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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,…
Systems of dynamical interactions between competing species can be used to model many complex systems, and can be mathematically described by {\em random} networks. Understanding how patterns of activity arise in such systems is important…
Many large cities are found at locations with certain first nature advantages. Yet, those exogenous locational features may not be the most potent forces governing the spatial pattern of cities. In particular, population size, spacing and…
A substantial share of the Earth's land surface is managed by humans, with cities representing the most extreme form of anthropogenic land use. There are zillion ways in which settlements can be arranged across a given area, and their…
Granular materials size segregate when exposed to external periodic perturbations such as vibrations. Moreover, mixtures of grains of different sizes spontaneously segregate in the absence of external perturbations: when a mixture is simply…
In this article we investigate the topological changes undergone by trajectory networks as a consequence of progressive geographical infiltration. Trajectory networks, a type of knitted network, are obtained by establishing paths between…
Mathematical models of spatial population dynamics typically focus on the interplay between dispersal events and birth/death processes. However, for many animal communities, significant arrangement in space can occur on shorter timescales,…
A stable population network is hard to interrupt without any ecological consequences. A communication blockage between patches may destabilize the populations in the ecological network. This work deals with the construction of a safe cut…
A model for the generation of fractal growth networks in Euclidean spaces of arbitrary dimension is presented. These networks are considered as the spatial support of reaction-diffusion and pattern formation processes. The local dynamics at…
For $\alpha \in (1,2]$, the $\alpha$-stable graph arises as the universal scaling limit of critical random graphs with i.i.d. degrees having a given $\alpha$-dependent power-law tail behavior. It consists of a sequence of compact measured…
Describing networks geometrically through low-dimensional latent metric spaces has helped design efficient learning algorithms, unveil network symmetries and study dynamical network processes. However, latent space embeddings are limited to…
Self-organizing processes shape Earth's surface, creating complex patterns from simple rules in most landforms. Rainfall-induced mass movements dramatically reshape landscapes through rapid sediment transfer, but whether they self-organize…
The dryland vegetation model proposed by Rietkerk and collaborators has been explored from a bifurcation perspective in several previous studies. Our aim here is to explore in some detail the bifurcation phenomena present when the…
We numerically investigate a diffusion-reaction model of an ombrotrophic peatland implementing a Turing instability relying on nutrient accumulation. We propose a systematic and quantitative sorting of the vegetation patterns, based on the…
A fragmented landscape reduces the impact of interspecies connectivity, leading to higher diversity levels than otherwise possible in a connected landscape. Reconnecting a previously fragmented landscape initiates an extinction event,…
A Random Geometric Graph (RGG) ensemble is defined by the disordered distribution of its node locations. We investigate how this randomness drives sample-to-sample fluctuations in the dynamical properties of these graphs. We study the…
The role of species interactions in controlling the interplay between the stability of an ecosystem and its biodiversity is still not well understood. The ability of ecological communities to recover after a small perturbation of the…
Many soft matter systems exhibit ordered, polycontinuous network morphologies, such as the cubic (double) gyroid or diamond, as well as disordered network morphologies known generically as ``random sponges". While presumed to share similar…
Social and biological contagions are influenced by the spatial embeddedness of networks. Historically, many epidemics spread as a wave across part of the Earth's surface; however, in modern contagions long-range edges -- for example, due to…
The spatial arrangement of trees in a tropical forest reflects the interplay between aggregating processes, like dispersal limitation, and negative feedback that induces effective repulsion among individuals. Monitoring the variance-mean…