EYE-TRACKING TECHNOLOGY IN THE STUDY OF COGNITIVE PROCESSES

. Instrumental algorithmic and software tools for building a non-parametric dynamic model of the oculo-motor system (OMS) of a person, taking into account its inertial and nonlinear properties, based on the data of « input-output » experimental studies using eye-tracking technology, have been developed. Information technology and software for obtaining experimental data for the identification of OMS using test visual stimuli and the use of eye-tracking to track eye movements have been developed. Experimental studies of OMS have been carried out and first-, second- and third-order transient functions have been determined on the basis of oculographic research data. An analysis of the varia bility of transient functions corresponding to different psychophysiological states of the individual was carried out. Conclusion . A method of experimental research of the human oculo-motor system (OMS) was developed and implemented using innovative eye -tracking technology to obtain empirical data for the identification of OMS in the form of multidimensional transient functions (MTF ) using video recording of responses to test visual stimuli; introduced methods and computational algorithms for building OMS models based on polynomials and the Volterra series in the form of MTF with the use of test visual stimuli and determining feedback using eye-tracking

their processing, allow monitoring and diagnosis of the state of cognitive processes during the educational activities of students. At the same time, an integral nonlinear dynamic model is used the Volterra polynomial, for the construction of which the data of experimental studies of «input-output» OMS using test visual stimuli are used [2,3].
The purpose of the work is developing a method and instrumental algorithmic and software tools for building a mathematical model of the OMS based on the Volterra polynomial according to the data of experimental studies of the OMS «input-output» using test visual stimuli and eye-tracking technology, applying the obtained models to assess the psychophysiological state of the individual with the aim of increasing efficiency educational activity.

Theoretical and practical significance of research.
The scientific novelty of the obtained results lies in the development and indepth theory and methodology of building Volterra models of the human oculo-motor system and their application in studies of cognitive processes.
Formal relations that represent universal expressions for estimating diagonal intersections of multidimensional transition functions (n-dimensional integrals from Volterra kernels) of OMS in the form of a linear combination of OMS responses to test visual stimuli with different distances from the starting position have been proposed and theoretically substantiated, which made it possible to algorithmize and simplify the software implementation of the identification procedure.
A new method of building an approximation model of the OMS based on the Volterra polynomial using test visual stimuli displayed on the monitor screen at different distances from the starting position is proposed, which, unlike known methods, uses a regularized method of least squares to determine the diagonal intersections of multidimensional transition functions, which allows improve the accuracy and computational stability of the identification procedure.
OMS models were built based on Volterra polynomials of the second and third orders according to eye-tracking data in the form of diagonal intersections of the corresponding transition functions, which differ from the known ones in that they The following software tools have been developed: • the «SignalManager» program (C#) -allows to generate deterministic or random test visual stimuli of any configuration on the computer monitor screen for conducting «input-output» identification experiments with human OMS using innovative eye-tracking technology; • the «eSmart» program (Java Android) -instrumental software for Android smartphones, which perform automatic recognition of images of objects (face, eye, pupil) on the sequence of video registration frames and calculation of pupil coordinates in the dynamics of the eye movement process; • the «VolterraApp» program (Matlab) -implements computational algorithms for nonlinear dynamic identification of OMS based on the Volterra polynomial in the form of multidimensional transition functions (MTF); • the «FeatureSpace» program (Matlab) -implements computational algorithms for determining heuristic features, which are used to build spaces of diagnostic features.

The intelligent information technology for diagnosing psychophysiological conditions of a person.
The proposed intelligent information technology for diagnosing states of neural processes, which is based on non-parametric identification of the oculo-motor system in the form of non-linear dynamic Volterra models. The technology involves the sequential solution of the following tasks: The minimization of criterion (4) is reduced to solving a system of normal Gaussian equations, which in vector-matrix form can be written as where . , 1 , , α , α A N n j a n j jn jn In the studies of each respondent, three experiments were performed sequentially for the three amplitudes a 1 , a 2 , a 3 (N=3) of the test signals in the horizontal direction. The distance between the starting position and the test stimuli is: Experimental studies of OMS were carried out using a high-tech device, the Tobii Pro TX300 (300 Hz) eye tracker, given by the Center for Innovation and Advanced Technologies of the Lublin Technological University (Lublin, Poland) [6].

Construction of a Bayesian
where x=(x 1 ,x 2 ,…,x n )' is a vector of features, n is the dimension of the space of features, m i is a vector of mathematical expectations of features of class i, i=1, 2;