Analysis of spatiotemporal patterns in a model of olfaction
Introduction
The dynamic neural filter (DNF) [3] is a recurrent binary neural network that maps regions of input space into spatiotemporal sequences. It has been motivated by locust olfaction research. Here we take up the task of using this model as a prototype of spatiotemporal patterns, and put it to tests of the kind employed by Stopfer et al., [5] for data obtained from the locust antennal lobes (ALs).
Since this kind of system is known to exhibit a local field potential with temporal width of [6], we take this time window as the basic temporal bin in our discrete system, obeyingwhere ni are the neural activity values, wij is the synaptic coupling matrix, Ri is an external input and θi is the threshold. H is the Heaviside step function taking the values 0 for negative arguments and 1 for positive ones.
In the next section we define all other details of the model, after which we turn to a series of numerical experiments and their analysis.
Section snippets
Model of olfaction
We use a fully connected binary network, defined by an asymmetric weight-matrix, with , having both positive and negative couplings taken from a normal distribution of width 4. In a previous work [2] we discussed some features of the response sequences generated in large networks, e.g. N=40, by changing R values. We found that close-by R values generate divergent spatiotemporal sequences. We also found that the center of R space is the region where the system leads to large
Analysis of the spatiotemporal data
Similar to the work of [5] the data we analyzed were spatiotemporal patterns of 100 neurons over a simulation time of . Fig. 1 depicts such patterns, derived from a network of 100 neurons, all of which received a constant odor during a simulation of 20 time steps. Each of the frames, representing five concentrations of the three different odors, will be referred to as a ‘spatiotemporal pattern’. We proceed then to ask for clustering properties of such patterns for different odors and
Discussion
We have obtained the desired odor and concentration clusters on all three levels of data analysis. Of particular importance is the fact that odors and concentrations clustered correctly for the local spatiotemporal analysis, which seems to be the most relevant to the biological system (inputs of Kenyon cells). In the recent experimental analysis of [5], the authors have demonstrated a representation of odors as manifolds with concentration as trajectories delineated by the temporal order of the
Acknowledgements
We wish to thank Vivek Jayaraman and Mark Stopfer for helpful discussions of their data and Gilles Laurent for the hospitality extended to one of us (OK).
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