A pseudospectral method for budget-constrained infinite horizon optimal control problems

In this paper a generalization of the indirect pseudo-spectral method, presented in [17], for the numerical solution of budget-constrained infinite horizon optimal control problems is presented. Consideration of the problem statement in the framework of weighted functional spaces allows to arrive at a good approximation for the initial value of the adjoint variable, which is inevitable for obtaining good numerical solutions. The presented method is illustrated by applying it to the budget-constrained linear-quadratic regulator model. The quality of approximate solutions is demonstrated by an example

Quantum communication through a spin chain with interaction determined by a Jacobi matrix

We obtain the time-dependent correlation function describing the evolution of a single spin excitation state in a linear spin chain with isotropic nearest-neighbour XY coupling, where the Hamiltonian is related to the Jacobi matrix of a set of orthogonal polynomials. For the Krawtchouk polynomial case an arbitrary element of the correlation function is expressed in a simple closed form. Its asymptotic limit corresponds to the Jacobi matrix of the Charlier polynomial, and may be understood as a unitary evolution resulting from a Heisenberg group element. Correlation functions for Hamiltonians corresponding to Jacobi matrices for the Hahn, dual Hahn and Racah polynomials are also studied. For the Hahn polynomials we obtain the general correlation function, some of its special cases, and the limit related to the Meixner polynomials, where the su(1,1) algebra describes the underlying symmetry. For the cases of dual Hahn and Racah polynomials the general expressions of the correlation functions contain summations which are not of hypergeometric type. Simplifications, however, occur in special cases

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

Impact of strain on electronic defects in (Mg,Zn)O thin films

We have investigated the impact of strain on the incorporation and the properties of extended and point defects in (Mg,Zn)O thin films by means of photoluminescence, X-ray diffraction, deep-level transient spectroscopy (DLTS), and deep-level optical spectroscopy. The recombination line Y2, previously detected in ZnO thin films grown on an Al-doped ZnO buffer layer and attributed to tensile strain, was exclusively found in (Mg,Zn)O samples being under tensile strain and is absent in relaxed or compressively strained thin films. Furthermore a structural defect E3′ can be detected via DLTS measurements and is only incorporated in tensile strained samples. Finally it is shown that the omnipresent deep-level E3 in ZnO can only be optically recharged in relaxed ZnO samples

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