Sustainability and long-term strategies in the modeling of biological processes

In this article, we intend to explore the role of using an”infinite time horizon” framework to address the issues of sustainability and long-term strategies in the control of biological processes. We use two case study models to explain why considering a fixed or moving endpoint does not lead to the desired long-term effects. The first biological model considered concerns the spread of an infectious disease and its treatment as an infinite horizon optimal control problem. The second one deals with the metronomic chemotherapy cancer treatment over the remaining lifetime horizon of the patient. The latter is consistent with the conception of cancer as a chronic disease. Both models show structural differences in the choice of the objective functional, the first one uses a stabilization functional containing a weight function, the second one contains a damage functional which involves a density function

The loyal dissident: N.A. Bernstein and the double-edged sword of Stalinism

Nikolai Aleksandrovich Bernstein (1896-1966) studied movement in order to understand the brain. Contra Pavlov, he saw movements (thus, the brain) as coordinated. For Bernstein, the cortex was a stochastic device; the more cortexes an animal species has, the more variable its actions will be. Actions are planned with a stochastic "model of the future," and relevance is established through blind mathematical search. In the 1950 neoPavlovian affair, he came under strong attack and had to stop experimenting. It is argued that the consistency of his work derived both from both dialectical materialism and the relentless attacks of the neoPavlovians. Copyright © Taylor & Francis Group, LLC

Duality theory for state-constrained control problems governed by a first order PDE system

In this paper we prove weak and strong duality results for optimal control problems with multiple integrals, first-order partial differential equations and state constraints. We formulate conditions under which the sequence of canonical variables [y^epsilon] in the [epsilon]-maximum principle, proved in Pickenhain and Wagner (2000), form a maximizing sequence in the dual problem

On the lower semicontinuity of functionals involving Lebesgue or improper Riemann integrals in infinite horizon optimal control problems

This paper deals with infinite horizon optimal control problems, which are formulated in weighted Sobolev spaces ... [wzór] and weighted Lp-spaces ... [wzór]. We ask for the consequences of the interpretation of the integral within the objective as a Lebesgue or an improper Riemann integral. In order to justify the use of both types of integrals, various applications of infinite horizon problems are presented. We provide examples showing that lower semicontinuity may fail for objectives involving Lebesgue as well as improper Riemann integrals. Further we prove a lower semicontinuity theorem for an objective with Lebesgue integral under more restrictive growth conditions on the integrand

Piecewise continuous controls in Dieudonne-Rashevsky type problems

SIGLEAvailable from TIB Hannover: RR 7760(2002,5) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman

Minimalfolgen in klassenbeschraenkten Depotproblemen (Neufassung)

Available from TIB Hannover: RR 7760(2001,2) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman