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Perturbative renormalization group theory is developed as a unified tool for global asymptotic analysis. With numerous examples, we illustrate its application to ordinary differential equation problems involving multiple scales, boundary…

Based on the classical Degree Corrected Stochastic Blockmodel (DCSBM) model for network community detection problem, we propose two novel approaches: principal component clustering (PCC) and normalized principal component clustering (NPCC).…

Block coordinate descent (BCD) methods and their variants have been widely used in coping with large-scale nonconstrained optimization problems in many fields such as imaging processing, machine learning, compress sensing and so on. For…

Model predictive control (MPC) is one of the most successful modern control methods. It relies on repeatedly solving a finite-horizon optimal control problem and applying the beginning piece of the optimal input. In this paper, we develop a…

Estimating high-quality images while also quantifying their uncertainty are two desired features in an image reconstruction algorithm for solving ill-posed inverse problems. In this paper, we propose plug-and-play Monte Carlo (PMC) as a…

We study the maximum-confidence (MC) measurement strategy for discriminating among nonorthogonal symmetric qudit states. Restricting to linearly dependent and equally likely pure states, we find the optimal positive operator valued measure…

The Variational Quantum Eigensolver (VQE) algorithm is gaining interest for its potential use in near-term quantum devices. In the VQE algorithm, parameterized quantum circuits (PQCs) are employed to prepare quantum states, which are then…

We investigate a number of recently reported exact algorithms for the maximum clique problem (MCQ, MCR, MCS, BBMC). The program code used is presented and critiqued showing how small changes in implementation can have a drastic effect on…

We develop a one-Newton-step-per-horizon, online, lag-$L$, model predictive control (MPC) algorithm for solving discrete-time, equality-constrained, nonlinear dynamic programs. Based on recent sensitivity analysis results for the target…

Bayesian classification and regression with high order interactions is largely infeasible because Markov chain Monte Carlo (MCMC) would need to be applied with a great many parameters, whose number increases rapidly with the order. In this…

Exact approximations of Markov chain Monte Carlo (MCMC) algorithms are a general emerging class of sampling algorithms. One of the main ideas behind exact approximations consists of replacing intractable quantities required to run standard…

Model predictive control (MPC) is a method to formulate the optimal scheduling problem for grid flexibilities in a mathematical manner. The resulting time-constrained optimization problem can be re-solved in each optimization time step…

Accurate quantum channel parameter estimation is essential for effective information reconciliation in continuous-variable quantum key distribution (CV-QKD). However, conventional maximum likelihood (ML) estimators rely on a large amount of…

A general approach to provide approximate parameterizations of the "small" scales by the "large" ones, is developed for stochastic partial differential equations driven by linear multiplicative noise. This is accomplished via the concept of…

Large-scale, fault-tolerant quantum computations will be enabled by quantum error-correcting codes (QECC). This work presents the first systematic technique to test the accuracy and effectiveness of different QECC decoding schemes by…

We present a general procedure for incorporating higher-order information into the scale-setting prescription of Brodsky, Lepage and Mackenzie. In particular, we show how to apply this prescription when the leading coefficient or…

We study the renormalization-scheme (RS) dependence of Pade Approximants (PA's), and compare them with the Principle of Minimal Sensitivity (PMS) and the Effective Charge (ECH) approaches. Although the formulae provided by the PA, PMS and…

Principal Component Analysis (PCA) is one of the most important methods to handle high dimensional data. However, most of the studies on PCA aim to minimize the loss after projection, which usually measures the Euclidean distance, though in…

Autonomous systems with machine learning-based perception can exhibit unpredictable behaviors that are difficult to quantify, let alone verify. Such behaviors are convenient to capture in probabilistic models, but probabilistic model…

The cyclic block coordinate descent-type (CBCD-type) methods, which performs iterative updates for a few coordinates (a block) simultaneously throughout the procedure, have shown remarkable computational performance for solving strongly…