Identification of Dendritic Processing in Spiking Neural Circuits

A large body of experimental evidence points to sophisticated signal processing taking place at the level of dendritic trees and dendritic branches of neurons. This evidence suggests that, in addition to inferring the connectivity between neurons, identifying analog dendritic processing in individual cells is fundamentally important to understanding the underlying principles of neural computation. In this thesis, we develop a novel theoretical framework for the identification of dendritic processing directly from spike times produced by spiking neurons. The problem setting of spiking neurons is necessary since such neurons make up the majority of electrically excitable cells in most nervous systems and it is often hard or even impossible to directly monitor the activity within dendrites. Thus, action potentials produced by neurons often constitute the only causal and observable correlate of dendritic processing. In order to remain true to the underlying biophysics of electrically excitable cells, we employ well-established mechanistic models of action potential generation to describe the nonlinear mapping of the aggregate current produced by the tree into an asynchronous sequence of spikes. Specific models of spike generation considered include conductance-based models such as Hodgkin-Huxley, Morris-Lecar, Fitzhugh-Nagumo, as well as simpler models of the integrate-and-fire and threshold-and-fire type. The aggregate time-varying current driving the spike generator is taken to be produced by a dendritic stimulus processor, which is a nonlinear dynamical system capable of describing arbitrary linear and nonlinear transformations performed on one or more input stimuli. In the case of multiple stimuli, it can also describe the cross-coupling, or interaction, between various stimulus features. The behavior of the dendritic stimulus processor is fully captured by one or more kernels, which provide a characterization of the signal processing that is consistent with the broader cable theory description of dendritic trees. We prove that the neural identification problem, stated in terms of identifying the kernels of the dendritic stimulus processor, is mathematically dual to the neural population encoding problem. Specifically, we show that the collection of spikes produced by a single neuron in multiple experimental trials can be treated as a single multidimensional spike train of a population of neurons encoding the parameters of the dendritic stimulus processor. Using the theory of sampling in reproducing kernel Hilbert spaces, we then derive precise results demonstrating that, during any experiment, the entire neural circuit is projected onto the space of input stimuli and parameters of this projection are faithfully encoded in the spike train. Spike times are shown to correspond to generalized samples, or measurements, of this projection in a system of coordinates that is not fixed but is both neuron- and stimulus-dependent. We examine the theoretical conditions under which it may be possible to reconstruct the dendritic stimulus processor from these samples and derive corresponding experimental conditions for the minimum number of spikes and stimuli that need to be used. We also provide explicit algorithms for reconstructing the kernel projection and demonstrate that, under natural conditions, this projection converges to the true kernel. The developed methodology is quite general and can be applied to a number of neural circuits. In particular, the methods discussed span all sensory modalities, including vision, audition and olfaction, in which external stimuli are typically continuous functions of time and space. The results can also be applied to circuits in higher brain centers that receive multi-dimensional spike trains as input stimuli instead of continuous signals. In addition, the modularity of the approach allows one to extend it to mixed-signal circuits processing both continuous and spiking stimuli, to circuits with extensive lateral connections and feedback, as well as to multisensory circuits concurrently processing multiple stimuli of different dimensions, such as audio and video. Another important extension of the approach can be used to estimate the phase response curves of a neuron. All of the theoretical results are accompanied by detailed examples demonstrating the performance of the proposed identification algorithms. We employ both synthetic and naturalistic stimuli such as natural video and audio to highlight the power of the approach. Finally, we consider the implication of our work on problems pertaining to neural encoding and decoding and discuss promising directions for future research

Channel Identification Machines

We present a formal methodology for identifying a channel in a system consisting of a communication channel in cascade with an asynchronous sampler. The channel is modeled as a multidimensional filter, while models of asynchronous samplers are taken from neuroscience and communications and include integrate-and-fire neurons, asynchronous sigma/delta modulators and general oscillators in cascade with zero-crossing detectors. We devise channel identification algorithms that recover a projection of the filter(s) onto a space of input signals loss-free for both scalar and vector-valued test signals. The test signals are modeled as elements of a reproducing kernel Hilbert space (RKHS) with a Dirichlet kernel. Under appropriate limiting conditions on the bandwidth and the order of the test signal space, the filter projection converges to the impulse response of the filter. We show that our results hold for a wide class of RKHSs, including the space of finite-energy bandlimited signals. We also extend our channel identification results to noisy circuits

A cooperative MAC protocol for ad hoc wireless networks

Abstract — Cooperative communications fully leverages the broadcast nature of the wireless channel and spatial diversity, thereby achieving tremendous improvements in system capacity and delay. By enabling additional collaboration from stations that otherwise will not directly participate in the transmission, cooperative communications ushers in a new design paradigm for wireless communications. In this paper, we extend a cooperative MAC protocol called CoopMAC [1] into the ad hoc network environment 1. The new protocol is based on the idea of involving in an ongoing communication an intermediate station that is located between the transmitter and the receiver. The intermediate station acts as a helper and forwards to the destination the traffic it receives from the source. Thus, a slow one-hop transmission is transformed into a faster two-hop transmission, thereby decreasing the transmission time for the traffic being handled. Extensive simulations in a large scale wireless adhoc network (150 stations) show that CoopMAC significantly improves the ad hoc network performance in terms of throughput and delay, and indicate how such cooperative schemes can boost the performance of traditional solutions (e.g., IEEE 802.11). Index Terms — Cooperative communications, MAC, 802.11, ad hoc networ