The computational brain: Patricia S. Churchland and Terrence J. Sejnowski (MIT Press, Cambridge, MA, 1992); xi, 544 pages, $39.95

http://doc.ml.tu-berlin.de/bbci/publications/HauMeiGoeDaeHayBlaBie13.pdf

On the interpretation of weight vectors of linear models in multivariate neuroimaging.

Lectures on Cauchy’s Problem in Linear Partial Differential Equations. By J. Hadamard. Pp. viii+316. 15s.net. 1923. (Per Oxford University Press.)

The BCI competition IV stands in the tradition of prior BCI competitions that aim to provide high quality neuroscientific data for open access to the scientific community. As experienced already in prior competitions not only scientists from the narrow field of BCI compete, but scholars with a broad variety of backgrounds and nationalities. They include high specialists as well as students. The goals of all BCI competitions have always been to challenge with respect to novel paradigms and complex data. We report on the following challenges: (1) asynchronous data, (2) synthetic, (3) multi-class continuous data, (4) session-to-session transfer, (5) directionally modulated MEG, (6) finger movements recorded by ECoG. As after past competitions, our hope is that winning entries may enhance the analysis methods of future BCIs.

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Review of the BCI Competition IV

Anthropometry of the head and face

This book for the first time unifies the theories of acoustic, electromagnetic, and elastic waves and discusses the many physical and geometric aspects of their interactions with obstacles It offers a complete introduction to scattering theory, and goes on to discuss low frequency scattering in particular A significant number of results are previously unpublished, and the book fills many gaps in the existing literature Included is an extended bibliography covering the whole existing literature on low frequency scattering, making this an invaluable reference for researchers

Low Frequency Scattering

EEG forward calculation in realistic volume conductors using the boundary element method suffers from the fact that the solutions become inaccurate for superficial sources. Here we propose to correct an analytical approximation of the respective lead fields with series of spherical harmonics with respect to multiple expansion points. The necessary correction depends very much on the chosen analytical approximation. We constructed the latter such that the correction can be modelled adequately within the chosen basis. Simulations for a 3-shell prolate spheroid demonstrate the accurate modelling of the lead fields. Explicit comparison with analytically known solutions was done for the 3-shell spherical volume conductor showing that relative errors are mostly far below 1% even for the most superficial sources placed directly on the innermost surface.

Analytic expansion of the EEG lead field for realistic volume conductors.

The stream function y/ for axisymmetric Stokes flow satisfies the wellknown equation E4y/ = 0. In spheroidal coordinates the equation E2y/ = 0 admits separable solutions in the form of products of Gegenbauer functions of the first and second kind, and the general solution is then represented as a series expansion in terms of these eigenfunctions. Unfortunately, this property of separability is not preserved when one seeks solutions of the equation E4i// = 0. The nonseparability of Ea >// = 0 in spheroidal coordinates has impeded considerably the development of theoretical models involving particle-fluid interactions around spheroidal objects. In the present work the complete solution for ^ in spheroidal coordinates is obtained as follows. First, the generalized 0-eigenspace of the operator E2 is investigated and a complete set of generalized eigenfunctions is given in closed form, in terms of products of Gegenbauer functions with mixed order. The general Stokes stream function is then represented as the sum of two functions: one from the 0-eigenspace and one from the generalized 0-eigenspace of the operator E . A rearrangement of the complete expansion, in such a way that the angular-type dependence enters through the Gegenbauer functions of successive order, leads to some kind of semiseparable solutions, which are given in terms of full series expansions. The proper solution subspace that provides velocity and vorticity fields, which are regular on the axis, is given explicitly. Finally, it is shown how these simple and generalized eigenfunctions reduce to the corresponding spherical eigenfunctions as the focal distance of the spheroidal system tends to zero, in which case the separability is regained. The usefulness of the method is demonstrated by solving the problem of the flow in a fluid cell contained between two confocal spheroidal surfaces with Kuwabara-type boundary conditions. Received March 18, 1992. 1991 Mathematics Subject Classification. Primary 76D07; Secondary 33A50, 33A70, 35C10, 35D99, 35J30.

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Generalized eigenfunctions and complete semiseparable solutions for Stokes flow in spheroidal coordinates

Prologue 1. The ellipsoidal system and its geometry 2. Differential operators in ellipsoidal geometry 3. Lame functions 4. Ellipsoidal harmonics 5. The theory of Niven and Cartesian harmonics 6. Integration techniques 7. Boundary value problems in ellipsoidal geometry 8. Connection between sphero-conal and ellipsoidal harmonics 9. The elliptic functions approach 10. Ellipsoidal bi-harmonic functions 11. Vector ellipsoidal harmonics 12. Applications to geometry 13. Applications to physics 14. Applications to low-frequency scattering theory 15. Applications to bioscience 16. Applications to inverse problems Epilogue Appendix A. Background material Appendix B. Elements of dyadic analysis Appendix C. Legendre functions and spherical harmonics Appendix D. The fundamental polyadic integral Appendix E. Forms of the Lame equation Appendix F. Table of formulae Appendix G. Miscellaneous relations Bibliography Index.

Ellipsoidal Harmonics: Theory and Applications

An exact analytic solution for the forward problem in the theory of biomagnetics of the human brain is known only for the (1D) case of a sphere and the (2D) case of a spheroid, where the excitation field is due to an electric dipole within the corresponding homogeneous conductor. In the present work the corresponding problem for the more realistic ellipsoidal brain model is solved and the leading quadrupole approximation for the exterior magnetic field is obtained in a form that exhibits the anisotropic character of the ellipsoidal geometry. The results are obtained in a straightforward manner through the evaluation of the interior electric potential and a subsequent calculation of the surface integral over the ellipsoid, using Lame functions and ellipsoidal harmonics. The basic formulas are expressed in terms of the standard elliptic integrals that enter the expressions for the exterior Lame functions. The laborious task of reducing the results to the spherical geometry is also included.

George Dassios

Papers

Low Frequency Scattering

Analytic expansion of the EEG lead field for realistic volume conductors.

Generalized eigenfunctions and complete semiseparable solutions for Stokes flow in spheroidal coordinates

Ellipsoidal Harmonics: Theory and Applications

Magnetoencephalography in ellipsoidal geometry