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)
 
 

 

    Books and Correspondence Courses:

  1. Potthast, R.: Point-sources and Multipoles in Inverse Scattering, Chapman & Hall, London 2001.

  2. Managers Introduction to Information Technology, Correspondence Course for the Henley Management College, Henley-On-Thames, Oxfordshire, UK (2000).

  3. Mathematical Foundations of Public Policy, Correspondence Course, University of Erfurt 2002.

    4. Preprints (full papers, submitted):

  4. Roland Potthast: Orthogonality Sampling for Object Visualization under revision.

  5. Potthast, R., Stratis, I and Yannacopoulos, A.: On the stochastic magnetic tomography problem, under revision.

    Publications in refereed scientific journals

    (see also MathSciNet)

    In Press

  6. Potthast, R., Fazi, F. and Nelson, Ph.: Source Splitting via the Point Source Method, Inverse Problems, accepted for publication.

  7. Ben Hassen, F., Erhard, K. and Potthast, R.: The singular sources method for 3d inverse acoustic obstacle scattering problems, IMA J. Appl. Math, accepted for publication.

  8. Burkard, C. and Potthast, R.: Three-dimensional Rough Surface Reconstruction by the Kirsch-Kress Method, Inverse Problems, accepted for publication.

    2009

  9. Potthast, R and beim Graben, P.: Dimensional reduction for the inverse problem of neural Field theory, Frontiers in Neuroscience, Vol.3, 2009, DOI 10.3389/neuro.10/017.2009. [PDF]

  10. Beim Graben, P. and Potthast, R.: Inverse Problems in Neural Field Theory, SIAM J. Appl. Dyn. Syst., Vol. 8, No. 4 (2009), 1405-1433. [PDF]

  11. Beim Graben, Peter and Potthast, R.: Existence and Properties of Solutions for Neural Field Equations, Math. Meth. Appl. Sci., 2009. [PDF]

  12. Burkard, C. and Potthast, R.: A Time-Domain Probe Method for Three-dimensional Rough Surface Reconstructions, Inverse Problems and Imaging, Volume 3, No. 2 (2009) 259274. [PDF]

  13. Beim Graben, P. and Potthast, R.: Inverse Problems in Dynamic Cognitive Modeling, CHAOS 19, 015103 (2009). [PDF]

  14. Potthast, R. and Wannert, M.: Uniqueness of Current Reconstructions for Magnetic Tomography in Multi-Layer Devices, SIAM J. Appl. Math. Volume 70, Issue 2, pp. 563- 578 (2009). [PDF]

  15. Potthast, R. and Sini, M.: The No Response Test for the Reconstruction of Polyhedral Objects in Electromagnetics, J. Comp. Appl. Math. (2009) DOI 10.1016/j.cam.2009.08.023.

  16. Liu, Jijun and Potthast, Roland: On the duality of the potential method and the point source method in inverse scattering problems, J. Int. Eq. Appl, Vol.21, No.2, (2009) doi:10.1216/JIE-2009-21-2-1.

    17. 2008

  17. Fabrice Delbary, Klaus Erhard, Rainer Kress, Roland Potthast and Jochen Schulz: Inverse electromagnetic scattering in a two-layered medium with an application to mine detection Inverse Problems 24 (2008) 015002 (18pp) doi:10.1088/0266-5611/24/1/015002

  18. Heinemeyer, E., Linder, M. and Potthast, R.: Convergence and numerics of a multi-section method for scattering by three-dimensional rough surfaces, SIAM J. Numer. Anal. 46, 1780 (2008), 1780-1798.

  19. Hauer, K.-H., Potthast, R. and Wannert, M: Algorithms for magnetic tomography - On the role of apriori knowledge and constraints, Inverse Problems 24 (2008) 045008 (18pp) doi:10.1088/0266-5611/24/4/045008.

