Related papers: A Sharp Bound on the $s$-Energy and Its Applicatio…
The homogeneous entropy for continuous systems in nonextensive statistics reads $S^{H}_{q}=k_B\,{(1 - (K \int d\Gamma \rho^{1/q}(\Gamma))^{q})}/({1-q})$, where $\Gamma$ is the phase space variable. Optimization of $S^{H}_{q}$ combined with…
This paper presents a sensitivity-based approach for the placement of distributed energy resources (DERs) in power systems. The approach is based on the fact that most planning studies utilize some form of optimization, and solutions to…
Coordinated optimization and control of distribution-level assets can enable a reliable and optimal integration of massive amount of distributed energy resources (DERs) and facilitate distribution system management (DSM). Accordingly, the…
This paper considers distributed optimization algorithms, with application in binary classification via distributed support-vector-machines (D-SVM) over multi-agent networks subject to some link nonlinearities. The agents solve a…
Spiking neural networks (SNNs) are energy-efficient neural networks because of their spiking nature. However, as the spike firing rate of SNNs increases, the energy consumption does as well, and thus, the advantage of SNNs diminishes. Here,…
Algorithms and dynamics over networks often involve randomization, and randomization may result in oscillating dynamics which fail to converge in a deterministic sense. In this paper, we observe this undesired feature in three applications,…
Neural networks, a central tool in machine learning, have demonstrated remarkable, high fidelity performance on image recognition and classification tasks. These successes evince an ability to accurately represent high dimensional…
A refinement of Bennett's inequality is introduced which is strictly tighter than the classical bound. The new bound establishes the convergence of the average of independent random variables to its expected value. It also carefully…
The rapid growth of deep neural networks (DNNs) has brought increasing attention to their energy use during training and inference. Here, we establish the thermodynamic bounds on energy consumption in quasi-static analog DNNs by mapping…
Motivated by applications to data networks where fast convergence is essential, we analyze the problem of learning in generic N-person games that admit a Nash equilibrium in pure strategies. Specifically, we consider a scenario where…
We consider several estimation and learning problems that networked agents face when making decisions given their uncertainty about an unknown variable. Our methods are designed to efficiently deal with heterogeneity in both size and…
The brightness theorem---brightness is nonincreasing in passive systems---is a foundational conservation law, with applications ranging from photovoltaics to displays, yet it is restricted to the field of ray optics. For general linear wave…
The operation of adding edges has been frequently used to the study of opinion dynamics in social networks for various purposes. In this paper, we consider the edge addition problem for the DeGroot model of opinion dynamics in a social…
This paper considers distribution systems with a high penetration of distributed, renewable generation and addresses the problem of incorporating the associated uncertainty into the optimal operation of these networks. Joint chance…
We derive and investigate lower bounds for the potential energy of finite spherical point sets (spherical codes). Our bounds are optimal in the following sense -- they cannot be improved by employing polynomials of the same or lower degrees…
In a Big Data setting computing the dominant SVD factors is restrictive due to the main memory requirements. Recently introduced streaming Randomized SVD schemes work under the restrictive assumption that the singular value spectrum of the…
Generalizing treatment effects from a randomized trial to a target population requires the assumption that potential outcome distributions are invariant across populations after conditioning on observed covariates. This assumption fails…
It has been recently proven that the semidefinite programming (SDP) relaxation of the optimal power flow problem over radial networks is exact under technical conditions such as not including generation lower bounds or allowing load…
In this paper we consider a sample of a linearly elastic heterogeneous composite in elastodynamic equilibrium and present universal theorems which provide lower bounds for the total elastic strain energy plus the kinetic energy, and the…
We consider the elastic energy of a hanging drape -- a thin elastic sheet, pulled down by the force of gravity, with fine-scale folding at the top that achieves approximately uniform confinement. This example of energy-driven pattern…