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The Shinnar-Le-Roux (SLR) algorithm is widely used to design frequency selective pulses with large flip angles. We improve its design process to generate pulses with lower energy (by as much as 26%) and more accurate phase profiles.…
This paper addresses the problem of planning under uncertainty in large Markov Decision Processes (MDPs). Factored MDPs represent a complex state space using state variables and the transition model using a dynamic Bayesian network. This…
Eigenvalue assignment problem of a linear scalar system with a single discrete delay is analytically and exactly solved. The existence condition of the desired eigenvalue is established when the current and delay states are present in the…
A simplified model of a redundant power grid is used to study integration of fluctuating renewable generation. The grid consists of large number of generator and consumer nodes. The net power consumption is determined by the difference…
Approximate resolution of linear systems of differential equations with varying coefficients is a recurrent problem shared by a number of scientific and engineering areas, ranging from Quantum Mechanics to Control Theory. When formulated in…
Multi-matrix invariants, and in particular the scalar multi-trace operators of $\mathcal{N}=4$ SYM with $U(N)$ gauge symmetry, can be described using permutation centraliser algebras (PCA), which are generalisations of the symmetric group…
We study the problem of pattern selection in an array of parametrically-driven nonlinear resonators with application to microelectromechanical and nanoelectromechanical systems (MEMS & NEMS), using an amplitude equation recently derived by…
We consider a new problem of designing a network with small $s$-$t$ effective resistance. In this problem, we are given an undirected graph $G=(V,E)$, two designated vertices $s,t \in V$, and a budget $k$. The goal is to choose a subgraph…
Integrated electricity and gas systems are constructed to facilitate the gas-fired generation, and the distributed operation of these integrated systems have received much attention due to the increased emphasis on data security and privacy…
We define a class of "algebraic" random matrices. These are random matrices for which the Stieltjes transform of the limiting eigenvalue distribution function is algebraic, i.e., it satisfies a (bivariate) polynomial equation. The Wigner…
A power assignment is an assignment of transmission power to each of the wireless nodes of a wireless network, so that the induced graph satisfies some desired properties. The cost of a power assignment is the sum of the assigned powers. In…
Quadratic harnesses are time-inhomogeneous Markov polynomial processes with linear conditional expectations and quadratic conditional variances with respect to the past-future filtrations. Typically they are determined by five numerical…
We study the problem of modeling multiple symmetric, weighted networks defined on a common set of nodes, where networks arise from different groups or conditions. We propose a model in which each network is expressed as the sum of a shared…
In the standard Mechanism Design framework, agents' messages are gathered at a central point and allocation/tax functions are calculated in a centralized manner, i.e., as functions of all network agents' messages. This requirement may cause…
We develop a new approach for construction of convex analytically simple regions where the AC power flow equations are guaranteed to have a feasible solutions. Construction of these regions is based on efficient semidefinite programming…
This paper considers automatic generation control over an information-sharing network of communicating generators as a multi-agent system. The optimization solution is distributed among the agents based on information consensus algorithms,…
In this paper, we study the Schr\"{o}dinger equation in the semiclassical regime and with multiscale potential function. We develop the so-called constraint energy minimization generalized multiscale finite element method (CEM-GMsFEM), in…
Quantum phase estimation is one of the most powerful quantum primitives. This work proposes a new approach for the problem of multiple eigenvalue estimation: Quantum Multiple Eigenvalue Gaussian filtered Search (QMEGS). QMEGS leverages the…
A shape optimization problem arising from the optimal reinforcement of a membrane by means of one-dimensional stiffeners or from the fastest cooling of a two-dimensional object by means of ``conducting wires'' is considered. The criterion…
The aim of this article is to analyze numerical schemes using two-layer neural networks withinfinite width for the resolution of high-dimensional Schr{\"o}dinger eigenvalue problems with smoothinteraction potentials and Neumann boundary…