Guaranteed Inertia Functions in Dynamical Games.

This paper deals with inertia functions in control theory introduced in Aubin, Bernardo and Saint-Pierre (2004, 2005) and their adaptation to dynamical games. The inertia function associates with any initial state-control pair the smallest of the worst norms over time of the velocities of the controls regulating viable evolutions. For tychastic systems (parameterized systems where the parameters are tyches, disturbances, perturbations, etc.), the palicinesia of a tyche measure the worst norm over time of the velocities of the tyches. The palicinesia function is the largest palicinesia threshold c such that all evolutions with palicinesia smaller than or equal to c are viable. For dynamical games where one parameter is the control and the other one is a tyche (games against nature or robust control), we define the guaranteed inertia function associated with any initial state-control-tyche triple the best of the worst of the norms of the velocities of the controls and of the tyches and study their properties. Viability Characterizations and Hamilton-Jacobi equations of which these inertia and palicinesia functions are solutions are provided.Viability; dynamical games; inertia function; Tychastic systems; palicinesia;

Dynamic Management of Portfolios with Transaction Costs under Tychastic Uncertainty.

We use in this chapter the viability/capturability approach for studying the problem of dynamic valuation and management of a portfolio with transaction costs in the framework of tychastic control systems (or dynamical games against nature) instead of stochastic control systems. Indeed, the very definition of the guaranteed valuation set can be formulated directly in terms of guaranteed viable-capture basin of a dynamical game. Hence, we shall “compute” the guaranteed viable-capture basin and find a formula for the valuation function involving an underlying criterion, use the tangential properties of such basins for proving that the valuation function is a solution to Hamilton-Jacobi-Isaacs partial differential equations. We then derive a dynamical feedback providing an adjustment law regulating the evolution of the portfolios obeying viability constraints until it achieves the given objective in finite time. We shall show that the Pujal—Saint-Pierre viability/capturability algorithm applied to this specific case provides both the valuation function and the associated portfolios.dynamic games; dynamic valuation; tychastic control systems; management of portfolio;

The method of characteristics revisited. A viability approach

This mini-course provides a presentation of the method of characteristics to initial/boundary-value problems for systems of first-order partial differential equations and to Hamilton-Jacobi variational inequalities. In particular, these results are indeed useful for the treatment of hybrid systems of control theory. We rely on tools forged by set-valued analysis and viability theory, which happen to be both efficient and versatile to cover many problems. They find here unexpected relevance

Viabilist and Tychastic Approaches to Guaranteed ALM Problem.

This study reconsiders the problem of hedging a liability by a portfolio made of a riskless asset and an underlying (underlying).Asset and Liability Management; Viability theory;

A Seizure Attributed to Ofloxacine in a Woman Undergoing Detoxification for Alcohol Dependence

Objective. To report one case of seizure following administration of ofloxacin. Case Summary. A 38-year-old woman with alcohol dependence but no prior history of seizure disorder admitted in our inpatient alcohol detoxification program was prescribed ofloxacin four days after admission for a lower urinary tract infection. She was currently prescribed diazepam 30 mg per day. This treatment was continued without modification following admission. Forty eight hours after starting ofloxacin and after receiving five doses of oral ofloxacin, the patient experienced a seizure. Ofloxacin treatment was stopped and no further seizures occurred. Neurological examination of the patient, laboratory tests, computerized tomography with contrast enhancement and electroencephalography did not detect any abnormalities. Up to the last consultation, six months after admission, the patient has reported no recurrence of the seizure. Discussion. Quinolone antibiotics vary in their ability to induce seizures, with ofloxacin having one of the least potentials. In the present case, the seizure could be attributed in all probability to taking ofloxacin; since she had no previous history of seizures, she did not present an alcohol withdrawal syndrome, benzodiazepine treatment was not modified, the seizure occurred 48 h after taking ofloxacin, but seven days after stopping drinking, no alternative aetiologies for the seizure could be identified and no seizure recurrence was reported over the following seven months. Of reported cases of seizures in patients treated with fluoroquinolones, none concerned patients with alcohol dependence or patients treated with benzodiazepines. Conclusions. The present case alerts us to the possibility that seizures may occur in alcohol dependent patients treated with benzodiazepines who concomitantly prescribed a fluoroquinolone. These widely-used antibiotics should thus be prescribed with caution to patients undergoing detoxification for alcohol dependence, particularly if they are also taking benzodiazepines, irrespective of whether they have a previous history of seizures or not

Ecosystem service framework and typology for an ecosystem approach to aquaculture

International audienceThe ecosystem approach to aquaculture (EAA) considers ecosystem services (ES) important but does not provide a conceptual framework or a typology to integrate and assess them. To supplement the EAA, a literature review of the ES conceptual framework and ES typologies was combined with selected criteria from the EAA and ES literature. Eight criteria of transition from a conventional approach to aquaculture to the EAA were used as selection criteria to choose a conceptual framework of ES relevant with the EAA. To select a typology, we determined that ES must be distinguished from benefits, be a part of nature, be usable directly and indirectly, and not contain support or habitat ES. The conceptual framework of the Intergovernmental Science-Policy Platform on Biodiversity and Ecosystem Services (IPBES) is the most compatible with the EAA but does not provide an ES typology. The Common International Classification of Ecosystem Services (CICES) provides the ES typology most consistent with EAA criteria to supplement the conceptual framework. We identified 10 provisioning ES, 20 regulation and maintenance ES, and 11 cultural ES. Integration of the IPBES conceptual framework with the CICES typology preserves the generic approach of the EAA. This integration could highlight the main interactions among an aquaecosystem, its ES supply, its management, and its relevant stakeholders at multiple spatial and temporal scales. Moreover, it fulfils the three main goals of the EAA by identifying them in a clear and common framework