| Location: | House 6, Lecture Hall - Campus Nord | ||
| Time: | Tue., 16:30-18:00 ( |
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| Contact: | |||
| Script: | Under construction epub pdf html | ||
| Literature: | ↓see below | ||
| Practical: | There will be a computer tutorial after the lecture ↓see below | ||
| Moodle: | Please be so kind as to register for the course on its Moodle webpage, Einschreibeschlüssel: ammb2016 |
It is still a great challenge to come up with quantitative assertions about complex biological systems. Especially, if one aims towards a functional understanding at the cell, tissue or organismic level, it typically leads to quite involved modells. Analytical progress can be made with simplifying assumptions and the restriction to limiting cases.
This course will discuss a potpourri of mathematical methods ranging from analytical techniques to numerical methods and inform the participant on how to apply them to answer biological question.
The mathematical techniques encompass stochastic systems, numerical bifurcation analysis, information theory, perturbation theory and Fourier analysis. The biological examples are chosen mostly from neurobiology, sensory ecology, but also bacterial communication and evolution.
The schedule is very likely to change.
| 18. Oct | No lecture | |||
| 25. Oct | Floquet theory | |||
| 01. Oct | The continuum limit of a membrane patch I | |||
| 08. Nov | The continuum limit of a membrane patch II | |||
| 15. Nov | The continuum limit of a membrane patch III | |||
| 22. Nov | Information theory I - Intro | |||
| 29. Nov | Information theory II - Spike coding (Reconstruction bound) | |||
| 06. Dec | Linear response theory | |||
| 13. Dec | Spike reliability | |||
| 20. Dec | No lecture | |||
| 27. Dec | No lecture | |||
| 03. Jan | No lecture | |||
| 10. Dec | Numerical bifurcation analysis of the resting state | |||
| 17. Jan | CANCELED (Lecturer has the influenza virus) | |||
| 24. Jan | Numerical bifurcation analysis of the resting state I | |||
| 31. Jan | Phase descriptions near bifurcations | |||
| 07. Feb | Synchronisation phenomena in biology | |||
| 14. Feb | Spike train statistics | |||
| 28. Feb | Project & Practical (whole afternoon) |
bachelor level mathematics, basic understanding of English (questions can be asked in German)
Quantitative Aussagen über komplexe biologische Systeme zu treffen stellt noch immer eine große Herausforderung da. Vor allem das Verstehen von funktionalen Zusammenhänge auf der Ebene von Zellen oder ganzer Organismen führt zu aufwendigen mathematischen Modellen. Analytische Ergebnisse erlangt man nur durch restriktive Annahmen oder die Betrachtung von Grenzfällen.
In diesem Kurs wird eine Vielzahl mathematischer Methoden, von analytischen Techniken bis hin zu numerischen Verfahren besprochen und zur Klärung biologischer Fragestellungen verwand.
Die mathematischen Techniken beinhalten stochastische Systeme, numerische Bifurkationsanalyse, Informationstheorie, Perturbationstheorie und Fourieranalyse. Biologische Beispiele kommen hauptsächlich aus der Neurobiologie, sensorischen Ökologie, aber auch bakterielle Kommunikation und Evolutionsbiologie.
David MacKay’s book on information theory is available here.
Eusebius Doedel’s continuation lecture notes are here.
Eugene Izhikevich’s book on bifurcation theory in neurobiology is partly here.
It will take place (unless we agree otherwise: yes, we can apply the time shift operator ) 28. Feb 14:00-18:00. Simplest solution is to bring your own linux laptop and install AUTO. There is also to the possibility to go the the BCCN computer pool.
Have a look at this webpage for material that you can install on you laptop prior to the tutorial.