Nonlinear Dynamical Systems and Adaptive Filters in Biomedicine Export

@article{citeulike:165112, abstract = { In this paper we present the application of a method of adaptive estimation using an algebra\&\#150;geometric approach, to the study of dynamic processes in the brain. It is assumed that the brain dynamic processes can be described by nonlinear or bilinear lattice models. Our research focuses on the development of an estimation algorithm for a signal process in the lattice models with background additive white noise, and with different assumptions regarding the characteristics of the signal process. We analyze the estimation algorithm and implement it as a stochastic differential equation under the assumption that the Lie algebra, associated with the signal process, can be reduced to a finite dimensional nilpotent algebra. A generalization is given for the case of lattice models, which belong to a class of causal lattices with certain restrictions on input and output signals. The application of adaptive filters for state estimation of the CA3 region of the hippocampus (a common location of the epileptic focus) is discussed. Our areas of application involve two problems: (1) an adaptive estimation of state variables of the hippocampal network, and (2) space identification of the coupled ordinary equation lattice model for the CA3 region.}, author = {Pardalos, P. M. and Sackellares, J. C. and Yatsenko, V. A. and Butenko, S. I.}, citeulike-article-id = {165112}, citeulike-linkout-0 = {http://www.ingentaconnect.com/content/klu/anor/2003/00000119/F0040001/05115479}, issn = {0254-5330}, keywords = {biomedicine, brain, differential, dynamical, equations, estimation, network, nonlinear, parameter, stochastic}, month = {March}, posted-at = {2005-04-19 19:19:12}, priority = {4}, title = {Nonlinear Dynamical Systems and Adaptive Filters in Biomedicine}, url = {http://www.ingentaconnect.com/content/klu/anor/2003/00000119/F0040001/05115479}, year = {2003} }

TY - JOUR ID - citeulike:165112 L3 - citeulike-article-id:165112 N2 - In this paper we present the application of a method of adaptive estimation using an algebra–geometric approach, to the study of dynamic processes in the brain. It is assumed that the brain dynamic processes can be described by nonlinear or bilinear lattice models. Our research focuses on the development of an estimation algorithm for a signal process in the lattice models with background additive white noise, and with different assumptions regarding the characteristics of the signal process. We analyze the estimation algorithm and implement it as a stochastic differential equation under the assumption that the Lie algebra, associated with the signal process, can be reduced to a finite dimensional nilpotent algebra. A generalization is given for the case of lattice models, which belong to a class of causal lattices with certain restrictions on input and output signals. The application of adaptive filters for state estimation of the CA3 region of the hippocampus (a common location of the epileptic focus) is discussed. Our areas of application involve two problems: (1) an adaptive estimation of state variables of the hippocampal network, and (2) space identification of the coupled ordinary equation lattice model for the CA3 region. SN - 0254-5330 TI - Nonlinear Dynamical Systems and Adaptive Filters in Biomedicine KW - biomedicine KW - brain KW - differential KW - dynamical KW - equations KW - estimation KW - network KW - nonlinear KW - parameter KW - stochastic AU - Pardalos, PM AU - Sackellares, JC AU - Yatsenko, VA AU - Butenko, SI PY - 2003/03// UR - http://www.ingentaconnect.com/content/klu/anor/2003/00000119/F0040001/05115479 ER -