Special Session: Complex-Valued Neural Networks
at
2010 IEEE World Congress on Computational Intelligence (WCCI-2010)
International Joint Conference on Neural Networks (IJCNN-2010)
Barcelona, Spain, July 18-23, 2010

Organizers/Chairs:
Igor Aizenberg, Texas A&M University-Texarkana, USA
e-mail: igor.aizenberg at tamut.edu
URL: http://www.eagle.tamut.edu/faculty/igor

Akira Hirose, University of Tokyo, Japan
e-mail: ahirose at ee.t.u-tokyo.ac.jp
URL: http://www.eis.t.u-tokyo.ac.jp/

Jacek M. Zurada, University of Louisville, USA
e-mail: jacek.zurada at louisville.edu URL: http://ci.louisville.edu/zurada

Please, take a look at the Detailed Scope of the Session:

· Theoretical Aspects of CVNNs and Complex-Valued Activation Functions
· Complex-Valued Associative Memories
· Dynamics of Complex-Valued Neurons
· Learning Algorithms for CVNNs
· Chaos in Complex Domain
· Feedforward CVNNs
· Pattern Recognition, Classification and Time Series Prediction using CVNNs
· Spatiotemporal CVNNs Processing
· Frequency Domain CVNNs Processing
· Phase-Sensitive Signal Processing
· Applications of CVNNs in Image Processing, Speech Processing and Bioinformatics
· Quantum Computation and Quantum Neural Networks
· CVNNs in Robotics
· Quaternion and Clifford Networks

All guidelines and instructions for authors will appear soon at the WCCI-2010 home page. We will also put a link to the instructions for authors and paper submission page here.

Important Dates:
January 31, 2010 Deadline for the paper submission
March 15, 2010 Notification of acceptance
May 2, 2010 Deadline for final paper submission
May 23, 2010 Deadline for early registration
July 18-23, 2010 Conference, Technical and social programs

We are looking forward to seeing you in Barcelona!

Simple five-dimensional wave-equation for a Dirac particle
by N. Redington (redingtn_at_MIT.EDU) and M. A. K. Lodhi

Although it’s a bit late, I would like to draw the community’s attention to a paper of mine of which no-one seems to be aware:

N. Redington and M. A. K. Lodhi:
“Simple five-dimensional wave-equation for a Dirac particle”,
Journal of Mathematical Physics 48 (22303) 2007
http://arxiv.org/abs/quant-ph/0512140

Although the abstract doesn’t say this, we present a five-dimensional generalisation of the Dirac-Hestenes equation which turns out to be remarkably similar to a wave equation discovered by Lanczos in 1929.

With kindest regards,

Norman Hugh Redington

Source: Email by N.H. Redington (01.11.2009)

Clifford (Geometric) Algebra Wavelet Transform

by Eckhard Hitzer
Department of Applied Physics, University of Fukui, 910-8507 Japan
Submitted (October 10, 2009) to:
Proceedings of GraVisMa 2009, 02-04 September 2009, Plzen, Czech Republic, edited by V. Skala and D. Hildenbrand.

Abstract
While the Clifford (geometric) algebra Fourier Transform (CFT) is global, we introduce here the local Clifford (geometric) algebra (GA) wavelet concept. We show how for n = 2,3(mod 4) continuous Cl_n-valued admissible wavelets can be constructed using the similitude group SIM(n). We strictly aim for real geometric interpretation, and replace the imaginary unit i of C therefore with a GA blade squaring to -1. Consequences due to non-commutativity arise. We express the admissibility condition in terms of a Cl_n CFT and then derive a set of important properties such as dilation, translation and rotation covariance,a reproducing kernel, and show how to invert the Clifford wavelet transform. As an explicit example, we introduce Clifford Gabor wavelets. We further invent a generalized Clifford wavelet uncertainty principle. Extensions of CFTs and Clifford wavelets to Cl_{0,n’}, n’ = 1,2 (mod 4) appear straight forward.

Source: E. Hitzer (hitzer_at_mech.fukui-u.ac.jp)

Real Clifford Algebra Cl(n,0), n = 2,3(mod 4) Wavelet Transform

by Eckhard Hitzer
(Department of Applied Physics, University of Fukui, 910-8507 Japan)
edited by T.E. Simos et al., AIP Proceedings of ICNAAM 2009, No. 1168, pp. 781-784 (2009).

Abstract
We show how for n = 2,3(mod 4) continuous Clifford (geometric) algebra (GA) Cl_n-valued admissible wavelets can be constructed using the similitude group SIM(n). We strictly aim for real geometric interpretation, and replace the imaginary unit i of C therefore with a GA blade squaring to -1. Consequences due to non-commutativity arise. We express the admissibility condition in terms of a Cl_n Clifford Fourier Transform and then derive a set of important properties such as dilation, translation and rotation covariance, a reproducing kernel, and show how to invert the Clifford wavelet transform. As an example, we introduce Clifford Gabor wavelets. We further invent a generalized Clifford wavelet uncertainty principle.

Keywords
Clifford geometric algebra, Clifford wavelet transform, multidimensional wavelets, continuous wavelets, similitude group

AMS Subj. Class.
15A66, 42C40, 94A12

Source: E. Hitzer, hitzer_at_mech.fukui-u.ac.jp

Quaternion Grassmann-Hamilton-Clifford algebras: new mathematical tools for classical and relativistic modeling

by Patrick R. Girard (University of Lyon; Creatis; Insa-Lyon; France)
in O. Doessel and W.C. Schlegel (Eds.): WC 2009, IFMBE Proceedings 25/IV,
pp. 65-68, 2009. www.springerlink.com

Abstract
The paper presents new mathematical tools for classical and relativistic modeling based on a quaternion formulation of Clifford algebras which we shall call Grassmann-Hamilton-Clifford algebras. These algebras allow to develop an associative exterior calculus for any metric and any dimension yielding probably the best representations of the covariance groups. As applications, the paper develops these algebras in euclidean three-space and pseudo-euclidean spacetime, and in particular the Frenet frame and the relativistic moving frame.

