HGS MathComp Curriculum & Events

Mixed-Integer Nonlinear Programming (MINLP) is a sub-field of Mathematical Programming (MP) specializing in modelling and solving one of the most general (and hard) classes of optimization problems: namely, problems including both nonlinear terms and integer variables. There are countless applications: in energy production, chemical engineering, scheduling, software verification, quantum chemistry, geometry, bioinformatics, nuclear engineering, and water distribution, to name a few.

Small and medium scale MINLPs are currently solved using a Branch-and-Bound variant called "spatial Branch-and-Bound" (sBB), where branching is allowed on continuous as well as discrete variables that contribute to the gap between the original problem and its convex relaxation. For large-scale variants one must currently resort to heuristics, such as VNS, Feasibility Pump, Local Branching; or exploit the problem structure to derive special-purpose methods.

Such special-purpose methods need to be applied, when the processes to be optimized are time-dependent. Mixed-integer optimal control problems (MIOCPs) are formally more general than MINLPs, but after a certain way of discretization a subclass of MINLPs with specific features that need to be exploited.

We revise many of these methods in theoretical lectures and apply them to challenging problems in afternoon hands-on practical exercises in the computer pool.

Electrochemical devices are essential in today_s society. For example Li-ion batteries can enable hybrid and plug-in hybrid electric vehicles and provide back-up for wind and solar energy, Solid Oxide Fuel Cells have unmatched efficiency direct conversion of chemical energy into electric energy. In addition to that these technologies are believed to be key for the development of the future sustainable economy.

The short-course + workshop aims at providing an introduction to solid state ionics to students, post-docs and researchers from scientific disciplines, such as mathematics, chemistry, physics and engineering.
The focus of the course is to overview the basic physico-chemical principles needed for modeling electrochemical processes and devices and to familiarize the audience with the jargon typically found in the solid state ionics literature.

Several application examples drawn from the areas of expertise of the lecturers, i.e., fuel cells, batteries, and solar fuel production, will be discussed.
Instruction is complemented by afternoon computer tutorials.

A 1-day workshop will complete the course.

Instruction: by Dr. Ciucci (HGs), Prof. Wei Lai (Michigan State), Dr. W.C. Chueh (Caltech & Sandia).

What is Software Engineering and how can it help me in developing better software? Software has become a solid part of research in many areas like physics, biology or medicine. It is used to simulate real world situations that are often too big or too small to be handles any other way. Error in Software can have an impact on research findings and at the end get very expensive. Researchers developing software for their own use would like to spend less time coding and concentrate on their research instead. They want to be able to trust the results the software is delivering.

Software Engineering is a profession and field of study dedicated to designing, implementing, and modifying software so that it is of higher quality, more affordable, maintainable, and faster to build (wikipedia). In this course you will learn about some essential Software Engineering principles and techniques. We will take a look at the different phases in a software development process (design, implementation, testing,…). You will learn to know the 10 software engineering practices (Version management, Issue Tracking,…) every scientific software project should use.

In the practical exercises we will take a look at some freeware Tools available to accomplish the benefits we have learned about in the lectures.

Location:
Monday July 19th and Tuesday July 20th 9am - 12 pm lecture in INF 368, room 432
Wednesday July 21th 9am - 12 pm lecture in INF 348, room 013 (please note that it_s a different building)
The exercises are always held 1pm - 4pm in OMZ, INF 350, room U011 (Cip-Pool).

This short course consists of two lecture series. Lecture series A provides
the fundamentals of state-space system identification to create mathematical
models from input-output measurements. In lecture series B numerical methods
for offline and online state and parameter estimation in systems of nonlinear
differential equations are presented.

The first part of lecture series A explains key linear state-space system
theory elements such as continuous and discrete-time state-space models, the
Markov parameters, observability, state estimation, various input-output
models, the Eigensystem Realization Algorithm (ERA), and the Observer/Kalman
filter Identification (OKID) method, and how these methods handle process and
measurement noises.

The second part of lecture series A deals with applications of state-space
system identification to High Performance Computing models, nonlinear system
identification with bilinear models, and identification by minimizing output
error.

