Toby Berger

A Mathematical Theory of Energy Efficient Neural Computation and Communication

A neuroscience-based mathematical model of how a neuron stochastically processes data and communicates information is introduced and analyzed. Call the neuron in question neuron j, or just j. The information j transmits approximately describes the time-varying intensity of the excitation j is continuously experiencing from neural spike trains delivered to its synapses by thousands of other neurons. Neuron j encodes this excitation history into a sequence of time instants at which it generates neural spikes of its own. By propagating these spikes along its axon, j acts as a multiaccess, partially degraded broadcast channel with thousands of input and output terminals that employs a time-continuous version of pulse position modulation. The mathematical model features three parameters, m, ¿, and b, which largely characterize j as an engine of computation and communication. Each set of values of these parameters corresponds to a long term maximization of the bits j conveys to its targets per joule it expends doing so, which is achieved by distributing the random duration between successive spikes j generates according to a gamma pdf with parameters ¿ and b and distributing b/A according to a beta probability density with parameters ¿ and m-¿, where A is the random intensity of the effectively Poisson process of spikes that arrive to the union of all of js synapses at a randomly chosen time instant.

Spatial channel reuse in wireless sensor networks

Wireless sensor networks (WSN) are formed by network-enabled sensors spatially randomly distributed over an area. Because the number of nodes in the WSNs is usually large, channel reuse must be applied, keeping co-channel nodes sufficiently separated geographically to achieve satisfactory SIR level. The most efficient channel reuse configuration for WSN has been determined and the worst-interference scenario has been identified. For this channel reuse pattern and worst-case scenario, the minimum co-channel separation distance consistent with an SIR level constraint is derived. Our results show that the two-hop co-channel separations often assumed for sensor and ad hoc networks are not sufficient to guarantee communications. Minimum co-channel separation curves given various parameters are also presented. The results in this paper provide theoretical basis for channel spatial reuse and medium access control for WSN s and also serve as a guideline for how channel assignment algorithms should allocate channels. Furthermore, because the derived co-channel separation is a function of the sensor transmission radius, it also provides a connection between network data transport capacity planning and network topology control which is administered by varying transmission powers.

Capacity Analysis for Integrate-and-Fire Neurons With Descending Action Potential Thresholds

Understanding how a biological neuron works has been a major goal in neuroscience. Under the Poisson-excitation assumption, results from earlier study by Suksompong and Berger on the timing jitter in the leaky integrate-and-fire (LIF) model of neurons are used to determine families of neural thresholding functions that are appropriate in certain interesting senses. Next, the neuron is treated as a communication channel for which information-theoretic quantities can be calculated. In particular, the optimal distribution of the Poisson excitation intensity is numerically evaluated along with the corresponding capacity using the Blahut-Arimoto algorithm. Simple formulas which approximate the optimal intensity distribution are given. Furthermore, the Jimbo-Kunisawa algorithm is used to explore energy-efficient operations for neuron. Finally, a rate-matching argument leads to a unique operating condition which turns out to agree with experimentally observed rate.

A Berger-Levy energy efficient neuron model with unequal synaptic weights

How neurons in the cerebral cortex process and transmit information is a long-standing question in systems neuroscience. To analyze neuronal activity from an information-energy efficiency standpoint, Berger and Levy calculated the maximum Shannon mutual information transfer per unit of energy expenditure of an idealized integrate-and-fire (IIF) neuron whose excitatory synapses all have the same weight. Here, we extend their IIF model to a biophysically more realistic one in which synaptic weights are unequal. Using information theory, random Poisson measures, and the maximum entropy principle, we show that the probability density function (pdf) of interspike interval (ISI) duration induced by the bits per joule (bpj) maximizing pdf fΛ(λ) of the excitatory postsynaptic potential (EPSP) intensity remains equal to the delayed gamma distribution of the IIF model. We then show that, in the case of unequal weights, fΛ(·) satisfies an inhomogeneous Cauchy-Euler equation with variable coefficients for which we provide the general solution form.

Performance analysis for maximal-ratio combining in correlated generalized Rician fading

In this paper, we perform the analysis of average symbol error probability (SEP) for a diversity system over generalized Rician fading channels with correlated branches. This class of fading subsumes generalized Rayleigh fading, Nakagami-q (Hoyt) fading, generalized gamma fading, Nakagami fading, Rician fading, and Rayleigh fading as special cases, which are among the most popular fading models considered in the published literature. We derive a series expression of the average SEP for a general class of M-ary modulation schemes (including MPSK, MQAM, BFSK, and MSK) with maximal-ratio combining (MRC). The series expression is in canonical form as a weighted sum of elementary closed-form expressions, which are the closed-form expressions for the average SEP of a single-branch system in Nakagami fading environments.

Energy Efficient Neurons With Generalized Inverse Gaussian Conditional and Marginal Hitting Times

Neuronal information processing is energetically costly. Energy supply restrictions on information processing have resulted in the evolution of brains to compute and communicate information with remarkable energy efficiency. Indeed, energy minimization subject to functional constraints is a unifying principle. Toward better comprehension of neuronal information processing and communication from an information-energy standpoint, we consider a continuous time, continuous state-space neuron model with a generalized inverse Gaussian (GIG) conditional density. This GIG model arises from a Levy diffusion that contains both homogeneous Poisson processes and Wiener processes with drift as special cases. We show that, when the energy constraints consist of a tripartite family apropos of the GIG model, the distribution of input excitation,

On Minimal Eigenvalues of a Class of Tridiagonal Matrices

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Energy efficient neurons with generalized inverse Gaussian conditional and marginal hitting times

, that maximizes bits per Joule (bpJ) generates an output interspike interval duration

Upper bound for the capacity of multiple access protocols on multipacket reception channels

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Mutual Information and Parameter Estimation in the Generalized Inverse Gaussian Diffusion Model of Cortical Neurons

that possesses a related GIG marginal distribution. Most importantly, we obtain the exact expression for the bpJ-maximizing distribution of