Related papers: Graph topology determines coexistence in the rock-…
The richness of many complex systems stems from the interactions among their components. The higher-order nature of these interactions, involving many units at once, and their temporal dynamics constitute crucial properties that shape the…
To understand the mechanisms underlying species coexistence, ecologists often study invasion growth rates of theoretical and data-driven models. These growth rates correspond to average per-capita growth rates of one species with respect to…
We investigate the scale-free behavior of the spatial rock-paper-scissors model with May-Leonard dynamics, analyzing specific quantifiers that engender the power-law feature. The main results show that an important parameter that drives the…
Dynamic graph theory is a novel, growing area that deals with graphs that change over time and is of great utility in modelling modern wireless, mobile and dynamic environments. As a graph evolves, possibly arbitrarily, it is challenging to…
A central question in dynamics is whether the topology of a system determines its geometry. This is known as rigidity. Under mild topological conditions rigidity holds for many classical cases, including: Kleinian groups, circle…
The spatio-temporal arrangement of interacting populations often influences the maintenance of species diversity and is a subject of intense research. Here, we study the spatio-temporal patterns arising from the cyclic competition between…
Cyclic dominant systems, like rock-paper-scissors game, are frequently used to explain biodiversity in nature, where mobility, reproduction and intransitive competition are on stage to provide the coexistence of competitors. A significantly…
A temporal graph is a graph whose edges only appear at certain points in time. Reachability in these graphs is defined in terms of paths that traverse the edges in chronological order (temporal paths). This form of reachability is neither…
The topological structure of complex networks has fascinated researchers for several decades, resulting in the discovery of many universal properties and reoccurring characteristics of different kinds of networks. However, much less is…
The topological structure of complex networks has fascinated researchers for several decades, resulting in the discovery of many universal properties and reoccurring characteristics of different kinds of networks. However, much less is…
Courcelle's Theorem is an important result in graph theory, proving the existence of linear-time algorithms for many decision problems on graphs whose tree-width is bounded by a constant. The purpose of this text is twofold: to provide an…
We construct graphs (trees of bounded degree) on which the contact process has critical rate (which will be the same for both global and local survival) equal to any prescribed value between zero and $\lambda_c(\mathbb{Z})$, the critical…
As the behavior of a system composed of cyclically competing species is strongly influenced by the presence of fluctuations, it is of interest to study cyclic dominance in low dimensions where these effects are the most prominent. We here…
We study the spatial rock-paper-scissors model, where resource competitors' cyclic dominance impacts organisms' energy levels. Our model assumes that failed selection interactions can lead to energy loss, reducing the chances of success in…
Cyclic dominance of competing species is an intensively used working hypothesis to explain biodiversity in certain living systems, where the evolutionary selection principle would dictate a single victor otherwise. Technically the…
Previous symmetry-based database searches have already revealed ubiquitous band topology in nature, while the destiny of band topology under symmetry-breaking is yet to be studied comprehensively. Here we first develop a framework allowing…
The formation of out-of-equilibrium patterns is a characteristic feature of spatially-extended, biodiverse, ecological systems. Intriguing examples are provided by cyclic competition of species, as metaphorically described by the…
We present a graph model for a background independent, relational approach to spacetime emergence. The general idea and the graph main features, detailed in [1], are discussed. This is a combinatorial (dynamical) metric graph, colored on…
Networks are important representations in computer science to communicate structural aspects of a given system of interacting components. The evolution of a network has several topological properties that can provide us information on the…
This work deals with the influence of the neighborhood in simple rock-paper-scissors models of biodiversity. We consider the case of three distinct species which evolve under the standard rules of mobility, reproduction and competition. The…