Lecture series B introduces the Multiple Shooting method and the Gauss-Newton
Method for state and parameter identification in systems of nonlinear
differential equations. The Moving Horizon Estimator is presented as a
powerful method for online state and parameter estimation. Finally,
techniques for online optimal experimental design are introduced, where
incoming measurement data of a running experiment are used to plan the
remaining experiment such that the unknown parameters are determined with
minimum variances.

This short course is intended to be introductory, yet insights into these
concepts and techniques are provided whenever possible for research purpose.
No advanced knowledge on the subject is assumed.


Lectures given by:

Prof. Dr. Jer-Nan Juang
National Cheng Kung University, Taiwan

Prof. Dr. Richard Longman
Columbia University, New York

Prof. Dr. Minh Q. Phan
Dartmouth, New Hampshire

Dr. Stefan Körkel,
IWR, Universität Heidelberg

Simon Lenz
HGS MathComp
Universität Heidelberg

Leonard Wirsching
HGS MathComp
Universität Heidelberg

In the last few years, a new interest in the understanding of networks has arisen, based on the surprising finding of some universal structures in very different networks: cooperation networks, metabolic, genetic, and protein-protein-interaction networks, electrical and neural networks, or acquaintance networks.
This course introduces the basic terminology and highlights some of the tools, methods, and measures with which networks can be characterized and analyzed. Important measures to characterize networks are, e. g., various centrality indices, the number and structure of significantly overrepresented subgraphs, or the distribution of cluster sizes. Based on these methods and measures, universal network structures and the network models that describe them will be discussed. Additionally, the behavior of some exemplary processes (disease spreading, cascading failures, robustness, etc.) in dependency of the structure will be discussed.
The course will help to understand how to characterize, describe, and model networks from all disciplines, ranging from graphical models as used in computer vision to biological or social networks.

This course is interdisciplinary and does not assume mathematical background. Thus, it is especially suitable for all students with a non-mathematical background. For those of the students with a deep interest in the mathematics behind network analysis, additional material will be available and can be discussed in detail.

Remark: The Course will be divided in two parts. Part 1 (26th-28th) will be held by K.Zweig; Part 2 (29th-30th) will be held by S.Iyengar and consist of an introduction on the topics of centrality indices and clustering algorithms.

Contents:
Introduction to the finite element software library deal.II

Requirements
Knowledge in C/C++. This compact course is based on the open-source software package deal.II. Participants should have basic knowledge in classes, pointers, references, templates.

Script:
Scripts for "C" and "C++" for self-study.
Helmut Erlenkötter, "C++ Objektorientiertes Programmieren von Anfang an", rororo, ISBN 3-499-60077-3

Target audience:
Students in the following fields: mathematics, physics, computer sciences with focus on
numerical analysis as well as all doctoral-)students who are interested in numerical solutions of PDEs.

Registration:
Please, write an e-mail to Bärbel Janssen baerbel.janssen@iwr.uni-heidelberg.de

Images are all around us! Inexpensive digital cameras, video cameras, computer web-cams, satellite imagery, images off the Internet give us access to vast numbers of spatial imagery of various sorts. The vast majority of these images will be of scenes at human scales, pictures of animals / houses / people / faces, for which countless algorithms have been developed to process / compress / segment such images, described in innumerable textbooks on image processing.

Somewhat less common, but of great research interest, are images which do allow some sort of mathematical characterization, and to which standard image-processing algorithms may not apply. In most cases we do not necessarily have images here, per se, rather spatial data sets, with one or more measurements taken over a two or higher dimensional space.

Although a great deal of research has been applied to scientific images, in most cases the resulting methods are not well-documented in common textbooks, such that many students and researchers will be unfamiliar with techniques in inverse problems, posterior sampling, and random fields.

The goal of this short course is to address methods for solving multidimensional statistical inverse problems. An outline will be provided at the start of the course.

