Various parameterizations of rotations are related through a unifying mathematical treatment, and transformations between coordinate systems are computed using the Campbell-Baker Hausdorff formula. Next, we describe Listing's law by means of the Lie algebra so(3). This enables us to demonstrate a direct connection to Donders' law, by showing that eye orientations are restricted to the quotient space 80(3)/80(2). The latter is equivalent to the sphere S2, which is exactly the space of gaze directions. Our analysis provides a mathematical framework for studying the oculomotor system and could also be extended to investigate the geometry of mUlti-joint arm movements.

The passeriformes or songbirds make up more than half of all bird species and are divided into two groups: the os cines which learn their songs and sub-oscines which do not. Oscines raised in isolation sing degraded species typical songs similar to wild song. Deafened oscines sing completely degraded songs (Konishi, 1965), while deafened sub-oscines develop normal songs (Kroodsma and Konishi, 1991) indicating that auditory feedback is crucial in oscine song learning. Innate structures in the bird brain regulate song learning. For example, song sparrows show innate preferences for their own species' songs and song structure (Marler, 1991). Innate preferences are thought to be encoded in an auditory template which limits the sounds young birds may copy. According to the auditory template hypothesis birds go through two phases during song learning, a memorization phase and a motor phase.

The nature of this reorganisation seems consistent with the behaviour of competitive neural networks, as has been demonstrated in the past by computer simulation.

While it is generally agreed that neurons transmit information about their synaptic inputs through spike trains, the code by which this information is transmitted is not well understood. An upper bound on the information encoded is obtained by hypothesizing that the precise timing of each spike conveys information. Here we develop a general approach to quantifying the information carried by spike trains under this hypothesis, and apply it to the leaky integrate-and-fire (IF) model of neuronal dynamics. We formulate the problem in terms of the probability distribution peT) of interspike intervals (ISIs), assuming that spikes are detected with arbitrary but finite temporal resolution. In the absence of added noise, all the variability in the ISIs could encode information, and the information rate is simply the entropy of the lSI distribution, H (T) (-p(T) log2 p(T)}, times the spike rate. H (T) thus provides an exact expression for the information rate. The methods developed here can be used to determine experimentally the information carried by spike trains, even when the lower bound of the information rate provided by the stimulus reconstruction method is not tight. In a preliminary series of experiments, we have used these methods to estimate information rates of hippocampal neurons in slice in response to somatic current injection. These pilot experiments suggest information rates as high as 6.3 bits/spike.

We have developed a computational theory of rodent navigation that includes analogs of the place cell system, the head direction system, and path integration. In this paper we present simulation results showing how interactions between the place and head direction systems can account for recent observations about hippocampal place cell responses to doubling and/or rotation of cue cards in a cylindrical arena (Sharp et at.,

The formation of associations between signals, which are considered to arise from the same external source, allows the organism to recognise significant patterns and relationships within the signals from each source without being confused by accidental coincidences between unrelated signals (Bregman, 1990). The intrinsically temporal nature of sound means that in addition to being able to focus on the signal of interest, perhaps of equal significance, is the ability to predict how that signal is expected to progress; such expectations can then be used to facilitate further processing of the signal. It is important to remember that perception is a creative act (Luria, 1980). The organism creates its interpretation of the world in response to the current stimuli, within the context of its current state of alertness, attention, and previous experience. The creative aspects of perception are exemplified in the auditory system where peripheral processing decomposes acoustic stimuli.

However, ANNs are usually costly to train, preventing one from trying many different representations. In this paper, we address this problem by introducing and evaluating three new measures for quickly estimating ANN input representation quality. Two of these, called [DBleaves and Min (leaves), consistently outperform Rendell and Ragavan's (1993) blurring measure in accurately ranking different input representations for ANN learning on three difficult, real-world datasets.

Most studies of attention have focused on the selection process of incoming sensory cues (Posner et al., 1980; Koch et al., 1985; Desimone et al., 1995). Emphasis was placed on the phenomena of causing different percepts for the same sensory stimuli. However, the selection of sensory input itself is not the final goal of attention. We consider attention as a means for goal-directed behavior and survival of the animal. In this view, dynamical properties of attention are crucial. While attention has to be maintained long enough to enable robust response to sensory input, it also has to be shifted quickly to a novel cue that is potentially important. Long-term maintenance and quick transition are critical requirements for attention dynamics.

Harmony networks have been proposed as a means by which connectionist models can perform symbolic computation. Indeed, proponents claim that a harmony network can be built that constructs parse trees for strings in a context free language. This paper shows that harmony networks do not work in the following sense: they construct many outputs that are not valid parse trees. In order to show that the notion of systematicity is compatible with connectionism, Paul Smolensky, Geraldine Legendre and Yoshiro Miyata (Smolensky, Legendre, and Miyata 1992; Smolen sky 1993; Smolen sky, Legendre, and Miyata 1994) proposed a mechanism, "Harmony Theory," by which connectionist models purportedly perform structure sensitive operations without implementing classical algorithms. Harmony theory describes a "harmony network" which, in the course of reaching a stable equilibrium, apparently computes parse trees that are valid according to the rules of a particular context-free grammar.

A significant limitation of neural networks is that the representations they learn are usually incomprehensible to humans.