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We investigate properties which ensure that a given finite graph is the commuting graph of a group or semigroup. We show that all graphs on at least two vertices such that no vertex is adjacent to all other vertices is the commuting graph…
This paper is concerned with the problem of goodness-of-fit for curve registration, and more precisely for the shifted curve model, whose application field reaches from computer vision and road traffic prediction to medicine. We give bounds…
Efficiency of routing on a regular digraph often involves finding opitmal properties of the graph. For example, the diameter of a digraph is the maximum distance between any two vertices. We show how we can study these problems…
This paper is devoted to the study of unparameterized simple curves in the plane. We propose diverse canonical parameterizations of a 2D-curve. For instance, the arc-length parameterization is canonical, but we consider other natural…
We develop criteria based on a calibration argument via discrete PDE and semidiscrete optimal transport, for finding sharp isoperimetric inequalities of the form $(\sharp \Omega)^{d-1} \le C (\sharp \overrightarrow{\partial\Omega})^d$ where…
The parameters of a linear compartment model are usually estimated from experimental input-output data. A problem arises when infinitely many parameter values can yield the same result; such a model is called unidentifiable. In this case,…
In transformation regression models the response is transformed before fitting a regression model to covariates and transformed response. We assume such a model where the errors are independent from the covariates and the regression…
In this paper we study a class of Riemannian metrics on the space of unparametrized curves and develop a method to compute geodesics with given boundary conditions. It extends previous works on this topic in several important ways. The…
In this paper we introduce the notion of rational Hausdorff divisor, we analyze the dimension and irreducibility of its associated linear system of curves, and we prove that all irreducible real curves belonging to the linear system are…
This paper presents a guidance algorithm for solving the problem of following parametric paths, as well as a curvature-varying speed setpoint for land-based car-type wheeled mobile robots (WMRs). The guidance algorithm relies on…
We develop the foundations of the theory of quasi-visual approximations of bounded metric spaces. Roughly speaking, these are sequences of covers of a given space for which the diameters of the sets in the covers shrink to zero and for…
A bounded curvature path is a continuously differentiable piece-wise $C^2$ path with bounded absolute curvature connecting two points in the tangent bundle of a surface. These paths have been widely considered in computer science and…
Reparameterization invariance, a symmetry of heavy quark effective theory, appears in different forms in the literature. The most commonly cited forms of the reparameterization transformation are shown to induce the same constraints on…
We study the persistence of quadratic estimates related to the Kato square root problem across a change of metric on smooth manifolds by defining a class of Riemannian-like metrics that are permitted to be of low regularity and degenerate…
In this paper we are concerned with the approach to shape analysis based on the so called Square Root Velocity Transform (SRVT). We propose a generalisation of the SRVT from Euclidean spaces to shape spaces of curves on Lie groups and on…
We study a large family of graph covering problems, whose definitions rely on distances, for graphs of bounded cyclomatic number (that is, the minimum number of edges that need to be removed from the graph to destroy all cycles). These…
We demonstrate the reparametrization invariance of perturbatively defined one-dimensional functional integrals up to the three-loop level for a path integral of a quantum-mechanical point particle in a box. We exhibit the origin of the…
Symmetry is an important aesthetic criteria in graph drawing and network visualisation. Symmetric graph drawings aim to faithfully represent automorphisms of graphs as geometric symmetries in a drawing. In this paper, we design and…
A main goal in the field of statistical shape analysis is to define computable and informative metrics on spaces of immersed manifolds, such as the space of curves in a Euclidean space. The approach taken in the elastic shape analysis…
In this paper we compare two regression curves by measuring their difference by the area between the two curves, represented by their $L^1$-distance. We develop asymptotic confidence intervals for this measure and statistical tests to…