In this compact course some basic features of the theory of extremal problems are presented. After a general introduction with historical and contextual remarks we focus on the following aspects:

1. Necessary optimality conditions for smooth, convex and non-smooth functions
2. Necessary optimality conditions for variational problems
3. Necessary optimality conditions for optimal control tasks
4. Sufficient optimality conditions
5. Condition of existence of optimal solutions

Depending on the target audience, the focus will be either on fellowship applications or on project grants. The basic structure of grant applications will be presented and parts of grant applications will be prepared and discussed (grant abstract, work plan). Participants are introduced to different strategies for the successful presentation of their projects. Special focus is put on the expectations of reviewers and on typical mistakes. In the two day course format, participants will evaluate the texts prepared within the group and a sample grant application, thus gaining important insights into the reviewer point of view.

Participants will:
- learn strategies for writing successful grant applications
- get introduced to general writing techniques
- write (and evaluate, 2 day course) part of a grant application
- be introduced to the funding opportunities and special conditions of various funding bodies (i.e. BMBF, DFG, EU)
- learn evaluation procedures and evaluate the texts produced in the group and a sample application (2 day course)

Effective teamwork is essential for the success of many research projects. Participants of this course will enhance their competencies of working in a team by learning about basic principles of team work as well as influencing team action.
This two-day course focuses on the following topics:

* Understanding the aspects of effective team work
* Defining individual preferences and roles within a team
* Reflecting your influence as a singular team member on the team
* Identifying and establishing norms and rules of team work
* Recognizing and preventing conflicts in the team
* Working towards a constructive resolution of conflicts
The workshop aims at enabling participants to further develop their team and communication skills. For this reason, the course work comprises of several aspects: short inputs on various topics, individual reflection of personal experiences, trying out news ways of behaviour (e.g. in role plays), feedback from the trainer and the participants.

In der Vorlesung werden wir Techniken kennen lernen die bei
der Untersuchung von Mehrskalensystemen eingesetzt werden, wie z.
B.: Zwei-Skalen asymptotische Entwicklung, Homogenisierung, Zwei-
Skalen Konvergenz. Diese Methoden erlauben uns ausgehend von
Beschreibungen der Prozesse auf mikroskopischer Skala, effektive
Modelle herzuleiten. Solche Methoden sind sehr wichtig für
Anwendungen aus Umweltphysik, Biologie, Materialwissenschaften u.a.
In der Vorlesung werden wir die erlernten Methoden an konkreten
Beispielen anwenden.

Optimale Versuchsplanungsprobleme für nichtlineare Differentialgleichungsmodelle, Parameterschätzung, Modelldiskriminierung, numerische Lösungsmethoden, BDF-Verfahren, automatische Differentiation, Anwendungsstrategien, Praxisbeispiele

Die Grundlagen der Graphikprogrammierung wie Koordinatensysteme, Projektionen, Transformationen, Zeichenalgorithmen, Bufferkonzepte (z-Buffer, Double-Buffer), Shading, Lichtmodelle und Texturverfahren werden vorgestellt und anhand der Graphikbibliothek OpenGl in den Übungen (Computerpool im OMZ, Fr 9:00-11:00) praktisch erprobt. Dabei werden die Vor- und Nachteile der Methoden des Dircet Rendering (lokale Verfahren) den globalen Verfahren wie Raytracing und Volume Rendering gegenübergestellt.

Scientific workflows are executable descriptions of automatable scientific processes
ranging from standalone desktop data analyses to complex monitoring and control workflows that
orchestrate large-scale computational science simulations on parallel compute clusters. Scientific
workflows are often expressed in terms of tasks and their (dataflow) dependencies. This course
provides an introduction and overview of scientific workflow management, ranging from underlying
foundations (e.g. dataflow computation models), to modeling, design, and optimization techniques,
and novel features such as data lineage and provenance support to validate and interpret work-
flow runs. The course includes practical examples and hands-on exercises from a different science
domains and disciplines such as bioinformatics (phylogenetics, metagenomics), ecoinformatics (eco-
logical niche modeling), and plasma fusion simulation, and is aimed at both practitioners, i.e.,
computational scientists, bioinformaticians, etc. who would like to learn more about new (and possibly
different) ways to think about their workflow automation tasks, and at computer scientists who are
looking for application-oriented research problems that can make a difference for their colleagues in
the natural sciences.
For further information, please come to the first event on Friday May 14th or send email
to ludaesch@ucdavis.edu with subject "Scientific Workflow Course".

