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Gaussian processes (GPs) are commonplace in spatial statistics. Although many non-stationary models have been developed, there is arguably a lack of flexibility compared to equipping each location with its own parameters. However, the…
Some iterative calculations can be carried out by parallel communicating processors, and yield the same results whether or not the processors are synchronized. We show that this is the case if and only if the iteration is a contraction that…
This work concerns the minimization of the pseudospectral abscissa of a matrix-valued function dependent on parameters analytically. The problem is motivated by robust stability and transient behavior considerations for a linear control…
The ever-growing size of modern space-time data sets, such as those collected by remote sensing, requires new techniques for their efficient and automated processing, including gap-filling of missing values. CUDA-based parallelization on…
A trajectory-following primal--dual interior-point method solves nonlinear optimization problems with inequality and equality constraints by approximately finding points satisfying perturbed Karush--Kuhn--Tucker optimality conditions for a…
I point out that standard two dimensional, asymptotically free, non-linear sigma models, supplemented with terms giving a mass to the would-be Goldstone bosons, share many properties with four dimensional supersymmetric gauge theories, and…
We study the fine geometric structure of bifurcation currents in the parameter space of cubic polynomials viewed as dynamical systems. In particular we prove that these currents have some laminar structure in a large region of parameter…
We construct parallel manipulators with one degree of freedom and admitting infinitely many legs lying on a curve of degree ten and genus six. Our technique relies upon a duality between the spaces parametrizing all the possible legs and…
Subspace clustering methods which embrace a self-expressive model that represents each data point as a linear combination of other data points in the dataset provide powerful unsupervised learning techniques. However, when dealing with…
In this paper we discuss some properties of resolvents of an accretive operator in linear 2-normed spaces, focusing on the concept of contraction mapping and the unique fixed point of contraction mappings in linear 2- normed spaces. Also,…
Nonlinear constrained optimization has a wide range of practical applications. In this paper, we consider nonlinear optimization with inequality constraints. The interior point method is considered to be one of the most powerful algorithms…
We develop a polynomial time $\Omega\left ( \frac 1R \log R \right)$ approximate algorithm for Max 2CSP-$R$, the problem where we are given a collection of constraints, each involving two variables, where each variable ranges over a set of…
We present an approach to solving problems in micromechanics that is amenable to massively parallel calculations through the use of graphical processing units and other accelerators. The problems lead to nonlinear differential equations…
We develop a method for optimization in shape spaces, i.e., sets of surfaces modulo re-parametrization. Unlike previously proposed gradient flows, we achieve superlinear convergence rates through a subtle approximation of the shape Hessian,…
In this paper we establish that several maximal operators of convolution type, associated to elliptic and parabolic equations, are variation-diminishing. Our study considers maximal operators on the Euclidean space $\mathbb{R}^d$, on the…
The theory of limiting modular symbols provides a noncommutative geometric model of the boundary of modular curves that includes irrational points in addition to cusps. A noncommutative space associated to this boundary is constructed, as…
Networks of coupled parametric resonators (parametrons) hold promise for parallel computing architectures. En route to realizing complex networks, we report an experimental and theoretical analysis of two coupled parametrons. In contrast to…
Resonances in open quantum systems depending on at least two controllable parameters can show the phenomenon of exceptional points (EPs), where not only the eigenvalues but also the eigenvectors of two or more resonances coalesce. Their…
This paper demonstrates that any general 3-DOF three-legged planar parallel robot with extensible legs can change assembly modes without passing through parallel singularities (configurations where the mobile platform loses its stiffness).…
This paper investigates two situations in which the forward kinematics of planar 3-RPR parallel manipulators degenerates. These situations have not been addressed before. The first degeneracy arises when the three input joint variables r1,…