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 neurons. Reconstruction or decoding is an inverse problem in which paper. The first goal is technical and is exemplified by the the physical variables are estimated from observed neural activity. population vector method applied to motor cortical activities Reconstruction is useful first in quantifying how much information during various reaching tasks (Georgopoulos et al. 1986, 1989; about the physical variables is present in the population and, second, Schwartz 1994) and the template matching method applied to 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

Sensorimotor transformations are nonlinear mappings of sensory inputs to motor responses. We explore here the possibility that the responses of single neurons in the parietal cortex serve as basis functions for these transformations. Basis function decomposition is a general method for approximating nonlinear functions that is computationally efficient and well suited for adaptive modification. In particular, the responses of single parietal neurons can be approximated by the product of a Gaussian function of retinal location and a sigmoid function of eye position, called a gain field. A large set of such functions forms a basis set that can be used to perform an arbitrary motor response through a direct projection. We com-pare this hypothesis with other approaches that are commonly used to model population codes, such as computational maps and vectorial representations. Neither of these alternatives can fully account for the responses of parietal neurons, and they are computationally less efficient for nonlinear transformations. Basis functions also have the advantage of not depending on any coordinate system or reference frame. As a consequence, the position of an object can be represented in multiple reference frames simultaneously, a property consistent with the behavior of hemineglect patients with lesions in the parietal cortex.

We analyze a model of navigational map formation based on correlation-based, temporally asymmetric potentiation and depression of synapses between hippocampal place cells. We show that synaptic modification during random exploration of an environment shifts the location encoded by place cell activity in such a way that it indicates the direction from any location to a fixed target avoiding walls and other obstacles. Multiple maps to different targets can be simultaneously stored if we introduce target-dependent modulation of place cell activity. Once maps to a number of target locations in a given environment have been stored, novel maps to previously unknown target locations are automatically constructed by interpolation between existing maps.

Gain modulation is a nonlinear way in which neurons combine information from two (or more) sources, which may be of sensory, motor, or cognitive origin. Gain modulation is revealed when one input, the modulatory one, affects the gain or the sensitivity of the neuron to the other input, without modifying its selectivity or receptive field properties. This type of modulatory interaction is important for two reasons. First, it is an extremely widespread integration mechanism; it is found in a plethora of cortical areas and in some subcortical structures as well, and as a consequence it seems to play an important role in a striking variety of functions, including eye and limb movements, navigation, spatial perception, attentional processing, and object recognition. Second, there is a theoretical foundation indicating that gain-modulated neurons may serve as a basis for a general class of computations, namely, coordinate transformations and the generation of invariant responses, which indeed may underlie all the brain functions just mentioned. This article describes the relationships between computational models, the physiological properties of a variety of gain-modulated neurons, and some of the behavioral consequences of damage to gain-modulated neural representations.

: : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : xiii I Introduction : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 1 A. Spatial representations and sensori-motor coordination : : : : : : : : : 1 B. The posterior parietal cortex : : : : : : : : : : : : : : : : : : : : : : : 2 C. Neural code for spatial representations : : : : : : : : : : : : : : : : : : 4 1. Dynamic remapping : : : : : : : : : : : : : : : : : : : : : : : : : : 4 2. Gain modulation : : : : : : : : : : : : : : : : : : : : : : : : : : : : 6 3. The Zipser and Andersen Network : : : : : : : : : : : : : : : : : : 6 D. Parallel vectorial representations : : : : : : : : : : : : : : : : : : : : : 9 E. Thesis Outline : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 10 1. Hierarchy in spatial representations : : : : : : : : : : : : : : : : : 10 2. A basis function approach for spatial representation : : : : : : : : 11 II Egocentric spatial representation in early vision : :...

Gain modulation is a nonlinear way in which neurons combine information from two (or more) sources, which may be of sensory, motor, or cognitive origin. Gain modulation is revealed when one input, the modulatory one, affects the gain or the sensitivity of the neuron to the other input, without modifying its selectivity or receptive field properties. This type of modulatory interaction is important for two reasons. First, it is an extremely widespread integration mechanism; it is found in a plethora of cortical areas and in some subcortical structures as well, and as a consequence it seems to play an important role in a striking variety of functions, including eye and limb movements, navigation, spatial perception, attentional processing, and object recognition. Second, there is a theoretical foundation indicating that gain-modulated neurons may serve as a basis for a general class of computations, namely, coordinate transformations and the generation of invariant responses, which indeed may underlie all the brain functions just mentioned. This article describes the relationships between computational models, the physiological properties of a variety of gain-modulated neurons, and some of the behavioral consequences of damage to gain-modulated neural representations. NEUROSCIENTIST 7(5):430-440, 2001 KEY WORDS Gain fields, Computational neuroscience, Computer model, Parietal cortex, Neglect, Coordinate transformations Neurons in the visual system represent the visual world;