In-situ revascularisation for secondary aorto-enteric fistulae: the success of silver-coated Dacron is closely linked to a suitable bowel repair.

OBJECTIVES: The purpose of this study was to assess short- and mid-term results of in-situ revascularisation (ISR) using silver-coated Dacron prostheses and bowel repair for management of secondary aorto-enteric fistulae (SAEF). DESIGN: Single-centre retrospective chart review. MATERIAL AND METHODS: This study includes all the patients treated by ISR using silver-coated Dacron for SAEF between 2006 and 2010. Primary end points were mortality and survival rates. Secondary end points were reinfection-free survival and secondary patency rates. RESULTS: Eighteen male patients with SAEF with a median age of 64 years were operated by ISR using silver-coated Dacron during the study period without operative death. The 30-day mortality was 22% and the in-hospital mortality rate was 39%. Indeed, during hospitalisation, a duodenal leak was observed in four patients including three who died. Four others patients died due to multi-system organ failure. Median follow-up was 16 months (range 1-66). The survival rate at 12 months was 55%. One duodenal leak was observed leading to death. The reinfection-free survival and the secondary patency rates at 12 months were 60% and 89%, respectively. CONCLUSION: In-situ revascularisation with silver-coated Dacron provides acceptable results in terms of mortality. This treatment may be useful for simple vascular reconstruction and allow greater attention to bowel repair that is a determinant in short- and mid-term survival.