Lecture note on NISS2003 Neuron model and synfire chain.

Theory of localized synfire chain

Neuron is a noisy information processing unit and conventional view is that information in the cortex is carried on the rate of neurons spike emission. More recent studies on the activity propagation through the homogeneous network have demonstrated that signals can be transmitted with millisecond fidelity; this model is called the Synfire chain and suggests the possibility of the spatio-tempor...

Lecture Note on Auctions

There has been a tremendous growth in both the number of internet auction websites, where individuals can put up items for sale under common auction rules, and the value of goods sold there. The objective of auction theory is to rigorously understand the properties and implications of auctions used in the real world. I mainly investigate four auction forms: (1) The open ascending price or Engli...

Lecture Note: Self-Selection — The Roy Model

Synfire chain in a balanced network

We investigate the formation of ordered spatiotemporal activations of pools of neurons in synfire chains (SFC) within a balanced network, both by simulations and by analytic tools. Using a suitable matrix of synaptic connections, we show that the results depend on the ratio between the size of an individual pool of neurons (w) and the total excitatory input of a neuron (K). In our simulations o...

Lecture note on convection and diffusion

The logic we are going to employ to survey the similarity structure of several kinds of PDEs is the following. The preliminary requirement is that the problem under consideration should be well-posed, or the uniqueness should be guaranteed at least. Let u(x, t) be a solution to such a problem and consider a rescaled function v given by u(x, t) = av(bx, ct), a, b, c > 0. (1.1) The main step is t...