Week 1.
Sections 1 and 2 of the notes. 
<br>
<br>

Week 2. Section 3 of the notes. <a href="prob1.html">Problem set 1</a>
<br>
<br>

Week 3. Set up Xpp, go through XPP tutorial. 
<br>
Draw your favorite phase plane and bifurcation diagram from Section 3 in XPP. <br>
Do problem 3 from <a href="http://www.jhu.edu/motn/homeworks/Homework_5_13.pdf">here</a>

<br>
<br>
Week 4. Section 4 of the notes. Catch up with problems from previous week. 
<br>
Exercises 1-3 from Section 5.8 of "Mathematical Foundations of Neuroscience" book (available
online from the library)

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<br>
Week 5. Section 5 of the notes.
<br> 
Explain the behavior of theta-model in Fig.23B using its phase plane and/or bifurcation diagrams.

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Week 6. Chapter 8 from "Dynamical systems in neuroscience" by Izhikevich (online in library), up tp 8.1.5
<br>
Excercises: - What is Ermentrout-Kopell theta model? What is its relationship with QIF model? 
<br>
- Program up QIF with adaptation or EIF with adaptation and study how their responses to constant depolarizing levels of current vary as you change the strength and time constant of adaptation . 
<br><br>
Week 7/8. Start with <a href="BrunelPRL01.pdf">Brunel et al. 2001</a>, 
<a href="IF_comparison_vilele_lindner.pdf">Vilela and Lindner</a> and 
<a href="richardson_etal2003">Richardson et al</a>.<br>

Focus on what the models are, and what are the results, not the analytical approaches (yet).
<br>

Exercises: program up one of the IF models with sinusoidally modulated 
white and (separately) low-pass-filtered
noise. 
<br>
Preferably in both matlab and XPP. 

<br><br>

Week 9. Review on <a href="http://www.ploscompbiol.org/article/info%3Adoi%2F10.1371%2Fjournal.pcbi.1002247">models of channel noise</a>, 
<a href="http://www.nature.com/nature/journal/v448/n7155/abs/nature06028.html">
correlations and firing rates</a>, <a href="http://www.math.utah.edu/~borisyuk/PAPERS/comp_neuro08.pdf">noise contributing to 
population oscillations</a>
<br>
Exercise: feed a leaky integrate and fire model with subthreshold time-varying applied current and sufficient noise to generate some spikes. Repeat with the 
same current input and indepentently generated noise several times and then 
look at the firing rate. Does it track the subthreshold stimulus?

<br><br>
Week 10. Chapter 10 from ERmentrout and Terman book (online in the library): 10.1
(except 10.1.3 and 10.1.4.1), 10.2.1.2-10.2.1.3, 10.2.3-10.2.5
<br>
Chapter 1 from "Phase response curves in Neuroscience", Schultheiss et al (Eds). Focus mostly on sections 1-3.

<br><br>
Week 11. Continue reading the PRC chapter.<br>
<a href="http://neurotheory.columbia.edu/~larry/VanVreeswijkJCN94.pdf">
More on synchrony</a>
<br>
Exercises: compute phase-response curve of the Morris-Lecar neuron in both
type I and type II regimes in XPP. 
<br>
Write Focker-Planck equation
for leaky integrat-and-fire neuron with additive white noise.
<br><br>

Week 12. 
<br>
PRC computation in XPP: <a href="http://www.math.pitt.edu/~bard/bardware/tut/xpptut4.html#reduction"> Tutorial</a>, <a href="PRC.pdf"> From XPP book</a> (Notice there are 2 different approaches to the computation, corresponding to 
2 different sections of last week's chapter
<br>
STDP: How does the model in <a href="http://neurotheory.columbia.edu/~larry/SongNatNeuro00.pdf"> this paper</a> relate to the description in 
<a href="http://www.scholarpedia.org/article/Spike-timing_dependent_plasticity">
Scholarpedia</a> 

<br><br>
Week13.
<br>
<a href="http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3308339/">Unlearning synchronization</a>
<br>
<a href="http://icwww.epfl.ch/~gerstner/SPNM/node85.html">Tuning of sound
localization system</a>
<br>
<a href="http://icwww.epfl.ch/~gerstner/SPNM/node74.html#SECTION04143000000000000000">Calcium-based model of synaptic plasticity</a>