Data Assimilation - Inverse Problems - Remote Sensing
Roland Potthast, Deutscher Wetterdienst - University of Reading/UK - University of Göttingen/Ger
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Science Flash
Recent results and activities in our group, 2010_09_07.

Working on Cognitive Neurodynamics

The neural field equation is an important and basic equation which reflects the structure of our brain. It summarizes the activity of millions of neurons into a mean field. The activity of neurons in some little area of the brain then leads to the spread of brain potentials, which is modelled by a kernel w(x,y), which describes the influence of the neurons at point y on the neurons at point x. The change in the potential at x is proportional to the integral of all influences over y in some region B of the space (B for "brain").

Recently, our group on cognitive neurodynamics with Peter beim Graben, R.P. and Dimitris Pinotsis analysed the existence of solutions of this integro- differential equation via the Banach fix point theorem. A global existence result for inhomogeneous kernels w could be proven. This builds the basis for further analysis, modelling and the treatment of inverse problems.

ResearchGroup
Gö: Uni Göttingen, Ger; J: Research Center Jülich, Ger; Rdg: Uni Reading, UK

    Further Group Members
  • Daniel Langhans
  • Tobias Schwab
  • Florian Lackert

    Local Collaborators
  • Dr. Timothy Astin (Archaeology)
  • Prof. Simon Chandler-Wilde (Maths)
  • Dr. David Ezra (Oxford)
  • Dr. Peter beim Graben (Linguistics)
  • Prof. Peter Grindrod (Maths)
  • Prof. Geoff Mitchell (Optics)
  • Dr. Tobias Kuna (Maths)
  • Dr. Slawek Nasuto (Engineering)
  • Prof. Doug Saddy (Linguistics)
 
 

 

Group Members 2009

  1. Roland Potthast. Group leader. Dr. Potthast has worked on scientific and industrial projects for more than 15 years, leading a range of new developments in the mathematical theory and applications of inverse modelling / inverse problems. He is a well-known author in the area, with book contributions and a range of well-cited publications on new methods, analysis and applications. Dr. Potthast serves on the steering committee of several international conferences on inverse problems and for the inverse problems international association (IPIA).

  2. Martin Wannert. In a collaboration with the Research Center Jülich Martin Wannert works on mathematical algorithms for Magnetic Tomography. He has developed several projection algorithms which incorporate different type of a-priori knowledge into the inversion schemes. Currently, he is working on a new uniqueness proof for current reconstructions from fuel cells. In general, the current reconstruction is highly non-unique (see Hauer, Kühn, Potthast 2005), however, for the special case of a fuel cell uniqueness can be shown. Further, Martin Wannert works on the evaluation of the maximal potential of magnetic tomography and on the application of the algorithms to real data by managing a measurement device jointly developed by TomoScience, Wolfsburg, the research center Jülich and our research group in Reading and Göttingen. One publication is submitted, a second publication is in preparation.

  3. Muhammad Zaighum-Zia. Muhammad Zaighum-Zia works on inverse problems in fluid dynamics. As a starting point he is formulating the point source method for flow field reconstructions for the Stokes and the Oseen equation and implemented the forward and inverse problems. A publication is in preparation. Further steps will be carried out by investigating the applicability of sampling and probe methods for these equations, in particular looking at the singular-sources method (Potthast 1998) and the no-response test (Luke-Potthast 2003).

  4. Corinna Burkard. On a project about Optical Security Devices Corinna Burkard investigates direct and inverse scattering in three dimensions. In a first step she has solved the inverse acoustic scattering problem by a rough surface in three dimensions using the Kirsch-Kress method, i.e. the adaption of the fields by a potential approach and the search for an unknown surface by a minimization technique. She develped the convergence analysis for this situation, which involves a number of sincere difficulties due to the unbounded geometry of the domain under consideration. Further, she has implemented the method and showed the numerical feasibility of the method. A first publication is in preparation. In a second step she now looks at the electromagnetic problem in three dimensions, where the design of new optical security devices by simulation of scattering processes is the target of this ambitious project in collaboration with Prof. Geoff Michell, Center for Advanced Microscopy, Prof. Chandler-Wilde, Mathematics and Dr David Ezra, Oxford.

  5. Boris Marx. As a diplom student Boris Marx has worked on the optimal choice of measurement points for Magnetic Tomography. He has formulated a hybrid evolutionary gradient method for the solution of this "meta"-inverse problem. The method consists of a two-population evolutionary algorithm where the mutations of the second population are deterministic and are carried out by several steps of a gradient method. This hybrid scheme combines the strength of both algorithms and avoids their disadvantages. Currently, Boris Marx is now a PhD student in the Graduiertenkolleg in Göttingen jointly supervised by Kress and Potthast. He continues work on magnetic tomography investigating stochastic algorithms and data assimilation techniques for time-dependent reconstruction problems.

  6. Ndifreke Etik. Electrical Resistance Tomography (ERT) is a basic and important technology employed for geophysics and archeology. Ndi is working on the optimization of measurement points for electrical resistance tomography in archeaological applications. The project is jointly supervised with Dr. Timothy Astin from the department of Archeaology at the Unviersity of Reading.

