相关论文: Loop Shaping with Scaled Relative Graphs

The strong resolving graph $G_{SR}$ of a connected graph $G$ was introduced in [Discrete Applied Mathematics 155 (1) (2007) 356--364] as a tool to study the strong metric dimension of $G$. Basically, it was shown that the problem of finding…

We apply the matrix-tree theorem to establish a link between various diagrammatic and determinant expressions, which naturally appear in scattering amplitudes of gravity theories. Using this link we are able to give a general…

The non-solvable graph of a finite group G is a simple graph whose vertices are the elements of G and there is an edge between x and y if and only if the subgroup generated by x and y is not solvable. The isolated vertices in the…

Assur graphs are a tool originally developed by mechanical engineers to decompose mechanisms for simpler analysis and synthesis. Recent work has connected these graphs to strongly directed graphs, and decompositions of the pinned rigidity…

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…

The phase structure of the scalar field theory with arbitrary powers of the gradient operator and a local non-analytic potential is investigated by the help of the RG in Euclidean space. The RG equation for the generating function of the…

Within a random-matrix-theory approach, we use the nearest-neighbor energy level spacing distribution $P(s)$ and the entropic eigenfunction localization length $\ell$ to study spectral and eigenfunction properties (of adjacency matrices) of…

Highly connected and yet sparse graphs (such as expanders or graphs of high treewidth) are fundamental, widely applicable and extensively studied combinatorial objects. We initiate the study of such highly connected graphs that are, in…

Graphs are ubiquitous real-world data structures, and generative models that approximate distributions over graphs and derive new samples from them have significant importance. Among the known challenges in graph generation tasks,…

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…

The definition of edge-regularity in graphs is a relaxation of the definition of strong regularity, so strongly regular graphs are edge-regular and, not surprisingly, the family of edge-regular graphs is much larger and more diverse than…

We construct a strongly regular graph with the parameters (65; 32; 15; 16). The idea is to search for an adjacency matrix that consists of circulant blocks. Equations with such matrices can be reduced to congruences with polynomials…

We discuss the meaning of geometrical constructions associated to loop quantum gravity states on a graph. In particular, we discuss the "twisted geometries" and derive a simple relation between these and Regge geometries.

There has been recent growing interest in graph theoretical properties known as r- and (r,s)-robustness. These properties serve as sufficient conditions guaranteeing the success of certain consensus algorithms in networks with misbehaving…

The visualization of any graph plays important role in various aspects, such as graph drawing software. Complex systems (like large databases or networks) that have a graph structure should be properly visualized in order to avoid…

A graph is regularizable if it is possible to assign weights to its edges so that all nodes have the same degree. Weights can be positive, nonnegative or arbitrary as soon as the regularization degree is not null. Positive and nonnegative…

Graphons are continuous models that represent the structure of graphs and allow the generation of graphs of varying sizes. We propose Scalable Implicit Graphon Learning (SIGL), a scalable method that combines implicit neural representations…

The graph of a real symplectic linear transformation is an R-Lagrangian subspace of a complex symplectic vector space. The restriction of the complex symplectic form is thus purely imaginary and may be expressed in terms of the generating…

A new alternative method to approximate the Visibility Graph (VG) of a time series has been introduced here. It exploits the fact that most of the nodes in the resulting network are not connected to those that are far away from them. This…

The monography examines the problem of constructing a group of automorphisms of a graph. A graph automorphism is a mapping of a set of vertices onto itself that preserves adjacency. The set of such automorphisms forms a vertex group of a…