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Recently there has been an increasing interest in studying dynamical processes on networks exhibiting higher-order structures, such as simplicial complexes, where the dynamics acts above and beyond dyadic interactions. Using simulations or…

Over the last decade, an enormous interest and activity in complex networks have been witnessed within the physics community. On the other hand, diffusion and its theory, have equipped the toolbox of the physicist for decades. In this…

Dynamical patterns in complex networks of coupled oscillators are both of theoretical and practical interest, yet to fully reveal and understand the interplay between pattern emergence and network structure remains to be an outstanding…

The capacity to adapt can greatly influence the success of systems that need to compensate for damaged parts, learn how to achieve robust performance in new environments, or exploit novel opportunities that originate from new technological…

Emergence and causality are two fundamental concepts for understanding complex systems. They are interconnected. On one hand, emergence refers to the phenomenon where macroscopic properties cannot be solely attributed to the cause of…

Complex numbers define the relationship between entities in many situations. A canonical example would be the off-diagonal terms in a Hamiltonian matrix in quantum physics. Recent years have seen an increasing interest to extend the tools…

Characterizing the emergence of chaotic dynamics of complex networks is an essential task in nonlinear science with potential important applications in many fields such as neural control engineering, microgrid technologies, and ecological…

In this paper, we consider the problem of exploring structural regularities of networks by dividing the nodes of a network into groups such that the members of each group have similar patterns of connections to other groups. Specifically,…

Dissipative phenomena manifest in multiple mechanical systems. In this dissertation, different geometric frameworks for modelling non-conservative dynamics are considered. The objective is to generalize several results from conservative…

There has recently been an explosion of interest in how "higher-order" structures emerge in complex systems. This "emergent" organization has been found in a variety of natural and artificial systems, although at present the field lacks a…

The need to harmonise apparently irreconcilable arrangements in an ecosystem --nestedness and segregation-- has triggered so far different strategies. Methodological refinements, or the inclusion of behavioural preferences to the network…

Quantum transport is strongly influenced by interference with phase relations that depend sensitively on the scattering medium. Since even small changes in the geometry of the medium can turn constructive interference to destructive, a…

Various natural and engineered systems, from urban traffic flow to the human brain, can be described by large-scale networked dynamical systems. These systems are similar in being comprised of a large number of microscopic subsystems, each…

Adaptivity is a dynamical feature that is omnipresent in nature, socio-economics, and technology. For example, adaptive couplings appear in various real-world systems like the power grid, social, and neural networks, and they form the…

To better understand the structure and function of complex systems, researchers often represent direct interactions between components in complex systems with networks, assuming that indirect influence between distant components can be…

We consider the frequency at which avoided crossings appear in an energy level structure when an external field is applied to a quantum chaotic system. The distribution of the spacing in the parameter between two adjacent avoided crossings…

Many systems exhibit complex interactions between their components: some features or actions amplify each other's effects, others provide redundant information, and some contribute independently. We present a simple geometric method for…

We study the distribution of the statistics 'number of fixed points' and 'number of excedances' in permutations avoiding subsets of patterns of length 3. We solve all the cases of simultaneous avoidance of more than one pattern, giving…

Abductive reasoning, reasoning for inferring explanations for observations, is often mentioned in scientific, design-related and artistic contexts, but its understanding varies across these domains. This paper reviews how abductive…

This work concerns a many-body deterministic model that displays life-like properties as emergence, complexity, self-organization, spontaneous compartmentalization, and self-regulation. The model portraits the dynamics of an ensemble of…