HGS MathComp Curriculum & Events

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Computational structure-based methods are currently routinely used in drug design process, when potential drug targets are known or can be identified. Simulations allow for better understanding of interactions between small molecules and their targets, and thus allow for efficient design and optimization of drugs, e.g., protein inhibitors.

In this course we will present principles of simulation methods applicable in drug design and practical aspects of structure-based drug design strategies. We will focus on such techniques as ligand docking, molecular dynamics and binding free energy estimation methods.

Please find more details about the course in the abstract attached.

The places are limited by the size of the room (14 participants)

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Abstract
The short course will introduce students to theoretical concepts and computational methods for modeling biochemical reaction rates. The rate problems of unimolecular and bimolecular reactions will be formulated mathematically, and then solved analytically for simple models. Finally computational algorithms for solving these problems for realistic models of biochemical systems will be presented. Students are expected to carry out analytical derivations to fill gaps left out of the lectures and write pseudocodes to implement the algorithms presented.

Content
1. Rate description
2. Concepts of unimolecular reactions
3. Rate theories for unimolecular reactions
4. Simulations for unimolecular reaction rates
5. Concepts of bimolecular reactions
6. Rate theories for bimolecular reactions
7. Brownian dynamics simulations for bimolecular reactions
8.Coupled Brownian and molecular dynamics simulations

Language
English

Prerequisite
Students should have taken calculus and be familiar with computer coding.

Please register here

Summary

deal.II is a free, open source library to solve partial differential equations using the finite element method. The aim of this course is to provide an introduction into this framework. After this course, students should be able to implement suitably easy problems in deal.II.

The course will take place in the PC-Pool SW 1 with a preinstalled deal.II version. Since you will need your own installation for your final project, it is recommended to install deal.II on your own notebook. For using amandus, you will need to use a developer version. Instructions for installing can be found here. Files used in the course can be found here.


Target group

Students of mathematics (BSc, MSc, PhD) as well as students of scientific computing (MSc, PhD).


Prior Knowledge

Basic knowledge of FEM and C++ is required.


Participation

The number of participants is limited to 25 students. Please register via MÜSLI (or e-mail containing subject of study, semester and academic degree). Preferrably, also state subjects of interest for the course and a problem you want to solve using deal.II in separate e-mail.

For the successful completion of the final project (project summary, short presentation) 6 CP are awarded.


Topics

We will loosely follow the following outline

Short introduction to FEM and deal.II
Creating and refining meshes. Setting up finite element spaces.
A first Poisson solver
A multilevel Poisson solver with discontinuous Galerkin methods
Meshworker
Mixed finite elements
Time-dependent problems
Eigenvalue problems
Exploring error estimation and adaptive refinement
Parallelization (MPI)



Project Summary

The project summary has to be written using
doxygen or LaTeX.
Code has to be suitably commented.

Die Bildverarbeitung am Interdisziplinären Zentrum für Wissenschaftliches Rechnen (IWR) hat sich über die Jahrzehnte aus kleinen Anfängen kontinuierlich und organisch weiterentwickelt. Von Anfang an war die Grundlagenforschung eng mit Applikationen aus den Umwelt- und Lebenswissenschaften und der Industrie verknüpft. Zehn Jahre erfolgreiche Zusammenarbeit zwischen Forschung und Industrie im HCI sind einen Rückblick auf das Konzept, die wichtigsten Forschungsergebnisse und einen Ausblick auf die Zukunft wert, in einer Sonderveranstaltung des Heidelberger Bildverarbeitungsforums und eines gemeinsamen Festkolloquiums der Fakultät für Physik und Astronomie und des IWR.

> Die Teilnahme ist kostenfrei - Anmeldung erforderlich <

Uncertainty quantification (UQ) is a fast growing research area which deals with the impact of parameter, data and model uncertainties in complex systems. We focus on models which are based on partial differential equations (PDEs) with random inputs. For deterministic PDEs there are many classical analytical results and numerical tools available. The treatment of PDEs with random inputs, however, requires novel ideas and tools. We illustrate the mathematical and algorithmic challenges of UQ for Bayesian inverse problems arising from geotechnical engineering and medicine, and an optimal control problem with uncertain PDE constraints.

This talk is part of the HGS MathComp Ladyzhenskaya Lecture Series.

