scientific workfields

Simulating early visual cortex dynamics (PhD-work)

We investigate sub- and suprathreshold activities in the early visual cortex. On the basis of so called voltage sensitive dye imaging pictures (Jun. Prof. Dr. D. Jancke, Prof. A. Grinvald and others at the Weizman Institute in Israel) of cat area 18 we derive a computational model of the early visual cortex to account for special effects caused by simple stimuli configurations.

The anatomical position of the LGN and early visual cortex within the visual pathway is depicted on the left.

On the left side a visual stimulus over space (y-axes) and time (x-axes) (left) and the corresponding membrane potential responses on the early visual cortex (cat, area 18) of a cat is presented (right). (measured with a voltage sensitive dye method by Jun. Prof. Dr. D. Jancke and others at the Weizman Institute in Israel)

Jancke and others (Jancke et. al, 2004) showed that there is evidence that the famous line-motion illusion (a square briefly flashed before presenting an aligned bar perceived as if the square gradually moves out to the bar, Hikosaka et. al, 1993) might already result in the early visual cortex by fast and wide spreading subthreshold activity. This subthreshold activity helps activity near the cued position to give spiking responses earlier, resulting in a gradual spread of spiking activity.

Neural fields are used to describe the dynamics of neural tissue by means of partial (integro) differential equations. We use a varified version of Wilson and Cowan's excitatory-inhibitory-network (Wilson and Cowan, 1972) to account for certain effects at the early visual cortex (see left figure) of cats describing the spread of subtheshold and spiking activities.
We simulate further effects of the lateral geniculate nucleus (LGN, see left figure) like contrast-gain control and smoothing effects.

With the dynamic neural field and a normalization LGN-model (see schematic picture left) we can simulate this effect and lateral spread of as well sub - and suprathreshold activity.

Raial basis function networks (Diploma Thesis, Mathematics)

On the left side you can see a function that represents a trained radial-basis-function-network:
You can approximate an analytically given function that has got unlimited grades of freedom with a function that has got limited grades of freedom. One class of functions with such limited grades of freedom are radial basis-function networks.
A radial-basis-function is for example a Gaussian-function. If you sum up these weighted basis-functions you get a new function which works as the approximation function.
You can use neural networks (see below) as function networks. The several types of networks differ on the used class(es) of transfer-functions (such as radial-basis-functions) and on the topology of the network (included the weights used at each neuron).
You can regard a neural network as a function

F : Rⁿ —> R^m

with n input arguments and m output arguments. The learning-problem is to find this function F (that means to find the best parameters for each function in a neuron) that best represents the analytical given function

f : Rⁿ —> R^m.

Of course you do not need an analytical given function to produce some learning-data: A learning-data has got the following form:
(x₁,y₁),...,(x_t,y_t), where t is the number of data-points and x_i is an n-dimensional and y_j is an m-dimensional vector (i,,j = 1..t).

The interesting side of the trained neural network is not only how good the given data- points are represented, it is also interesting what the network puts out, if you put new unknown data-points in it.