B.S.  Biomedical Engineering

Columbia

2004

Reverse Engineering the Mouse Visual Cortex

Background:  Many of the brain's functions are network phenomenon which depend on the interaction of many neurons. Investigating these phenomenon requires recording from many neurons simultaneously. Rafael Yuste et Al. have developed a technique for recording from many neurons using calcium sensitive dyes and two photon microscopy. Since changes in calcium concentration are ubiquitous with spiking, Yuste et Al. have measured a cell's spike train by using two photon microscopy and calcium sensitive dyes to track calcium concentration. Multiple neurons can be recorded from simultaneously by loading a layer with dye and then scanning the microscope across the layer to sequentially record the intensity at multiple sights. A movie can then be constructed showing the intensity of each pixel in each frame.

In their analysis of this data, Cossart et Al. collapsed the analog calcium signals to a digital code that consisted only of the times when the calcium signal for a neuron exceeded some threshold.  Cossart and et Al. then used a statistical analysis of the correlations between events of different neurons to draw conclusions about the dynamics of spontaneous activity in cortical networks. Cossart and et Al found that neurons were characterized by UP states, periods of increased activity. The UP states of different neurons formed spatial and temporal patterns.

Project Goals:

· Use dynamic, generative models such as SLDS's to automatically classify UP states

· Use correlations between UP states of different neurons to determine network connectivity - PCA, ICA are used to find correlations

Tracking: An Example of Probabilistic Inference

Background: Since Hubel and Wiesel proposed their model for explaining the receptive fields of cortical neurons in 1962, neuroscience has leaned heavily on linear systems theory. The brain, however, is highly non-linear. In addition, the deterministic nature of linear systems theory makes it ill-suited for performing the integration and inference tasks that confront living organisms. Probability theory offers a better suited mathematical framework for performing such tasks.

To investigate how the brain might implement probabilistic inference we considered how the brain might implement the Condensation Algorithm of Michael Isard and Andrew Blake.Michael Isard and Andrew Blake devised an algorithm called the Condensation Algorithm. (Contour Tracking By Stochastic Propagation of Conditional Density. In proceedings European Conference of Computer Vision, 1996 pp. 343-356 Cambridge, Uk) Basically, the condensation algorithm is an adaptation of the kalman filter. Isard and Blake created a method for sampling that allows them to use the Kalman filter for any pdf. So they are no longer restricted to just using gaussians like Kalman Filters. 

Project Goals:

· Use the Condensation Algoirthm to perform real-time tracking.

· Implement the Condensation Alogirthm using spike based computations.

· As a first step we implemented the algorithm using discrete nodes. Conceivably the operations at each node could be performed a neuron or group of neurons.