LIF and Neurodynamics Flashcards
What is stochasticity?
The combined effect of multiple sources of perturbation that give a phenomenon the appearance of randomness.
Where can you find stochasticity in the brain?
Stochasticity is present across all levels of brain activity. At the neuronal level, synaptic transmission is mediated by the stochastic release of neurotransmitters. Additionally, membrane potentials fluctuate due to the stochastic opening and closing of ion channels. Sensory input has stochastic components.
How to produce a Poisson spike train?
(1) Choose a rate “r” for random events (spikes per second - Hz)
(2) Decide on a bin size (1ms)
(3) For each bin take a random number “R”. If R < r place a spike in that bin.
How to model a postsynaptic potential in the IF model?
An pre-synaptic spike induces a tiny post-synaptic voltage increment (e.g., +5mV)
When is the poisson process a good model for a neuronal spike train?
When:
1) the average rate of the neuron is well defined
2) there is no influence on the appearance of a spike on the next
One can statistically test a spike train vs the poisson process to check for these properties.
They are especially adequate for modeling pyramidal cells, the main cells of the human cortex.
Why are LIF neurons good encoders of information?
The firing rate is proportional to the inputs intensity (for a given stimulus range).
Name three spiking phenomena that basic LIF models cannot capture?
They do not display
(1) No threshold adaptation
(2) No adaptive firing
(3) No resonant spiking
(4) No burst spiking
(5) No subthreshold oscillations
(6) No hyperpolarization spikes
What is in this diagram?
A phase portrait for a 1D dynamical system.
It shows the rate of change of a process as a function of its state.
The rate dx/dt = f(x) is in the vertical axis. The state variable x is in the horizontal axis.
How many fixed-points are found in this 1D phase plane?
- 3 -
The intersections with the horizontal axis are fixed points (dx/dt=0)
There are two attractors and one repellor
Describe the axis and what is visualized in this bifurcation diagram
The horizontal axis is a parameter, the vertical axis indicates the locations of equilibria.
The location, type and number of equilibria changes as parameter is change. Abrupt changes are called bifurcations.
Between I1 and I2 there are three equilibria, 2 stable, 1 unstable.
Describe the fate of the 5 trajectories for different initial conditions.
There are two stable states in this system, and trajectories in their range converge to them. There is also one unstable equilibrium, which repels trajectories.
In this phase portrait, what happens with the equilibria as the parameter I is increased from I0 to I2?
We see a stable attractor merging with an unstable attractor and subsequently disappearing.
(i.e, a saddle node bifurcation)
