1. Introduction to Computational Neuroscience (Lecture 1) Harry R. Erwin, PhD COMM2E University of Sunderland

2. Resources Shepherd, G., ed., 2004, The Synaptic Organization of the Brain, 5th edition, Oxford University Press. Nicholls et al. Kandel et al. Koch, 2004, Biophysics of Computation, OUP. Koch and Segev, 1998, Methods in Neuronal Modelling, 2nd edition, MIT Press. Bower and Beeman, 1998, The Book of Genesis, second edition, TELOS, ISBN: 0-387-94938-0 Rieke et al, 1999, Spikes: Exploring the Neural Code, Bradford Books. Churchland and Sejnowski, 1994, The Computational Brain, Bradford Books.

3. Responsibility Dr. Harry Erwin is the Module Leader for COMM2E at the University of Sunderland. Bob Pullen and I team-teach this module. My primary research areas are computational neuroscience and auditory neuroethology—‘How bats do it.’ My PhD is in natural philosophy (experimental science), not computing. I also have 34 years of experience as a software systems engineer (mostly at TRW) on high-reliability systems. I supervise final year/MSc projects and PhD research in intelligent systems, security, and software engineering. E-mail: harry.erwin@sunderland.ac.uk.harry.erwin@sunderland.ac.uk

4. Purpose COMM2E is intended to help you understand how the topics presented in the other modules relate to animal behaviour and neuroscience. My role in the HIS research group is twofold: 1.To keep the engineers honest by explaining to them how animals don’t produce behaviour, and 2.To give the engineers insight into the mechanisms by which animals do produce behaviour. – So Bob teaches the biology and I teach the computational neuroscience.

5. Examples of Advice Vector-based algorithms are very hard to implement in neural networks. Local-processing-based algorithms are easy. Brains typically don’t have grandmother cells. Instead they tend to use distributed representations. However, brains sometimes do have single cells with a unique function. Brains are self-calibrating during learning.

6. Goals To give you an understanding of how biological neural networks actually perform in vivo. More specifically to provide: –an understanding and knowledge of the structure and basic function of the human neurone; –knowledge of the generation of a nerve ‘impulse’; –knowledge of the processes of operation of the synapse; –a knowledge of the essential structures of the human central nervous system; –an understanding of the cellular architecture and dynamics of the cerebral cortex; cell assemblies and mirror neurons –evaluate and develop various computational models of the neurone; –evaluate the contribution of neural science to artificial intelligence; –form an evaluation and critique of restrictive functional localisation in the human brain.

7. Outline Twelve lectures Seven tutorials Two laboratory assignments A take-home assessment (‘exam’)

8. My Informal Marking Criteria A first is supposed to mean that the student is clearly qualified to do a research degree with a significant computational component. An upper second is supposed to mean that the student is qualified to do a research degree with a significant computational component. A lower second is supposed to mean that the student may be qualified to do a research degree with a significant computational component. A third is supposed to mean that the student has reached a minimum level of skill in computational science. I expect almost all of you to earn a first or upper second.

9. Ethics and Academic Freedom Conrad Russell (Academic Freedom, Routledge, 1993) discusses the underlying principles: “the freedom for academics within the law to question and test received wisdom, and to put forward new ideas and controversial or unpopular opinions without placing themselves in jeopardy. It is the freedom to follow a line of research where it leads, regardless of the consequences, and the corresponding freedom to teach the truth as we see it, with suitable acknowledgement of views which differ from our own....”

10. Obligations of Scholars This discipline must be acquired by anyone who wishes to be a scholar: the willingness to speak the truth, not listening to pleas of convenience. This also implies duties of –truthfulness, –avoidance of willful error, and –avoidance of plagiarism. Remember the University is a community of scholars, not simply some buildings and facilities, and you are members of that community.

11. My Position on Collaboration The following are acceptable: –Cooperation in developing an understanding of requirements. –Cooperation in the diagnosis of bugs and problems as long as the helper does not provide solutions. –These are pedagogically valuable and allowed. The following are not acceptable: –Collaboration in developing laboratory report documentation and figures. Write your own report! –Collaboration in doing the take-home assessment. We are assessing you, not your friend!

12. The Role of the Scientist and of the Engineer If the engineer is trying to model animal behaviour, the scientist is responsible for identifying appropriate data for comparison to the model. If the engineer is building a biomimetic robot, the scientist is responsible for providing guidance on the behaviour and how it is generated.

13. Complexity Biological systems are ‘complex’. –The cost of accurately modelling the folding of a medium-sized protein exceeds the computational resources of the universe. –Since the shapes of proteins defines their function, this means accurately modelling a small cell (or neuron) also requires enormous computational resources. –Brains contain enormous numbers of complex neurons. –The only way to model biological systems accurately is to use the systems to model themselves.

14. What is a body to do? Since we are already in a ‘state of sin’, we do the best we can with the tools we have. We use numerical methods to approximate the behaviour of neurons and neural networks in the expectation that even approximations will provide insight. These numerical methods solve ordinary and partial differential equations describing what happens in cells. GENESIS is a package for doing this.

15. Conclusions So welcome to a module that is intended to give you insight. Do the labs—you’ll learn from them. Do the laboratory reports—they’re practice in writing up experiments. Do the take-home—it assesses your critical thinking. And enjoy yourselves!

16. Numerical Preliminaries (Mascagni and Sherman, 1998, in Segev and Koch) The fundamental reason for error (loss of accuracy) is the finite nature of computers. Three important concepts: –Convergence (the error can be made arbitrarily small) –Consistency (the method solves a discrete problem that is the same as the continuous problem) –Stability (the solution remains bounded as the grid parameters go to zero)

17. Lax Equivalence Theorem (Richtmyer and Morton, 1967) A finite difference method for linear DEs is convergence if and only if it is consistent and stable. There is no general Lax equivalence theorem for non-linear systems.

18. ODE ‘Stiffness’ An ODE is stiff if it is difficult to solve. Stiff systems are characterised by disparate time scales. Non-stiff systems can be solved by explicit methods coded by amateurs. Stiff systems must be solved by implicit methods (usually in a professionally-written package). Compartmental models of neurons tend to be stiff, particularly as the number of compartments increases.