  20. Beim Graben, Peter, Pinotsis, Dimitris, Saddy, Douglas and Potthast, Roland: Language Processing with Dynamic Fields, Cognitive Neurodynamics Vol 2, No2 (2008), 79-88. [PDF]

  21. P. Jakubik, R. Potthast: Testing the integrity of some cavity - the Cauchy problem and the range test, Applied Numerical Mathematics (2007), doi:10.1016/j.apnum.2007.04.007

    2007

  22. Ben Hassen, F., Liu, J. and Potthast, R.: On Source Analysis by Wave Splitting with Applications in Inverse Scattering of Multiple Obstacles, J. Comput. Math. 25 (2007), no. 3, 266--281.

  23. Eckel, H. and Potthast, R.: An evolutionary Newton method for shape reconstruction. J. Integral Equations and Applications, Vol 19, No 3 (2007) 261-288.

  24. Potthast, R. and Schulz, J.: A multi-wave range test for obstacle reconstructions with unknown physical properties. J. Comput. Appl. Math. 205 (2007), no. 1, 53--71.

  25. Honda, N., Nakamura, R., Potthast, R. and Sini, M.: The no-response approach and its relation to non-iterative methods in inverse scattering. , Annali di Matematica Pura ed Aplicata, at press, published online 20 September 2006.

  26. Potthast, R.: On the convergence of the no response test. SIAM J. Math. Anal. 38 (2007), no. 6, 1808--1824.

  27. Liu, J., Nakamura, G. and Potthast, R.: A new approach and improved error analysis for reconstructing the scattered wave by the point source method. Journal of Computational Mathematics, Vol.25, No.2, 2007, pp113-130.

    28. 2006

  28. Nakamura, G., Potthast, R. and Sini, M.: A comparative study between some non-iterative methods for inverse scattering. Contemporary Matheamtics, Volume 408, 2006.

  29. Nakamura, G., Potthast, R. and Sini, M. Unification of the probe and singular sources methods for the inverse boundary value problem by the no-response test. Communications in Partial Differential Equations, 31, 2006, 1505-1528

  30. Erhard, K. and Potthast, R.: A numerical study of the probe method. SIAM J. Sci. Comput. 28, 1597 (2006)

  31. Luke, D.R. and Potthast, R.: The point source method for inverse scattering in the time domain. Math. Meth. Appl. Sci. Volume 29, Issue 13 (2006) 1501-1521

  32. Ben Hassen, F., Erhard, K. And Potthast, R.: The point source method for 3d reconstructions for the Helmholtz and Maxwell equations. Inverse Problems 22 (2006), 331-353.

  33. Chandler-Wilde, S., Heinemeyer, E. and Potthast, R.: Acoustic Scattering by Mildly Rough Unbounded Surfaces in Three Dimensions. SIAM J. Appl. Math Vol. 66, Issue 3 (2006), 1001-1026.

  34. Chandler-Wilde, S.N., Heinemeyer, E. and Potthast, R. A well-posed integral equation formulation for three-dimensional rough surface scattering Proceedings of the Royal Society a-Mathematical Physical and Engineering Sciences, 462, 2006, 3683-3705

  35. Potthast, R.: A survey on sampling and probe methods for inverse problems Topical Review for Inverse Problems 22 (2006), R1-R47.

    36. 2005

  36. Hauer, K.-H., Potthast, R., Stolton, D. and Wüster, T.: Magnetotomography - A New Method for Analysing Fuel Cell Performance and Quality. Journal of Power Sources 143 (2005), 67-74.

  37. Hauer, K.-H., Kühn, L. and Potthast, R.: On uniqueness and non-uniqueness for current reconstruction from magnetic fields Inverse Problems 21 (2005) 1-13.

  38. Potthast, R.: Sampling and Probe Methods - An Algorithmical View Computing 75 (2005) 215-236.

  39. Potthast, R. and Stratis, I.: The singular sources method for an inverse transmission problem. together with Ioannis Stratis, Athens. Computing 75 (2005), 237-255.

    40. 2004

  40. Potthast, R.: A set-handling approach for the no-response test and related methods. Mathematics and Computers in Simulation, Vol. 66, No 4-5 (2004), 281-296.

  41. Potthast, R.: A new non-iterative singular sources method for the reconstruction of piecewise constant media. Numerische Mathematik, Vol 98 (2004), 703-730.

