================================================================================================== McNaughton, B.~L., F.~P.~Battaglia, O.~Jensen, E.~I.~Moser, and M.-B. Moser (2006) "Path integration and the neural basis of the cognitive map." Nature Reviews Neuroscience Vol. 7, pp. 663-678 ================================================================================================== Neural network models for path integration Mechanisms based on self-organizing and self-sustaining neural activity, or attractor dynamics, such as those originally proposed in Hebb's [13] cell assembly theory, have been essential components in several models accounting for path integration and the head direction system in rats [14]. [13] Hebb, D. O. The Organization of Behavior (Wiley, New York, 1949). (A seminal work on which much of modern neural network theory is founded, including the concepts of associative synaptic plasticity, cell assemblies and phase sequences.) [14] McNaughton, B. L., Chen, L. L. & Markus, E. J. "Deadreckoning, landmark learning, and the sense of direction: a neurophysiological and computational hypothesis." J. Cog. Neurosci. 3, 190.202 (1991). (An early version of the head direction path integrator model which formed the conceptual basis of subsequent continuous attractor models for path integration.) => not available for free In path integration, the information to be maintained and updated is not a set of discrete items (as are found in Hopfield-type attractor networks for discrete memories); rather, it is a continuous variable representing position or head direction. A continuum of cell assemblies, or a continuous attractor [15.19], is therefore needed to encode position or head direction. Such a continuum can exist in one dimension, as in the case of direction; two dimensions, as in the case of location in the plane; or many dimensions. It is equivalent to a large set of correlated discrete attractors, in which the energy barriers between neighbouring attractors become negligible [20,21]. [15] Wilson, H. R. & Cowan, J. D. A mathematical theory of the functional dynamics of cortical and thalamic nervous tissue. Kybernetik 13, 55.80 (1973). => not available for free [19] Tsodyks, M. & Sejnowski, T. "Associative memory and hippocampal place cells. " Int. J. Neural Syst. 6, S81.S86 (1995). => done My-paper ================================================================================================== In their good review paper Since O'keefe's {\it "first theoretical suggestion of a landmark independent navigational system up stream of the hippocampus," as McNaughton et al.~(2006) wrote in their nice review paper, OfKeefe, J.~(1976) "Place units in the hippocampus of the freely moving rat." Exp. Neurol. 51, 78.109 (1976). the discovery of spatially selective place cells in the hippocampus and the proposal that the hippocampus is the neural substrate of a ecognitive mapf3, OfKeefe, J. & J. Dostrovsky. The hippocampus as a spatial map: preliminary evidence from unit activity in the freely moving rat. Brain Res. 34, 171.175. (1971). 3. OfKeefe, J. & Nadel, L. The Hippocampus as a Cognitive Map (Clarendon, Oxford, 1978). 4. Mittelstaedt, M. L. & Mittelstaedt, H. Homing by path integration in a mammal. Naturwissenschaften 67, 566.567 (1980) (in German). The first report of path integration in a mammal. 5. Taube, J. S., Muller, R. U. & Ranck, J. B. Jr. Headdirection cells recorded from the postsubiculum in freely moving rats. I. Description and quantitative analysis. J. Neurosci. 10, 420.435 (1990). The first quantitative description of head directionsensitive cells in the brain. 6. Ranck, J. B. in Electrical Activity of the Archicortex (eds. Buzsaki, G. & Vanderwolf, C. H.) 217.220 (Akademiai Kiado, Budapest, 1985). The first report of head direction-sensitive cells in the brain.