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_08.

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_08.

C-Text - Christian Blog: Migration 3 - Faith Issues ...

Wednesday, September 8, 2010. What is the role of faith in migration issues today? Is there a problem? Or perhaps no problem at all?

Faith plays a role in the discussion of migration. The driving force here is that migrants often have a different faith than the majority of people in a country. Or one has to say that migrants have a different culture which has developed in strong interaction with some faith.

Faith as a threat?

Is faith a threat? Often, it is received or perceived as a threat. The threat is not the faith itself, but particular customs or actions which are linked to faith. People in several European countries feel some kind of threat when migrants who belive in Islam build their churches in the middle of western communities. It is possible to build these churches, Islam can be practiced rather freely in western society since we believe in the right of every human to follow his or her beliefs (as long as this does not strongly limit the rights of others). It is even a right to invite to faith - whatever faith this may be, Jewish, Muslim, Christian, Hindu, Buddhist etc etc.

On the other side, in Muslim societies Christian churches and Christian faith are perceived as a clear threat. Most mission in Muslim countries is forbidden. Not seldom, people who invite to Christian faith must fear for their life. Even existing churches are closed or education for priests is destroyed. So the reaction to Muslim faith in Christian countries reflects this state. Islam is feared as a set of believes with a suppressive and violent face.

It is very difficult to make a distinction between the actions of the so-called "Christian" societies when they shape world politics and the faith of Jesus, the Christ. Western influence is perceived as "Christian", even if it is not Christian at all. This might also be true for Islam, there might be a calm side of it, though not every state is following it. Remember that "Christian" states started wars in the past, Jesus did not tell them to do so!

Faith as an Invitation

Faith is an invitation to the migrant. Faith was the invitation to Abraham, when he moved from Iraq to Palestine thousands of years ago. When you move, you leave all securities behind. You start something new. You go into a new environment. When you go into the unknown, God offers you faith as a better security.

We want to invite all migrants to faith, as God has done this in the past. For so many people in the past their journey into a new country was a challenge and test for their faith - and it was the invitation to fully dedicate themselves to the living God. The "promised land" has even become the key picture for the kingdom of heaven. Going into a new land is what we all will do, when we go to God finally.

Migration is a wonderful chance to come to the living God. So our invitation today will pick up the old invitation of the New Testament: come to faith in Jesus! Look at him, he shows more than a human can be, you will discover the face and voice of God. Open yourself, your ears and your eyes to the presence of the most high. Faith is an invitation to the migrant! [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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