Related papers: Topological Reduction of Tight-Binding Models on C…

Designing topological materials with specific topological indices is a complex inverse problem, traditionally tackled through manual, intuition-driven methods that are neither scalable nor efficient for exploring the vast space of possible…

The empirical results suggest that the learnability of a neural network is directly related to its size. To mathematically prove this, we borrow a tool in topological algebra: Betti numbers to measure the topological geometric complexity of…

Network theory has played a dominant role in understanding the structure of complex systems and their dynamics. Recently, quantum complex networks, i.e. collections of quantum systems in a non-regular topology, have been explored leading to…

This paper studies reduced-order modeling of dynamic networks with strongly connected topology. Given a graph clustering of an original complex network, we construct a quotient graph with less number of vertices, where the edge weights are…

Network topology is a fundamental aspect of network science that allows us to gather insights into the complicated relational architectures of the world we inhabit. We provide a first specific study of neighbourhood degree sequences in…

Modeling distributed computing in a way enabling the use of formal methods is a challenge that has been approached from different angles, among which two techniques emerged at the turn of the century: protocol complexes, and directed…

Complex network theory has recently been proposed as a promising tool for characterising interactions between aircraft, and their downstream effects. We here explore the problem of networks' topological predictability, i.e. the dependence…

Long lived topological features are distinguished from short lived ones (considered as topological noise) in simplicial complexes constructed from complex networks. A new topological invariant, persistent homology, is determined and…

Parameterized tight-binding models fit to first principles calculations can provide an efficient and accurate quantum mechanical method for predicting properties of molecules and solids. However, well-tested parameter sets are generally…

As Internet of Things (IoT) devices become both cheaper and more powerful, researchers are increasingly finding solutions to their scientific curiosities both financially and computationally feasible. When operating with restricted power or…

We propose the n-clique network as a powerful tool for understanding global structures of combined highly-interconnected subgraphs, and provide theoretical predictions for statistical properties of the n-clique networks embedded in a…

Inferring network topology from smooth signals is a significant problem in data science and engineering. A common challenge in real-world scenarios is the availability of only partially observed nodes. While some studies have considered…

This system paper presents the Topology ToolKit (TTK), a software platform designed for topological data analysis in scientific visualization. TTK provides a unified, generic, efficient, and robust implementation of key algorithms for the…

Much of the complexity of social, biological, and engineered systems arises from a network of complex interactions connecting many basic components. Network analysis tools have been successful at uncovering latent structure termed…

With this contribution, we give a complete and comprehensive framework for modeling the dynamics of complex mechanical structures as port-Hamiltonian systems. This is motivated by research on the potential of lightweight construction using…

Flat bands - single-particle energy bands - in tight-binding networks have attracted attention due to the presence of macroscopic degeneracies and their extreme sensitivity to perturbations. This makes them natural candidates for emerging…

Networks constitute efficient tools for assessing universal features of complex systems. In physical contexts, classical as well as quantum, networks are used to describe a wide range of phenomena, such as phase transitions, intricate…

Motivated by new capabilities to realise artificial gauge fields in ultracold atomic systems, and by their potential to access correlated topological phases in lattice systems, we present a new strategy for designing topologically…

Convolutional neural networks (CNN's) are powerful and widely used tools. However, their interpretability is far from ideal. One such shortcoming is the difficulty of deducing a network's ability to generalize to unseen data. We use…

Entangled networks are ubiquitous in tissues, polymers, and fabrics. However, their mechanics remain insufficiently understood due to the complexity of the topological constraints at the network level. Here, we develop a mathematical…