  7. Natalie Lowery Jointly supervised with Dr Maria Vahdati from Engineering the project investigates the use of discrimination algorithms in connection with inversion as it is used for example in static or dynamic magnetic tomography. The interplay of methods which are popular in artificial intelligence and the broad collection of tools which has been developed in the field of tomography and inverse problems is one of the basic research challenges for applied inverse problems.

  8. Alexander Moodey. Data assimilation techniques are widely used in weather forecasting and hydrology. The basic task is to determine the current state of a complex system by combining measurements and model calculations using the past state of the system. The dynamical systems under consideration are usually highly complex and nonlinear and one needs to employ a huge number of unknown system parameters. It is well-known that these problems are ill-conditioned, i.e. data error can be strongly amplified. Thus, proper stabilization methods need to be employed for the stable determination of system states and are integrated into assimilation schemes. Various variational and stochastic assimilation algorithms have been developed, e.g. 3DVar, 4DVar and the ensemble Kalman Filter. The task of the project is the investigation of the instability and the stabilization properties of current assimilation algorithms with tools from regularization theory and the theory of ill-posed problems. In particular, we will study assimilation for a hierarchy of typical nonlinear systems ranging from very simple to complex systems with the task to derive general results on the stabilization behaviour of the algorithms under particular error types which naturally occur within important applications. This project is jointly supervised with Prof. Peter Jan van Leeuven from Meteorology and Dr Amos Lawless from Math at Reading.

  9. Tobias Schwab. As assistant Tobias is working on scientific and industrial projects as well as the public engagement projects of the group, in particular on the open scientist initiative.

  10. Daniel Langhans. Daniel is software programmer. He is supporting the work of the group on the programming side, both for scientific, industrial and public engagement projects.

  11. Florian Lackert. System Administrator. Florian is working on the administration of various computer systems which are used by the group.

Previous Research Students and Postdocs

  1. Eric Heinemeyer (PhD 2004-2007, PostDoc 2007-8), Graduate School
  2. Fabrice Delbary (PostDoc 2006), BMBF
  3. Jochen Schulz (PhD 2001-2007)
  4. Fahmi ben Hassen (PostDoc 2004-2005), NFG
  5. Klaus Erhard (PhD 2002-2005), NFG
  6. Russell Luke (PostDoc 2001-2003), NFG
  7. Lars Kühn (PhD 2001-2005), NFG
  8. Kuo-Ming Lee (PhD 2003, Kress first supervisor), NFG

NFG = Nachwuchs-Forscher Gruppe (Young Researchers Group)

 
Christian Blog
Thoughts and reasoning about christian faith today. Date: 2010_09_07.

C-Text - Christian Blog: Migration 2 - How can I know? ...

Tuesday, September 7, 2010. We are talking about migration currently. Do you have experiences with migration? Have you ever lived in another country? We have twice moved from Germany to the UK and back as a family. I have lived in the US for a year and have worked in France as visiting professor. And today I am working actively in both Germany and the UK. I would like to reflect the experience in the light of the current debates.

Many things you do not know! ...

First of all: probably my experience is special. When I came to the UK first, I spoke the language already. I came to work and had been offered an academic job. So to some extent I was integrated into some social processes from the very beginning. But even the things we experienced with our particular background made us think differently about migration.

When you come into a country, there are many things you do not know - even if you learned the language at school. Often these are little things, but they can slow you down extremely. How to buy some medicine? In the pharmacies in the UK that works differently from the pharmacies in Germany. There are many administrative things which are completely different in the two countries. Getting a social security number or a bank account can be a real adventure. You go from here to there and try to find out what you need to do. For this you need the language, and even then special vocabulary is often used in special situations - you are not prepared for this!

Every country has special ways do to things. In the UK you queue up, in Germany you do this much less, usually. However, this is considered to be very important, even a key social competence! Another thing: Whom do you approach how? That is another important topic. In the UK, the way to talk to others is sometimes different from the way you would do that in Germany. France and Germany have the forms "Vous" or "Sie" when you address another person. It is extremely impolite to use a personal form which is common in the UK. When you move into France or Germany, you need to know this!

We found Christian brothers and sisters ... it's the Lord's world!

We have been active Christians in a Christian environment. In Germany, we have attended a free evangelical church - and in the UK we looked around to find a church right away. This was very successful and we found brothers and sisters in the Lord very soon. I would say that moving country as Christians is very different from moving without such background. You get contacts very quickly, and these contacts are often sustainable, characterized by sincere friendship and start with a reasonable depth.

It is fantastic that the Lord is everywhere. It is his world. The world does not belong to you or to me. It does not belong to a particular group. It belongs to the Lord. He has created it and given it to us to live in it and to use it. We all are visitors in our world.

I am extremely grateful for the experiences I made as foreigner in the USA, in the UK, in Japan and in France. We have learned so much, and today I feel quite at home in different environments. That does not mean that I know everything all the time! We need to learn to live with imperfections everywhere. We need to learn how to learn from each other, locals and strangers, how to communicate the key expectations and processes which our society uses to the foreigners, and we need to be open to errors and difficulties and help each other. We need to be open to learn, eager to learn, all of us! [R.W.E.P., Jesus-Network.eu]

My Christian Blog can be found on the site of the Jesus-Network

For online Bible texts please visit our translation project Jesus Network Bible, where our team works on a translation of the bible into modern English and provide notes, comments and disucssions on the texts.

 
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