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Магистратура 2022/2023

Научно-исследовательский семинар "Вычислительные науки"

Лучший по критерию «Полезность курса для Вашей будущей карьеры»
Лучший по критерию «Полезность курса для расширения кругозора и разностороннего развития»
Лучший по критерию «Новизна полученных знаний»
Направление: 37.04.01. Психология
Когда читается: 2-й курс, 1-3 модуль
Формат изучения: без онлайн-курса
Охват аудитории: для своего кампуса
Прогр. обучения: Когнитивные науки и технологии: от нейрона к познанию
Язык: английский
Кредиты: 8
Контактные часы: 72

Course Syllabus


The research seminar “Research Seminar: Computational Sciences” consists of two parts: “Advanced data analysis of neurophysiological data” and «Dynamical theory of neural activity». The first part provides the understanding of algorithmic pipelines routinely used in the analysis of EEG and MEG data. Given the quick development of analysis tools, it is always challenging to fully comprehend the machinery hidden behind the typical button-press toolbox packages. Instead of approaching data analysis packages as a “black box”, at the end of the course the students will be able to fully comprehend the meaning of their choices while setting options in their data analysis workflow. During this course, we will go through the details of data acquisition, data processing and step by step implementation of most advanced data analysis pipeline and the understanding of the main parameters involved. After quickly reviewing the physical principles of signal acquisition and introducing some mathematical tools, the course dives into the main topics of time-frequency analysis, functional connectivity and statistical analysis. The second part “Dynamical theory of neural activity” aims to introduce masters graduate students to basic theory of dynamical systems as applied to neurodynamics: mathematical modeling of neuronal activity and techniques of model analysis. This shall prove to be useful for the students who interested in learning computational features of brain neuronal populations. During the course we are going to consider how neurons perform information processing and learn how to develop mathematical descriptions of these phenomena. We will start from the classification of different types of neuronal behavior and show the ways to motivate model choice as well as relations between the features of neuronal activity and dynamical properties of the models. Then we will explore different techniques to study the neuronal models: evolution of the phase portraits, bifurcation analysis, parameters showing level of synchronization, etc. Starting from the single neuron models we will proceed to the mathematical description of neuronal ensembles, impact of neuronal intrinsic activity and network connection topology in collective neuronal dynamics. We will study methods for estimation of network synchrony among other measures of network activity. The research seminar provides the students with the basic theory of neurophysiological data analysis and dynamical basis of neuronal activity which are useful not only in neuroscience and cognitive sciences but also in other scientific areas using similar mathematical framework.
Learning Objectives

Learning Objectives

  • Gain skills in biophysics of EEG/MEG
  • Gain skills in analysis in the time-frequency domain
  • Gain skills in connectivity analysis
  • Gain skills in statistical analysis
  • Gain understanding of the basic terms of nonlinear dynamics: attractors and repellers, steady states, limit cycles, stability, attraction domain, bifurcations
  • Gain skills in geometrical methods such as phase space plotting and bifurcations analysis
  • Gain understanding of the basic ionic mechanisms of neuronal electrophysiology
  • Gain skills in construction (choosing and development) of neuronal models
  • Gain skills in analysis of collective dynamics of neuronal networks
Expected Learning Outcomes

Expected Learning Outcomes

  • Ability to build a time-frequency projection of EEG/MEG data
  • Basic knowledge about nonlinear dynamical systems on the line (one-dimentional flows). Basic skills on analysis of equilibrium stability and bifurcations analysis of such systems.
  • Basic knowledge on the analysis of synchronization processes in neuronal networks
  • Know basic methods for phase space plotting and bifurcations analysis.
  • Know basic terms of nonlinear dynamical systems on the plane (two-dimensional flows): attractors and repellers, steady states, limit cycles, stability, attraction domain, bifurcations.
  • Know the basic ionic mechanisms of neuronal electrophysiology. Know basis of the neuronal model construction.
  • Know the basic neuronal models describing bursting activity
  • Know the basic neuronal models describing bursting activity. Basic skills on analysis the spiking neuronal models
  • Knowledge of characterization of cross-spectral relations in the data
  • Knowledge of computation and interpretation of connectivity analysis
  • Knowledge of statistical evaluation of analysis outcome
  • Knowledge of the basic physical principles of signal acquisition
  • Understanding of frequency signal analysis and its parametrization
Course Contents

Course Contents

  • Biophysics of EEG/MEG signal and data acquisition
  • Connectivity analysis: coherence, Granger causality and their interpretability
  • One-dimensional flows. Equilibria, its stability. Attraction domain. Bifurcations. One-dimensional neuron models.
  • Two-dimensional flows. Equilibria, its stability. Nullclines, evolution of phase portraits. Multistability and attraction domains. Local and nonlocal bifurcations.
  • Synchronization in neuronal populations. Connectivity and adjacency matrix. Characteristics showing level of synchronizations.
  • Bursting neuron models. Classification based on the fast subsystem bifurcations.
  • Statistical analysis of multidimensional data: non parametric testing
  • Cross-frequency coupling
  • Elements of Fourier Transform and its implementation
  • Spiking neuron models. Neuronal excitability. Hodgkin’s classification. Features of neurons of different types. Integrators and Resonators.
  • Electrophysiology of neurons. Equivalent circuit. Ionic currents and conductances. Conductance-based neuron models.
  • Time-frequency analysis: from Fourier to wavelet and multitapers
Assessment Elements

Assessment Elements

  • non-blocking Bifurcation analysis of a neuron model
  • non-blocking the study of synchronization processes in neuronal networks
  • blocking Exam
Interim Assessment

Interim Assessment

  • 2022/2023 2nd module
    No components to evaluate, the whole evaluation formula of this module is provided for the 3rd module.
  • 2022/2023 3rd module
    0.5 * Exam + 0.25 * Bifurcation analysis of a neuron model + 0.25 * the study of synchronization processes in neuronal networks


Recommended Core Bibliography

  • Eugene M. Izhikevich. (2007). Dynamical Systems in Neuroscience : The Geometry of Excitability and Bursting. The MIT Press.
  • Mike X Cohen. (2014). Analyzing Neural Time Series Data : Theory and Practice. The MIT Press.
  • Strogatz, S. H. (2000). Nonlinear Dynamics and Chaos : With Applications to Physics, Biology, Chemistry, and Engineering (Vol. 1st pbk. print). Cambridge, MA: Westview Press. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=421098

Recommended Additional Bibliography

  • Nekorkin, V. I. (2015). Introduction to Nonlinear Oscillations. Weinheim: Wiley-VCH. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=1099772