Putting reaction-diffusion systems into port-Hamiltonian framework

Reaction-diffusion systems model the evolution of the constituents distributed in space under the influence of chemical reactions and diffusion [6], [10]. These systems arise naturally in chemistry [5], but can also be used to model dynamical processes beyond the realm of chemistry such as biology, ecology, geology, and physics. In this paper, by adopting the viewpoint of port-controlled Hamiltonian systems [7] we cast reaction-diffusion systems into the portHamiltonian framework. Aside from offering conceptually a clear geometric interpretation formalized by a Stokes-Dirac structure [8], a port-Hamiltonian perspective allows to treat these dissipative systems as interconnected and thus makes their analysis, both quantitative and qualitative, more accessible from a modern dynamical systems and control theory point of view. This modeling approach permits us to draw immediately some conclusions regarding passivity and stability of reaction-diffusion systems. It is well-known that adding diffusion to the reaction system can generate behaviors absent in the ode case. This primarily pertains to the problem of diffusion-driven instability which constitutes the basis of Turing’s mechanism for pattern formation [11], [5]. Here the treatment of reaction-diffusion systems as dissipative distributed portHamiltonian systems could prove to be instrumental in supply of the results on absorbing sets, the existence of the maximal attractor and stability analysis. Furthermore, by adopting a discrete differential geometrybased approach [9] and discretizing the reaction-diffusion system in port-Hamiltonian form, apart from preserving a geometric structure, a compartmental model analogous to the standard one [1], [2] is obtaine

Brain signal analysis in space-time-frequency domain : an application to brain computer interfacing

In this dissertation, advanced methods for electroencephalogram (EEG) signal analysis in the space-time-frequency (STF) domain with applications to eye-blink (EB) artifact removal and brain computer interfacing (BCI) are developed. The two methods for EB artifact removal from EEGs are presented which respectively include the estimated spatial signatures of the EB artifacts into the signal extraction and the robust beamforming frameworks. In the developed signal extraction algorithm, the EB artifacts are extracted as uncorrelated signals from EEGs. The algorithm utilizes the spatial signatures of the EB artifacts as priori knowledge in the signal extraction stage. The spatial distributions are identified using the STF model of EEGs. In the robust beamforming approach, first a novel space-time-frequency/time-segment (STF-TS) model for EEGs is introduced. The estimated spatial signatures of the EBs are then taken into account in order to restore the artifact contaminated EEG measurements. Both algorithms are evaluated by using the simulated and real EEGs and shown to produce comparable results to that of conventional approaches. Finally, an effective paradigm for BCI is introduced. In this approach prior physiological knowledge of spectrally band limited steady-state movement related potentials is exploited. The results consolidate the method.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

MS FT-2-2 7 Orthogonal polynomials and quadrature: Theory, computation, and applications

Quadrature rules find many applications in science and engineering. Their analysis is a classical area of applied mathematics and continues to attract considerable attention. This seminar brings together speakers with expertise in a large variety of quadrature rules. It is the aim of the seminar to provide an overview of recent developments in the analysis of quadrature rules. The computation of error estimates and novel applications also are described