The lecture will be held in German. It also includes a practical session.

4-6 SWS

For a long time there have been two kinds of mathematical computation: symbolic and numerical. Symbolic computing manipulates algebraic expressions exactly, but it is unworkable for many applications since the space and time requirements grow combinatorially. Numerical computing avoids the combinatorial explosion by rounding to 16 digits at each step, but it works just with individual numbers, not algebraic expressions.

This talk will describe a new kind of computing that aims combines the feel of symbolics with the speed of numerics. The starting idea was to represent functions by Chebyshev expansions whose length is determined adaptively to maintain an accuracy of close to machine precision. The chebfun system is implemented in object-oriented Matlab, with familiar vector operations such as sum and diff being overloaded to analogues for functions such as integration and differentiation. But by now, the capabilities of chebfun have developed far beyond what this short description may suggest -- including, for example, the high-precision automatic solution of linear and nonlinear differential equations by executing "backslash". Chebfun is a joint project with Rodrigo Platte, Nick Hale, Toby Driscoll, Ricardo Pachon, and others.

Neben klassischen Experimenten wird die mathematische Modellierung ein immer wichtigerer Bestandteil biomechanischer Forschungen. Das Seminar beschäftigt sich insbesondere mit der Biomechanik des menschlichen Bewegungsapparates. Themen, die anhand aktueller Literatur erarbeitet werden, sind u. a. Muskelmodelle, Mehrkörpermodelle und charakteristische Größen der menschlichen Fortbewegung, sowie Modelle des Energieverbrauchs. Das Seminar ist eine ideale Vorbereitung für Diplom- und Doktorarbeiten im Wissenschaftlichen Rechnen mit biomechanischen Anwendungen.

Weitere Informationen unter kmombaur@uni-hd.de

The multiconfigurational time-dependent Hartree (MCTDH) method
is considered at present the most efficient wave-packet
propagation approach for systems of distinguishable
degrees-of-freedom, like molecular vibrations, etc. It was
invented in Heidelberg 20 years ago by H. D. Meyer, U. Manthe,
and L. S. Cederbaum, and has since led to a mirage of exciting
scientific advancements in "Quantum Dynamics". In recent years,
there have been ongoing scientific activities to extend the
MCTDH method to be applicable and efficient for physical
systems made of indistinguishable particles. For systems made
of electrons (fermions) the MCTDH for fermions (MCTDHF) was
developed whereas to describe the quantum dynamics of
interacting cold atoms (bosons) the MCTDH for bosons (MCTDHB)
was developed. These have opened the door to an intricate,
reliable, and accurate many-body non-equilibrium physics of
interacting particles beyond the classical text-book models of
the Hartree-Fock approximation for fermions and
Gross-Pitaevskii equation for bosons.

In my extended seminar at the HGS/MathComp I will open with a
general, unified description of multiconfigurational
time-dependent Hartree methods for systems of identical
particles and mixtures thereof, and elaborate on the utilization
of field operators, reduced-density matrices, and the
time-dependent variational principle to derive a compact and
efficient-to-work-with set of the equations of motion.

In the next part I will review some of the exciting applications
and breakthroughs achieved with MCTDHB in the prediction of
many-body phenomena of Bose-Einstein condensates. The concept of
condensate fragmentation will be defined and shown to dominate
the physics of Bose-Einstein condensates in many physical
scenarios, previously thought not to involve fragmentation at
all.

What lies ahead of us in the deciphering and description of
non-equilibrium dynamics of complex many-body quantum systems?

