HGS MathComp Curriculum & Events

Planned topics

Monday 13. July 2009
10:15 - 11:45
Introduction and overview, principles of photon sensing: external and internal photo effect, thermal effects;
Performance characteristics, noise sources & characteristics, linearity, saturation, speed, the ideal image sensor
13:15 - 14:45
Charge-coupled devices (CCD): principle of analog charge transfer, types of CCD-sensors: frame transfer, interline, EM-CCD; electronic shutter,
15:15 - 16:45
Analog-digital conversion, standard digital camera interfaces: CameraLink, IEEE 1994 (Firewire), synchronization and triggering

Tuesday 14. July 2009
10:15 - 11:45
CMOS image sensors: active pixels, logarithmic image sensors, high-dynamic range imaging, high-speed image sensors
13:15 - 14:45
Color sensors, thermal imaging & non-silicon image sensors: PtSi, InSb, HgCdTe, quantum well infrared photodetectors (QWIPs), InAs/GaSb superlattice detectors
15:15 - 16:45
Non-uniformity of image sensors, pixel defects, blooming, smearing, and other artifacts

Wednesday 15. July 2009
10:15 - 11:45
Sensors for depth imaging & fluorescence lifetime imaging
13:15 - 14:45
Geometry & radiometry of imaging: which parameters influence the size & brightness of digital images?
15:15 - 16:45
Diffraction-limited imaging, linear system theory of imaging, sensor MTF

Thursday 16. July 2009
10:15 - 11:45
Methods and equipment for image sensor characterization, photon transfer method, EMVA 1288 standard
13:15 - 16:45
Practical demonstrations

The block course will give a tutorial introduction to optimization with differential equations. It will build on a compact overview of deterministic optimization algorithms, derivative generation, and extensions towards optimal control. The theoretic overview will be complemented by practical hands-on exercises in the computer pool of IWR. The introduction part will be followed by one and a half days with external speakers reporting on state-of-the-art projects in the field of optimization with differential equations.

This compact course is geared towards doctoral and master students who work with models of ordinary differential equation (ODE) type.

Starting from the foundations of high-school mathematics the course develops both theoretical foundations and numerical examples of solving initial value problems of ODE type. The main focus lies on understanding the concepts of the theoretical examples and the successful application of software to solve such systems.

In various application exercises course members will get an understanding of *how* numerical software treats such initial value problems and *what* can go wrong in this solution process.

Application examples will use the software package ODESIM which was developed at IWR, Heidelberg University.

Often a biological system will span either multiple time or spatial scales. The spring school aims at giving an introduction into methods and research allowing a better understanding of such multiscale systems from the point of view of mathematics, physics, biology, and informatics.

Hyper-sensitivity to unknown boundary conditions is a well-known issue for indirect shooting methods in solving optimal control problems. This feature may however imply an underlying geometric structure in the state-costate space for the flow of the corresponding Hamiltonian system. This geometric structure suggests a solution approximation strategy that eliminates the hyper-sensitivity. To exploit this opportunity requires placing initial and final points on certain invariant manifolds. Finite-time Lyapunov analysis is used to quantify the hyper-sensitivity and determine the tangent space geometry. Then the tangent space geometry is used to define properties of points on the invariant manifolds of interest. A simple example is used to illustrate the approach.

How a 12th Century Angkorian Monument in Cambodia undergoes restoration using traditional skills and innovative technology.

John Sanday is a British architect who has spent the last 35 years living and working in Asia. As one of the region’s leading architectural conservators, he has travelled and worked all over the sub-continent on a wide and varied assortment of archaeological sites, historic buildings, monasteries in the high Himalaya, palaces in India, and, since 1989, in the Angkor complex in Cambodia. For his long term dedication to architectural conservation and training in Asia, John was awarded the Order of the British Empire (OBE) by Her Majesty Queen Elizabeth II in the honours list of 2006. John Sanday joined Global Heritage Fund at the beginning of 2007 as GHF’s Field Director in Asia and Pacific.

Interdisciplinary Center for Scientific Computing (IWR) and Heidelberg Graduate School of Mathematical and Computational Methods for the Sciences (HGS MathComp) also work in different projects in Asia and will intensify the research for Cultural Heritage in Cambodia together with John Sanday, using high-tech equipment, for example 3D scanning.

In this talk John Sanday will give an inspiring insight in his fascinating work in Cambodia.

The dynamics of liquid droplets driven by induced polarization effects was studied both experimentally and theoretically. During experiments droplets were isolated from all other effects using microgravity environment. The evolution of droplets was captured using a high-speed movie camera. Theoretical analysis, which involved numerical simulation of the deforming droplet, was able to reproduce various stages of the deformation process in time up to the formation of Taylor cones.

Many scientific and engineering applications involve both discrete decisions and nonlinear dynamics that affect the optimality of the final design. Mixed-integer nonlinear programs (MINLPs) combine the difficulty of discrete variable sets with the challenges of nonlinear functions. The discrete components of an MINLP model phenomena such as fixed charges, dichotomies, and general logical relationships. Nonlinearities often describe phenomena such as covariance, economies of scale, or physical properties such as pressure, stress, and equilibrium. We survey recent advances in branch-and-cut methods that have resulted in the new solver FilMINT.

In Archaeology it is often necessary to reassemble
fractured objects. Due to the large number of parts,
the size of the individual broken pieces, or a possible dislocation to different parts of the world
(excavation site, museums, ...), a digital reassembly
may be very useful. In this talk I will present a system for automatically reassembling broken 3D solids.
Using techniques that belong to geometry processing,
3D digital models of the fragments are first geometrically
analyzed. Then, using a variety of methods matching pieces are identified. Using constrained optimization
they are mutually registered into their respective spatial position in the unbroken object. Illustrative
examples showing the effectiveness of the algorithm
include matching pieces of the Forma Urbis Romae and the Octagon in Ephesus.

The title of my contribution is “Mathematical Function Evaluation in High Performance Computing” :
- A new “Chebyshev Algebra”, yielding a comprehensive set of optimal polynomial approximations for the elementary functions;
- VML (Vector Math Library), a set of ITANIUM codes for mass production of elementary functions. These VLM codes were implemented as “two-core” codes, running two parallel threads for two arguments; adapting these codes for a multi-core computer with GPU-s seems obvious.

A course on advanced C++ programming will be held before the DUNE workshop.

In many areas of science and engineering numerical simulation is an
important tool for research and development. Current simulation
trends range from multiscale-/multiphysics modelling to the usage of
parallel machines with PetaFlops performance. The Distributed and
Unified Numerics Environment (DUNE) tries to fit these
heterogeneous requirements inside a single environment with novel
numerical techniques as well as state-of-the-art software development
methods.

By participating in this course scientists have the opportunity to get
a hands-on introduction to the DUNE framework. Main focus is to give a
detailed introduction to the DUNE core modules: the grid interface
including IO methods with its numerous grid implementations and the
iterative solver module ISTL. In the exercises elliptic and hyperbolic
model problems will be solved with various methods.

Der Workshop wird einen Überblick über mathematische Methoden der
modellbasierten Parameterschätzung und zahlreiche Anwendungen in
unterschiedlichen Fachbereichen geben. Zielgruppe des Workshops sind
alle Wissenschaftler der Universität Heidelberg und ihre Projektpartner.

Organisation:
* H. G. Bock
* T. Carraro
* W. Jäger
* S. Körkel
* R. Rannacher
* J. P. Schlöder

Kontakt: mpta@uni-hd.de