Abstract
Traditionally analog signals are encoded in the amplitude domain. The reduction of the signal amplitude due to the drastically lower power supply in nanoscale semiconductors results in a very significant reduction in the encoding accuracy of analog circuits. A paradigm shift is in order. Instead of encoding the analog signal in the amplitude domain, time domain encoding should be used. Encoding signal information in the time domain leverages the trends in nanoscale semiconductors towards higher operational speeds and thus higher precision for time measurements.

The interest in temporal encoding in neuroscience is closely linked with the natural representation of sensory stimuli (signals) as a sequence of action potentials (spikes). Spikes are discrete time events that carry information about stimuli. Time encoding lies therefore at the interface between information/ communication theory and asynchronous signal processing, on the one hand, & theoretical/computational neuroscience on the other. We shall demonstrate how fundamental questions of information representation and neural encoding can be successfully addressed with methods and intuitive arguments in all these fields.

More formally, Time Encoding Machines (TEMs) are asynchronous signal processors that encode analog information in the time domain. Asynchronous Sigma/Delta modulators as well as neural circuits based on integrate-and-fire (IAF) neurons and more general Hodgkin-Huxley neurons with feedback are instances of TEMs.

We show that for bandlimited signals (stimuli) with a known bandwidth, a perfect stimulus recovery from the train of spikes is possible provided that the spike density is above the Nyquist rate. These results are based on the key insight that neural encoding with a population of IAF neurons is akin to taking a set of measurements on the stimulus. These measurements or encodings can be represented as projections (inner products) of the stimulus on a set of sampling functions. We further show how to extend these findings to signals encoded with neural circuits with random thresholds and feedback.

Finally, we describe architectures for time encoding and time decoding of visual stimuli such as natural and synthetic video streams (movies, animation). The architecture for time encoding is akin to models of the early visual system. It consists of a bank of filters in cascade with single-input multioutput neural circuits with feedback. We demonstrate that bandlimited video streams of finite energy can be faithfully recovered from the spike trains and provide a stable algorithm for perfect recovery. The key condition for recovery calls for the number of neurons in the population to be larger than a threshold value.

References
Aurel A. Lazar, Population Encoding with Hodgkin-Huxley Neurons, IEEE Transactions on Information Theory, Volume 56, Number 2, pp. 821-837, February, 2010, Special Issue on Molecular Biology and Neuroscience, doi:10.1109/TIT.2009.2037040.

Aurel A. Lazar and Eftychios A. Pnevmatikakis, Video Time Encoding Machines, IEEE Transactions on Neural Networks, Volume 22, Number 3, pp. 461-473, March, 2011, doi:10.1109/TNN.2010.2103323.

Aurel A. Lazar, Eftychios A. Pnevmatikakis and Yiyin Zhou, Encoding Natural Scenes with Neural Circuits with Random Thresholds, Vision Research, Volume 50, Number 22, pp. 2200-2212, October, 2010, Special Issue on Mathematical Models of Visual Coding, doi:10.1016/j.visres.2010.03.015.

Bio
Aurel A. Lazar is a Professor of Electrical Engineering at Columbia University. In the mid 80s and 90s, he pioneered investigations into networking games and programmable networks . In addition, he conducted research in broadband networking with quality of service constraints; and in architectures, network management and control of telecommunications networks.

His current research interests are at the intersection of computational, theoretical and systems neuroscience. The computational/theoretical work builds on methods of communications/networking, information theory, machine learning, nonlinear dynamical systems, signal processing and systems identification. The experimental work employs methods of genetics, neurophysiology and nanotechnology.

In silico, his focus is on neural encoding in and systems identification of sensory systems, and, spike processing and neural computation in the cortex. In this work, he investigates rigorous methods of encoding information in the time domain, functional identification of spiking neural circuits as well as massively parallel neural computation algorithms in the spike domain.

In vivo, his focus is on the olfactory system of the Drosophila. His current work primarily addresses the nature of odor signal processing in the antennal lobe of the fruit fly.