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Many materials, processes, and structures in science and engineering have important features at multiple scales of time and/or space; examples include biological tissues, active matter, oceans, networks, and images. Explicitly extracting,…

Transport is an important function in many network systems and understanding its behavior on biological, social, and technological networks is crucial for a wide range of applications. However, it is a property that is not well-understood…

A key goal in studies of ecology and evolution is understanding the causes of phenotypic diversity in nature. Most traits of interest, such as those relating to morphology, life-history, immunity and behaviour are quantitative, and…

Ecological systems show a variety of characteristic patterns of biodiversity in space and time. It is a challenge for theory to find models that can reproduce and explain the observed patterns. Since the advent of island biogeography these…

Characteristic scale is a notion that pervades the geophysical sciences, but it has no widely accepted precise definition. The wavelet transform decomposes a time series into coefficients that are associated with different scales. The…

Spatial ecological networks are widely used to model interactions between georeferenced biological entities (e.g., populations or communities). The analysis of such data often leads to a two-step approach where groups containing similar…

Ecologists and conservation biologists need to identify the relative importance of species to make sound management decisions and effectively allocate scarce resources. We introduce a new method, termed environ centrality, to determine the…

We study the spatial patterns formed by a system of interacting particles where the mobility of any individual is determined by the population crowding at two different spatial scales. In this way we model the behavior of some biological…

Understanding how size influences the internal characteristics of a system is a crucial concern across various fields. Concepts like scale invariance, universalities, and fractals are fundamental to this inquiry and find application in…

Spatial patterns are widely observed in numerous nonequilibrium natural systems, often undergoing complex transitions and bifurcations, thereby exhibiting significant importance in many physical and biological systems such as embryonic…

The theory of evolution by natural selection cannot be used to evaluate the truth value of the following proposition: Through evolution, there exists at least one species that can adapt to any one given environment. To address this issue,…

To comprehend the multipartite organization of large-scale biological and social systems, we introduce a new information theoretic approach that reveals community structure in weighted and directed networks. The method decomposes a network…

A celebrated and controversial hypothesis conjectures that some biological systems --parts, aspects, or groups of them-- may extract important functional benefits from operating at the edge of instability, halfway between order and…

The current science of cities can provide a useful foundation for future urban policies, provided that these proposals have been validated by correct observations of the diversity of situations in the world. However, international…

The spatial scale of population synchrony gives the characteristic distance at which the population fluctuations are correlated. Therefore, it gives also the characteristic size of the regions of simultaneous population depletion, or even…

The modelling and analysis of biological systems has deep roots in Mathematics, specifically in the field of Ordinary Differential Equations. Alternative approaches based on formal calculi, often derived from process algebras or term…

One of the themes that have been approached more and more within the specialised literature is being represented by economic cycles. The analysis of these is very useful in the long term predictions, in finding solutions for the economic…

Human mobility is known to be distributed across several orders of magnitude of physical distances , which makes it generally difficult to endogenously find or define typical and meaningful scales. Relevant analyses, from movements to…

Evolutionary dynamics are shaped by a variety of fundamental, generic drivers, including spatial structure, ecology, and selection pressure. These drivers impact the trajectory of evolution, and have been hypothesized to influence…

The structure of real-world networks is usually difficult to characterize owing to the variation of topological scales, the nondyadic complex interactions, and the fluctuations in the network. We aim to address these problems by introducing…