Vortragsreihe Didaktik

Wo gibt es Mathematik zu entdecken? Wie kann der aktive und neugierige mathematische Blick von Lernenden gestärkt und erweitert werden? Dialogisches und forschendes Lernen sind zwei Ansätze für den Mathematikunterricht, die den individuellen Fragen, Ansätzen und Erarbeitungswegen der Lernenden Raum geben. Gleichzeitig gelingt es, ausgehend von alltäglichen, ja oft sogar eher banal erscheinenden Fragestellungen tiefergehend mathematisch zu arbeiten. Sehr häufig kommt man dabei sogar auf aktuelle mathematische Forschungsfragen. Nicht einfach ist die Frage, wie forschendes Lernen im Fach Mathematik überhaupt authentisch gestaltet werden kann. Es wird über aktuelle Forschung sowie über Erfahrungen aus der Lehramtsausbildung und der wissenschaftlichen Begleitung des Programms „Mathe.Forscher“ der Stiftung Rechnen berichtet. Der Vortrag bietet konkrete Unterrichtsideen und Anregungen für den Unterricht in den Sekundarstufen.

We survey our recent and ongoing work [1,2] on finite element methods for contact problems. Our approach is to first write the problem in mixed form, in which the contact pressure act as a Lagrange multiplier. In order to avoid the problems related to a direct mixed finite element discretisation, we use a stabilised formulation, in which appropriately weighted residual terms are added to the discrete variational forms. We prove that the formulation is uniformly stable, which implies an optimal a priori error estimate. Using the stability of the continuous problem, we also prove a posteriori estimates, the optimality of which is ensured by local lower bounds. In the implementation of the methods, the discrete Lagrange multiplier is locally eliminated, leading to a Nitsche-type method [3].

For the problems of a membrane and plate subject to solid obstacles, we present numerical results.

Joint work with Tom Gustafsson (Aalto) and Juha Videman (Lisbon).

[1] T. Gustafsson, R. Stenberg, J. Videman. Mixed and stabilized finite element methods for the obstacle problem. SIAM Journal of Numerical Analysis 55 (2017) 2718–2744
[2] T. Gustafsson, R. Stenberg, J. Videman. Stabilized methods for the plate obstacle problem. https://arxiv.org/abs/1707.08396
[3] E. Burman, P. Hansbo, M.G. Larson, R. Stenberg. Galerkin least squares finite element method for the obstacle problem. Computer Methods in Applied Mechanics and Engineering 313 (2017) 362–374

This talk will present a unifying theme among the various effects of protein charges and polar groups. Simple models will be used to illustrate basic ideas about electrostatic interactions in proteins, and these ideas in turn will be used to elucidate the roles of electrostatic interactions in protein structure, folding, binding, condensation, and related biological functions. In particular, I will examine how charged side chains are spatially distributed in various types of proteins and how electrostatic interactions affect thermodynamic and kinetic properties of proteins. Both important historical developments and recent experimental and theoretical advances in quantifying electrostatic contributions of proteins will be highlighted.

Working as a PhD student you have the challenging task of developing research findings and write you doctoral thesis within three years. This alone is a demanding job. In addition, it is vital to the scientific process that your findings are presented to the scientific community. For most PhD students this is the first big project in their professional life and it could have a crucial impact on their future professional career. PhD students are highly motivated when they start their PhD studies but may underestimate the need for professional management for this three-year project "doctoral thesis".
This seminar demonstrates how to approach the doctoral thesis in a professional way. Project management tools and techniques are used, tailored to the specific situation of PhD students. You will learn how to set a project vision, define clear objectives, gain buy-in from your supervisor and other colleagues in your group, and how to develop a project plan, which is structured and at the same time flexible enough to easily adjust to unexpected findings. You will establish a "controlling cycle" which helps you to recognise risks and problems as early as possible, and you will learn how to manage critical situations and deal with ups and downs. Furthermore, networking with colleagues, supervisors and other people are important topics of this seminar.
Throughout the seminar, you will work on your own doctoral thesis and share your experience with others. This seminar is most beneficial for PhD students who are in the early phases of their doctoral thesis. At the end of the seminar you will have established a strategy on how to approach your own doctoral thesis. During the follow-up REVIEW we will share experience and best practices and deal with open questions from the first module.
This seminar will help you to make the most effective use of your three years and finish your doctoral thesis on time.
You will also learn and practise the basic concepts of project management – a prerequisite in industries and research institutions.

