The problem considered here is that of wireless information and power transfer across a noisy coupled-inductor circuit, which is a frequency-selective channel with additive white Gaussian noise. The optimal tradeoff between the achievable rate and the power transferred is characterized given the total power available. The practical utility of such systems is also discussed.

We provide novel coded computation strategies for distributed matrix–matrix products that outperform the recent “Polynomial code” constructions in recovery threshold, i.e., the required number of successful workers. When a fixed $1/m$ fraction of each matrix can be stored at each worker node, Polynomial codes require $m^{2}$ successful workers, while our MatDot codes only require $2m-1$ successful workers. However, MatDot codes have higher computation cost per worker and higher communication cost from each worker to the fusion node. We also provide a systematic construction of MatDot codes. Furthermore, we propose “PolyDot” coding that interpolates between Polynomial codes and MatDot codes to trade off computation/communication costs and recovery thresholds. Finally, we demonstrate a novel coding technique for multiplying $n$ matrices ( $n \geq 3$ ) using ideas from MatDot and PolyDot codes.

We consider the problem of computing a matrix-vector product Ax using a set of P parallel or distributed processing nodes prone to “straggling,” i.e., unpredictable delays. Every processing node can access only a fraction 8/N of the N-length vector x, and all processing nodes compute an equal number of dot products.We propose a novel error correcting code – that we call “Short-Dot” – that introduces redundant, shorter dot products such that only a subset of the nodes’ outputs are sufficient to compute Ax. To address the problem of straggling in computing matrix-vector products, prior work uses replication or erasure coding to encode parts of the matrix A, but the length of the dot products computed at each processing node is still N. The key novelty in our work is that instead of computing the long dot products as required in the original matrix-vector product, we construct a larger number of redundant and short dot products that only require a fraction of x to be accessed during the computation. Short-Dot is thus useful in a communication constrained scenario as it allows for only a fraction of x to be accessed by each processing node. Further, we show that in the particular regime where the number of available processing nodes is greater than the total number of dot products, Short-Dot has lower expected computation time under straggling under an exponential model compared to existing strategies, e.g. replication, in a scaling sense. We also derive fundamental limits on the trade-off between the length of the dot products and the recovery threshold, i.e., the required number of processing nodes, showing that Short-Dot is near-optimal.

Objective: This paper obtains strategies that can achieve spatially precise noninvasive deep brain stimulation using electrical currents. Methods: We provide the Spatio-Temporal Interference-based stiMULation focUsing Strategy (STIMULUS) that generates rich patterns of spatiotemporally interfering currents to stimulate precisely and deep inside the brain. To calibrate and compare the accuracy of stimulation using different techniques, we utilize computational Hodgkin–Huxley-type models for neurons and a model of current dispersion in the head. Results: In this computational model, STIMULUS dramatically outperforms the recently proposed Temporal Interference (TI) stimulation strategy in spatial precision. Our results also suggest that STIMULUS can attain steerable and multisite stimulation, which can be important in giving feedback in brain–machine interfaces. Finally, by examining more mammalian neuron types, we also observe that not every neuron exhibits temporal-interference stimulation. Conclusions: Computer simulations suggest that the proposed STIMULUS strategy has potential to achieve noninvasive electrical deep brain stimulation with high spatial precision and, further, has the flexibility of generating rich stimulation patterns. The fact that some neuron types do not exhibit TI stimulation suggests that caution is needed in evaluating conclusions of application of TI stimulation on large mammalian brains. Significance: A technique to reliably, noninvasively, and precisely stimulate deep inside the human brain could revolutionize human neuroscience and clinical treatments. We obtain the first computational demonstration of the recently proposed TI stimulation. Advancing on that, we propose a novel strategy that can perform stimulation with high precision and flexibility.

Standard human EEG systems based on spatial Nyquist estimates suggest that 20–30 mm electrode spacing suffices to capture neural signals on the scalp, but recent studies posit that increasing sensor density can provide higher resolution neural information. Here, we compared “super-Nyquist” density EEG (“SND”) with Nyquist density (“ND”) arrays for assessing the spatiotemporal aspects of early visual processing. EEG was measured from 128 electrodes arranged over occipitotemporal brain regions (14 mm spacing) while participants viewed flickering checkerboard stimuli. Analyses compared SND with ND-equivalent subsets of the same electrodes. Frequency-tagged stimuli were classified more accurately with SND than ND arrays in both the time and the frequency domains. Representational similarity analysis revealed that a computational model of V1 correlated more highly with the SND than the ND array. Overall, SND EEG captured more neural information from visual cortex, arguing for increased development of this approach in basic and translational neuroscience.

We consider the problem of computing a binary linear transformation when all circuit components are unreliable. Two models of unreliable components are considered: probabilistic errors and permanent errors. We introduce the “ENCODED” technique that ensures that the error probability of the computation of the linear transformation is kept bounded below a small constant independent of the size of the linear transformation even when all logic gates in the computation are noisy. By deriving a lower bound, we show that in some cases, the computational complexity of the ENCODED technique achieves the optimal scaling in error probability. Further, we examine the gain in energy-efficiency from the use of a “voltage-scaling” scheme, where gate-energy is reduced by lowering the supply voltage. We use a gate energy-reliability model to show that tuning gate-energy appropriately at different stages of the computation (“dynamic” voltage scaling), in conjunction with ENCODED, can lead to orders of magnitude energy-savings over the classical “uncoded” approach. Finally, we also examine the problem of computing a linear transformation when noiseless decoders can be used, providing upper and lower bounds to the problem.