Loewen H

Bio: Loewen H is an academic researcher. The author has an hindex of 1, co-authored 1 publications receiving 634 citations.

Scale-free networks are rare

Abstract: Real-world networks are often claimed to be scale free, meaning that the fraction of nodes with degree k follows a power law k−α, a pattern with broad implications for the structure and dynamics of complex systems. However, the universality of scale-free networks remains controversial. Here, we organize different definitions of scale-free networks and construct a severe test of their empirical prevalence using state-of-the-art statistical tools applied to nearly 1000 social, biological, technological, transportation, and information networks. Across these networks, we find robust evidence that strongly scale-free structure is empirically rare, while for most networks, log-normal distributions fit the data as well or better than power laws. Furthermore, social networks are at best weakly scale free, while a handful of technological and biological networks appear strongly scale free. These findings highlight the structural diversity of real-world networks and the need for new theoretical explanations of these non-scale-free patterns. Real-world networks are often said to be ”scale free”, meaning their degree distribution follows a power law. Broido and Clauset perform statistical tests of this claim using a large and diverse corpus of real-world networks, showing that scale-free structure is far from universal.

Are there general mechanisms of animal home range behaviour? A review and prospects for future research

Abstract: Home range behaviour is a common pattern of space use, having fundamental consequences for ecological processes. However, a general mechanistic explanation is still lacking. Research is split into three separate areas of inquiry - movement models based on random walks, individual-based models based on optimal foraging theory, and a statistical modelling approach - which have developed without much productive contact. Here we review recent advances in modelling home range behaviour, focusing particularly on the problem of identifying mechanisms that lead to the emergence of stable home ranges from unbounded movement paths. We discuss the issue of spatiotemporal scale, which is rarely considered in modelling studies, as well as highlighting the need to consider more closely the dynamical nature of home ranges. Recent methodological and theoretical advances may soon lead to a unified approach, however, conceptually unifying our understanding of linkages among home range behaviour and ecological or evolutionary processes.

On partial contraction analysis for coupled nonlinear oscillators

Abstract: We describe a simple yet general method to analyze networks of coupled identical nonlinear oscillators and study applications to fast synchronization, locomotion, and schooling. Specifically, we use nonlinear contraction theory to derive exact and global (rather than linearized) results on synchronization, antisynchronization, and oscillator death. The method can be applied to coupled networks of various structures and arbitrary size. For oscillators with positive definite diffusion coupling, it can be shown that synchronization always occurs globally for strong enough coupling strengths, and an explicit upper bound on the corresponding threshold can be computed through eigenvalue analysis. The discussion also extends to the case when network structure varies abruptly and asynchronously, as in "flocks" of oscillators or dynamic elements.

Scale-free networks are rare

Abstract: A central claim in modern network science is that real-world networks are typically "scale free," meaning that the fraction of nodes with degree $k$ follows a power law, decaying like $k^{-\alpha}$, often with $2 < \alpha < 3$. However, empirical evidence for this belief derives from a relatively small number of real-world networks. We test the universality of scale-free structure by applying state-of-the-art statistical tools to a large corpus of nearly 1000 network data sets drawn from social, biological, technological, and informational sources. We fit the power-law model to each degree distribution, test its statistical plausibility, and compare it via a likelihood ratio test to alternative, non-scale-free models, e.g., the log-normal. Across domains, we find that scale-free networks are rare, with only 4% exhibiting the strongest-possible evidence of scale-free structure and 52% exhibiting the weakest-possible evidence. Furthermore, evidence of scale-free structure is not uniformly distributed across sources: social networks are at best weakly scale free, while a handful of technological and biological networks can be called strongly scale free. These results undermine the universality of scale-free networks and reveal that real-world networks exhibit a rich structural diversity that will likely require new ideas and mechanisms to explain.