Please register here:
http://hgs.iwr.uni-heidelberg.de/Portfolio_HGS/VERANSTALTUNGEN/reg_form/reg_form.php?id=187

We consider a population consisting of two species. Each type gives birth and dies independently of the other one. Population size is regulated by intra- and interspecific competition events letting the model follow generalized Lotka-Volterra dynamics. A quantity of interest in finite populations is the probability of fixation/extinction of one type. While it has been studied broadly in the context of fixed or deterministically varying population sizes we approximate the fixation probability in populations with stochastically fluctuating sizes. In order to do so we will take the limit of weak selection, i.e. the "fitness" benefit of one type over the other is very small.

This talk is organized by “Mathematics of Life” - a special interest group of doctoral students of the HGS MathComp.

Motion of mobile robotic systems can be based on specific motions of auxiliary internal masses inside the main body of the robot. Such robots have no outward devices, can be hermetic and operate in various environment, including tubes, vulnerable or hazardous media. Control of rigid bodies by means of internal mobile masses can be useful also for spacecraft. Control of one-dimensional and two-dimensional motions of bodies with internal masses is discussed. Optimal controls for such systems are obtained.

Biography:

Professor Felix Chernousko is a specialist in optimal control, mechanics and robotics. He graduated from Moscow Institute of Physics and Technology and has been working at the Institute for Problems of Mechanics of the Russian Academy of Sciences in Moscow for many years. He had been the director of this institute from 2004 until 2015. Professor Chernousko has published more than 500 papers and 14 books on mechanics of spacecraft, optimal control and robotics. His last book was published by Springer in 2017. Chernousko is a Full Member of the Russian Academy of Sciences, the European Academy of Sciences, the International Academy of Astronautics, Fellow of the European Mechanics Society, Honorary Professor of the Moscow Institute of Physics and Technology and others. He is laureate of the Russian State Prize for Science (twice), the Körber European Science Prize, the Alexander von Humboldt Research Award, the Chaplygin Gold Medal of the Russian Academy of Sciences, the Euler Gold Medal and others. His recent publications are devoted to mobile robots.

The global flow picture for the steady Boltzmann equation is studied (jointly with Shih-Hsien Yu). The time-asymptotic analysis is based on explicit construction of the Green's function. For the resonance situation when one of the Euler characteristic speeds is near zero, there are coupling of Knudsen-type and fluid-like waves. The construction of Bifurcation and Sone Manifolds yields finite dimensional reduction of the center manifold. Fluid nonlinearity is recognized and applied to study the global flow picture.

A plasma target for high neutralization of powerful beams of negative ions is considered. The plasma is held in a magnetic trap with multipole magnetic walls. The inverse of the magnetic tube was proposed to limit the expiration of the plasma through the inlet and outlet ports in the target. Mathematical modeling of plasma dynamics in the trap was performed by the PIC method. The basic idea of the PIC method and new analytical tests for numerical models and codes are presented. Plasma distribution in the trap the efficiency estimate of particle confinement in the magnetic field were obtained. Simulation results were compared with experimental data.

The splitting of poyharmonic equations into lower-order equations is subtle as the obvious splitting requires smoothness of the solution that might not be guaranteed by the elliptic regularity of the underlying PDE. This talk introduces a new splitting based on a Helmholtz-type decomposition. This splitting does only require the natural Sobolev regularity that is given by the weak formulation. The new mixed formulation allows for standard Lagrange ansatz functions of arbitrary polynomial degree. This talk will also state a posteriori error estimates and will illustrate the new method in numerical experiments. Applications include, e.g., the biharmonic problem from plate theory.

Mathematical modelling and simulation of physiological processes in organs and organisms are confronted with the challenge that the processes take place in complex structures, often on branching networks. In this lecture we consider networks arising in plants (“trees”, root-systems, vessel systems in leaves) and in vascular systems - in particular in cardio vascular systems. We are going to focus on the following topics:

1. characterization of the arising complex networks and construction of a coding system, including the essential information required in real applications;
2. requirements for the data, methods for data collection and processing;
3. algorithms to solve the geometric inverse problem to determine from CT-data the geometry and the developed code of the underlying network;
4. presentation and discussion of results obtained in recent research at IWR for the blood vessel system for the human heart, based on real CT-data;
5. open problems, requirements from the applications.