All quantum systems we have dealt with so far in my talk -- and
for which multiconfigurational time-dependent Hartree methods
have been developed and implemented -- assume the number of
particles (molecular vibrations, electrons, or cold atoms) in
the system to be conserved. However, there are many quantum
systems in which particles_ conversion, i.e., the
"transformation" of particles of one kind to another, governs
the basic behavior of the physical system under investigation.
These include "chemical reactions", transitions between
hyperfine states in ultracold atoms, and association and
dissociation of electrons to Cooper-pairs in solid-state
targets. Using the theoretical tools presented above I will
present the extension of the standard, particle-conserving
multiconfigurational time-dependent methods to systems with
particles_ conversion. I will conclude my seminar with a
discussion of prospects and future plans along the
"multiconfigurational time-dependent way" to researching the
quantum dynamics around us.

Based on the material presented in the Courant Lecture, Prof. Trefethen will give a short intorduction into the CHEBFUN concepts using a Matlab implementation.

Solid-gas interfaces are crucial in a wide variety of electrochemical systems,
such as fuel cells, electrolyzers, and air batteries. Electrode reactions occurring
in these devices involve ions, electrons and gas-phase species and take place
across multiple surfaces, such as those of metals, semiconductors, and ionic
conductors. Improving electrode reactions rate are critical for increasing energy
conversion efficiencies, lowering system costs, and eliminating the use of
precious materials. In the first half of the talk, I will discuss new insight into the
reaction pathways for nickel-doped cerium oxide composite fuel cell anodes.
Lithographically patterned thin film structures and two-dimensional electrostatickinetics
models were employed to decouple multi-phase reaction-diffusion
interactions. These insights enabled the design and fabrication of several highperformance
anode microstructures. In the second half of the talk, I will present a
novel cerium oxide-based thermochemical cycle for dissociating H2O and/or CO2
into H2, CO, CH4 or synthesis gas at record rates. In this cycle, cerium oxide is
first thermally reduced and then reoxidized by H2O and/or CO2 at a lower
temperature to produce fuel(s). The unfavorable deposition of carbon on the
surface of cerium oxide can be readily manipulated, in conjunction with a base
metal catalyst, to tune the selectivity of the products.

Numerous mechanisms for soot formation are known, capable for describing soot formation under specific conditions, but just a few have been developed for describing soot formation in various combustion systems. A detailed kinetic model has been developed and validated against the experimentally obtained concentration profiles of the main gas-phase species, measured in shock tube experiments and soot particle characteristics.

For the application in a multi-dimensional computational fluid dynamics (CFD) code for turbine combustion simulation, merely simple empirical models with few variables must be used. Therefore, a two-equation model has been developed for simulation of time-dependent homogeneous reaction systems. The model has been calibrated by the reaction kinetics of the detailed chemical mechanism. The complex phenomenon of soot formation is described in terms of several global steps: inception, growth, coagulation and oxidation, where two differential equations are solved for the temporal change of soot concentration and soot volume fraction.

We present a criterion for the Cohen-Macaulayness of a monomial ideal
in terms of its primary decomposition. This criterion allows us to use
tools of integer programming to study powers of Stanley-Reisner
ideals.
It turns out that all symbolic powers are Cohen-Macaulay if and only
if the associated simplicial complex is a matroid. This result leads
to the solution of several problems in this topics.

The Computerized Archaeological Laboratory, at the Hebrew University of Jerusalem started to operate on January 1st 2010. Its purpose is to harness mathematical and computational methods to support archaeological research, documentation and visualization. The laboratory is equipped with modern, high precision scanners which provide digital three dimensional models of archaeological finds. We concentrated on ceramic and lithic artifacts, and developed several tools and algorithms which are used routinely as the standard procedure for their analysis and publications. The presentation shall summarize the main novel features which are relevant to ceramics:
1) Efficient, high precision data acquisition using 3D scanners.
2) A stable and reliable algorithm which automatically finds the symmetry axis of pottery fragments.
3) A user friendly interface which creates print quality drawings of the objects.
4) A new procedure for automatic typology and classification of ceramic assemblages, which is based on mathematical representations of the cross-section profiles.
These four steps of documentation and analysis are now the routine tasks in the lab. So far we have successfully tested the procedure for more than 10,000 fragments from a large variety of archaeological excavations.

