Related papers: Hidden geometry and dynamics of complex networks: …

Real complex systems are not rigidly structured; no clear rules or blueprints exist for their construction. Yet, amidst their apparent randomness, complex structural properties universally emerge. We propose that an important class of…

Our work is concerned with simplicial complexes that describe higher-order interactions in real complex systems. This description allows to go beyond the pairwise node-to-node representation that simple networks provide and to capture a…

The study of complex networks is a significant development in modern science, and has enriched the social sciences, biology, physics, and computer science. Models and algorithms for such networks are pervasive in our society, and impact…

Multiple scales coexist in complex networks. However, the small world property makes them strongly entangled. This turns the elucidation of length scales and symmetries a defiant challenge. Here, we define a geometric renormalization group…

Many observables of brain dynamics appear to be optimized for computation. Which connectivity structures underlie this fine-tuning? We propose that many of these structures are naturally encoded in the space that more directly relates to…

Neuronal networks constitute a special class of dynamical systems, as they are formed by individual geometrical components, namely the neurons. In the existing literature, relatively little attention has been given to the influence of…

Open-shell nanographenes provide a versatile platform to host unconventional magnetic states within their {\pi}-conjugated networks. Particularly appealing are graphene architectures that incorporate spatially separated radicals and tunable…

Clustering is typically measured by the ratio of triangles to all triples, open or closed. Generating clustered networks, and how clustering affects dynamics on networks, is reasonably well understood for certain classes of networks…

The response of driven frustrated media stems from interacting hysteretic elements. We derive explicit mappings from networks of hysteretic springs to their abstract representation as interacting hysterons. These maps reveal how the…

The fundamental idea of embedding a network in a metric space is rooted in the principle of proximity preservation. Nodes are mapped into points of the space with pairwise distance that reflects their proximity in the network. Popular…

One important question in neuroscience is how global behavior in a brain network emerges from the interplay between network connectivity and the neural dynamics of individual nodes. To better understand this theoretical relationship, we…

We propose a two-dimensional geometrical model, based on the concept of geometrical frustration, conceived for the study of compaction in granular media. The dynamics exhibits an interesting inverse logarithmic law that is well known from…

The understanding of neural activity patterns is fundamentally linked to an understanding of how the brain's network architecture shapes dynamical processes. Established approaches rely mostly on deviations of a given network from certain…

The Ising model, often seen as the paradigmatic spin model, has been heavily studied for its mathematical description of ferromagnetism in statistical mechanics. We explore a quantum version of this model, the transverse field Ising model,…

Complex networks describe a wide range of systems in nature and society, much quoted examples including the cell, a network of chemicals linked by chemical reactions, or the Internet, a network of routers and computers connected by physical…

Compound graphs are networks in which vertices can be grouped into larger subsets, with these subsets capable of further grouping, resulting in a nesting that can be many levels deep. In several applications, including biological workflows,…

This thesis is a compendium of research which brings together ideas from the fields of Complex Networks and Computational Neuroscience to address two questions regarding neural systems: 1) How the activity of neurons, via synaptic changes,…

In the dense metal-organic framework Na[Mn(HCOO)$_3$], Mn$^{2+}$ ions ($S=\frac{5}{2}$) occupy the nodes of a `trillium' hyperkagome net. We show that this material exhibits a variety of behaviour characteristic of geometric frustration:…

Network models with latent geometry have been used successfully in many applications in network science and other disciplines, yet it is usually impossible to tell if a given real network is geometric, meaning if it is a typical element in…

Nature is a blossoming of regular structures, signature of self-organization of the underlying microscopic interacting agents. Turing theory of pattern formation is one of the most studied mechanisms to address such phenomena and has been…