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In agricultural landscapes, the composition and spatial configuration of cultivated and semi-natural elements strongly impact species dynamics, their interactions and habitat connectivity. To allow for landscape structural analysis and…
Studies regarding knowledge organization and acquisition are of great importance to understand areas related to science and technology. A common way to model the relationship between different concepts is through complex networks. In such…
The paper investigates the properties of a class of resource allocation algorithms for communication networks: if a node of this network has $x$ requests to transmit, then it receives a fraction of the capacity proportional to $\log(1+x)$,…
Several network growth models have been proposed in the literature that attempt to incorporate properties of citation networks. Generally, these models aim at retaining the degree distribution observed in real-world networks. In this work,…
We show how scale-free degree distributions can emerge naturally from growing networks by using random walks for selecting vertices for attachment. This result holds for several variants of the walk algorithm and for a wide range of…
In network flow problems, there is a well-known one-to-one relationship between extreme points of the feasibility region and trees in the associated undirected graph. The same is true for the dual differential problem. In this paper, we…
We try to perform geometrization of cognitive science and psychology by representing information states of cognitive systems by points of {\it mental space} given by a hierarchic $m$-adic tree. Associations are represented by balls and…
In many real world networks, the number of links increases nonlinearly with the number of nodes. Models of such accelerated growth have been considered earlier with deterministic and stochastic number of links. Here we consider stochastic…
Pattern formation often occurs in confined systems, yet how boundaries shape patterning dynamics is unclear. We develop techniques to analyze confinement effects in nonlocal advection-diffusion equations, which generically capture the…
The organizational development of growing random networks is investigated. These growing networks are built by adding nodes successively and linking each to an earlier node of degree k with attachment probability A_k. When A_k grows slower…
In this paper, we propose DeepTree, a novel method for modeling trees based on learning developmental rules for branching structures instead of manually defining them. We call our deep neural model situated latent because its behavior is…
In this work we propose a computational scheme inspired by the workings of human cognition. We embed some fundamental aspects of the human cognitive system into this scheme in order to obtain a minimization of computational resources and…
Most complex networks serve as conduits for various dynamical processes, ranging from mass transfer by chemical reactions in the cell to packet transfer on the Internet. We collected data on the time dependent activity of five natural and…
Geometric constraints impact the formation of a broad range of spatial networks, from amino acid chains folding to proteins structures to rearranging particle aggregates. How the network of interactions dynamically self-organizes in such…
The adoption of agroecological practices will be crucial to address the challenges of climate change and biodiversity loss. Such practices favor the cultivation of plants in complex mixtures with layouts differing from the monoculture…
The behavior of complex systems is determined not only by the topological organization of their interconnections but also by the dynamical processes taking place among their constituents. A faithful modeling of the dynamics is essential…
The interplay between topology and dynamics in complex networks is a fundamental but widely unexplored problem. Here, we study this phenomenon on a prototype model in which the network is shaped by a dynamical variable. We couple the…
The availability of large scale streaming network data has reinforced the ubiquity of power-law distributions in observations and enabled precision measurements of the distribution parameters. The increased accuracy of these measurements…
Systems as diverse as genetic networks or the world wide web are best described as networks with complex topology. A common property of many large networks is that the vertex connectivities follow a scale-free power-law distribution. This…
The occurrence and the distribution of patterns of trees associated to natural numbers are investigated. Bounds from above and below are proven for certain natural quantities.