# Alois Grimbach

After a degree in electrical engineering and several years of professional experience in computer networks, I learnt about the CSiS master’s programme in Wuppertal. That gave me the chance to reanimate my latent interests in particle physics and cosmology, hence being able to both gaining interdisciplinary knowledge and performing an appealing thesis in computer simulation in physics.

During my CSiS studies in Wuppertal, I was warmly supported by all participating lecturers and professors and the work in small groups caused an efficient increase of new knowledge. I appreciated the lab courses which contained some theory and then demonstrated numerical applications in various fields. After all, CSiS was much work but the benefit was a solid education in both computer and natural sciences.

The topic of my thesis fell into the theoretical particle physics track which, although prepared by a tutored course in lattice gauge theory, was very challenging to me. But at the end, it even lead to a publication in the journal of High Energy Physics on the Lattice in cooperation with Prof. Knechtli and other scientists from CERN and DESY.

Here’s a trial to sum up the idea of the thesis: In Lattice QCD, the space-time continuum is discretised on a 4-dimensional Euclidean hypercubic lattice. Both gauge and fermion actions are computed on the lattice and reproduce the Yang-Mills theory in the continuum limit. Some non-physical effects emerge on the lattice and need to be eliminated by numerical counterterms. Those can be won by examining symmetries; merely the according coefficients have to be determined to achieve the desired improvement. My thesis aimed at determining the improvement coefficient for the static-light axial current, being induced by a meson consisting of a light and a static quark. That happened at one-loop order perturbation theory, especially under consideration of HYP smeared actions, a technique which originally had been introduced by Prof. Knechtli.

Clearly, I had to delve into deep theory to bring together the main concepts and Prof. Knechtli was patient enough to answer my many questions, also about the basics. Besides learning the principles of lattice gauge theory, I needed to review the calculation of the involved Feynman diagrams and to understand the herein applied tools and methodologies. Based on an already existing C++ program package and with the support of the participating scientists, I could calculate and extend the Feynman diagrams to the smeared action. Finally, the improvement coefficient could be extracted as depicted in the pictures.

The final presentation about my thesis can be found here. The thesis itself is available under Theses (see left menu)

Although I did not pursue an initially intended Phd in particle physics afterwards, I was able to move into a new job within interdisciplinary research projects in the fields of informatics and physics, with a strong emphasis on software development. I found my studies in CSiS highly worthwhile as they enabled me to work in a research environment with points of contact to scientists from different fields of knowledge.

# Asong Lekealem

The topic of my thesis was Applying Multivariate Statistical Methods for Forecasting Electricity Price Contributors. I wrote it at Vattenfall Energy Trading GmbH (VET) in Hamburg and my Supervisors were Mr. Erik Svensson from VET and Univ. Prof. Dr. Barbara Rüdiger-Mastandrea of the University of Wuppertal.

The objective of the thesis was to develop flexible models for forecasting short and long term electricity price “contributors”, and comparing these models and the present models used at Vattenfall Energy Trading. The case studies of the electricity price “contributors” were Cross-border flows of Electricity and Margins.

Cross-border flows is the transportation of electricity between two market areas (e.g. Germany is a market area) through transmission lines linking the two different market areas. A market area is a geographical region where electricity can be transported freely, that is, without network congestion.

Coming from a mathematical background, the M.Sc. in Computer Simulation in Science with specialization in Financial Mathematics was the right programme to attend for me. It not only allowed me to make use of the Mathematical knowledge I possessed, but also allowed me to learn a lot about numerical computing and (financial) mathematical modeling concepts.

Also, I did get the tools and level of understanding required to be able to go through interviews and be selected for challenging roles. Having been working as a Forecast Analyst since graduating, I keep confirming how solid the foundations I got from the M.Sc. programme are, as well as realizing the advantage I have on the job in the combination of theory and practice I obtained from the programme.

# Germán I. Ramírez Espinoza

Being a student at the master program was a great experience. I hold a B.Sc. in Engineering Physics and my interest in computing and science lead me to the CSiS master. I was looking for something more focused on the numerical analysis and the development of high performance algorithms rather than a program focused on the development of general purpose systems, like is the case in some IT master courses.

I had the opportunity to get taught by great professors from a wide range of areas of science: from physics to computer science to mathematics. This surely gives the student a better approach to the topics taught, the possibilities of research, and the connection between areas of science that, at first sight, seem disparate, like economics and physics.

After the completion of the master I was offered a job at EON, an energy company which also engages in trading for hedging purposes, in the area of risk management as developer of mathematical algorithms to support decision making and risk compliance.

The computational representation of partial differential equations (PDE) can be challenging in some cases and special numerical algorithms must be created to achieve reliable results. My thesis deals with the convection-dominated behavior present in the computational simulation of convection-diffusion PDEs. This behavior is caused by the parameters of the PDE and lead to incorrect approximations of the function of interest. Moreover, the derivatives of this approximation are even worst. In financial mathematics, the derivatives of the price of the option are required to measure the sensibility of the price to different parameters like the volatility.

In computational finance, there exist various methods for the pricing of Options, and one of them is the numerical simulation of the celebrated model called the Black-Scholes equation. This model is a convection-diffusion PDE and in many cases the parameters are such that convection-dominated behavior is present.