The theory of elliptic differential-difference equations has many interest-ing applications e.g. to
• the theory of sandwich shells and plates,
• the Kato problem concerning the analyticity of the square root of an analytic function of dissipative operators,
• nonlocal boundary value problems arising in plasma theory,
• the theory of multidimensional diffusion processes,
• nonlinear optics, …

This theory is based on the properties of difference operators acting in Sobolev spaces. Most important property of a regular difference operator:

It maps the Sobolev space of the first order with the homogeneous Dirichlet boundary condition onto the subspace of the Sobolev space of the first order with nonlocal boundary conditions continuously and bijectively. This result allows to reduce boundary value problems for strongly elliptic differential-difference equations to elliptic equations with nonlocal boundary conditions. Conversely, in some cases nonlocal elliptic boundary value problems can be reduced to elliptic differential-difference equations.

Evolutionary game theory (EGT) has recently become a popular modelling framework for understanding, modeling, and treating cancer. EGT is a quantitative framework for modeling evolution and natural selection. The purpose of this event is to introduce the attendees to the topic, the limitations of EGT and the research questions that are being tackled in the field. The event features an introductory talk to this research area by Dr. Jeffrey West and a scientific lecture from Prof. David Basanta. Both speakers are researchers from the Integrated Mathematical Oncology Department at H. Lee Moffitt Cancer Center, Tampa, USA.

The short course concerns different aspects of the bromine explosion in the polar troposphere, which is associated with the ozone depletion in the polar spring. Both numerical simulations of the auto-catalytic chemical reaction mechanism as well as observations in field campaigns are addressed. The short course provides fundamental information on the physical and chemical processes involved. Moreover, the current status of research in this area as well as future research is emphasized.

Who I am:
My name is Jonathan Griffiths (Jonnie). I have extensive experience in both freelance academic English-language proofreading and in tutoring of various kinds (workshops, classes, one-on-one tuition). I am simultaneously writing a PhD in Ancient Philosophy at UCL, UK.

Suggested Content and Breakdown of Workshop:
I am altogether flexible and happy to tailor an academic English-language workshop to the specific needs and requests of those in attendance. However, from my experience of the workshop environment in the past, I have often found it helpful to isolate certain core features of successful & stylish English writing technique. The below headings are only a handful of examples:

- Argumentation: use of connectives of different kinds (e.g. to contrast or rebut an argument previously made, to advance a complementary argument, to cross-reference and connect parts of your argument and written work together)
- Introductions & Conclusions
- Scholarly etiquette: acknowledging previous opinion, arguing against it in a professional manner; or creating an academic space for your own original contribution (e.g. to a scholarly field)
- Footing: shorthand and cross-reference (including correct use of Latin and/or abbreviated terms: see, cf. pp., ff., etc.)
- Writing Abstracts (or other materials that preface your main paper): tips & tricks to synthesise your argument into a digestible package (e.g. of 250 words or shorter).

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Max. Teilnehmerzahl 15 Personen

Mathematische Modelle kommen in unserem Alltag in vielfältigen Varianten vor. Dabei spielt die Lokalisierung eine besonders wichtige Rolle: Ein abstraktes Modell wird konkretisiert, indem es mit lokalen Daten angereichert und so präzise für einen Kunden angepasst wird.

Die geografische Komponente ist vor allem in der modellgestützten Optimierung eine entscheidende Größe. Ein Beispiel mag dies verdeutlichen: Während die Fahrroutenoptimierung in nicht-geobasierten Modellen auf abstrakte Grundgrößen wie durchschnittliche Fahrtzeit von Ort zu Ort zurückgreifen muss, können in Modellen mit detaillierten geografischen Daten exakte Vorhersagen für die Fahrtdauer beim Einsatz unterschiedlicher Fahrzeuge der zur Verfügung stehenden Flotte errechnet und in die Planoptimierung eingespeist werden. Die Kopplung mit aktuellen Verkehrsdaten erlaubt sogar eine tagesabhängige Nachoptimierung und so eine noch bessere Anpassung der Fahrpläne an die realen Gegebenheiten.

Diese Verbesserungen können auch in vielen anderen Bereichen erreicht werden:

- Modellierung der Ausbreitung von Infektionserkrankungen in Abhängigkeit von regionalem Klima und Wetter
- Hochwasservorhersage auf Basis detaillierter Geländekarten
- Planung von Funknetzwerken unter Berücksichtigung von Bebauungsplänen

Der Zusammenhang zu geografischen Daten ist so offensichtlich, dass die Anbindung geografischer Informationssysteme oft selbstverständlich erscheint. Auf dem Modellierungstag wollen wir uns mit dieser Facette der Modellbildung beschäftigen und auf Schwierigkeiten bei der Modellerstellung, Risiken in der Datengenerierung und Chancen im wirtschaftlichen Einsatz eingehen. Experten aus Wissenschaft, Forschung und Praxis geben dazu Einblicke in aktuelle Projekte und neue Entwicklungen.

