Strong solutions for stochastic porous media equations with jumps

We prove global well-posedness in the strong sense for stochastic generalized porous media equations driven by locally square integrable martingales with stationary independent increments.

Electronic compliance monitoring in resistant hypertension: the basis for rational therapeutic decisions.

OBJECTIVE: Incomplete compliance is one of several possible causes of uncontrolled hypertension. Yet, non-compliance remains largely unrecognized and is falsely interpreted as treatment resistance, because it is difficult to confirm or exclude objectively. The goal of this study was to evaluate the potential benefits of electronic monitoring of drug compliance in the management of patients with resistant hypertension. METHODS: Forty-one hypertensive patients resistant to a three-drug regimen (average blood pressure 156/ 106 +/- 23/11 mmHg, mean +/- SD) were studied prospectively. They were informed that for the next 2 months, their presently prescribed drugs would be provided in electronic monitors, without any change in treatment, so as to provide the treating physician with a measure of their compliance. Thereafter, patients were offered the possibility of prolonging the monitoring of compliance for another 2 month period, during which treatment was adapted if necessary. RESULTS: Monitoring of compliance alone was associated with a significant improvement of blood pressure at 2 months (145/97 +/- 20/15 mmHg, P < 0.01). During monitoring, blood pressure was normalized (systolic < 140 mmHg or diastolic < 90 mmHg) in one-third of the patients and insufficient compliance was unmasked in another 20%. When analysed according to tertiles of compliance, patients with the lowest compliance exhibited significantly higher achieved diastolic blood pressures (P = 0.04). In 30 patients, compliance was monitored up to 4 months and drug therapy was adapted whenever necessary. In these patients, a further significant decrease in blood pressure was obtained (from 150/100 +/- 18/15 to 143/94 +/- 22/11 mmHg, P = 0.04/0.02). CONCLUSIONS: These results suggest that objective monitoring of compliance using electronic devices may be a useful step in the management of patients with refractory hypertension, as it enables physicians to take rational decisions based on reliable and objective data of drug compliance and hence to improve blood pressure control.

A Model of Near-Rational Exuberance

We study how the use of judgement or “add-factors” in forecasting may disturb the set of equilibrium outcomes when agents learn using recursive methods. We isolate conditions under which new phenomena, which we call exuberance equilibria, can exist in a standard self-referential environment. Local indeterminacy is not a requirement for existence. We construct a simple asset pricing example and find that exuberance equilibria, when they exist, can be extremely volatile relative to fundamental equilibria.

Does Ricardian Equivalence Hold When Expectations are not Rational?

This paper considers the Ricardian Equivalence proposition when expectations are not rational and are instead formed using adaptive learning rules. We show that Ricardian Equivalence continues to hold provided suitable additional conditions on learning dynamics are satisfied. However, new cases of failure can also emerge under learning. In particular, for Ricardian Equivalence to obtain, agents’ expectations must not depend on government’s financial variables under deficit financing.

Rational Expectations Dynamics: A Methodological Critique

This paper analyses RE macromodels from the methodological perspective. It proposes a particular property, robustness, which should be considered a necessary feature of scienti cally valid models in economics, but which is absent from many RE macromodels. To restore this property many macroeconomists resort to detailed and implausible assumptions, which take their models a long way from simple Rational Expectations. The paper draws attention to the problems inherent in the technique of local linearisation and concludes by proposing the use of nonlinear models, analysed globally.

Positive solutions of nonlinear problems involving the square root of the Laplacian

We consider nonlinear elliptic problems involving a nonlocal operator: the square root of the Laplacian in a bounded domain with zero Dirichlet boundary conditions. For positive solutions to problems with power nonlinearities, we establish existence and regularity results, as well as a priori estimates of Gidas-Spruck type. In addition, among other results, we prove a symmetry theorem of Gidas-Ni-Nirenberg type.

The rational search for natural neolignans

A rational method of search for natural neolignans of desired structures is outlined. This involves consultation of a collection of chemical profiles of plant families. The profiles are assembled considering the biosynthetic class (in the present case lignoids), subclass (neolignans), structural types (neolignan skeleta) and relative frequency of substitutional derivatives belonging to each type (known compounds). The method is of course applicable to ani class of natural products. Its use in the case of neolignans is here selected as an exemple in view of the recently discovered antagonism towards PAF of kadsurenone, a representative of this subclass of phytochemicals. Application of the chemical profiles to phylogenetic studies is illustrated.

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.