Scientific discoveries in the natural sciences are increasingly data-driven and computationally intensive, providing unprecedented data analysis and scientific computing challenges and opportunities. Scientific workflow systems and tools aim at simplifying the process of designing, executing, and maintaining complex "code aggregates", i.e., consisting of, e.g., a mix of simulation, data management, analysis, and visualization steps. Thus, scientific workflows target similar use cases as do scripting languages such as Perl or Python and can be seen as the "glue" for assembling and executing complex computational science experiments from pre-existing tools and programs. In addition, scientific workflow systems can provide further functionality, e.g., to capture the "provenance" (i.e., processing history and data lineage) of workflow outputs, thus allowing scientists to interpret, debug, and reproduce their computational experiments, or to provide fault-tolerance and scalability for well-designed scientific workflows.


In this talk, I will give an overview of this new and active research area, using real-world examples to illustrate the potential as well as current limitations of scientific workflow technology. At the end, I will also provide an overview of a course on scientific workflow management that will start one week after this talk. The course is aimed at both practitioners, i.e., computational scientists, bioinformaticians, etc. who would like to learn more about new (and possibly different) ways to think about their workflow automation tasks, and at computer scientists who are looking for application-oriented research problems that can make a difference for their colleagues in the natural sciences.

Information visualization can be invaluable in making sense
out of large data sets. However, traditional graph visualization methods
often fail to capture the underlying structural information, clustering,
and neighborhoods. Our algorithm for visualizing graphs as maps
provides a way to overcome some of the shortcomings with the help of the
geographic map metaphor. While graphs, charts, and tables often require
considerable effort to comprehend, a map representation is more
intuitive, as most people are very familiar with maps and even enjoy
carefully examining maps. The effectiveness of the algorithm is
illustrated with examples from several domains: TV shows, movies, books,
and music.

The use of dry powder inhalers (DPIs) in the therapy of asthma bronchiale and COPD (chronic obstructive pulmonary disease) has become more and more popular in the last decades: One of the reasons for this is the environmental friendliness of DPIs in comparison to conventionally used pressurized metered dose inhalers (MDIs), which deliver a solution or suspension of the drug by using environmentally harmful propellants. The challenge of designing a well performing dry powder inhalate is to cope with cohesivity and poor flowability of the drug particles, which, in order to target the deep parts of the lung, have to exhibit aerodynamic diameters between 0.5 µm and 5 µm.
There are several solutions to the problem of poor flowability, the most prominent approach being the attachment of the drug particles to coarse carrier particles of 50 µm to 200 µm, which flow sufficiently well. However, upon inhalation, the drug particles have to be detached from the carrier again in order to ensure, that the drug particles travel along the narrow airways finally reaching the deep lung. So interparticle interactions between the drug and the carrier are crucial with respect to the performance of the inhalate. Another approach is the decrease of interparticle interactions between drug particles of carrier free formulations by covering the drug particle surface with nanoparticles acting as spacers between the drug particles thereby reducing interparticle interactions.
Recent advances in the field of carrier based as well as carrier free formulations targeting the modification and optimization of interparticle interactions will be the main topic of the presentation.

The workshop brings together several experts in the field of solid-state electro-chemistry for applications in energy storage and conversion:

Prof. W. Lai (Michigan State)
Dr. W.C. Chueh (Caltech and Sandia National Lab)
Dr. G. Gregori (Max Planck Institute Stuttgart)
Dr. A. Leonide (Karlsruhe Institute of Technology)

Talks and discussions by users as well as developers in the following areas:

- application areas of the library
- what users think would be useful directions for the library to go into, what things are missing, and possibly getting people together who can help implement those parts
- newer parts of the library (e.g. hp, multithreading,
optimization, etc) and how these could help in your programs.

9. Workshop über Sprays, Techniken der Fluidzerstäubung und Untersuchungen von Sprühvorgängen

International Workshop on Optimal Control in Image Processing



The aim of this workshop is to present the current state of the art of research as well as to discuss current research interests. Through these discussions, novel impulses can be generated to tackle problems and shortcomings of the methodologies as well as to identify needs within
the application areas. Invited scientists are leading experts in the fields of optimal control theory, numerics, image processing and environmental sciences. This workshop will thus try to bridge the gap between methodologies and application areas.