Die Veranstaltung ist öffentlich. Der Eintritt ist frei. Um Anmeldung bis zum 28. Januar 2018 wird gebeten.

„Heimfahrten, Laptop, Fachliteratur & Semesterbeiträge“; kurzum an nahezu allen Kosten, die euch vom Beginn des Masters bis zum Ende der Promotion begleiten, könnt ihr das Finanzamt beteiligen – sogar rückwirkend für die letzten Jahre.
Der Effekt: Eine bis zu 5-stellige Steuerru?ckerstattung fließt nach dem Berufseinstieg auf euer Konto.
Gleichzeitig gibt es wirtschaftliche Themen, die ihr in der Promotion bewegen solltet, um fru?hzeitig und langfristig von wiederkehrenden Erstattungen zu profitieren. Dies wird ebenfalls aufgezeigt und besprochen.

Inhalt
Nach dem Training werden die Teilnehmer:
- die Vorgehensweise kennen, wie sie ihre Studienkosten ru?ckerstattet bekommen.
- fu?r sich wichtige Finanzthemen erkennen und einen der größten Steuerhebel nutzen können.
- wissen, wie sie einen Verlustvortrag generieren & Werbungskosten und Sonderausgaben steueroptimiert einordnen können.

Anmeldung:
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Spätestens zum Berufseinstieg sollten Sie eine klare Gehaltsvorstellung haben. Üben Sie Werbung in eigener Sache zu betreiben, sich optimal auf das Gehaltsgespräch vorzubereiten
und dieses selbstbewusst durchzufu?hren. Der erste Eindruck ist von entscheidender
Bedeutung und sollte das erste Ausrufezeichen setzen. Lernen Sie daru?ber hinaus die
eigenen Stärken und Schwächen allgemein und bei Verhandlungen im Speziellen kennen.
Ziel ist es, den TeilnehmerInnen aufzuzeigen, wie man authentisch und u?berzeugend auftritt, welche Gehaltsbestandteile es gibt und was man eigentlich verhandeln kann.

Inhalt
- Ermittlung des eigenen Marktwerts
- Tipps fu?r ein erfolgreiches Verhandlungsgespräch
- Rollenspiele zum Üben anhand realer Fallbeispiele
- Stärken und Schwächen im Bewerbungs- und Verhandlungskontext
Nach dem Seminar werden die TeilnehmerInnen
- Wissen, was ihr Marktwert ist
- Besser verhandeln in allen Lebenslagen
- Tools zur Identifikation der eigenen Stärken und auch zur Evaluierung des Einstiegsgehalts zur Verfu?gung gestellt bekommen

Anmeldung
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Hochschulabsolventen werden in Bewerbungsverfahren nicht selten mit einem Assessment Center (AC) konfrontiert. Mit Hilfe von verschiedenen Übungen, Aufgaben und Tests werden die Fähigkeiten und Kompetenzen der AC-Teilnehmerinnen im Rahmen eines Bewerberauswahlverfahrens eingeschätzt. Ziel dieses Workshops ist es, den Teilnehmern neben Vorbereitungsstrategien ein sicheres und überzeugendes Auftreten sowohl im Vorstellungsgespräch als auch im AC beizubringen.

Inhalt:
- Die Teilnehmer durchlaufen reale Übungen wie Selbstpräsentation, Rollenspiel, Vorstellungsgespräch, Stressinterview.
- Sie lernen sicherer und souveräner aufzutreten.
- Die Teilnehmer erfahren Techniken, einen Vortrag packender zu gestalten.
- Durch Übungen wird die Schlagfertigkeit im Gespräch und vor der Gruppe erhöht.
Nach dem Seminar werden die Teilnehmer:
- Souverän und sicher vor der Gruppe präsentieren.
- Körpersprache und Gesagtes besser verbinden können.
- Mit ihren neuen Kompetenzen aus der Masse hervorstechen.
- Ein präziseres Sprachbild haben.
- Sich auf das nächste Assessmentcenter oder Vorstellungsgespräch freuen!

Anmeldung
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