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Over the past four decades, the dominant view of visual processing in primates is that the complexity of feature analysis increases as information flows from primary visual cortex rostrally through regions of the temporal lobe, into area TE, where whole complex objects are represented. This view is consistent with observations that TE neurons are selective for complex objects such as hands and faces. We test a major prediction: bilateral removal of area TE will damage high-level visual object categorization, such as distinguishing cats from dogs. After removal of TE, this type of categorical classification is only mildly impaired in old-world monkeys. However, when the images are degraded by a small amount of visual noise, the monkeys are virtually unable to correctly classify morphs of cats versus dogs. This raises the possibility that area TE makes it possible to identify partially obscured objects, that is, it is critical for pattern completion.

Monkeys can learn discrete categories (such as 'cat' / 'dog') while performing a behavioral task without explicit instruction related to the categories [1]. The reward protocol is such that the monkey always gains some reward if it performs correctly an easy learnable task, but it can considerably increase its cumulative reward if it can make a proper use of categorical cues, which requires being able to distinguish between the two categories. These experiments have not allowed to compare the acquired knowledge of categories with the standard phenomenon of categorical perception [2]. Notably, the main characteristic features of categorical perception show up in the psychophysics when the stimuli are ambiguous, near the boundary between categories in stimulus space. On the theoretical side, these features have been shown to emerge as byproduct of optimal neural coding, optimality being defined in terms of information content and Bayesian decision, when the task is to decide which category the stimulus belongs to (identification task) [3,4]. In new experiments we have focused on the transition between categories, controlling for the degree of ambiguity of the cue. The experimental protocol is otherwise similar to the one in [1]. We have modeled these behavioral experiments with a focus on learning. Our experiments indicate that the monkey acquires 'categorical perception' (results to be presented in detail elsewhere). The modeling shows that a reinforcement learning scheme [5,6] can reproduce the main behavioral results, and gives some insight on how categorical perception builds up through learning. The neural and behavioral properties in the model are qualitatively similar to those derived for an identification task assuming optimal coding. Quantitatively, the details depend on the reward protocol. The model parameters can be fitted to match the experimental behavioral results quantitatively. In the model, the visual cues are encoded by a population of neurons with tuning curves sharing a single global shape (e. g. a sigmoid form), but with idiosyncratic parameters. This assembly feeds a decision layer, producing the behavioral choice function - the probability to make one of two possible choices given the cue. We study the optimal choice function resulting from maximizing the cumulative reward over all the tuning curves parameters. We demonstrate a universality property, namely, for a large enough population code, the same optimal behavioral choice function is obtained whatever the shape of the tuning curves (subject to some weak restrictions). We show an exact mathematical procedure to construct the optimal set of parameters for a large class of shapes of tuning curves. We believe the method is applicable to a wide range of neural models.

We analyse the low temperature properties of a system of classical Heisenberg spins on a hexagonal lattice with Kitaev couplings. For a lattice of 2N sites with periodic boundary conditions, we show that the ground states form an (N+1) dimensional manifold. We show that the ensemble of ground states is equivalent to that of a solid-on-solid model with continuously variable heights and nearest neighbour interactions, at a finite temperature. For temperature T tending to zero, all ground states have equal weight, and there is no order-by-disorder in this model. We argue that the bond-energy bond-energy correlations at distance R decay as 1/R^2 at zero temperature. This is verified by Monte Carlo simulations. We also discuss the relation to the quantum spin-S Kitaev model for large S, and obtain lower and upper bounds on the ground state energy of the quantum model., Comment: 11 pages, 8 figures

We construct clusters of classical Heisenberg spins with two-spin $\vec{S}_i.\vec{S}_j$-type interactions for which the ground state manifold consists of disconnected pieces. We extend the construction to lattices and couplings for which the ground state manifold splits into an exponentially large number of disconnected pieces at a sharp point as the interaction strengths are varied with respect to each other. In one such lattice we construct, the number of disconnected pieces in the ground state manifold can be counted exactly., Comment: Accepted for publication in Physica A; 6 pages, 4 figures

Adding grains at a single site on a flat substrate in the Abelian sandpile models produce beautiful complex patterns. We study in detail the pattern produced by adding grains on a two-dimensional square lattice with directed edges (each site has two arrows directed inward and two outward), starting with a periodic background with half the sites occupied. The size of the pattern formed scales with the number of grains added $N$ as $\sqrt{N}$. We give exact characterization of the asymptotic pattern, in terms of the position and shape of different features of the pattern., 5 pages, 4 figures, submitted to Phys. Rev. Lett

We construct a class of lattices in three and higher dimensions for which the number of dimer coverings can be determined exactly using elementary arguments. These lattices are a generalization of the two-dimensional kagome lattice, and the method also works for graphs without translational symmetry. The partition function for dimer coverings on these lattices can be determined also for a class of assignments of different activities to different edges., Comment: 4 pages, 2 figures; added results on partition function when different edges have different weights; modified abstract; added references

We study the ground state energy E(G)(n) of N classical O(n) vector spins with the Hamiltonian H=-Sigma(i>j)J(ij)S(i).S(j) where the coupling constants {J(ij)} are arbitrary. We prove that E(G)(n) is independent of n for all n>n(max)(N)= left floor(sq rt[8N+1]-1)/2 right floor. We show that this bound is the best possible. We also derive an upper bound for E(G)(m) in terms of E(G)(n), for m j) J(ij) + E(G)(n)]/Sigma(i>j) J(ij). We describe a procedure for constructing a set of J(ij)'s such that an arbitrary given state, {S(i)}, is the ground state. We show that the problem of finding the ground state for the special case n=N is equivalent to finding the ground state of a corresponding soft-spin problem.

We study the ground state energy E(G)(n) of N classical O(n) vector spins with the Hamiltonian H=-Sigma(ij)J(ij)S(i).S(j) where the coupling constants {J(ij)} are arbitrary. We prove that E(G)(n) is independent of n for all nn(max)(N)= left floor(sq rt[8N+1]-1)/2 right floor. We show that this bound is the best possible. We also derive an upper bound for E(G)(m) in terms of E(G)(n), for mn . We obtain an upper bound on the frustration in the system, as measured by F(n) triple bond [Sigma(ij) J(ij) + E(G)(n)]/Sigma(ij) J(ij). We describe a procedure for constructing a set of J(ij)'s such that an arbitrary given state, {S(i)}, is the ground state. We show that the problem of finding the ground state for the special case n=N is equivalent to finding the ground state of a corresponding soft-spin problem.