Isotropic covariance functions on graphs and their edges

We develop parametric classes of covariance functions on linear networks and their extension to graphs with Euclidean edges, i.e., graphs with edges viewed as line segments or more general sets with a coordinate system allowing us to consider points on the graph which are vertices or points on an edge. Our covariance functions are defined on the vertices and edge points of these graphs and are isotropic in the sense that they depend only on the geodesic distance or on a new metric called the resistance metric (which extends the classical resistance metric developed in electrical network theory on the vertices of a graph to the continuum of edge points). We discuss the advantages of using the resistance metric in comparison with the geodesic metric as well as the restrictions these metrics impose on the investigated covariance functions. In particular, many of the commonly used isotropic covariance functions in the spatial statistics literature (the power exponential, Mat{\'e}rn, generalized Cauchy, and Dagum classes) are shown to be valid with respect to the resistance metric for any graph with Euclidean edges, whilst they are only valid with respect to the geodesic metric in more special cases.Comment: 6 figures, 1 tabl

Isometric Immersions and the Waving of Flags

In this article we propose a novel geometric model to study the motion of a physical flag. In our approach a flag is viewed as an isometric immersion from the square with values into $\mathbb R^3$ satisfying certain boundary conditions at the flag pole. Under additional regularity constraints we show that the space of all such flags carries the structure of an infinite dimensional manifold and can be viewed as a submanifold of the space of all immersions. The submanifold result is then used to derive the equations of motion, after equipping the space of isometric immersions with its natural kinetic energy. This approach can be viewed in a similar spirit as Arnold's geometric picture for the motion of an incompressible fluid.Comment: 25 pages, 1 figur

A relaxed approach for curve matching with elastic metrics

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 model and resulting matching algorithm integrate within one common setting both the family of $H^2$-metrics with constant coefficients and scale-invariant $H^2$-metrics on both open and closed immersed curves. These families include as particular cases the class of first-order elastic metrics. An essential difference with prior approaches is the way that boundary constraints are dealt with. By leveraging varifold-based similarity metrics we propose a relaxed variational formulation for the matching problem that avoids the necessity of optimizing over the reparametrization group. Furthermore, we show that we can also quotient out finite-dimensional similarity groups such as translation, rotation and scaling groups. The different properties and advantages are illustrated through numerical examples in which we also provide a comparison with related diffeomorphic methods used in shape registration.Comment: 27 page

Do Foreign Experts Increase the Productivity of Domestic Firms?

While most countries welcome (and some even subsidise) high-skilled immigrants, there is very limited evidence of their importance for domestic firms. To guide our empirical analysis, we first set up a simple theoretical model to show how foreign experts may impact on the productivity and wages of domestic firms. Using matched worker-firm data from Denmark and a difference-indifferences matching approach, we then find that firms that hire foreign experts – defined as employees eligible for reduced taxation under the Danish "Tax scheme for foreign researchers and key employees" – both become more productive (pay higher wages) and increase their exports of goods and services.foreign experts, export, immigrants, productivity, difference-in-differences matching

Do Immigrants Take the Jobs of Native Workers?

In this paper, we focus on the short-run adjustments taking place at the workplace level when immigrants are employed. Specifically, we analyse whether individual native workers are replaced or displaced by the employment of immigrants within the same narrowly defined occupations at the workplace. For this purpose, we estimate a competing risks duration model for job spells of native workers that distinguishes between job-to-job and job-to-unemployment transitions. In general, we do not find any signs of native workers being displaced by immigrants. Furthermore, we find only very limited signs of replacement of native workers by immigrants. Instead, in particular low-skilled native workers are less likely to lose or leave their jobs when the firms hire immigrants.immigration, adjustment costs, displacement, job spells, duration model