Elad Gilboa

Parallel Load Schedule Optimization With Renewable Distributed Generators in Smart Grids

We propose a framework for demand response in smart grids that integrates renewable distributed generators (DGs). In this model, some users have DGs and can generate part of their electricity. They can also sell extra generation to the utility company. The goal is to optimize the load schedule of users to minimize the utility companys cost and user payments, while considering user satisfaction. We employ a parallel autonomous optimization scheme, where each user requires only the knowledge of the aggregated load of other users, instead of the load profiles of individual users. All the users can execute distributed optimization simultaneously. The distributed optimization is coordinated through a soft constraint on changes of load schedules between iterations. Numerical examples show that our method can significantly reduce the peak-hour load and costs to the utility and users. Since the autonomous user optimization is executed in parallel, our method also significantly decreases the computation time and communication costs.

Image interpolation and denoising for division of focal plane sensors using Gaussian processes

Image interpolation and denoising are important techniques in image processing. These methods are inherent to digital image acquisition as most digital cameras are composed of a 2D grid of heterogeneous imaging sensors. Current polarization imaging employ four different pixelated polarization filters, commonly referred to as division of focal plane polarization sensors. The sensors capture only partial information of the true scene, leading to a loss of spatial resolution as well as inaccuracy of the captured polarization information. Interpolation is a standard technique to recover the missing information and increase the accuracy of the captured polarization information. Here we focus specifically on Gaussian process regression as a way to perform a statistical image interpolation, where estimates of sensor noise are used to improve the accuracy of the estimated pixel information. We further exploit the inherent grid structure of this data to create a fast exact algorithm that operates in ����(N(3/2)) (vs. the naive ���� (N³)), thus making the Gaussian process method computationally tractable for image data. This modeling advance and the enabling computational advance combine to produce significant improvements over previously published interpolation methods for polarimeters, which is most pronounced in cases of low signal-to-noise ratio (SNR). We provide the comprehensive mathematical model as well as experimental results of the GP interpolation performance for division of focal plane polarimeter.

Estimating Electrical Conductivity Tensors of Biological Tissues Using Microelectrode Arrays

Finding the electrical conductivity of tissue is highly important for understanding the tissue’s structure and functioning. However, the inverse problem of inferring spatial conductivity from data is highly ill-posed and computationally intensive. In this paper, we propose a novel method to solve the inverse problem of inferring tissue conductivity from a set of transmembrane potential and stimuli measurements made by microelectrode arrays (MEA). We first formalize the discrete forward model of transmembrane potential propagation, based on a reaction–diffusion model with an anisotropic inhomogeneous electrical conductivity-tensor field. Then, we propose a novel parallel optimization algorithm for solving the complex inverse problem of estimating the electrical conductivity-tensor field. Specifically, we propose a single-step approximation with a parallel block-relaxation optimization routine that simplifies the joint tensor field estimation problem into a set of computationally tractable subproblems, allowing the use of efficient standard optimization tools. Finally, using numerical examples of several electrical conductivity field topologies and noise levels, we analyze the performance of our algorithm, and discuss its application to real measurements obtained from smooth-muscle cardiac tissue, using data collected with a high-resolution MEA system.

Adaptive smoothing based on Gaussian processes regression increases the sensitivity and specificity of fMRI data

Temporal and spatial filtering of fMRI data is often used to improve statistical power. However, conventional methods, such as smoothing with fixed‐width Gaussian filters, remove fine‐scale structure in the data, necessitating a tradeoff between sensitivity and specificity. Specifically, smoothing may increase sensitivity (reduce noise and increase statistical power) but at the cost loss of specificity in that fine‐scale structure in neural activity patterns is lost. Here, we propose an alternative smoothing method based on Gaussian processes (GP) regression for single subjects fMRI experiments. This method adapts the level of smoothing on a voxel by voxel basis according to the characteristics of the local neural activity patterns. GP‐based fMRI analysis has been heretofore impractical owing to computational demands. Here, we demonstrate a new implementation of GP that makes it possible to handle the massive data dimensionality of the typical fMRI experiment. We demonstrate how GP can be used as a drop‐in replacement to conventional preprocessing steps for temporal and spatial smoothing in a standard fMRI pipeline. We present simulated and experimental results that show the increased sensitivity and specificity compared to conventional smoothing strategies. Hum Brain Mapp 38:1438–1459, 2017.

Distributed optimization via adaptive regularization for large problems with separable constraints

Many practical applications require solving an optimization over large and high-dimensional data sets, which makes these problems hard to solve and prohibitively time consuming. In this paper, we propose a parallel distributed algorithm that uses an adaptive regularizer (PDAR) to solve a joint optimization problem with separable constraints. The regularizer is adaptive and depends on the step size between iterations and the iteration number. We show theoretical convergence of our algorithm to an optimal solution, and use a multi-agent three-bin resource allocation example to illustrate the effectiveness of the proposed algorithm. Numerical simulations show that our algorithm converges to the same optimal solution as other distributed methods, with significantly reduced computational time.

Estimating electrical conductivity tensors of biological tissues using microelectrode arrays

Finding the electrical conductivity of tissue is important for understanding the tissues structure and functioning. However, the inverse problem of inferring spatial conductivity from data is highly ill-posed and computationally intensive. In this paper, we propose a novel method to solve the inverse problem of inferring tissue conductivity from a set of transmembrane potential and stimuli measurements made by microelectrode arrays (MEA). We propose a parallel optimization algorithm based on a single-step approximation with a parallel alternating optimization routine. This algorithm simplifies the joint tensor field estimation problem into a set of computationally tractable subproblems, allowing the use of efficient standard optimization tools.

GP-grid image interpolation and denoising for division of focal plane sensors

Image interpolation and denoising are important techniques in image processing. Recently, there has been a growing interest in the use of Gaussian processes (GP) regression for interpolation and denoising of image data. However, exact GP regression suffers from 0 (N3) runtime for data size N, making it intractable for image data. Our GP-grid algorithm reduces the runtime complexity of GP from 0 (N3) to 0 (N312). We provide comprehensive mathematical model as well as experimental results of the GP interpolation performance for division of focal plane polarimeter. The GP interpolation method outperforms the commonly used bilinear interpolation method for polarimeters.