CISR Research Seminar Series - 2012

This research project investigates the ability for human participants to feel the visual information contained within 2D visual art. Haptic interaction is utilised as the basis for the development of mapping algorithms allowing participants to feel the visual information contained within 2D images. The human user will grasp a haptic interface with one or both hands and then 'feel' forces and vibrations representing colour, intensity and other visual elements of 2D images. The ability of visually impaired and able sighted users to perceive the visual information using the mapping algorithms and haptic interfacing will be evaluated.

In vitro multichannel recordings from neurons have been used as important evidence in neuroscientific studies to understand the fundamentals of neural network mechanisms in the brain. Consequently, accurate detection and sorting of neural activity waveforms becomes a key requirement for creating meaningful machine brain interfaces and to understand the working principles of neural networks. Number of spikes detection and sorting algorithms are proposed based on the variance maximisation of the sum of distances between the waveform clusters. Wavelet coefficients are also employed to exploit the time-frequency localisation and scale-space representation of the waveforms [1, 2] however in a very simple way.

To exploit the maximum potential of wavelet transform and available statistical technique, we propose a unified framework for unsupervised neural spike clustering. Proposed framework exploits the features of wavelets scale-space representation and time-frequency localisation through the use of wavelet transform modulus maxima (WTMM). WTMM are translation invariant high profile multiscale wavelet coefficients that remain unaltered by the shifted versions of the same action potential spike. Multiscale principle component analysis minimises the dimensionality of the raw data at different scales prior to clustering. Principle component analysis provides variance-distribution of the waveforms at different scales and spaces, generated by wavelets transform, and help in estimating the optimised number of clusters.

Professor Gao received his B.A. in Manufacturing/Material Science, M.A. in Aerospace Engineering. His PhD was obtained from Tsinghua University in Engineering Mechanics and Applied Math. Since then, he has held research and teaching positions in different institutes including MIT (Math), Yale (Engineering), Harvard (Math), the University of Michigan, and Virginia Tech. Currently, he is the Alexander Rubinov Chair Professor at the University of Ballarat, Australia.

Professor Gao's research interests range over nonconvex/nonsmooth analysis and mechanics, operations research, scientific computation, modeling, simulation, optimization and control of complex systems. He has published one research monograph (454 pp), one handbook, seven books, and about 130 scientific and philosophic papers. His main research contributions include a canonical duality-triality theory, several mathematical models in engineering mechanics and material science, a series of complete solutions to a class of nonconvex/nonsmooth problems in nonlinear analysis and mechanics, and some deterministic methods/algorithms for solving certain NP-hard problems in global optimization and computational science. The main part of the canonical duality theory, i.e., the complementary-dual variational principle he proposed in 1997 is playing an important role in large deformation solid mechanics.

Professor Gao is an editor-in-chief for Springer Encyclopedia of Duality, Springer book series of Advances in Mechanics and Mathematics, and Taylor & Francis book series of Optimization and Control of Complex Systems. He serves as an associate editor for several journals of applied math, optimization, solid mechanics, dynamical systems, and industrial and management engineering. Currently he is the Secretary-General and Vice President of International Society of Global Optimization http://isogop.org/

Complex systems theory is a multidisciplinary scientific field which studies the common properties of systems that are considered fundamentally complex. The fundamental difficulty in complex systems theory is mainly due to nonsmooth and nonconvexity. In static systems, the nonconvexity usually leads to multi-solutions in the related governing equations. Each of these solutions represents certain possible state of the system. How to identify the global and local stability and extremality of these critical solutions is a challenge task. It turns out that many nonconvex problems in global optimization and computational science are considered to be NP-hard. In nonlinear dynamics, the so-called chaotic behavior is due to nonconvexity of the objective functions. In complex systems, even some qualitative questions such as regularity and stability are considered as the outstanding open problems.

In this talk, the speaker will first present some fundamental principles for modeling complex systems. Based on the definitions of objectivity and isotropy in continuum physics, a potentially powerful canonical duality theory is naturally developed. Based on the traditional oriental philosophy and some basic rules in systems theory, he will show a unified framework in complex systems and a fundamental reason that leads to challenging problems in different fields, including chaotic dynamics, NP-hard problems in global optimization, and the paradox of Buridan's donkey in decision sciences. By using the canonical duality theory, a unified analytical solution form can be obtained for a large class of problems in nonconvex systems and global optimization, both global and local optimality conditions can be identified by a triality theory. For many nonconvex variational problems, the global optimal solutions are usually nonsmooth, and cannot be captured by any traditional Newton-type direct approaches. Applications will be illustrated by certain well-known challenging problems in analysis (such as phase transitions and control of chaotic systems) and NP-hard problems in global optimization and computational science (such as integer programming, network optimization, and TSP etc). Finally, some open problems and very recent solutions regarding the triality and unified theory will be addressed.

The speaker hopes this talk will bring some new insights into complex systems theory and decision science.