Related papers: Core Decomposition in Multilayer Networks: Theory,…
We focus on two central themes in this dissertation. The first one is on decomposing polytopes and polynomials in ways that allow us to perform nonlinear optimization. We start off by explaining important results on decomposing a polytope…
Decycling and dismantling of complex networks are underlying many important applications in network science. Recently these two closely related problems were tackled by several heuristic algorithms, simple and considerably sub-optimal, on…
Multilayer networks offer a powerful framework for modeling complex systems across diverse domains, effectively capturing multiple types of connections and interdependent subsystems commonly found in real world scenarios. To analyze these…
The segmentation of ultra-high resolution images poses challenges such as loss of spatial information or computational inefficiency. In this work, a novel approach that combines encoder-decoder architectures with domain decomposition…
The use of multimode fibers offers advantages in the field of communication technology in terms of transferable information density and information security. For applications using physical layer security or mode division multiplexing, the…
In complex networks, many elements interact with each other in different ways. A hypergraph is a network in which group interactions occur among more than two elements. In this study, first, we propose a method to identify influential…
Modelling relationships between entities in real-world systems with a simple graph is a standard approach. However, reality is better embraced as several interdependent subsystems (or layers). Recently the concept of a multilayer network…
Kernelization algorithms, usually a preprocessing step before other more traditional algorithms, are very special in the sense that they return (reduced) instances, instead of final results. This characteristic excludes the freedom of…
Centrality measures for simple graphs/networks are well-defined and each has numerous main-memory algorithms. However, for modeling complex data sets with multiple types of entities and relationships, simple graphs are not ideal. Multilayer…
A typical way in which network data is recorded is to measure all the interactions among a specified set of core nodes; this produces a graph containing this core together with a potentially larger set of fringe nodes that have links to the…
Core-periphery detection aims to separate the nodes of a complex network into two subsets: a core that is densely connected to the entire network and a periphery that is densely connected to the core but sparsely connected internally. The…
As networks grow in size and complexity, backbones become an essential network representation. Indeed, they provide a simplified yet informative overview of the underlying organization by retaining the most significant and structurally…
The analysis of the modular structure of networks is a major challenge in complex networks theory. The validity of the modular structure obtained is essential to confront the problem of the topology-functionality relationship. Recently,…
Community detection, the decomposition of a graph into essential building blocks, has been a core research topic in network science over the past years. Since a precise notion of what constitutes a community has remained evasive, community…
For subspace recovery, most existing low-rank representation (LRR) models performs in the original space in single-layer mode. As such, the deep hierarchical information cannot be learned, which may result in inaccurate recoveries for…
Networks are largely used for modelling and analysing data and relations among them. Recently, it has been shown that the use of a single network may not be the optimal choice, since a single network may misses some aspects. Consequently,…
Given an undirected graph, the $k$-core is a subgraph in which each node has at least $k$ connections. This is widely used in graph analytics to identify core subgraphs within a larger graph. The sequential $k$-core decomposition algorithm…
With the advent of era of Big Data and Internet of Things, there has been an exponential increase in the availability of large data sets. These data sets require in-depth analysis that provides intelligence for improvements in methods for…
Graphlets are induced subgraph patterns that are crucial to the understanding of the structure and function of a large network. A lot of efforts have been devoted to calculating graphlet statistics where random walk based approaches are…
A useful approach to the mathematical analysis of large-scale biological networks is based upon their decompositions into monotone dynamical systems. This paper deals with two computational problems associated to finding decompositions…