Formal Computational Skills

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Formal Computational Skills

• Introduction

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My research areas Neuroethology visual
learning (mainly homing) in insects combining
behavioural experiments with modelling. Also
involves computer vision, especially object
recognition Diffusible neuromodulators in real
brains and robots. Mathematical modelling of
diffusion development and analysis of the GasNet
(for autonomous robotics). Evolutionary
robotics, evolution as optimisation, neural
Networks Also do bits of pattern
recognition/data mining and image processing
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Course Aims
Not everyone has the necessary mathematical tools
or experience to engage fully with MSc
courses This course will provide mathematical
background needed to understand several subjects
in later courses. In particular Neural Networks
and Computational Neuroscience Also, useful for
building simulations, analysing neural networks,
optimisation (by GAs or other) and basic
statistics Why called Formal Computational
Skills? Dont know
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Learning Outcomes

• By the end of the course you will be able to
• Use matrices to perform neural network operations
  NNs
• Use gradient descent for function optimisation
  NNs, ALife, GAs/artificial evolution
• Construct and analyse 1st order differential
  equations Comp Neuro, ALife
• Calculate the entropy of a random variable NNs,
  Comp Neuro and just in general
• Use the matlab programming language Useful
  generally

Stealth Outcomes Pass on enjoyment of maths by
showing interesting maths problems and
highlighting deeper aspects Also aim to
demystify scary maths terminology eg entropy
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What I Wont Do

• Make you all expert mathematicians
• Prove all the mathematical theory
• Explain all of the example topics such as Neural
  Networks
• However it is often difficult for me to gauge
  what to leave out or put in
• It will really really help if you tell me I am
  going too fast, have left out too much detail am
  incomprehensible etc etc

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General Structure

• Lectures will give mathematical details/theory on
  a subject
• Seminars will (mainly) be practical computer
  classes which reinforce theory using a topic from
  future courses
• Idea is to build a model and experiment with it
  empirically to understand the theory and see what
  happens in practice
• Next week some basics on functions
• Next 3 weeks on NNs and optimisation
• Next 3 on constructing and analysing neural
  models (1st order differential equations)
• Last 1/2 on probability, statistics

Lectures/seminars will build on each other so
early weeks are introductory, containing
knowledge needed in later weeks
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Topics
Lectures 1. Functions and notation 2. Matrices
and Vectors 3. Matlab (minimal lecture) 4.
Differentiation 5. Numerical integration of
differential equations 6-7. Dynamical systems
analysis 7-8. Probability and statistics
Seminars 1. Practice with functions/notation 2.
NN operations via matrices 3. Networks in
matlab 4. Gradient descent 5. Integration of
neuron model 6-7. CTRNN/GasNet analysis 7-8.
Entropy and information theory
Last 2 weeks(-ish) are for a mini-project
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References

• Very difficult to give references as some topics
  are school-level, some undergraduate and some
  very specialised
• Also, maths text-books are notorious for being
  suited to particular people/levels of expertise,
  so what I think is excellent you might hate
• Best thing is to search for a key-word in the
  library and check the short-loan books for one
  that suits you/your level
• Document from the course web-site has good
  introductory stuff but is a little out of date
  regarding some topics
• Numerical Recipes in C (Press et al., 79) is
  excellent but quite high level
• http//mathworld.wolfram.com/ is good for
  reference (many others sites out there for
  particular subjects)

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Organisation
There are differing mathematical abilities in the
group. I will go as slowly as I feel is necessary
LET ME KNOW IF TOO FAST. However, you dont
have to come to the lectures. Eg

• This weeks topic is functions
• Common functions and how to visualise functions
• Equation of a straight line and linear equations
• Summation notation
• (briefly) What a polynomial is
• (V briefly) notion of ex and logarithms
• DONT come if you know these things or you will
  be bored. If not sure, look at lecture material
  and the worksheet and see if you can do it
• You all have to complete the worksheet

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Assessment
70 weekly(-ish) worksheets handed in on
subsequent weeks 30 by a mini-project handed in
at the end of term

• Worksheets (apart from first 2 weeks)
  empirically test a mathematical topic through
  computer simulation
• Aims and outcomes
• Intro to the topic
• Description of task
• Breakdown/lead through of tasks
• Questions to be answered/investigated.
• Seminars will get you all to the level where you
  can investigate each topic. Attendance and
  participation should give 50. Partly
  peer-assessed

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Mini Project
Idea is to find a mathematical topic that you
DONT already know and that will be useful in
doing the course (some will be suggested) You
then need to describe it and investigate/analyse
it and so you show you have understood it good
way is to imagine you are explaining how it works
to somebody else (me) Marks will NOT be based on
the mathematical complexity of the topic but on
demonstration of comprehension and learning
More details later
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Finally

• Idea of the course is to help you with later
  subjects
• Assessments are needed as maths is often learnt
  by practice
• Topics are things you WILL USE in later courses
• There is NO point in simply going through the
  motions rather than working on the basics
• Time (mine and yours) would be MUCH better spent
  elsewhere