Related papers: Directed graphs and interferometry
The elecrooptical response of graphene due to heating and drift of carriers is studied theoretically. Real and imaginary parts of the dynamic conductivity tensor are calculated for the case of effective momentum relaxation, when anisotropic…
We extend the notion of intersection graphs for knots in the theory of finite type invariants to string links. We use our definition to develop weight systems for string links via the adjacency matrix of the intersection graph, and show…
Let ${\cal G}=(G,w)$ be a weighted simple finite connected graph, that is, let $G$ be a simple finite connected graph endowed with a function $w$ from the set of the edges of $G$ to the set of real numbers. For any subgraph $G'$ of $G$, we…
This work introduces a novel algorithm for finding the connected components of a graph where the vertices and edges are grouped into sets defining a Set--Based Graph. The algorithm, under certain restrictions on those sets, has the…
In the theory of line graphs of undirected graphs there exists an important theorem linking the incidence matrix of the root graph to the adjacency matrix of its line graph. For directed or mixed graphs, however, the exists no analogous…
We present a conceptually new approach to describe state-of-the-art photonic quantum experiments using Graph Theory. There, the quantum states are given by the coherent superpositions of perfect matchings. The crucial observation is that…
A weighted graph is a graph in which every edge is assigned a non-negative real number. In a weighted graph, the weight of a path is the sum of the weights of its edges, and the weighed degree of a vertex is the sum of the weights of the…
A novel approach for measuring fast oscillations of an absolute value of interferometer optical path difference (OPD) has been developed. The principles of frequency-scanning interferometry are utilized for registration of the…
Consider the setting of \emph{randomly weighted graphs}, namely, graphs whose edge weights are chosen independently according to probability distributions with finite support over the non-negative reals. Under this setting, properties of…
A new type of an optical interferometer is discussed the phase difference between the interfering beams in which is substantially wavelength dependent. It is shown that the function measured with this device is an integral transform of the…
Metric graphs are often introduced based on combinatorics, upon "associating" each edge of a graph with an interval; or else, casually "gluing" a collection of intervals at their endpoints in a network-like fashion. Here we propose an…
We present a simple iterative strategy for measuring the connection strength between a pair of vertices in a graph. The method is attractive in that it has a linear complexity and can be easily parallelized. Based on an analysis of the…
In this article we try to describe the physics of a standard optical interferometer fed by "quantum" photons in terms of primitive, nevertheless accurate formulation. We derive explicit interferene patterns and show how they vary depending…
We consider an interferometer based on the concept of induced coherence, where two photons that originate in different second-order nonlinear crystals can interfere. We derive a complementarity relationship that links the first-order…
The complexity of a graph can be obtained as a derivative of a variation of the zeta function or a partial derivative of its generalized characteristic polynomial evaluated at a point [\textit{J. Combin. Theory Ser. B}, 74 (1998), pp.…
In this paper it is shown that it is possible to associate several polynomial ideals to a directed graph $D$ in order to find properties of it. In fact by using algebraic tools it is possible to give appropriate procedures for automatic…
The electron transmission through a {\it closed} Aharonov-Bohm mesoscopic solid-state interferometer, with a quantum dot (QD) on one of the paths, is calculated exactly for a simple model. Although the conductance is an even function of the…
In this note, we formulate the notions of the direct and inverse problems and contact points for the Feynman diagrams. For the electron-photon interaction case, the solutions of these direct and inverse problems are presented. The…
This paper gives a method that maps the static magnetic field due to a system of parallel current-carrying wires to a complex function. Using this function simplifies the calculation of the magnetic field energy density and inductance per…
Entanglement is a complexity measure of directed graphs that origins in fixed point theory. This measure has shown its use in designing efficient algorithms to verify logical properties of transition systems. We are interested in the…