FB 6 Mathematik/Informatik/Physik

Institut für Mathematik


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Neurodynamics

Prerequisites and Abstract
8.3047

Dozenten

Beschreibung

Prerequisites: Lineare Algebra, Analysis I

In this lecture, we will discuss cutting-edge science that uses dynamical systems, such as networks of neurons to implement computational principles and cognitive functions. We will start with basic concepts of modelling the activity of single neurons. This includes bio-physical models as well as generative models of spiking activity. We learn essential concepts such as attractors, bifurcations, Poincare maps etc to describe and understand the behaviour of dynamical systems. In the second part, we will move to complex dynamical systems such as spiking neuronal networks. We will use these networks to compute information using the concept of Liquid State Machines. To link the knowledge acquired in this course with scientific questions every second lecture a 30 min 3W session is offered. The three big W are: why should I learn this / what for can I use it / how can it be important for my bachelor and master thesis The lecture will be supplemented by a seminar (Neurodynamics) on dynamical systems in neuroscience. This course is intended for Bachelor students in their third term and master students as a compulsory module.

Weitere Angaben

Ort: 66/E34: Do. 14:00 - 16:00 (13x) Donnerstag, 23.05.2024, Donnerstag, 04.07.2024 16:00 - 18:00, 93/E31: Fr. 12:00 - 14:00 (12x)
Zeiten: Do. 14:00 - 16:00 (wöchentlich), Ort: 66/E34, Fr. 12:00 - 14:00 (wöchentlich) - Tutorial Session, Ort: 93/E31, Termine am Donnerstag, 23.05.2024, Donnerstag, 04.07.2024 16:00 - 18:00, Ort: 66/E34
Erster Termin: Donnerstag, 04.04.2024 14:00 - 16:00, Ort: 66/E34
Veranstaltungsart: Vorlesung (Offizielle Lehrveranstaltungen)

Studienbereiche

  • Cognitive Science > Bachelor-Programm
  • Cognitive Science > Master-Programm
  • Human Sciences (e.g. Cognitive Science, Psychology)

Past and Forthcoming Events

Publications

  • Asymptotics of a time-bounded cylinder model, with N. Aschenbruck and S. Bussmann, Probability in the Engineering and Informational Sciences, https://doi.org/10.1017/S0269964822000420
  • The method of cumulants for the normal approximation, with S. Jansen and K. Schubert, Probability Surveys 2022, Vol. 19, 185-270, https://doi.org/10.1214/22-PS7
  • Sedentary Random Waypoint, with C. Betken, arXiv:2009.02941
  • The Impact of Bit Errors on Intra-Session Network Coding with Heterogeneous Packet Lengths, with B. Schütz, N. Aschenbruck, S. Bussmann and M. Juhnke-Kubitzke, Proc. of the 45th IEEE LCN Symposium on Emerging Topics in Networking LCN, virtually hosted in Sydney, Australia, Nov. 16–19, 2020.
  • Stationarity for the Small World in Motion Mobility Model, with Nils Aschenbruck, Christian Heiden und Matthias Schwamborn, MSWIM '19: Proceedings of the 22nd International ACM Conference on Modeling, Analysis and Simulation of Wireless and Mobile Systems, Nov 25-29, 2019, https://doi.org/10.1145/3345768.3355935
  • Crossing Numbers and Stress of Random Graphs, with Markus Chimani and Matthias Reitzner, In Proceedings 26th International Symposium, GD 2018, Barcelona, Spain, 255--268, 2018 available here and for an extended journal version here: https://arxiv.org/abs/1808.07558
  • Fluctuations in a general preferential attachment model via Stein's method, with Carina Betken and Marcel Ortgiese, Random Structures & algorithms, vol.55, no.4, 2019 available here
  • Connection times in large ad-hoc mobile networks, Bernoulli, vol.22, no.4, 2143--2176, 2016 available here
    with Gabriel Faraud, Wolfgang König
  • The random disc thrower problem, Proceedings of the 90th European Study Group Mathematics with Industry, 59-78, 2013  available here with T. van der Aalst, D. Denteneer, M. Hong Duong, R. J. Kang, M. Keane, J. Kool, I. Kryven, T. Meyfroyt, T. Müller, G. Regts, J. Tomczyk
  • Edge fluctuations of eigenvalues of Wigner matrices, High Dimensional Probability VI: the Banff volume, Progress in Probability, vol.66, 261-275, Springer, Basel, 2013 available here
    with Peter Eichelsbacher
  • Moderate deviations for the determinant of Wigner matrices, Dedicated to Friedrich Götze on the occasion of his sixtieth birthday, Limit Theorems in Probability, Statistics and Number Theory, Springer Proceedings in Mathematics & Statistics, vol.42, 253-275, 2013, available here
    with Peter Eichelsbacher
  • Moderate deviations for the eigenvalue counting function of Wigner matrices, ALEA, Lat. Am. J. Probab. Math. Stat. 10 (1), 27-44, 2013, available here
    with Peter Eichelsbacher
  • Moderate deviations via cumulants, Journal of Theor. Probability, 2012, available here
    with Peter Eichelsbacher
  • Moments of recurrence times for Markov chains, Electronic Comm. Probab., 16(28), 296-303, 2011, available here
    with Frank Aurzada, Marcel Ortgiese, Michael Scheutzow
  • Moderate deviations in a random graph and for the spectrum of Bernoulli random matrices, Electronic Journal of Probability, Vol. 14, Paper no. 92, 2636-2656, 2009, available here
    with Peter Eichelsbacher
  • Perpendicular transport of charged particles in slab turbulence: recovery of diffusion for realistic wave-spectra?, Journal of Physics G: Nuclear and Particle Physics, 35, 025202, 2008
    with Andreas Shalchi
  • Velocity correlation functions of charged test particles, Journal of Physics G: Nuclear and Particle Physics, 34, 859, 2007
    with Andreas Shalchi