We present an information-geometric measure to systematically investigate neuronal firing patterns, taking account not only of the second-order but also of higher-order interactions. We begin with the case of two neurons for illustration and show how to test whether or not any pairwise correlation in one period is significantly different from that in the other period. In order to test such a hypothesis ofdifferent firing rates, the correlation term needs to be singled out'orthogonally' to the firing rates, where the null hypothesis mightnot be of independent firing. This method is also shown to directly associate neural firing with behavior via their mutual information, which is decomposed into two types of information, conveyed by mean firing rate and coincident firing, respectively. Then, we show that these results, using the'orthogonal' decomposition, arenaturally extended to the case of three neurons and n neurons in general. 1 Introduction Based on the theory of hierarchical structure and related invariant decomposition of interactions by information geometry [3], the present paper briefly summarizes methods useful for systematically analyzing a population of neural firing [9].

Recent biological experimental findings have shown that the synaptic plasticitydepends on the relative timing of the pre-and postsynaptic spikeswhich determines whether Long Term Potentiation (LTP) occurs or Long Term Depression (LTD) does. The synaptic plasticity has been called "Temporally Asymmetric Hebbian plasticity (TAH)".Many authors have numerically shown that spatiotemporal patternscan be stored in neural networks.

Neurons receive excitatory inputs via both fast AMPA and slow NMDA type receptors. We find that neurons receiving input via NMDA receptors can have two stable membrane states which are input dependent. Action potentials can only be initiated from the higher voltage state. Similar observations have been made in several brainareas which might be explained by our model. The interactions betweenthe two kinds of inputs lead us to suggest that some neurons may operate in 3 states: disabled, enabled and firing. Suchenabled, but non-firing modes can be used to introduce context-dependent processing in neural networks. We provide a simple example and discuss possible implications for neuronal processing andresponse variability. 1 Introduction Excitatory interactions between neurons are mediated by two classes of synapses: AMPA and NMDA.

Integration in the head-direction system is a computation by which horizontal angularhead velocity signals from the vestibular nuclei are integrated toyield a neural representation of head direction. In the thalamus, the postsubiculum and the mammillary nuclei, the head-direction representation has the form of a place code: neurons have a preferred head direction in which their firing is maximal [Blair and Sharp, 1995, Blair et al., 1998,?]. Integration is a difficult computation, given that head-velocities can vary over a large range. Previous models of the head-direction system relied on the assumption that the integration is achieved in a firing-rate-based attractor network with a ring structure. In order to correctly integrate head-velocity signals during high-speed head rotations, very fast synaptic dynamics had to be assumed. Here we address the question whether integration in the head-direction system is possible with slow synapses, for example excitatory NMDA and inhibitory GABA(B) type synapses. For neural networks with such slow synapses, rate-based dynamics are a good approximation of spiking neurons[Ermentrout, 1994]. We find that correct integration during high-speed head rotations imposes strong constraints on possible network architectures.

Statistical learning and probabilistic inference techniques are used to infer thehand position of a subject from multi-electrode recordings of neural activityin motor cortex. First, an array of electrodes provides training dataof neural firing conditioned on hand kinematics. We learn a nonparametric representationof this firing activity using a Bayesian model and rigorously compare it with previous models using cross-validation. Second, we infer a posterior probability distribution over hand motion conditioned on a sequence of neural test data using Bayesian inference. The learned firing models of multiple cells are used to define a non-Gaussian likelihood term which is combined with a prior probability for the kinematics. A particle filtering method is used to represent, update, and propagate the posterior distribution over time. The approach is compared withtraditional linear filtering methods; the results suggest that it may be appropriate for neural prosthetic applications.

The usual observable at the level of neuronal populations is the populationaveraged instantaneousfiring rate A(t), with A(t)6.t

Acetylcholine (ACh) has been implicated in a wide variety of tasks involving attentional processes and plasticity. Following extensive animal studies, it has previously been suggested that ACh reports on uncertainty and controls hippocampal, cortical and cortico-amygdalar plasticity. We extend this view and consider its effects on cortical representational inference, arguing that ACh controls the balance between bottom-up inference, influenced by input stimuli, and top-down inference, influenced by contextual information. We illustrate our proposal using a hierarchical hidden Markovmodel.

The way groups of auditory neurons interact to code acoustic information isinvestigated using an information theoretic approach. We develop measures of redundancy among groups of neurons, and apply them to the study of collaborative coding efficiency in two processing stations in the auditory pathway: the inferior colliculus (IC) and the primary auditory cortex (AI). Under two schemes for the coding of the acoustic content, acoustic segments coding and stimulus identity coding, we show differences both in information content and group redundancies between IC and AI neurons. These results provide for the first time a direct evidence for redundancy reduction along the ascending auditory pathway, as has been hypothesized fortheoretical considerations [Barlow 1959,2001]. The redundancy effects under the single-spikes coding scheme are significant onlyfor groups larger than ten cells, and cannot be revealed with the redundancy measures that use only pairs of cells. The results suggest that the auditory system transforms low level representations thatcontain redundancies due to the statistical structure of natural stimuli, into a representation in which cortical neurons extractrare and independent component of complex acoustic signals, that are useful for auditory scene analysis.

The model can predict the response ofindividual cells and populations to parametric manipulations of both geometric (e.g.O'Keefe & Burgess, 1996) and orientational (Fenton et aI., 2000a) cues, extending a previous geometric model (Hartley et al., 2000). It provides a functional description of how these cells' spatial responses are derived from the rat's environment and makes easily testable quantitative predictions. Consideration ofthe phenomenon of remapping (Muller & Kubie, 1987; Bostock et aI., 1991) indicates that the model may also be consistent with nonparametric changesin firing, and provides constraints for its future development.

Driven by the progress in the field of single-trial analysis of EEG, there is a growing interest in brain computer interfaces (BCIs), i.e., systems that enable human subjects to control a computer only by means of their brain signals. In a pseudo-online simulation our BCI detects upcoming finger movements in a natural keyboard typing condition and predicts their laterality. Thiscan be done on average 100-230 ms before the respective key is actually pressed, i.e., long before the onset of EMG. Our approach is appealing for its short response time and high classification accuracy ( 96%) in a binary decision where no human training is involved. We compare discriminative classifiers like Support Vector Machines (SVMs) and different variants of Fisher Discriminant that possess favorable regularization propertiesfor dealing with high noise cases (inter-trial variablity).