Related papers: Notion of a virtual derivative

The parametric geometry of numbers has allowed to visualize the simultaneous approximation properties of a collection of real numbers through the combined graph of the related successive minima functions. Several inequalities among…

Multicrossings, which have previously been defined for classical knots and links, are extended to virtual knots and links. In particular, petal diagrams are shown to exist for all virtual knots.

Given a multivariate complex polynomial ${p\in\mathbb{C}[z_1,\ldots,z_n]}$, the imaginary projection $\mathcal{I}(p)$ of $p$ is defined as the projection of the variety $\mathcal{V}(p)$ onto its imaginary part. We focus on studying the…

There are many possible definitions of derivatives, here we present some and present one that we have called generalized that allows us to put some of the others as a particular case of this but, what interests us is to determine that there…

This paper builds on the connection between graph neural networks and traditional dynamical systems. We propose continuous graph neural networks (CGNN), which generalise existing graph neural networks with discrete dynamics in that they can…

The Integral Image algorithm is often applied in tasks that require efficient integration over images, such as object detection. In this paper we discuss theoretical aspects of the algorithm's continuous version. We suggest to define the…

Vector-space word representations obtained from neural network models have been shown to enable semantic operations based on vector arithmetic. In this paper, we explore the existence of similar information on vector representations of…

We demonstrate that the notions of derivative representation of a Lie algebra on a vector bundle, of semi-linear representations of a Lie group on a vector bundle, and related concepts, may be understood in terms of representations of Lie…

Differential Calculus is a staple of the college mathematics major's diet. Eventually one becomes tired of the same routine, and wishes for a more diverse meal. The college math major may seek to generalize applications of the derivative…

The fractional integrals and fractional derivatives problem is tackled by using the operator approach. The definition domain E of operators is causal functions.Many properties of fractional integrals are given. Fractional derivatives…

We construct arithmetic terms representing the partial sums of binomial coefficients, and we extend these results to obtain arithmetic terms representing the multisections of binomial coefficient sums. We also introduce an arithmetic term…

We give a detailed exposition of the "vectorized" notation for dealing with quantum operations. This notation is used to highlight the relationships between representations of completely-positive dynamics. Vectorization considerably…

The search for linguistic patterns, stylometry and forensic linguistics have in the theory of complex networks, their structures and associated mathematical tools, allies with which to model and analyze texts. In this paper we present a new…

A graph theoretic perspective is taken for a range of phenomena in continuum physics in order to develop representations for analysis of large scale, high-fidelity solutions to these problems. Of interest are phenomena described by partial…

In the recent years, several polynomial algorithms of a dynamical nature have been proposed to address the graph isomorphism problem. In this paper we propose a generalization of an approach exposed in cond-mat/0209112 and find that this…

The Wiener index is a graphical invariant that has found extensive application in chemistry. We define a generating function, which we call the Wiener polynomial, whose derivative is a q-analog of the Wiener index. We study some of the…

A Gauss paragraph is a combinatorial formulation of a generic closed curve with multiple components on some surface. A virtual string is a collection of circles with arrows that represent the crossings of such a curve. Every closed curve…

This book objective is to develop an algebraization of graph grammars. Equivalently, we study graph dynamics. From the point of view of a computer scientist, graph grammars are a natural generalization of Chomsky grammars for which a purely…

Graph-based semantic representations are valuable in natural language processing, where it is often simple and effective to represent linguistic concepts as nodes, and relations as edges between them. Several attempts has been made to find…

A point visibility graph is a graph induced by a set of points in the plane, where every vertex corresponds to a point, and two vertices are adjacent whenever the two corresponding points are visible from each other, that is, the open…