Computational neuroscience

OpenStax

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Dynamics of a network of single compartmental cells

2 Network dynamics

3 Leak current and active current

4 Network current

5 External current

6 Model of a hypercolumn in primary visual cortex

Dynamics of the firing rate of single compartmental cells

Cell assemblies: a binary integer programming problem

3 Mathematics of cell assemblies

4 Adjacency matrix ( A d )

5 Threshold ( k )

6 The excitation map, e(x,k)

7 Graph theory and cell assemblies

9 Algorithms for finding a k -assembly

10 Finding minimal k -cores:

11 Algorithm examples

12 bintprog Example

13 Closure example

14 Finding k -assemblies

15 Future work for finding cell assemblies

17 Acknowledgements

A model of a grid cell

Modeling cell assemblies

5 Mathematical model

7 Synaptic connections

8 Computational methods for solving differential equations

9 Building networks

10 Picking weights

11 Hooking up the network

13 Network size and patterns

14 Parameters for cells

15 Remaining parameters

16 Running simulations

17 Simulation 1

18 Simulation 2 - pattern competition

20 Acknowledgements

Cell assembly enumeration in random graphs

5 Finding k-assemblies

6 K-core enumeration

8 Assembly enumeration

9 Experimentation

10 Random graph generation

Mathematical models of hippocampal spatial memory

2 Modeling hippocampal place cells

3 Conductance-based integrate and fire model

4 Synaptic conductance

5 Synaptic plasticity

6 Spike-time dependent plasticity

7 Calcium dependent plasticity: a better model?

8 Plasticity equations

9 Calcium equations

10 Metaplasticity

11 Spike-time dependence of cadp

12 Comparison: stdp vs. cadp

13 Experimental setup revisited

14 Stdp dynamics

15 Cadp dynamics

16 Applying metaplasticity to cadp

17 Conclusions/future work

Mathematical modeling of hippocampal spatial memory with place cells

1 Background: place cells in the hippocampus

3 Motivation: double rotation experiment

5 Neuron as a circuit: integrate and fire

6 Model of dre: 120-cell ring

8 Model for analysis

9 Computational method

10 Analytic method

11 Problems and results

12 Minimum input weight for activity

13 Computational vs. analytic method

14 Number of input spikes versus input weight

15 Computational vs. analytic method

16 Application of findings

Exploring the biochemical and mechanical effects of intestinal edema on

5 Mathematical model

6 Biochemical model

7 Ach simulation

8 Calcium control

9 Myosin activation

10 Force generation

11 Mechanical model

Source: OpenStax, The art of the pfug. OpenStax CNX. Jun 05, 2013 Download for free at http://cnx.org/content/col10523/1.34

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