Kuno Huisman: Decision Making Under Uncertainty
In this talk I start with sketching the situation where ASML is in. The highly volatile semiconductor market, producing lithography equipment in a market with three players: ASML, Nikon, and Canon. I will explain how the decision support department facilitates decision making under uncertainty by using the decision dialogue process. Next I want to explain a little more about the mathematical tools that are used in that process, such as determenistic analysis (discounted cash flow and sensitivity analysis) and stochastic analysis (monte carlo simulation, decision trees, real options analysis). Lastly I will focus a little more on real options analysis as that is my academic speciality.
Fahima Nekka: Information-loaded Formalism to Assess the Causal Effect of Drug Intake on Therapeutic Outcomes
The determination of an optimal dosing regimen is a critical step to enhance the drug efficacy and avoid toxicity. Rational dosing recommendations based on mathematical considerations are increasingly being adopted in the process of drug development and use. In this work, we propose a quantitative approach to evaluate the efficacy of antibiotic agents. By integrating both pharmacokinetic (PK) and pharmacodynamic (PD) information, this approach gives rise to a unified formalism able to measure the cause-effect of dosing regimens. This new pharmaco-metric allows covering a whole range of antibiotics, including the two well known concentration and time dependent classes, through the introduction of the Hill-dependency concept. As a direct fallout, our formalism opens a new path towards the bioequivalence evaluation in terms of PK and PD, which associates the in vivo drug concentration and the in vitro drug effect. Using this new approach, we succeeded to reveal unexpected, but relevant behaviours of drug performance when different drug regimens and drug classes are considered. Of particular notice, we found that the doses required to reach the same therapeutic effect, when scheduled differently, exhibit completely different tendencies for concentration and time dependent drugs. Moreover, we theoretically confirmed the previous experimental results of the superiority of the once daily regimen of aminoglycosides. The proposed methodology is appealing for its computational features and can easily be applicable to design fair clinical protocols or rationalize prescription decisions.
Carsten Othmer: Adjoint Methods for Car Aerodynamics
The adjoint method has long been considered as the tool of choice for gradient-based optimisation in computational fluid dynamics (CFD). It is the independence of the computational cost from the number of design variables that makes it particularly attractive for problems with large design spaces. Originally developed by Lions and Pironneau in the 70′s, the adjoint method has therefore evolved towards a standard tool within the development processes of the aeronautical industries. Its uptake in the automotive industry, however, lags behind. The first systematic applications of adjoint methods in automotive CFD are interestingly not in the classical shape design arena, but in a relatively young discipline of sensitivity-based optimisation: fluid dynamic topology optimisation. While being an established concept in structure mechanics for decades already, its transfer to fluid dynamics took place as late as 2003 [Borrvall and Petersson, Klimetzek et al.]. Specifically for ducted flow applications, like airducts for cabin ventilation or engine intake ports, it constitutes a very powerful tool and has matured over the last years to a level that allowed its systematic usage for various automotive applications, some of which will be presented in the talk. To drive adjoint-based shape optimisation to the same degree of maturity and robustness for car applications is the subject of ongoing research collaborations between academia, software vendors and the car industry. The achievements and challenges encountered on this strive will be addressed in the talk.
Svetozar Margenov: Robust multilevel methods for strongly heterogeneous anisotropic problems and simulations in porous media
The first part of the talk is devoted to construction and analysis of Algebraic MultiLevel Iteration (AMLI) methods in the case of coefficient jumps which are aligned with the interfaces of the initial mesh. The condition number estimates are uniform with respect to both mesh and/or coefficient anisotropy, the coefficient jumps, as well as the size of the discrete problem. The computational complexity is proportional to the number of degrees of freedom. The presented theoretical results are in the spirit of the monograph: J. Kraus, S. Margenov, Robust Algebraic Multilevel Methods and Algorithms, Radon Series on Computational and Applied Mathematics, 5, de Gruyter, 2009.
Three applications related to computer simulations in porous media are discussed in the second part: a) problems of high-frequency and high contrast; b) voxel analysis of bone microstructure; c) simulation of radio-frequency hepatic tumor ablation. They demonstrate both, robust discretizations and robust multilevel solution methods and algorithms. Some of the problems have coefficient jumps which are not aligned with the interfaces of the initial mesh. Complex microstructures obtained from high resolution computer tomography are studied. For such problems, some advantages of nonconforming finite elements are discussed. The numerical tests include supercomputing simulations on IBM Blue Gene/P.
Nicole Marheineke: Stochastic production processes of technical textiles – mathematical model-chain for optimal design
Technical textiles, especially nonwoven materials find their application in various branches of industry, e.g. in textile, hygiene, automobile and building industry. Typical products are clothing textiles, baby diapers, oil/water filters, sound proofing, etc. Depending on their use, the textiles have to satisfy certain properties. A long-term objective in industry is the optimal design of the production process with respect to the desired product specification. Hence, it is necessary to model, simulate and control the manufacturing. Differing in details, the processes have in principle four things in common: melting, spinning, entanglement and lay-down. The individual fibers are obtained by a continuous extrusion of a molten granular through narrow nozzles. Then, they are stretched and entangled by acting turbulent air flows to form a three-dimensional texture, while laying down onto a moving conveyor belt. The production process might be considered as a multiphase problem, i.e. visco-elastic polymer in interaction with a turbulent air flow in a highly complex geometry of a machine. A monolithic numerical treatment of this multiscale problem is impossible because of the enormous computational effort.
Therefore, we developed a mathematical chain of appropriate models for single aspects (asymptotic and computational models as well as stochastic surrogates). The models are coupled via perturbation theory, similarity estimates and parameter identification. The simulation results demonstrate not only the practical relevance and applicability, in fact the presented methodology is already successfully used for improving the design of industrial processes.
Alistair Fitt: Modelling of Disease and Medical Procedures in the Human Eye
In the past 10 years mathematics has been used by a range of authors to study diseases and medical procedures in the human eye. This development mirrors other branches of medicine and biology, where it is increasingly becoming understood that mathematical modelling constitutes a key tool in helping to both explain and optimize procedures, diseases and diagnoses. In this talk I will illustrate some of the progress that has been made in understanding both how the eye works, and what might be happening when things go wrong and an individual’s sight is threatened: I will also give some examples of problems that have been investigated by mathematicians, but are still not satisfactorily resolved.
Matti Heiliö: Charm and Impact. Is there something like pedagogy for industrial mathematics?
The early years of ECMI were driven by an educational mission. Applied mathematics education should respond to the challenges of modern technology agenda and a changing world. Room for development was recognized at curriculum level and in the ways of interaction between research, education and applications. In this talk I will discuss some features and changes in the educational scene in the past 25 years and their reflections on university pedagogy for real world oriented applied mathematics. A prevailing challenge is the general awareness about mathematics and the ability to get the new generation fascinated about it. We should show to the students the beauty and “charm of theorems” and at the same time teach the practical tool-value and real world impact, as for instance the role of mathematics in sustainability issues. I will refer to Alan Tayler’s pathfinding role as an educator. I will also give a somewhat personal story how I was drawn into the germination phase of ECMI and I will report how the 25 years of in the network have been an inspiration-factor in building our own department.