Related papers: A Model Theory Approach to Structural Limits
We study first-order model checking, by which we refer to the problem of deciding whether or not a given first-order sentence is satisfied by a given finite structure. In particular, we aim to understand on which sets of sentences this…
We prove that for any weakly convergent sequence of finite graphs with bounded vertex degrees, there exists a topological limit graphing.
The notion of 1-planarity is among the most natural and most studied generalizations of graph planarity. A graph is 1-planar if it has an embedding where each edge is crossed by at most another edge. The study of 1-planar graphs dates back…
We prove a general multi-dimensional central limit theorem for the expected number of vertices of a given degree in the family of planar maps whose vertex degrees are restricted to an arbitrary (finite or infinite) set of positive integers…
We consider general structures where formulas have truth values in the real unit interval as in continuous model theory, but whose predicates and functions need not be uniformly continuous with respect to a distance predicate. Every general…
In this paper we develop homotopy theoretical methods for studying diagrams. In particular we explain how to construct homotopy colimits and limits in an arbitrary model category. The key concept we introduce is that of a model…
The aim of the present article is to establish the connection between the existence of the limit along the normal and an admissible limit at a fixed boundary point for holomorphic functions of several complex variables.
A thesis submitted for the degree of Doctor of Philosophy of The Australian National University. In this work we introduce several new optimisation methods for problems in machine learning. Our algorithms broadly fall into two categories:…
Automatic Text Summarization strategies have been successfully employed to digest text collections and extract its essential content. Usually, summaries are generated using textual corpora that belongs to the same domain area where the…
The study of nonplanar drawings of graphs with restricted crossing configurations is a well-established topic in graph drawing, often referred to as beyond-planar graph drawing. One of the most studied types of drawings in this area are the…
Large models have emerged as the most recent groundbreaking achievements in artificial intelligence, and particularly machine learning. However, when it comes to graphs, large models have not achieved the same level of success as in other…
In the vast landscape of visualization research, Dimensionality Reduction (DR) and graph analysis are two popular subfields, often essential to most visual data analytics setups. DR aims to create representations to support neighborhood and…
Modeling networks as different graph types and researching on route finding strategies, to avoid congestion in dense subnetworks via graph-theoretic approaches, contributes to overall blocking probability reduction in networks. Our main…
Recent advancements in graph learning have revolutionized the way to understand and analyze data with complex structures. Notably, Graph Neural Networks (GNNs), i.e. neural network architectures designed for learning graph representations,…
In communication field, an important issue is to group users and base stations to as many as possible subnetworks satisfying certain interference constraints. These problems are usually formulated as a graph partition problems which…
A matching in a graph is uniquely restricted if no other matching covers exactly the same set of vertices. We establish tight lower bounds on the maximum size of a uniquely restricted matching in terms of order, size, and maximum degree.
We present a new approach to graph limit theory which unifies and generalizes the two most well developed directions, namely dense graph limits (even the more general $L^p$ limits) and Benjamini--Schramm limits (even in the stronger…
Many real life networks present an average path length logarithmic with the number of nodes and a degree distribution which follows a power law. Often these networks have also a modular and self-similar structure and, in some cases -…
We consider the edge-triangle model, a two-parameter family of exponential random graphs in which dependence between edges is introduced through triangles. In the so-called replica symmetric regime, the limiting free energy exists together…
We present some results on (co)limits of diagrams in $\infty$-categories, as well as those in $(n, 1)$-categories. In particular, we deduce a way to reshape colimit diagrams into simplicial ones, and a characterisations of $n$-cofinality…