We study functional central limit theorems for persistent Betti numbers obtained from networks defined on a Poisson point process. The is formed in large volumes of cylindrical shape stretching only one dimension. results cover directed sublevel-filtration stabilizing and the ?ech Vietoris–Rips complex random geometric graph. presented open door to variety statistical applications topological d...

We prove that if a system has superpolynomial (faster than any power law) decay of correlations (with respect to Lipschitz observables), then the time τ(x, Sr) is needed for a typical point x to enter for the first time a set Sr = {x : f(x) ≤ r} which is a sublevel of a Lipschitz function f scales as 1 μ(Sr) i.e., lim r→0 log τ(x, Sr) − log r = lim r→0 log μ(Sr) log r . This generalizes a previ...

A well-defined cluster containing 12 equivalent platinum atoms was prepared by ion exchange of an NaY zeolite, followed by hydrogen reduction. It was characterized by electron paramagnetic resonance (EPR) spectroscopy, hyperfine sublevel correlation (HYSCORE), and theoretical calculations. Combing the results of the experiments with density functional calculations, the likely structure of this ...

(in alphabetic order by speaker surname) Speaker: Dominique Attali (CNRS, Grenoble) Title: Persistence-sensitive simplification of functions on surfaces in linear time. Abstract: Let f be a real-valued function defined on a triangulated surface S. The persistence diagram of f encodes the homological variations in the sequence of sublevel sets St = f−1(−∞, t]. A point (x, y) in the persistence d...

We investigate which elliptic PDEs have the property that every viscosity supersolution belongs to a Sobolev space $$W^{1,q}_{loc}(\Omega )$$ , $$\Omega \subseteq \mathbb {R}^n$$ . The asymptotic cone of operator’s sublevel set seems be essential. It turns out much can said if we know how is related dominative p-Laplacian, with $$p = \frac{n-1}{n}q + 1$$ show that, in certain sense, this minima...

LKAB’s Kiruna Mine, located in northern Sweden, produces about 24 million tons of iron ore yearly using an underground mining method known as sublevel caving. To efficiently run the mills that process the iron ore, the mine must deliver planned quantities of three ore types. We used mixed-integer programming to schedule Kiruna’s operations, specifically, which production blocks to mine and when...

The constrained stabilization of linear uncertain systems is investigated via the set-theoretic framework of control Lyapunov R-functions. A novel composition rule allows the design of a composite control Lyapunov function with external level set that exactly shapes the maximal controlled invariant set and inner sublevel sets arbitrarily close to any choice of smooth ones, generalizing both pol...

Motivated by applications in robotics and computer vision, we study problems related to spatial reasoning of a 3D environment using sublevel sets of polynomials. These include: tightly containing a cloud of points (e.g., representing an obstacle) with convex or nearly-convex basic semialgebraic sets, computation of Euclidean distances between two such sets, separation of two convex basic semalg...

A novel state feedback control technique to stabilise linear differential inclusions through composite quadratic Lyapunov functions is presented. By using a gradient-based control technique, the minimum effort control is composed through intersection and union operations, derived from the theory of R-functions. While conventional min and max compositions are recovered as a special case, it is s...