Related papers: Directed graphs and interferometry
The computation of the optical conductivity of strained and deformed graphene is discussed within the framework of quantum field theory in curved spaces. The analytical solutions of the Dirac equation in an arbitrary static background…
Folded graphene flakes are a natural byproduct of the micromechanical exfoliation process. In this Letter we show by a combination of analytical and numerical methods that such systems behave as intriguing interferometers due to the…
Recently, one has seen a surge of interest in developing such methods including ones for learning such representations for (undirected) graphs (while preserving important properties). However, most of the work to date on embedding graphs…
Interferometry provides highly sensitive access to optical phase and is central to much of modern metrology and phase imaging methods. Conventional implementations, however, often face trade-offs between mechanical stability and…
A geometrical approach to calculate the electric field due to a uniformly charged rod is presented. The result is surprisingly simple and elegant. Using pure geometrical quantities like length and angle, the direction of the electric field…
This paper considers the problem of embedding directed graphs in Euclidean space while retaining directional information. We model a directed graph as a finite set of observations from a diffusion on a manifold endowed with a vector field.…
We consider the issue of validating the relationship between electric fields and optical intensity as proposed by the classical theory of electromagnetism. We describe an interference scenario in which this can be checked using only…
A graphical model provides a compact and efficient representation of the association structure of a multivariate distribution by means of a graph. Relevant features of the distribution are represented by vertices, edges and other…
We explore pseudometrics for directed graphs in order to better understand their topological properties. The directed flag complex associated to a directed graph provides a useful bridge between network science and topology. Indeed, it has…
We introduce a new arc in directed graphs of integers. Among other things, we determine the positive integers that have arcs to all except a finite number of positive integers. We also propose some possible research problems at the end of…
In the field of graph signal processing (GSP), directed graphs present a particular challenge for the "standard approaches" of GSP to due to their asymmetric nature. The presence of negative- or complex-weight directed edges, a graphical…
Bidirected graphs are multigraphs where every edge has an independent direction at each end. In the paper, with an arbitrary bidirected graph we associate a non-negative integral quadratic form (called the incidence form of the graph), and…
A theory of orientation on gain graphs (voltage graphs) is developed to generalize the notion of orientation on graphs and signed graphs. Using this orientation scheme, the line graph of a gain graph is studied. For a particular family of…
Given a finite directed graph with $n$ vertices, we define a metric $d_G$ on $\mathbb{F}_q^n$, where $\mathbb{F}_q$ is the finite field with $q$ elements. The weight of a word is defined as the number of vertices that can be reached by a…
Intense laser fields have been proposed as a means to generate light-induced gravitational effects, providing a novel approach to investigate gravity and its coupling to electromagnetism in a controlled laboratory setting. In this article,…
It is shown that classical control diagrams can be mapped one-to-one onto quantum path integrals over measurement amplitudes. To show the practical utility of this method, exact closed-form expressions are derived for the control dynamics…
Interference effects are usually observed by intensity measurement. Path indistinguishability by quantum complementarity principle requires projection of the interfering fields into a common indistinguishable mode before detection. On the…
This paper provides an overview of results, concerning longest or heaviest paths, in the area of random directed graphs on the integers along with some extensions. We study first-order asymptotics of heaviest paths allowing weights both on…
A path graph is the intersection graph of paths in a tree. A directed path graph is the intersection graph of paths in a directed tree. Even if path graphs and directed path graphs are characterized very similarly, their recognition…
This paper is aimed to review and promote the main applications of the methods of Quantum Field Theory to description of quantum effects in graphene. We formulate the effective electromagnetic action following from the Dirac model for the…