Related papers: Bratteli--Vershik models and graph covering models
GARCH models are useful tools in the investigation of phenomena, where volatility changes are prominent features, like most financial data. The parameter estimation via quasi maximum likelihood (QMLE) and its properties are by now well…
In this paper, we introduce a generalized concept of vertex transitivity in graphs called generalized vertex transitivity. We put forward a new invariant called transitivity number of a graph. The value of this invariant in different…
Context-free graph grammars have shown a remarkable ability to model structures in real-world relational data. However, graph grammars lack the ability to capture time-changing phenomena since the left-to-right transitions of a production…
A {\em $3$-graph} is a connected cubic graph such that each vertex is is equipped with a cyclic order of the edges incident with it. A {\em weight system} is a function $f$ on the collection of $3$-graphs which is {\em antisymmetric}:…
This note is a modest addition to the work arXiv:2109.13952. Here we construct an embedding of the space of electrical networks to the totally non-negative Lagrangian Grassmannian in a generic situation with the help of the technique of…
This work develops a flexible and mathematically sound framework for the design and analysis of graph scattering networks with variable branching ratios and generic functional calculus filters. Spectrally-agnostic stability guarantees for…
Global variational approximation methods in graphical models allow efficient approximate inference of complex posterior distributions by using a simpler model. The choice of the approximating model determines a tradeoff between the…
Graph theoretical ideas are highly utilized by computer science fields especially data mining. In this field, a data structure can be designed in the form of tree. Covering is a widely used form of data representation in data mining and…
Many real networks are equipped with short diameters, high clustering, and power-law degree distributions. With preferential attachment and network growth, the model by Barabasi and Albert simultaneously reproduces these properties, and…
The comparison of graphs is a vitally important, yet difficult task which arises across a number of diverse research areas including biological and social networks. There have been a number of approaches to define graph distance however…
Recent investigations address transport through ballistic charge-neutral graphene strips coupled to doped graphitic leads. This paper shows that identical transport properties arise when the leads are replaced by quantum wires. This duality…
In this article we study the notion of capacity of a vertex for infinite graphs over non-Archimedean fields. In contrast to graphs over the real field monotone limits do not need to exist. Thus, in our situation next to positive and null…
Knowledge graph is a popular format for representing knowledge, with many applications to semantic search engines, question-answering systems, and recommender systems. Real-world knowledge graphs are usually incomplete, so knowledge graph…
We define a new integer invariant of a finite graph G, the freeness index, that measures the extent to which G can be embedded in the 3-sphere so that it and its subgraphs have ``simple" complements, i.e., complements which are homeomorphic…
Statistical techniques are needed to analyse data structures with complex dependencies such that clinically useful information can be extracted. Individual-specific networks, which capture dependencies in complex biological systems, are…
Coverings of undirected graphs are used in distributed computing, and unfoldings of directed graphs in semantics of programs. We study these two notions from a graph theoretical point of view so as to highlight their similarities, as they…
The immensely fruitful concept of Grothendieck topology or covering issued from the efforts of algebraic geometers to study "sheaf-like" objects defined on categories more general than the lattice of open sets on a topological space. In the…
We consider infinite weighted graphs $G$, i.e., sets of vertices $V$, and edges $E$ assumed countable infinite. An assignment of weights is a positive symmetric function $c$ on $E$ (the edge-set), conductance. From this, one naturally…
We develop a tool for embedding almost spanning degenerate graphs of small bandwidth. As an application, we extend the blow-up lemma to degenerate graphs of small bandwidth, the bandwidth theorem to degenerate graphs, and make progress on a…
In these Notes, a comprehensive description of the universal fractal geometry of conformally-invariant scaling curves or interfaces, in the plane or half-plane, is given. The present approach focuses on deriving critical exponents…