Keywords
Quaternions, biquaternions, tetraquaternions, Grassmann-Hamilton-Clifford algebras, classical and relativistic modeling.

Source: Email by P. Girard (21 Oct. 2009), patrick.girard_at_insa-lyon.fr

Applied Geometric Algebras in Computer Science and Engineering 2010, June 14-16th 2010, Amsterdam, The Netherlands

The 4th conference on Applied Geometric Algebras in Computer Science and Engineering will be held in the Doelenzaal, which is part of the University of Amsterdam Library and situated in central Amsterdam.

Conference Chairs: Leo Dorst (L.Dorst_at_uva.nl ) and Joan Lasenby (jl221_at_cam.ac.uk)
AGACSE 2010 homepage: http://www-sigproc.eng.cam.ac.uk/~jl/AGACSE2010/index.html

Conference Aims
AGACSE 2010 is the 4th in this series of conferences and will bring together researchers from different disciplines within the Mathematics, Physics, Engineering and Computer Science communities. The conference will explore algebraic techniques for geometrical problems, study the relationships between them, and establish new links.

Topics (including but not limited to)
Engineering
Vision and robotics
Motion capture and analysis
Signal and image processing
Computer graphics and gaming
Mechanics
Mathematics and Computer Science
Geometry
Numerics and implementation
Efficient computation (GPUs etc)
Symbolic algebra

Proceedings will probably be published as an issue of Lecture Notes in Computer Science, Springer.

Important Dates
1 A4 page abstract submission: 10th March 2010
Notification of acceptance: 30th April 2010

Provisional schedule: here

Committees: here

Venue details: here

Registration and housing details will appear here shortly.

Proceedings and Photos of GraVisMa 2009

by Vaclav Skala (skala_at_kiv.zcu.cz)
12 September 2009

Dear friends,

I hope that it was a nice time in Plzen. I hope that GraVisMa workshop was productive for you and I do hope we will meet somewhere again. I will try to keep you in touch.

I hope you got back safely and enjoying life at your working place.

I will keep the GraVisMa pages updated – I put there a common photo and proceedings if you would like to use them, feel free to download both.

Please, disseminate info about GraVisMa workshop around you.

Yours,

Vaclav

GraVisMa 2009 homepage: http://geometryalgebra.zcu.cz/GraVisMa/
GraVisMa Extended Abstracts Proceedings [3,2 MB]: http://geometryalgebra.zcu.cz/GraVisMa/!_2009_GraVisMa_Abstract_proceedings.pdf

A simple tool to make easy learning geometric algebra

by Bernard Eyheramendy
Date: Tues, Aug 25 2009 1:43pm

I am novice with geometric algebra, and have developed a simple tool, EVA, to help me understand this large matter. This tool is working under a nice software named SpaceTime running on windows, mac, windows ce ( pocket PC like ipaq, Dell axiom etc ..). This tool is available for anybody interested by geometric algebra. I have checked my tool by comparing the computing results with Clical (from P. Lounesto). I need your help to be sure that what I wrote on my EVA site (beyhfr.free.fr) is correct, what parts need to be enhanced, and suggestions to complete the tool. My goal with EVA is to make available to anybody interrested, a simple software for learning GA, with easy customisation (don’t need C++ expertise) and user friendly interface. SpaceTime is a good substitute for Mapple or Mathematica if no professional use. Programming language is easy to learn (about 1 day), and allow symbolic computation (not possible with Clical, GaViewver …). OpenGl.support for 3D graphics need some enhancement to get nice presentation as (specialized) GAViewver or CLUcalc, A 30 day trial version is available at www.spacetime.us. EVA. and EVA_tutorial may be downloaded from www.spacetime.us/graphbook/files.

Thanks for your help.

Bernard

Source: http://groups.google.com/group/geometric_algebra?hl=en (26 August 2009)

Geometric (Clifford) algebra and its applications
by Douglas Lundholm
(Submitted on 10 May 2006)

Abstract
In this Master of Science Thesis I introduce geometric algebra both from the traditional geometric setting of vector spaces, and also from a more combinatorial view which simplifies common relations and operations.

Download: http://arxiv.org/abs/math/0605280

Source: http://groups.google.com/group/geometric_algebra?hl=en (01 August 2009)

Clifford algebra, geometric algebra, and applications

by Douglas Lundholm, Lars Svensson
(Submitted on 30 Jul 2009)

Abstract:
These are lecture notes for a course on the theory of Clifford algebras, with special emphasis on their wide range of applications in mathematics and physics. Clifford algebra is introduced both through a conventional tensor algebra construction (then called geometric algebra) with geometric applications in mind, as well as in an algebraically more general form which is well suited for combinatorics, and for defining and understanding the numerous products and operations of the algebra. The various applications presented include vector space and projective geometry, orthogonal maps and spinors, normed division algebras, as well as simplicial complexes and graph theory.

Download: http://arxiv.org/abs/0907.5356

Source: http://groups.google.com/group/geometric_algebra?hl=en (01 August 2009)