Related papers: Various Properties of Various Ultrafilters, Variou…
Hypergraphs, increasingly utilised for modelling complex and diverse relationships in modern networks, gain much attention representing intricate higher-order interactions. Among various challenges, cohesive subgraph discovery is one of the…
Data are represented as graphs in a wide range of applications, such as Computer Vision (e.g., images) and Graphics (e.g., 3D meshes), network analysis (e.g., social networks), and bio-informatics (e.g., molecules). In this context, our…
Our capacity to learn representations from data is related to our ability to design filters that can leverage their coupling with the underlying domain. Graph filters are one such tool for network data and have been used in a myriad of…
An extension of the divisibility relation on $\mathbb{N}$ to the set $\beta\mathbb{N}$ of ultrafilters on $\mathbb{N}$ was defined and investigated in several papers during the last ten years. Here we make a survey of results obtained so…
Graph density profiles are fundamental objects in extremal combinatorics. Very few profiles are fully known, and all are two-dimensional. We show that even in high dimensions ratios of graph densities and numbers often form the power-sum…
Over the past decade, we witness an increasing amount of interest in the design of exact exponential-time and parameterized algorithms for problems in Graph Drawing. Unfortunately, we still lack knowledge of general methods to develop such…
Graphs are a fundamental abstraction for modeling relational data. However, graphs are discrete and combinatorial in nature, and learning representations suitable for machine learning tasks poses statistical and computational challenges. In…
Graphs are fundamental objects that find widespread applications across computer science and beyond. Graph Theory has yielded deep insights about structural properties of various families of graphs, which are leveraged in the design and…
A recent line of research has concentrated on exploring the links between analytic and combinatorial theories of submodularity, uncovering several key connections between them. In this context, Lov\'asz initiated the study of matroids from…
In most work to date, graph signal sampling and reconstruction algorithms are intrinsically tied to graph properties, assuming bandlimitedness and optimal sampling set choices. However, practical scenarios often defy these assumptions,…
The structural properties of graphs are usually characterized in terms of invariants, which are functions of graphs that do not depend on the labeling of the nodes. In this paper we study convex graph invariants, which are graph invariants…
The performance of large language models (LLMs) is strongly influenced by the quality and diversity of data used during supervised fine-tuning (SFT). However, current data selection methods often prioritize one aspect over the other,…
Mathematical morphology (MM) helps to describe and analyze shapes using set theory. MM can be effectively applied to binary images which are treated as sets. Basic morphological operators defined can be used as an effective tool in image…
Geometric graphs are a special kind of graph with geometric features, which are vital to model many scientific problems. Unlike generic graphs, geometric graphs often exhibit physical symmetries of translations, rotations, and reflections,…
Existing multiplex graph models often assume homophily, where connected nodes tend to belong to the same class or share similar attributes. Consequently, these models may struggle with graphs exhibiting heterophily, where connected nodes…
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…
Recently, graph neural networks have been widely used for network embedding because of their prominent performance in pairwise relationship learning. In the real world, a more natural and common situation is the coexistence of pairwise…
We study the parametrized complexity of fundamental relations between multidimensional subshifts, such as equality, conjugacy, inclusion, and embedding, for subshifts of finite type (SFTs) and effective subshifts. We build on previous work…
In a recent work, we introduced a parametric framework for obtaining obstruction characterizations of graph parameters with respect to a quasi-ordering $\leqslant$ on graphs. Towards this, we proposed the concepts of class obstruction,…
Networks are useful representations for complex systems. Especially, heterogeneous and asymmetrical relations commonly found in complex systems can be converted to weighted directed edges between nodes. The disparity filter (Serrano et al.,…