/ James M. Goodwin / Professor
/ John Sarraille / Visiting Professor
/ Yasushi Kikuchi / Assistant Professor
The present members of the Multimedia Software Systems Laboratory have diverse backgrounds and research interests. The primary areas of expertise of the current members include numerical analysis, the study of fractals and fractal dimension, nonlinear dynamics, complex systems, real and artificial neural networks, the application of physical principles to computing, genetic algorithms, fuzzy logic, fuzzy systems, nonlinear optimization algorithms and the like.
Research being done in this laboratory includes studying the use of visualization techniques to enhance the understanding of mathematical problems, for example, investigation of 3D graphs of complex functions using time, color, sound, as the necessary ``fourth dimension". The display of zeros or critical points of functions appears to aid in understanding underlying mathematical structures.
Investigation of the role of fractals and fractal dimension is being used to aid in describing complex systems, and in particular in describing the behavior of the human brain. Graphical and mathematical software, including extension and application of FD3, a fast algorithm developed and implemented by one of our members, for fractal dimension computation is being developed. This is being applied to the analysis of mathematical fractals, and of real-life data sets. Among these are digitized responses to various psychological testing procedures, obtained in cooperative research with universities in the U.S. Display and transformation techniques to allow non-linear data to be understood in several ways, using Fourier transforms, phase space plots, Poincare sections, lagging, and other approaches, are also under investigation.
Other research underway in the laboratory lies in nonlinear and complex systems and dynamics, real and artificial neural networks, the application of physical principles to computing, genetic algorithms, fuzzy logic and the like. Multimedia applications related to these ideas, are also being developed, as is the development of educational courseware and joint projects using Multimedia, hypertext, hypermedia, and virtual reality techniques.
Nonlinear dynamics methods for the control of unstable or chaotic systems (e.g. human heart, multiple trailer trucks backing up, high performance aircraft, economic systems) are becoming prominent, and are under study in this laboratory. Because these methods draw heavily on topology, they can be clarified by interactive graphical presentations. Multimedia display and interaction with controller and controlled system can enhance understanding and support the research.
The laboratory has recently added a new member, Professor N. Asada, previously at the Osaka National Research Institute (MITI) where his main research covered Laser Application Measurement Techniques. He will be involved in the development of a new infra-red video system to measure a human's physiological condition, and in a variety of multimedia activities.
Laboratory members have participated actively in scientific meetings, both in Japan and abroad. They are involved in joint research projects involving faculty from such institutions as the University of California, Los Angeles (UCLA) and the University of Texas, in the U.S. They have presented and participated in seminars, and in presentation of scientific results in fully refereed publications.
The laboratory is the coordinator for coursework in computer music and in the interaction of brain waves with physical devices. It has a wide variety of equipment available for use by students and faculty, typically interconnected via the campus network. The equipment includes two graphics workstations by Silicon Graphics, two workstations using the NeXTSTEP operating system, a UNIX based system supporting multimedia interface development, an Amiga 4000 with a Video Toaster for real time analog video presentation, a number of Macintosh computers, a number of PCs running DOS, Windows, and OS/2, together with several Sun workstations.
Refereed Journal Papers
The notion that behavior may be unpredictable is not new. However the idea is new that, within a deterministic nonlinear dynamical system, unpredictable behavior may be considered chaotic. It is supposed that chaotic behavior results from the existence of a fractal attractor having complex structure at arbitrary scales of measurement. FD3 is a computer program that estimates fractal dimension. It was used to determine the fractal dimension of hand-drawn Bender-Gestalt figures. The analysis of these figures is currently one of the most widely used psychological tests. It is employed primarily to detect brain damage in adults and visual-motor deficits in children.
Consider the problem of computing a
given number N of the smallest positive zeros jm, 1,..., jm, N of Bessel
function Jm(z) of a given nonnegative order m with a given relative accuracy
. In this paper, we implement the matrix algorithm for this
computation for the case
,
and
.
The algorithm can be extended for the case where m is negative. However, if m
is close to a negative integer then the problem turns out to be
ill-conditioned.
Consider computing simple eigenvalue
of a given compact infinite matrix regarded as operating in the complex
Hilbert space by computing the eigenvalues of the truncated finite
matrices and taking an obvious limiting process. In this paper we deal with a
special case where the given matrix is compact, complex and symmetric (but
not necessarily Hermitian). Two examples of application are studied. The
first is concerned with the equation J0(z)-iJ1(z)=0 appearing in the analysis
of the solitary wave runup on a sloping beach, and the second with the zeros
of the Bessel function Jm(z) of any real order m. In each case, the problem
is reformulated as an eigenvalue problem for a compact complex symmetric
tridiagonal matrix operator in
whose eigenvalue are all simple. A
complete error analysis for the numerical solution by truncation is given
based on the general theorems proved in this paper, where the usefulness of
the seldom-used generalized Rayleigh quotient is demonstrated.
Refereed Proceeding Papers
We describe a method for avoiding local minima in nonlinear optimization tasks or in neural network training problems, by combining Very Fast Simulated Reannealing (VFSR) with backpropagation. Network training algorithms can be viewed as solving global optimization problems. Although networks trained with VFSR may take longer to converge, than gradient descent methods in cases where gradient descent is successful, they are faster than other simulated annealing network training methods. In addition, convergence to the optimal weight set is mathematically guaranteed in our case. VFSR training is also amenable to recurrent networks. We demonstrate VFSR network training on a variety of test problems including the classic xor and parity problems, and two time series prediction problems, predicting a noisy ARMA time series, and predicting the chaotic time series produced by the Mackey Glass equation. We compare performances of VFSR network training with conjugate gradient trained backpropagation networks.
This paper describes large scale parallel simulation of a spin glass associative memory. As a massively parallel neural network architecture, it resembles the Boltzmann Machine, but it is based on the material and physical characteristics of spin glasses, and on the use of opto-magnetic control. The system is designed to learn, store, and recall very high dimensional binary pattern vectors. It is therefore amenable to image processing, recognition, and recall of large patterns or images. In this paper we describe massively parallel Monte Carlo style simulations of the physical and computational behavior of the spin glass memory. The simulations were run on a CM-2 Connection Machine with 65536 processing units. The study shows performance results of the system's autoassociative learning and recall capabilities on a 4996 bit Coca-Cola trademark image.
The Backward Error Propagation (BEP) procedure which is commonly used to train artificial neural networks has substantial convergence problems for problems with complex error surface geometries. We present a method for avoiding either premature convergence to suboptimal local minima or network paralysis, by combining Very Fast Simulated Reannealing with BEP. In a number of examples which are hard for BEP, we demonstrate the utility of the new method. We consider both linearly separable problems which are nonetheless hard for BEP, and produce long training times or no convergence at all, and also problems which are notlinearly separable, that have complex but unknown error geometries. We compare this with other advanced methods, in addition to BEP.
Books
Academic Activities
Participant, NIPS-93, Denver Colo., Nov. 1993.
Participant, Neural Information Processing Workshop, Vail Colo., Dec. 1993.
Participant, 1993 International Symposium on Nonlinear Theory and its Applications, NOLTA'93, Honolulu HI.
Participant, NOLTA Workshop on Recent Results on Neural Networks and Emergent Computation, Honolulu HI.
Participant, NOLTA Workshop on Chua's Circuit: Chaotic Phenomena and Applications, Honolulu HI.
Participant, First ACM International Conference on Multimedia, Anaheim CA.
Participant, SIGGRAPH 93, Anaheim CA. Aug. 1993.
Participant, French-Japanese Workshop on Synthetic Worlds, Dec. 1993. Chaired one session and presented a paper (to be published).