Let d 2, and let fXv; v 2 Z d g be an i.i.d. family of non-negative random variables with common distribution F. Let N (n) be the maximum value of P v2 Xv over all connected subsets of Z d of size n which contain the origin. This model of \greedy lattice animals" was introduced by Cox et al. (1993) and Gandoll and Kesten (1994), who showed that if E X d 0 (log + X0) d+ < 1 for some > 0, then N ...

If we let p(f) ∝ e, we obtain a probability distribution over assignments of binary states to the vertices of the machine. Let A(V ) denote the set of assigments of {0, 1} values to V , i.e. A(V ) = {a | a : V → {0, 1}}. A restricted boltzmann machine(RBM), introduced in [Smo86], is a boltzmann machine where the underlying graph is a complete bipartite graph. Let V = V1∪V2 be the partition of t...

A super (d, )-regular graph on 2n vertices is a bipartite graph on the classes of vertices V1 and V2, where |V1| = |V2| = n, in which the minimum degree and the maximum degree are between (d− )n and (d+ )n, and for every U ⊂ V1,W ⊂ V2 with |U | ≥ n, |W | ≥ n, | e(U,W ) |U ||W | − e(V1,V2) |V1||V2| | < . We prove that for every 1 > d > 2 > 0 and n > n0( ), the number of perfect matchings in any ...

By combining optical imaging, single unit electrophysiology and cytochrome oxidase (CO) histology, we sought to reveal in greater detail the functional organization within the CO stripes of visual area V2 of primates. To visualize the disparity selective regions of V2, the imaging of binocular interaction was employed. These imaging maps guided single unit penetrations that then revealed a colu...

By combining optical imaging, single unit electrophysiology and cytochrome oxidase (CO) histology, we sought to reveal in greater detail the functional organization within the CO stripes of visual area V2 of primates. To visualize the disparity selective regions of V2, the imaging of binocular interaction was employed. These imaging maps guided single unit penetrations that then revealed a colu...