    42. 2003

  42. Luke, D.R. and Potthast, R.: The no response test - a sampling method for inverse scattering problems. SIAM Journal of Applied Math No.4, Vol. 63 (2003), 1292--1312.

  43. Erhard, K. and Potthast, R.: Reconstructing an inclusion from boundary measurements in electrical impedance tomography and acoustic scattering. Inverse Problems, 19 (2003), 1139-1157.

  44. Kusaik, S., Potthast, R. and Sylvester, R.: A 'range test' for determining scatterers with unknown physical properties. Inverse Problems 19, 533-547 (2003).

  45. Potthast, R. and Stratis, I.: On the domain derivative for scattering by impenetrable obstacles in chiral media IMA J. Appl. Math., 68 (2003) 621 - 635.

  46. Kühn, L. and Potthast, R.: On the convergence of the finite integration technique for the anisotropic boundary value problem of magnetic tomography Math. Meth. Appl. Sciences 26 (2003), 739-757.

    47. 2002

  47. Kühn, L., Kreß, R. and Potthast, R.: The reconstruction of a current distribution from its magnetic fields Inverse Problems 18, 1127-1146 (2002).

  48. Chandler-Wilde, S. and Potthast, R.: The Domain Derivative in Rough Surface Scattering and Rigorous Estimates for First Order Perturbation Theory Proceedings of the Royal Society, London 458 (2002), 2967-3001.

    49. 2001

  49. Potthast, R.: On the Convergence of Newton's Method in Inverse Scattering. Inverse Problems 17, 1419-1434 (2001).

    50. 2000

  50. Potthast, R.: Stability estimates and reconstructions in inverse acoustic scattering using singular sources. J. Comp. Appl. Math. (2000) 114, 247-274.

  51. Potthast, R.: Integral equation methods in electromagnetic scattering from anisotropic media. Mathematical Methods in the Applied Sciences 23, 1145-1159 (2000).

    52. 1999

  52. Colton, D. and Potthast, R.: The inverse electromagnetic scattering problem for an anisotropic medium. Q. J. Appl. Math 52 (3) (1999) 349-372

  53. Potthast, R.: Electromagnetic scattering from an orthotropic medium. Journal of Integral Equations and Applications 11 No. 2 (1999) 197-215.

    54. 1998

  54. Potthast, R.: A point-source method for inverse acoustic and electromagnetic obstacle scattering problems. IMA Journal of Appl. Math 61 (1998) 119-140.

  55. Potthast, R.: On a concept of uniqueness in inverse scattering for a finite number of incident waves. Siam J. Appl. Math 58 (1998) 666-682 .

    56. 1997

  56. Colton, D., Piana, M. and Potthast, R.: A simple method using Morozov's discrepancy principle for solving inverse scattering problems., Inverse Problems 13 (1997) 1477-1493.

    57. 1996

  57. Potthast, R.: A fast new method to solve inverse scattering problems." Inverse Problems 12 (1996) 731-742.

  58. Potthast, R.: Domain Derivatives in electromagnetic scattering. " Mathematical Methods in the Applied Sciences Vol 19, (1996) 1157-1175.

  59. Potthast, R.: Fréchet differentiability of the solution to the acoustic Neumann scattering problem with respect to the domain." Journal on Inverse and Ill-posed Problems Vol.4, No.1 (1996) 67 - 84.

    60. 1994

  60. Potthast, R.: Fréchet differentiability of boundary integral operators in inverse acoustic scattering." Inverse Problems 10 (1994), 431-447.

    61. Proceedings Paper (refereed):

    62. Potthast R., Fazi F.M., Nelson P.A. and Seo J.: Two Sound Field Reconstruction Techniques Based on Integral Equations, Hands-Free Speech Communication and Microphone Arrays, Trento, Italy, 2008.

  62. Burkard, C. and Potthast, R.: Field and Surface Reconstructions for 3d Rough Surface Problems, Institute of Acoustics Spring Conference Reading, UK, 2008.

