Related papers: Systoles in translation surfaces
The homological scaffold leverages persistent homology to construct a topologically sound summary of a weighted network. However, its crucial dependency on the choice of representative cycles hinders the ability to trace back global…
The transmission of a connected hypergraph is defined as the summation of distances between all unordered pairs of distinct vertices. We determine the unique uniform unicyclic hypergraphs of fixed size with minimum and maximum…
A statistical mechanics argument relating partition functions to martingales is used to get a condition under which random geometric processes can describe interfaces in 2d statistical mechanics at criticality. Requiring multiple SLEs to…
Machine translation is the discipline concerned with developing automated tools for translating from one human language to another. Statistical machine translation (SMT) is the dominant paradigm in this field. In SMT, translations are…
A square-tiled surface (STS) is a (finite, possibly branched) cover of the standard square-torus with possible branching over exactly 1 point. Alternately, STSs can be viewed as finitely many axis-parallel squares with sides glued in…
The purpose of this paper is to present the critical cases of the trace theorems for the restriction of functions to closed surfaces, and to give the asymptotics for the norms of the traces under dilations of the surface. We also discuss…
Though intuitively appealing, the concept of spinodal is rigourously defined only in systems with infinite range interactions (mean field systems). In short-range systems, a pseudo-spinodal can be defined by extrapolation of metastable…
This paper defines a subregular class of functions called the tier-based synchronized strictly local (TSSL) functions. These functions are similar to the the tier-based input-output strictly local (TIOSL) functions, except that the locality…
Tractograms are mathematical representations of the main paths of axons within the white matter of the brain, from diffusion MRI data. Such representations are in the form of polylines, called streamlines, and one streamline approximates…
We introduce the persistent homotopy type distance dHT to compare real valued functions defined on possibly different homotopy equivalent topological spaces. The underlying idea in the definition of dHT is to measure the minimal shift that…
Hysteresis can be defined from a dynamical systems perspective with respect to equilibrium points. Consequently, hysteresis naturally lends itself as a topic to illustrate and extend concepts in a dynamical systems course. A number of…
The interaction strength I(X) of a compact hyperbolic surface X is the best upper bound for the intersection number of two closed geodesics divided by the product of their lengths. Let $M_g$ be the moduli space of compact hyperbolic…
For a functional defined on the class of closed one-dimensional connected subsets of ${\mathbb R}^n$ we consider the corresponding minimization problem and we give suitable first order necessary conditions of optimality. The cases studied…
The goal of this chapter is to review recent analytical results about the growth of a (static) correlation length in glassy systems, and the connection that can be made between this length scale and the equilibrium correlation time of its…
We consider infinite staircase translation surfaces with varying step sizes. For typical step sizes we show that the translation flow is uniquely ergodic in almost every direction. Our result also hold for typical configurations of the…
Putman introduced a notion of a partitioned surface which is a surface with boundary with decoration restricting how the surface can be embedded into larger surfaces, and defined the Torelli group of the partitioned surfaces. In this paper,…
Notions of (pointwise) tangential dimension are considered, for measures of R^n. Under regularity conditions (volume doubling), the upper resp. lower dimension at a point x of a measure can be defined as the supremum, resp. infimum, of…
Analytical expressions for coordinates of stationary points and conditions for their existence in the ABC flow are received. The type of the stationary points is shown analytically to be saddle-node. Exact expressions for eigenvalues and…
The development of mechanised language specification based on structured operational semantics, with applications to verified compilers and sound program analysis, requires huge effort. General theory and frameworks have been proposed to…
We consider the distance function from an arbitrary point $p$ on a flat surface, and determine the set $F_{p}$ of all \emph{farthest points} (i.e., points at maximal distance) from $p$.