A Numerical Slow Manifold Approach to Model Reduction for Optimal Control of Multiple Time Scale ODE

Time scale separation is a natural property of many control systems that can be ex- ploited, theoretically and numerically. We present a numerical scheme to solve optimal control problems with considerable time scale separation that is based on a model reduction approach that does not need the system to be explicitly stated in singularly perturbed form. We present examples that highlight the advantages and disadvantages of the method

A numerical approach to model reduction for optimal control of multiscale ODE

The topic of this thesis is model (order) reduction in the context of numerical optimal control. Complex mathematical models based on ordinary differential equations can often be reduced in order to decrease computational complexity and enable their use in control algorithms. A feature that can be exploited for the purpose of model reduction is time scale separation, which means that the system dynamics are comprised of fast and slow processes. Fast states relax to a slow invariant manifold in the state space, which is parametrized by the slow states. This manifold is approximated numerically and the fast species can be eliminated from the full model and thus also from the optimal control problem. To this end multivariate interpolation based on radial basis functions is used and compared with an online approach that solves the model reduction problem ad hoc. Singular perturbation theory is employed to illustrate the theoretical background and illustrate how reduced models influence the solution of the optimal control problem. It is shown via numerical experiments that the application of the model reduction techniques can lead to significant savings in computation time without compromising the quality of the optimal control solution

The prognostic value of serum methotrexate area under curve in elderly primary CNS lymphoma patients

Studies on pharmacokinetics and pharmacodynamics of high-dose methotrexate chemotherapy (HD-MTX) in elderly primary central nervous system lymphoma (PCNSL) patients are rare. MTX exposure time has recently been proposed as an outcome determining factor in PCNSL. We investigated 49 immunocompetent PCNSL patients (female N=30, male N=19, median age 73 years) who were treated according to HD-MTX-based protocols. A two-compartment pharmacokinetic model was used to describe the MTX clearance. Response to treatment was assessed by MRI. We used multivariable models to investigate the association between MTX exposure and tumor response as well as survival. Dose normalized MTX peak serum levels [C (max), μmol/L g] and dose normalized area under the curve [AUC(dn), μmol h/L g] were higher in females than in males, respectively [59.4 (f) vs. 48.1 (m), P<0.001; 373.2 (f) vs. 271.9 (m), P=0.008]. Increasing AUC was inversely correlated with tumor response. AUC values above 2,126 h μmol/L were independently associated with shorter overall and progression-free survival [hazard ratio (HR), 4.56, 95 % CI 1.74-11.94; HR 2.87, 95 % CI 1.18-7.00]. Exceedingly high MTX AUC levels can have a negative impact on progression-free and overall survivals in elderly PCNSL patients

Unbuffered and buffered supply chains in human metabolism

The investigation of very complex dynamical systems like the human metabolism requires the comprehension of important subsystems. The present paper deals with energy supply chains as subsystems of the metabolism on the molecular, cellular, and individual levels. We form a mathematical model of ordinary differential equations and we show fundamental properties by Fourier techniques. The results are supported by a transition from a system of ordinary differential equations to a partial differential equation, namely, a transport equation. In particular, the behavior of supply chains with dominant pull components is discussed. A special focus lies on the role of buffer compartments

History of the Book in Canada. Volume III : 1918-1980

"The History of the Book in Canada is one of this country's great scholarly achievements, with three volumes spanning topics from Aboriginal communication systems established prior to European contact to the arrival of multinational publishing companies. Each volume observes developments in the realms of writing, publishing, dissemination, and reading, illustrating the process of a fledgling nation coming into its own. The third and final volume follows book history and print culture from the end of the First World War to 1980, discussing the influences on them of the twentieth century, including the country's growing demographic complexity and the rise of multiculturalism." -- Front flap of jacket