Related papers: Two characterizations of crooked functions
We consider several coding discretizations of continuous functions which reflect their variation at some given precision. We study certain statistical and combinatorial properties of the sequence of finite words obtained by coding a typical…
Finite differences have been widely used in mathematical theory as well as in scientific and engineering computations. These concepts are constantly mentioned in calculus. Most frequently-used difference formulas provide excellent…
It is known that there exists a function interpolating a given data set such that the graph of the function is the attractor of an iterated function system which is called fractal interpolation function. We generalize the notion of fractal…
Functionals in geometric probability are often expressed as sums of bounded functions exhibiting exponential stabilization. Methods based on cumulant techniques and exponential modifications of measures show that such functionals satisfy…
In this paper we will estimate the main parameters of some evaluation codes which are known as projective parameterized codes. We will find the length of these codes and we will give a formula for the dimension in terms of the Hilbert…
We revisit a new type of a Voronoi diagram, in which distance is measured from a point to a pair of points. We consider a few more such distance functions, based on geometric primitives, and analyze the structure and complexity of the…
We show that the graph of a bent function is a Salem set in an appropriate sense. We also establish a simple result that quantifies redundancies in the difference operators of a function, which applies to bent functions over fields of odd…
In this paper, two novel algorithms for features selection are proposed. The first one is a filter method while the second is wrapper method. Both the proposed algorithms use the crowding distance used in the multiobjective optimization as…
We provide algorithms involving edge slides, for a connected simple graph to evolve in a finite number of steps to another connected simple graph in a prescribed configuration, and for the regularization of such a graph by the minimization…
Highly-regular graphs can be regarded as a combinatorial generalization of distance-regular graphs. From this standpoint, we study combinatorial aspects of highly-regular graphs. As a result, we give the following three main results in this…
In this paper we give two characterizations of the $p \times q$-grid graphs as co-edge-regular graphs with four distinct eigenvalues.
Large-scale graphs are widely used to represent object relationships in many real world applications. The occurrence of large-scale graphs presents significant computational challenges to process, analyze, and extract information. Graph…
Numerical functions, which characterize Dynkin schemes, Coxeter graphs and tame marked quivers, are considered.
Computing the similarity between two probability distributions is a recurring theme across control. We introduce a unified family of distances between the probability distributions of two random variables that is based on the discrepancy…
The functionality of a graph $G$ is the minimum number $k$ such that in every induced subgraph of $G$ there exists a vertex whose neighbourhood is uniquely determined by the neighborhoods of at most $k$ other vertices in the subgraph. The…
The directions of an infinite graph $G$ are a tangle-like description of its ends: they are choice functions that choose compatibly for all finite vertex sets $X\subseteq V(G)$ a component of $G-X$. Although every direction is induced by a…
We give an overview of different approaches to measuring the similarity of, or the distance between, two graphs, highlighting connections between these approaches. We also discuss the complexity of computing the distances.
We define two classes of functions, called regular (respectively, first-order) list functions, which manipulate objects such as lists, lists of lists, pairs of lists, lists of pairs of lists, etc. The definition is in the style of regular…
We generalize the class of split graphs to the directed case and show that these split digraphs can be identified from their degree sequences. The first degree sequence characterization is an extension of the concept of splittance to…
Let $X$ be a finite, simple graph with vertex set $V(X)$. The $2$-distance graph $T_2(X)$ of $X$ is the graph with the same vertex set as $X$ and two vertices are adjacent if and only if their distance in $X$ is exactly $2$. A graph $G$ is…