In this paper, we consider the problem of designing in-place algorithms for computing the maximum area empty rectangle of arbitrary orientation among a set of points in 2D, and the maximum volume empty axisparallel cuboid among a set of points in 3D. If n points are given in an array of size n, the worst case time complexity of our proposed algorithms for both the problems is O(n); both the alg...

An in-place algorithm is one in which the output is given in the same location as the input and only a small amount of additional memory is used by the algorithm. In this paper we describe three in-place algorithms for computing the convex hull of a planar point set. All three algorithms are optimal, some more so than others. . .

We propose a computational model of the CA3 region of the rat hippocampus that is able to reproduce the available experimental data concerning the dependence of directional selectivity of the place cell discharge on the environment and on the spatial task. The main feature of our model is a continuous, unsupervised Hebbian learning dynamics of recurrent connections, which is driven by the neuro...

Tolman proposed that complex animal behavior is mediated by the cognitive map, an integrative learning system that allows animals to reconfigure previous experience in order to compute predictions about the future. The discovery of place cells in the rodent hippocampus immediately suggested a plausible neural mechanism to fulfill the 'map' component of Tolman's theory. Recent work examining hip...

The activity of ensembles of hippocampal place cells represents a hallmark of an animal's spatial experience. The neuronal mechanisms that enable the rapid expression of novel place cell sequences are not entirely understood. Here we report that during sleep or rest, distinct sets of hippocampal temporal sequences in the rat preplay multiple corresponding novel spatial experiences with high spe...

The rat hippocampus contains cells that are characterized by location-specific firing. Previous work has shown that the angular position of hippocampal place cell firing fields is accurately controlled by the position of visual cues, suggesting that vision plays a important role in triggering place cell activity. However, a role for other types of information has also been suggested because pla...

The hippocampal formation is involved in navigation, and its neuronal activity exhibits a variety of spatial correlates (e.g., place cells, grid cells). The quantification of the information encoded by spikes has been standard procedure to identify which cells have spatial correlates. For place cells, most of the established metrics derive from Shannon's mutual information (Shannon, 1948), and ...

Hippocampal place cells fire selectively when a rat occupies a particular location. Under certain conditions, the cells briefly represent trajectories along locations away from the rat's current location. New results lend important insight into this phenomenon and demonstrate spatiotemporally coherent, cognitive representations that are independent of current sensory input.

As subjects perceive the sensory world, different stimuli elicit a number of neural representations. Here, a subjective distance between stimuli is defined, measuring the degree of similarity between the underlying representations. As an example, the subjective distance between different locations in space is calculated from the activity of rodent's hippocampal place cells and lateral septal ce...