We study a family of Teichmüller curves T (n,m) constructed by Bouw and Möller, and previously by Veech and Ward in the cases n = 2, 3. We simplify the proof that T (n,m) is a Teichmüller curve, avoiding the use Möller’s characterization of Teichmüller curves in terms of maximally Higgs bundles. Our key tool is a description of the period mapping of T (n,m) in terms of Schwarz triangle mappings...

The Laplace-Beltrami operator of a smooth Riemannian manifold is determined by the Riemannian metric. Conversely, the heat kernel constructed from its eigenvalues and eigenfunctions determines the Riemannian metric. This work proves the analogy on Euclidean polyhedral surfaces (triangle meshes), that the discrete Laplace-Beltrami operator and the discrete Riemannian metric (unique up to a scali...

Perfect matchings and maximum weight matchings are two fundamental combinatorial structures. We consider the ratio between the maximum weight of a perfect matching and the maximum weight of a general matching. Motivated by the application in triangle meshes, where we seek to convert a triangulation into a quadrangulation by merging pairs of adjacent triangles, we focus on bridgeless cubic graph...

An algorithm for striping triangle meshes in the context of OpenSG is presented. The technique is similar to STRIPE, however, a careful yet simple implementation leads to significant faster execution. Furthermore, we propose to randomly sample several partitions and chose the one that minimizes a given cost function. More samples are expected to lead to better solutions, thus, introducing a par...

Children with an obstetric brachial plexus injury have an elevated risk of long-term impairment if they do not fully recover by the age of 3 months. Persistent nerve damage leads to muscle abnormalities and progressive muscle and bone deformities. Several procedures have been described to treat this severe deformity. We have demonstrated the benefits of the triangle tilt procedure in young chil...

A 2-matching in an undirected graph G = (V G,EG) is a function x : EG → {0, 1, 2} such that for each node v ∈ V G the sum of values x(e) on all edges e incident to v does not exceed 2. The size of x is the sum ∑ e x(e). If {e ∈ EG | x(e) 6= 0} contains no triangles then x is called triangle-free. Cornuéjols and Pulleyblank devised a combinatorial O(mn)-algorithm that finds a triangle free 2-mat...

Fitness is typically represented in heavily simplified terms in evolutionary genetics, often using constant selection coefficients, to make it easier to infer or predict how type frequencies change over time. This excludes fundamental ecological factors such as dynamic population size or density-dependence from the most genetically-realistic treatments of evolution, a problem that inspired MacA...

We call our approach geometrical as instead of considering 6-fold integral in abstract space we consider random triangle (RT) inside the plane rectangle when all possible cases are explicitly apparent. Area of triangle with vertices p1=(x1,y1), p2=(x2,y2), p3=(x3,y3) is equal to s = 1 2 (x1(y2− y3) + x2 (−y1 + y3) + x3 (y1− y2)). (1) Let points p1, p2, p3 are randomly (with constant differentia...