Vitaliy A. Yatsenko

Seizure warning algorithm based on optimization and nonlinear dynamics

Abstract.There is growing evidence that temporal lobe seizures are preceded by a preictal transition, characterized by a gradual dynamical change from asymptomatic interictal state to seizure. We herein report the first prospective analysis of the online automated algorithm for detecting the preictal transition in ongoing EEG signals. Such, the algorithm constitutes a seizure warning system. The algorithm estimates STLmax, a measure of the order or disorder of the signal, of EEG signals recorded from individual electrode sites. The optimization techniques were employed to select critical brain electrode sites that exhibit the preictal transition for the warning of epileptic seizures. Specifically, a quadratically constrained quadratic 0-1 programming problem is formulated to identify critical electrode sites. The automated seizure warning algorithm was tested in continuous, long-term EEG recordings obtained from 5 patients with temporal lobe epilepsy. For individual patient, we use the first half of seizures to train the parameter settings, which is evaluated by ROC (Receiver Operating Characteristic) curve analysis. With the best parameter setting, the algorithm applied to all cases predicted an average of 91.7% of seizures with an average false prediction rate of 0.196 per hour. These results indicate that it may be possible to develop automated seizure warning devices for diagnostic and therapeutic purposes.

Analysis of EEG data using optimization, statistics, and dynamical system techniques

Abstract The use of dynamical system techniques, optimization methods and statistical algorithms to estimate the characteristics of brain electrical activity are explored. A system approach for characterizing EEG (electroencephalogram) signals, based on nonlinear estimation of dynamical characteristics and modeling the evolution of dynamical processes over time is applied. The dynamical characteristics can be used to better visualize the “state vector” of epileptic EEG signals and for the purpose of pattern recognition. An optimization method for reconstructing parameter spaces of dynamical systems is applied to systems with one or more hidden variables, and can be used to reconstruct maps or differential equations of the brain dynamics. The methods are illustrated by using numerically generated data and EEG data from epileptic patients.

Statistical information approaches for the modelling of the epileptic brain

First, the theory of random process is linked with the statistical description of epileptic human brain process. A statistical information approach to the adaptive analysis of the electroencephalogram (EEG) is proposed. Then, the problem of time window recognition of the global stochastic model based upon Bayesian estimation and the use of global optimization for restricted experimental data are proposed. A robust algorithm for estimating unknown parameters of stochastic models is considered. The ability of nonlinear time-series analysis to extract features from brain EEG signal for detecting epileptic seizures is evaluated.

Optimal Estimation of Signal Parameters Using Bilinear Observations

The paper considers the problem of optimal input signal estimation for bilinear systems under output measurements. The invertibility notion is introduced for a controlled bilinear system. Lie algebraic invertibility criteria are obtained for bilinear systems in R 2. The necessary conditions are given for invertibility of a nonlinear sensor class, which includes bilinear systems. A parameter identification method is proposed, when parameters occur nonlinearly in a regression function of a known structure. The so-called periodogram estimates of parameters are studied. The possibility to construct a finite-dimensional adaptive estimator for a causal dynamic system class is shown. The robust signal estimation problem is solved, when signals are estimated via application of neural networks and when nonlinear measurements are used.

An Optimization Approach for Finding a Spectrum of Lyapunov Exponents

In this chapter, we consider an optimization technique for estimating the Lyapunov exponents from nonlinear chaotic systems. We then describe an algorithm for solving the optimization model and discuss the computational aspects of the proposed algorithm. To show the efficiency of the algorithm, we apply it to some well-known data sets. Numerical tests show that the algorithm is robust and quite effective, and its performance is comparable with that of other well-known algorithms.

Nonlinear Dynamical Systems and Adaptive Filters in Biomedicine

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.

Classical and Quantum Controlled Lattices: Self-Organization, Optimization and Biomedical Applications

This paper presents new mathematical models of classical (CL) and quantum-mechanical lattices (QML). System—theoretic results on the observability, controllability and minimal realizability theorems are formulated for CL. The cellular dynamaton (CD) based on quantum oscillators is presented. We investigate the conditions when stochastic resonance can occur through the interaction of dynamical neurons with intrinsic deterministic noise and an external periodic control. We found a chaotic motion in phase—space surrounding the separatrix of dynamaton. The suppression of chaos around the hyperbolic saddle arises only for a critical external control field strength and phase. The possibility of the use of bilinear lattice models for simulating the CA3 region of the hippocampus (a common location of the epileptic focus) is discussed. This model consists of a hexagonal CD of nodes, each describing a controlled neural network model consisting of a group of prototypical excitatory pyramidal cells and a group of prototypical inhibitory interneurons connected via excitatory and inhibitory synapses. A nonlinear phenomenon in this neural network is studied.

Global optimization of cryogenic-optical sensors

We describe a phenomenon in which a macroscopic superconducting probe, as large as 2 - 6 cm, is chaotically and magnetically levitated. We have found that, when feedback is used, the probe chaotically moves near an equilibrium state. The global optimization approach to highly sensitive measurement of weak signal is considered. Furthermore an accurate mathematical model of asymptotically stable estimation of a limiting weak noisy signal using the stochastic measurement model is considered.

A monitoring system for agricultural crops on chlorophyll basis

It is shown that the spectral curve of reflectance of vegetation contains the sufficient information to create a set of parameters for effective monitoring of agricultural crops. Most of them are based on the chlorophyll estimation or characteristics, which are dependent on specific influence of inner structure of plant tissues on leaf reflection in the region of chlorophyll absorption. New chlorophyll indices are proposed for estimation of chlorophyll content in leaves using the shape of leaf reflectance curves. The ratio of two maxima in the 1-st derivative plot from reflectance spectral curve in 680-750 nm region has been shown to correlate with chlorophyll content in winter wheat leaves. Independent component analysis of reflectance spectral curves has been applied as well. An interrelation between the chlorophyll concentration and vectors of principal components has been found. The estimates of the chlorophyll content by using of these parameters and regression equations gave suitable results. Comparison of two approaches has been performed. Stability of both approaches with regard to incomplete project covering have been tested. Usage of physical and graphical models permits to estimate stability in calculation results of chlorophyll concentration influence of soil reflection. It has been shown that the ratio of two maxima in the 1-st derivative plot was changed now more than 5% and 11% under 50 % and 25 % projective cover, respectively, on a background of dark soil or sand. The reflectance coefficient at 550 nm correlates with chlorophyll content but it is highly sensitive to contribution of soil reflectance. Therefore combination of chlorophyll estimates obtained by red edge parameters and the reflectance coefficient at 550 nm gives possibility to estimate a projective covering. We shown that principal components approach is resistant to influence of project covering.

Quantum optimization and maximum clique problems

This paper describes a new approach to global optimization and control uses geometric methods and modern quantum mathematics. Polynomial extremal problems (PEP) are considered. PEP constitute one of the most important subclasses of nonlinear programming models. Their distinctive feature is that an objective function and constraints can be expressed by polynomial functions in one or several variables. A general approach to optimization based on quantum holonomic computing algorithms and instanton mechanism. An optimization method based on geometric Lie - algebraic structures on Grassmann manifolds and related with Lax type flows is proposed. Making use of the differential geometric techniques it is shown that associated holonomy groups properly realizing quantum computation can be effectively found concerning polynomial problems. Two examples demonstrating calculation aspects of holonomic quantum computer and maximum clique problems in very large graphs, are considered in detail.