Related papers: Cubature formulas on combinatorial graphs
We develop a purely combinatorial theory of limit linear series on metric graphs. This will be based on the formalisms of hypercube rank functions and slope structures. We provide a full classification of combinatorial limit linear series…
We study the scenario of graph-based clustering algorithms such as spectral clustering. Given a set of data points, one first has to construct a graph on the data points and then apply a graph clustering algorithm to find a suitable…
In this paper, we introduce a new combinatorial curvature on two and three dimensional triangulated manifolds, which transforms in the same way as that of the smooth scalar curvature under scaling of the metric and could be used to…
The Numerical Recipes series of books are a useful resource, but all the algorithms they contain cannot be used within open-source projects. In this paper we develop drop-in alternatives to the two algorithms they present for cubic spline…
In this article we furnish a new simple proof of a hard identity from the theory of cubature formulas via the method of coefficients.
We explore the relationship between convex and subharmonic functions on discrete sets. Our principal concern is to determine the setting in which a convex function is necessarily subharmonic. We initially consider the primary notions of…
Necessary and sufficient conditions for a finite connected graph with a strict partial order on vertices to be a combinatorial invariant of pseudoharmonic function are obtained.
In this work, we present some new integration formulas for any order of accuracy as an application of the B-spline relations obtained in [1]. The resulting rules are defined as a perturbation of the trapezoidal integration method. We prove…
This paper investigates some combinatorial and algebraic properties of a Witt type formula for graphs.
Let $G=(V,E)$ be a finite, combinatorial graph. We define a notion of curvature on the vertices $V$ via the inverse of the resistance distance matrix. We prove that this notion of curvature has a number of desirable properties. Graphs with…
Given two regular graphs with consistent rotation maps, we produce a constructive method for a consistent rotation map on their Cartesian product. This method will be given as a simple set of rules of addition and table look ups. We assume…
In this paper we develop an approach to conformal geometry of piecewise flat metrics on manifolds. In particular, we formulate the combinatorial Yamabe problem for piecewise flat metrics. In the case of surfaces, we define the combinatorial…
For a flexible labeling of a graph, it is possible to construct infinitely many non-equivalent realizations keeping the distances of connected points constant. We give a combinatorial characterization of graphs that have flexible labelings.…
Building on techniques developed by Lyons and Victoir, we present the first explicit construction of a degree-7 cubature formula for Wiener space over $\mathbb{R}^3$. We then examine and compare two approaches for computing cubature…
Graph generative model evaluation necessitates understanding differences between graphs on the distributional level. This entails being able to harness salient attributes of graphs in an efficient manner. Curvature constitutes one such…
Existing approaches to solving combinatorial optimization problems on graphs suffer from the need to engineer each problem algorithmically, with practical problems recurring in many instances. The practical side of theoretical computer…
We establish for the first time the explicit curvature formulas for the horizontal and vertical edges of the strong product of two regular graphs. We complement this result with showing that there does not exist an analogous formula for the…
The aim of this paper is to extend classic results of the theory of CMC surfaces in the product spaces to the class of immersed surfaces in $\mathbb{M}^2(\kappa)\times\mathbb{R}$ whose mean curvature is given as a $C^1$ function depending…
We prove a stochastic Taylor expansion for SPDEs and apply this result to obtain cubature methods, i. e. high order weak approximation schemes for SPDEs, in the spirit of T. Lyons and N. Victoir. We can prove a high-order weak convergence…
In this article we present theoretical and computational results on the existence of polyhedral embeddings of graphs. The emphasis is on cubic graphs. We also describe an efficient algorithm to compute all polyhedral embeddings of a given…