Three methods are presented and emphasis is put on the Kurganov-Tadmor (KT) scheme. The KT scheme delivers excellent results and handles discontinuities or non-smoothness on the initial condition satisfactorily. In comparison to other methods like Crank-Nicolson or F inite Volume Methods, the KT scheme performs competitively and, additionally, it is easy to implement.

In the image, the approximation to the first derivative of price of the option is shown. Unrealistic oscillations artificially introduced by the method appear.

In many cases, Monte Carlo methods are used because of the ease of implementation and flexibility. Nevertheless, when the dimensionality of the problem is not high, using an scheme like the KT represents advantages and a considerable optimization in terms of computing time. This method could help the financial analyst to obtain approximations to the price of an option and its derivatives in an accurately manner.

# Octavian Sandu

CSiS program at Bergische Universität Wuppertal was a great experience to me, even though I did not finish the master program. I cannot say what I value more, the multicultural experience of living in Germany alongside people from all over the world, or the master program itself. I really appreciated the lectures that I had, they gave me a new overview about the world and, if I had the appropriate age, I would go for it again. On the other hand, a new career opportunity appeared in another country (Canada) as a consequence of my hobby (programming) and the Computer Science module studied here, and, as I already had a master of science degree in another field, I decided not to waste it and leave the CSiS program.

One important piece of advice that I would give to anyone coming here is to make sure they study the German language as well.

Overall, I thank everyone that helped me get here and do my studies, it was a great experience and a great opportunity.

# Ruilin Shao

CSiS program is an excellent interdisciplinary master course, which combines science theory with modern computational technology and can build strong theoretic background in the future study in simulations. During the course, I was enjoying the concept world of physics, math and programming. This promotes the capability of reasoning, construction and logic thinking, which is a great help for the students, who wants to work in the area of informatization in the manufacturing industry.

The topic of my thesis is Validation of Atmospheric Infrared Sounder Temperature Retrieval. It is about the intercomparison of the temperature mean and RMS value between three different data source for four different atmospheric conditions, the work was carried out in research centre Jülich, and was supervised by an expert in remote sensing, Prof. Martin Riese, as well as Dr. Lars Hoffmann.

# Michèle Wandelt

After a diploma in pure mathematics I detected the master degree course Computer Simulation in Science I decided to take part in this study because I wanted to change my focus to an interdisciplinary subject, and this course is a mixture between mathematics, physics and computer science with focus on the computer simulation.

I gained good experience with it: There were only a few students in the class and very kind and helpful lecturers.

During the studies, I liked the compulsory subject Computer Simulation at most, especially the simulation of physical systems. Before, I had no experience with physics and learned a lot thanks to patient lecturers and much work.

Moreover, for me it is impressing that the compulsory subjects enable you to choose one of the quite different elective subjects. For example, I visited lectures in mathematical modelling, theoretical particle and atmospheric physics.

At the end, I wrote an multdisciplinary thesis including numerical mathematics and theoretical particle physics in the subject Mathematical Modelling. This work was very good supervised by a mathematician, Prof. Dr. Michael Günther, as well as a physicist, the CSiS chairman Prof. Dr. Francesco Knechtli.

The title of my master thesis is Implicit partitioned Runge-Kutta integrators for simulations of gauge theories and can be described as follows:

In the simulations of gauge theories, expectation values of certain operators have to be calculated. This is usually performed using a Hybrid Monte Carlo (HMC) method that combines a Metropolis step with a Molecular Dynamics step. During the Molecular Dynamics step, Hamiltonian equations of motion have to be solved through an integration scheme.

Thereby, the integrator has to fulfill the properties time-reversibility and area-preservation. There are state-of-the-art integration methods with these properties, e. g. the Leapfrog scheme as well as splitting methods. At the beginning of this thesis, there was the question if there are any higher order numerical integration schemes for simulations of gauge theories besides the aforementioned methods.

I investigated implicit Runge-Kutta schemes on Lie groups. First of all, I have rewritten the Leapfrog scheme as Runge-Kutta scheme of second order. Afterwards, I focused on higher-order Runge-Kutta methods and developed a time-reversible scheme of order 3. Finally, I implemented a code and performed a HMC simulation using the different integrators.

In the image, the convergence order of the different integration methods can be observed.

After the studies, I started to work in the University of Wuppertal. I have been an employee in the atmospheric physics sector for 1.5 years and changed to the applied mathematics / numerical analysis. At the moment, I write a PhD thesis that proceeds with the work done in the master thesis.

# Konstantinos A. Sofos

A question that anyone could have when applying for a master degree, particularly in a different country, is likely to be, “What am I going to get out of this?” It is difficult to foresee your future and estimate the long-term outcome of your decisions. For this reason, it is rewarding to see that your efforts came through and thank people who helped you on your way.

As aptly put forth by Sir Isaac Newton: “If I have seen further it is by standing on the shoulders of giants”. The academic guidance and support I received as part of the CSiS program was exemplary.Coming from a Physics background, I felt very excited about the opportunity that by attending this program I would be able to gain a deep understanding of various mathematical methods and their applications in Finance. Here, I gained expertise in simulation and optimization techniques, stochastic calculus, financial mathematics, statistical data analysis and discrete mathematics.

The topic of my thesis was “Numerical Pricing and Risk Management of Energy Commodities Derivatives” and the aim was to study pricing and hedging strategies of energy derivatives (Options, forwards, futures) using single and multi-factor pricing models. A good understanding of the stochastic price dynamics was required for these purposes.

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