Related papers: Two characterizations of crooked functions
A (Euclidean) greedy drawing of a graph is a drawing in which, for any two vertices $s,t$ ($s \neq t$), there is a neighbor vertex of $s$ that is closer to $t$ than to $s$ in the Euclidean distance. Greedy drawings are important in the…
Eight different refinements of trapped surfaces are proposed, of three basic types, each intended as potential stability conditions. Minimal trapped surfaces are strictly minimal with respect to the dual expansion vector. Outer trapped…
The theory of graphons has proven to be a powerful tool in many areas of graph theory. In this paper, we introduce several foundational aspects of the theory of digraphons -- asymmetric two-variable functions that arise as limits of…
We derive two sufficient conditions for a function of a Markov random field (MRF) on a given graph to be a MRF on the same graph. The first condition is information-theoretic and parallels a recent information-theoretic characterization of…
The main aim of this note is to provide characterization theorems concerning real derivations. Among others the following implication will be verified: Assume that $\xi\colon \mathbb{R}\to \mathbb{R}$ is a given differentiable function and…
If a point particle moves chaotically through a periodic array of scatterers the associated transport coefficients are typically irregular functions under variation of control parameters. For a piecewise linear two-parameter map we analyze…
We propose a geometric method for quantifying the difference between parametrized curves in Euclidean space by introducing a distance function on the space of parametrized curves up to rigid transformations (rotations and translations).…
In this paper we consider the concept of preintersection numbers of a graph. These numbers are determined by the spectrum of the adjacency matrix of the graph, and generalize the intersection numbers of a distance-regular graph. By using…
Minimal linear codes have significant applications in secret sharing schemes and secure two-party computation. There are several methods to construct linear codes, one of which is based on functions over finite fields. Recently, many…
We consider a biased nearest-neighbor random walk on $\Z$ which at each step is trapped for some random time with random, site-dependent mean. We derive a simple formula for the speed function in terms of the model parameters.
We enumerate the independent sets of several classes of regular and almost regular graphs and compute the corresponding generating functions. We also note the relations between these graphs and other combinatorial objects and, in some…
We discuss some properties of the distance functions on Riemannian manifolds and we relate their behavior to the geometry of the manifolds. This leads to alternative proofs of some "classical" theorems connecting curvature and topology.
Recently there has been much interest in graph-based learning, with applications in collaborative filtering for recommender networks, link prediction for social networks and fraud detection. These networks can consist of millions of…
Among various distance functions for graphs, graph and subgraph edit distances (GED and SED respectively) are two of the most popular and expressive measures. Unfortunately, exact computations for both are NP-hard. To overcome this…
A method of estimating sums of multiplicative functions braided with Dirichlet characters is demonstrated, leading to a taxonomy of the characters for which such sums are large.
In this paper we exploit the concept of extended Pareto grid to study the geometric properties of the matching distance for $\mathbb{R}^2$-valued regular functions defined on a Riemannian closed manifold. In particular, we prove that in…
In this paper we consider two properties of variadic functions, namely associativity and preassociativity, that are pertaining to several data and language processing tasks. We propose parameterized relaxations of these properties and…
We prove a discrete approximation of functionals with jumps and creases.
Graphings are special bounded-degree graphs on probability spaces, representing limits of graph sequences that are convergent in a local or local-global sense. We describe a procedure for turning the underlying space into a compact metric…
We study arithmetic functions $\Phi(x;d,a)$, called prime running functions, whose value at $x$ sums the gaps between primes $p_k \equiv a\ (\text{mod}\ d)$ below $x$ and the next following prime $p_{k+1}$, up to $x$. (The following prime…