  63. Potthast, R.: Acoustic Tomography by Orthogonality Sampling, Institute of Acoustics Spring Conference, Reading, UK 2008.

  64. Fazi F.M., Nelson P.A., Potthast R. and Seo J.: The Study of Sound Field Reconstruction as an Inverse Problem, Institute of Acoustics Spring Conference, Reading, UK 2008.

  65. Hauer, K.H. and Potthast, R.: Magnetic Tomography for Fuel Cells - Current Status and Problems. Proceedings of the international conference on inverse problems, Sapporo, Japan 2006.

  66. Nakamura G., Potthast R. and Sini M.: A comparative study between some non-iterative methods for inverse scattering. In {\em Inverse Problems, Multi-Scale Analysis and Homogenization.} Proceedings of the Workshop in Seoul, June 2005. Contemporary Mathematics Volume, AMS (Edition by H. Ammari and H. Kang), 2006.

  67. Nakamura, R., Potthast, R. and Sini, M.: The convergence of the no response test for localizing and inclusion. The 5th International Conference on Inverse Problems in Engineering - Theory and Practice, Oxford, UK 2005.

  68. Potthast, R. and Schulz, J.: From the Kirsch-Kress method via the range test to the singular sources method. The 2nd International Conference on Inverse Problems, Shanghai, China 2004.

  69. Erhard, K. and Potthast, R.: On Masking Operations for the Point-Source Method solving Inverse Boundary Value Problems. The Sixth International Conference on Mathematical and Numerical Aspects of Wave Propagation, Jyväskylä, Finland, June 30 - July 4, 2003.

  70. Luke, D.R. and Potthast, R.: The point source method in acoustic scattering: numerical reconstruction of the scattered field from far field measurements of inhomogeneous media., Int. Conf. on Acoustics, Speech and Signal Processing, Orlando, Florida, May 13-17, 2002.

  71. Potthast, R.: A Newton method for inverse scattering by a rough surface. European Symposium on Numerical Methods in Electrodynamics, Toulouse, March 2002.

  72. Akduman, I. and Potthast, R.: On the reconstruction of buried objects from surface measurements of electromagnetic fields., European Symposium on Numericl Methods in Electrodynamics, Toulouse 2002.

  73. Potthast, R.: On the Convergence of Newton's Method in Inverse Scattering. 5th International Workshop on Mathematical Methods in Scattering Theory and Biomedical Technoloy, Corfu, Greece, October 18-19, 2001.

  74. Potthast, R.: Uniqueness and stability in inverse acoustic scattering for finite data with limited aperture. in {\em Inverse Problems and Experimental Design in Thermal and Mechanical Engineering} Petit, Ingham, Jarny and Plourde (Eds.) March 5-7, 2001, Poitiers, France.

  75. Potthast, R.: A point-source method in inverse electromagnetic scattering." Proceedings of the Fourth International Conference on Mathematical and Numerical Aspects of Wave Propagation, June 1-5, 1998, at Colorado School of Mines, Golden, Colorado.

  76. Potthast, R.: A point-source method in inverse acoustic scattering." Proceedings of the International Symposium on Inverse Problems in Engineering Mechanics ISIP'98, March 23-28, 1998, Nagano, Japan.

  77. Potthast, R.: A fast new method in inverse scattering. " Proceedings of the Conference on Inverse Problems in Engineering: Theory and Practice, held June 9-14, 1996 in Le Croisic, France

  78. Potthast, R.: On two new methods in inverse scattering. " Proceedings of the Conference on Inverse Problems: Geophysical Applications, held Dec 1995 in Fish Camp, Yosemite, California

    79. Habilitation Thesis ('Second Book'):

  79. "Point-sources and Multipoles in Inverse Scattering", Habilitation Thesis, University of Göttingen 1999.

    Doctoral Dissertation:

  80. Fréchet Differenzierbarkeit von Randintegraloperatoren und Randwertproblemen zur Helmholtzgleichung und den zeithharmonischen Maxwellgleichungen." PHD-Thesis, Göttingen 1994 (in german)

 
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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