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Anomaly Detection in multivariate time series is a major problem in many fields. Due to their nature, anomalies sparsely occur in real data, thus making the task of anomaly detection a challenging problem for classification algorithms to…
This paper considers the efficient minimization of the infinite time average of a stationary ergodic process in the space of a handful of design parameters which affect it. Problems of this class, derived from physical or numerical…
Time delay estimation plays a critical role in control, stabilization and state estimation of many practical system with time delay. In this paper, we propose a method to estimate delay for discrete time linear multiple-input…
We consider time-harmonic elastodynamic problems in heterogeneous media.cWe focus on scattering problems in the high-frequency regime and incnearly incompressible media, where the the angular frequency $\omega$ and ratio of the Lam\'e…
In this paper, we consider the problem of joint delay-Doppler estimation of moving targets in a passive radar that makes use of orthogonal frequency-division multiplexing (OFDM) communication signals. A compressed sensing algorithm is…
We develop the method of stochastic modified equations (SME), in which stochastic gradient algorithms are approximated in the weak sense by continuous-time stochastic differential equations. We exploit the continuous formulation together…
We propose a novel formulation for phase synchronization -- the statistical problem of jointly estimating alignment angles from noisy pairwise comparisons -- as a nonconvex optimization problem that enforces consistency among the pairwise…
We show that accelerated gradient descent, averaged gradient descent and the heavy-ball method for non-strongly-convex problems may be reformulated as constant parameter second-order difference equation algorithms, where stability of the…
We study a family of numerical schemes applied to a class of multiscale systems of stochastic differential equations. When the time scale separation parameter vanishes, a well-known homogenization or Wong--Zakai diffusion approximation…
Progressive Hedging is a popular decomposition algorithm for solving multi-stage stochastic optimization problems. A computational bottleneck of this algorithm is that all scenario subproblems have to be solved at each iteration. In this…
This article is devoted to the analysis of semilinear, parabolic, Stochastic Partial Differential Equations, with slow and fast time scales. Asymptotically, an averaging principle holds: the slow component converges to the solution of…
In this paper, the optimal convergence rate $O\left(N^{-1/2}\right)$ (where $N$ is the total number of iterations performed by the algorithm), without the presence of a logarithmic factor, is proved for mirror descent algorithms with…
When the eigenvalues of the coefficient matrix for a linear scalar ordinary differential equation are of large magnitude, its solutions exhibit complicated behaviour, such as high-frequency oscillations, rapid growth or rapid decay. The…
Modern time series are usually composed of multiple oscillatory components, with time-varying frequency and amplitude contaminated by noise. The signal processing mission is further challenged if each component has an oscillatory pattern,…
We study the averaging of fronts moving with positive oscillatory normal velocity, which is periodic in space and stationary ergodic in time. The problem can be reformulated as the homogenization of coercive level set Hamilton-Jacobi…
Statistical static timing analysis deals with the increasing variations in manufacturing processes to reduce the pessimism in the worst case timing analysis. Because of the correlation between delays of circuit components, timing model…
This work investigates the distributed constrained optimization problem under inter-agent communication delays from the perspective of passivity. First, we propose a continuous-time algorithm for distributed constrained optimization with…
This work is devoted to the development and analysis of a linearization algorithm for microscopic elliptic equations, with scaled degenerate production, posed in a perforated medium and constrained by the homogeneous Neumann-Dirichlet…
We study the problem of estimating the time delay between two signals representing delayed, irregularly sampled and noisy versions of the same underlying pattern. We propose and demonstrate an evolutionary algorithm for the (hyper)parameter…
We extend the piecewise orthogonal collocation method to computing periodic solutions of coupled renewal and delay differential equations. Through a rigorous error analysis, we prove convergence of the relevant finite-element method and…