Related papers: Monotonicity and Contraction on Polyhedral Cones
Chains are vector-valued signals sampling a curve. They are important to motion signal processing and to many scientific applications including location sensors. We propose a novel measure of smoothness for chains curves by generalizing the…
It has been observed that certain classical chains admit topologically protected zero-energy modes that are localized on the boundaries. The static features of such localized modes are captured by linearized equations of motion, but the…
Monotonicity and convex analysis arise naturally in the framework of multi-marginal optimal transport theory. However, a comprehensive multi-marginal monotonicity and convex analysis theory is still missing. To this end we study extensions…
We propose a third order dynamical system for solving a nonlinear equation in Hilbert spaces where the operator is cocoercive with respect to the solutions set. Under mild conditions on the parameters, we establish the existence and…
It has been known for some time that the topological entropy is a nondecreasing function of the parameter in the real quadratic family, which corresponds to the intuitive idea that more nonlinearity induces more complex dynamical behavior.…
Various kinds of Bose-Einstein condensates are considered, which evolve without any geometric constraints or external trap potentials including gravitational. For studies of their collective oscillations and stability, including the…
The purpose of this paper is to characterize the concept of monotonicity according to a direction related to a set of n random variables in terms of its associated n-copula C. We start establishing relationships in the bivariate and…
We present a novel notion of $\lambda$-monotonicity for an $n$-species system of partial differential equations governed by mass-preserving flow dynamics, extending monotonicity in Banach spaces to the Wasserstein-2 metric space. We show…
This paper synthesizes anytime algorithms, in the form of continuous-time dynamical systems, to solve monotone variational inequalities. We introduce three algorithms that solve this problem: the projected monotone flow, the safe monotone…
A convex cone is homogeneous if its automorphism group acts transitively on the interior of the cone, i.e., for every pair of points in the interior of the cone, there exists a cone automorphism that maps one point to the other. Cones that…
We introduce new sufficient conditions for verifying stability and recurrence properties in singularly perturbed stochastic hybrid dynamical systems. Specifically, we focus on hybrid systems with deterministic continuous-time dynamics that…
This paper studies the problem of testing whether a function is monotone from a nonparametric Bayesian perspective. Two new families of tests are constructed. The first uses constrained smoothing splines, together with a hierarchical…
In this paper, we present an algorithm for stability analysis of systems described by coupled linear Partial Differential Equations (PDEs) with constant coefficients and mixed boundary conditions. Our approach uses positive matrices to…
We analyze networked heterogeneous nonlinear systems, with diffusive coupling and interconnected over a generic static directed graph. Due to the network's hetereogeneity, complete synchronization is impossible, in general, but an emergent…
We derive conditions for monotonicity properties that characterize general flows of a commodity over a network, where the flow is described by potential and flow dynamics on the edges, as well as potential continuity and Kirchhoff-Neumann…
An antinorm is a concave nonnegative homogeneous functional on a convex cone. It is shown that if the cone is polyhedral, then every antinorm has a unique continuous extension from the interior of the cone. The main facts of the duality…
For polyhedral convex cones in ${\mathbb R}^d$, we give a proof for the conic kinematic formula for conic curvature measures, which avoids the use of characterization theorems. For the random cones defined as typical cones of an isotropic…
A general class of nonconvex optimization problems is considered, where the penalty is the composition of a linear operator with a nonsmooth nonconvex mapping, which is concave on the positive real line. The necessary optimality condition…
A dynamical system is called contractive if any two solutions approach one another at an exponential rate. More precisely, the dynamics contracts lines at an exponential rate. This property implies highly ordered asymptotic behavior…
In this paper, we study the contractivity of Lur'e dynamical systems whose nonlinearity is either Lipschitz, incrementally sector bounded, or monotone. We consider both the discrete- and continuous-time settings. In each case, we provide…