Self-Wiring of Neural Networks

In order to form the intricate network of synaptic connections in the brain, the growth cones migrate through the embryonic environment to their targets using chemical communication. As a first step to study self-wiring, 2D model systems of neurons have been used. We present a simple model to reproduce the salient features of the 2D systems. The model incorporates random walkers representing the growth cones, which migrate in response to chemotaxis substances extracted by the soma and communicate with each other and with the soma by means of attractive chemotactic "feedback".Comment: 10 pages, 10 PostScript figures. Originally submitted to the neuro-dev archive which was never publicly announced (was 9710001

Mean field analysis of Williams-Bjerknes type growth

We investigate a class of stochastic growth models involving competition between two phases in which one of the phases has a competitive advantage. The equilibrium populations of the competing phases are calculated using a mean field analysis. Regression probabilities for the extinction of the advantaged phase are calculated in a leading order approximation. The results of the calculations are in good agreement with simulations carried out on a square lattice with periodic boundaries. The class of models are variants of the Williams- Bjerknes model for the growth of tumours in the basal layer of an epithelium. In the limit in which only one of the phases is unstable the class of models reduces to the well known variants of the Eden model.Comment: 21 pages, Latex2e, Elsevier style, 5 figure

Do firms buy their stock at bargain prices? : Evidence from actual stock repurchase disclosure

We use new data from SEC filings to investigate how S&P 500 firms execute their open market repurchase programs. We find that smaller S&P 500 firms repurchase less frequently than larger firms, and at a price which is significantly lower than the average market price. Their repurchase activity is followed by a positive and significant abnormal return which lasts up to three months after the repurchase. These findings do not hold for large S&P 500 firms. Our interpretation is that small firms repurchase strategically, whereas the repurchase activity of large firms is more focused on the disbursement of free cash. JEL Classification: G14, G30, G35 Keywords: Stock Repurchases, Stock Buybacks, Payout Policy, Timing, Bid-Ask Spread, Liquidit

Holographic Entanglement Entropy of Multiple Strips

We study holographic entanglement entropy (HEE) of $m$ strips in various holographic theories. We prove that for $m$ strips with equal lengths and equal separations, there are only 2 bulk minimal surfaces. For backgrounds which contain also "disconnected" surfaces, there are only 4 bulk minimal surfaces. Depending on the length of the strips and separation between them, the HEE exhibits first order "geometric" phase transitions between bulk minimal surfaces with different topologies. We study these different phases and display various phase diagrams. For confining geometries with $m$ strips, we find new classes of "disconnected" bulk minimal surfaces, and the resulting phase diagrams have a rich structure. We also study the "entanglement plateau" transition, where we consider the BTZ black hole in global coordinates with 2 strips. It is found that there are 4 bulk minimal surfaces, and the resulting phase diagram is displayed. We perform a general perturbative analysis of the $m$-strip system: including perturbing the CFT and perturbing the length or separation of the strips.Comment: 32 pages; v2: citations adde