The head-direction (HD) cells found in the limbic system in freely mov ing rats represent the instantaneous head direction of the animal in the horizontal plane regardless of the location of the animal. The internal direction represented by these cells uses both self-motion information for inertially based updating and familiar visual landmarks for calibration. Here, a model of the dynamics of the HD cell ensemble is presented. The stability of a localized static activity profile in the network and a dynamic shift mechanism are explained naturally by synaptic weight distribution components with even and odd symmetry, respectively. Under symmetric weights or symmetric reciprocal connections, a stable activity profile close to the known directional tuning curves will emerge. By adding a slight asymmetry to the weights, the activity profile will shift continuously without disturbances to its shape, and the shift speed can be controlled accurately by the strength of the odd-weight component. The generic formulation of the shift mechanism is determined uniquely within the current theoretical framework. The attractor dynamics of the system ensures modality-independence of the internal representation and facilitates the correction for cumulative error by the putative local-view detectors. The model offers a specific one-dimensional example of a computational mechanism in which a truly world-centered representation can be derived from observer-centered sensory inputs by integrating self-motion information.

Zhang, Kechen, Iris Ginzburg, Bruce L. McNaughton, and Ter-decoding problems have been studied previously (Abbott rence J. Sejnowski. Interpreting neuronal population activity by re-1994; Bialek et al. 1991;Optican and Richmond 1987; Saliconstruction: unified framework with application to hippocampal nas and Abbott 1994; Seung and Sompolinsky 1993; Snippe place cells. J. Neurophysiol. 79: 1017-1044, 1998. Physical variables 1996Zemel et al. 1997;Zohary et al. 1994).such as the orientation of a line in the visual field or the location of Two main goals for reconstruction are approached in this the body in space are coded as activity levels in populations of paper. The first goal is technical and is exemplified by the neurons. Reconstruction or decoding is an inverse problem in which population vector method applied to motor cortical activities the physical variables are estimated from observed neural activity.during various reaching tasks (Georgopoulos et al. 1986(Georgopoulos et al. , 1989 Reconstruction is useful first in quantifying how much information Schwartz 1994) and the template matching method applied to about the physical variables is present in the population and, second, in providing insight into how the brain might use distributed represen-disparity selective cells in the visual cortex (Lehky and Sejnowtations in solving related computational problems such as visual ob-ski 1990) and hippocampal place cells during rapid learning of ject recognition and spatial navigation. Two classes of reconstruction place fields in a novel environment (Wilson and McNaughton methods, namely, probabilistic or Bayesian methods and basis func-1993). In these examples, reconstruction extracts information tion methods, are discussed. They include important existing methods from noisy neuronal population activity and transforms it to a as special cases, such as population vector coding, optimal linear more explicit and convenient representation of movement and estimation, and template matching. As a representative example for position. In this paper, various reconstruction methods that are the reconstruction problem, different methods were applied to multitheoretically optimal under different frameworks are considelectrode spike train data from hippocampal place cells in freely ered; the ultimate theoretical limits on the best achievable accumoving rats. The reconstruction accuracy of the trajectories of the racy for all possible methods also are derived. rats was compared for the different methods. Bayesian methods were especially accurate when a continuity constraint was enforced, and Our second goal for reconstruction is biological. Because the best errors were within a factor of two of the information-theoretic the brain extracts information distributed among the activity limit on how accurate any reconstruction can be and were comparable of populations of neurons to solve various computational with the intrinsic experimental errors in position tracking. In addition, problems, the question arises as to which algor...

Neocortex, a new and rapidly evolving brain structure in mammals, has a similar layered architecture in species over a wide range of brain sizes. Larger brains require longer fibers to communicate between distant cortical areas; the volume of the white matter that contains long axons increases disproportionally faster than the volume of the gray matter that contains cell bodies, dendrites, and axons for local information processing, according to a power law. The theoretical analysis presented here shows how this remarkable anatomical regularity might arise naturally as a consequence of the local uniformity of the cortex and the requirement for compact arrangement of long axonal fibers. The predicted power law with an exponent of 4͞3 minus a small correction for the thickness of the cortex accurately accounts for empirical data spanning several orders of magnitude in brain sizes for various mammalian species, including human and nonhuman primates.