IMDB network revisited: unveiling fractal and modular properties from a typical small-world network

We study a subset of the movie collaboration network, imdb.com, where only adult movies are included. We show that there are many benefits in using such a network, which can serve as a prototype for studying social interactions. We find that the strength of links, i.e., how many times two actors have collaborated with each other, is an important factor that can significantly influence the network topology. We see that when we link all actors in the same movie with each other, the network becomes small-world, lacking a proper modular structure. On the other hand, by imposing a threshold on the minimum number of links two actors should have to be in our studied subset, the network topology becomes naturally fractal. This occurs due to a large number of meaningless links, namely, links connecting actors that did not actually interact. We focus our analysis on the fractal and modular properties of this resulting network, and show that the renormalization group analysis can characterize the self-similar structure of these networks.Comment: 12 pages, 9 figures, accepted for publication in PLOS ON

Approximate modularity: Kalton's constant is not smaller than 3

Kalton and Roberts [Trans. Amer. Math. Soc., 278 (1983), 803--816] proved that there exists a universal constant $K\leqslant 44.5$ such that for every set algebra $\mathcal{F}$ and every 1-additive function $f\colon \mathcal{F}\to \mathbb R$ there exists a finitely-additive signed measure $\mu$ defined on $\mathcal{F}$ such that $|f(A)-\mu(A)|\leqslant K$ for any $A\in \mathcal{F}$. The only known lower bound for the optimal value of $K$ was found by Pawlik [Colloq. Math., 54 (1987), 163--164], who proved that this constant is not smaller than $1.5$; we improve this bound to $3$ already on a non-negative 1-additive function.Comment: 9 pages, accepted to Proc. Am. Math. So

Comparing community structure identification

We compare recent approaches to community structure identification in terms of sensitivity and computational cost. The recently proposed modularity measure is revisited and the performance of the methods as applied to ad hoc networks with known community structure, is compared. We find that the most accurate methods tend to be more computationally expensive, and that both aspects need to be considered when choosing a method for practical purposes. The work is intended as an introduction as well as a proposal for a standard benchmark test of community detection methods.Comment: 10 pages, 3 figures, 1 table. v2: condensed, updated version as appears in JSTA

An Investigation into how concepts of modularity affect the evolution of complex morphologies

There are many different ways in which complex morphologies can be represented. While a simple string representation could be sufficient, often the most impressive artificial life simulations utilise. Context Free Grammars (1994, Karl Sims) or Recursive Tree Structures. When modelling a complex morphology using these encodings, it is possible to harness the creatures complex modularity to create more sensible and fit individuals. This article aims to compare and contrast the varying affects of evolutionary algorithms which utilise or disregard the organisms modularity

A Model of Genome Size Evolution for Prokaryotes in Stable and Fluctuating Environments

Temporal variability in ecosystems significantly impacts species diversity and ecosystem productivity and therefore the evolution of organisms. Different levels of environmental perturbations such as seasonal fluctuations, natural disasters, and global change have different impacts on organisms and therefore their ability to acclimatize and adapt. Thus, to understand howorganisms evolve under different perturbations is a key for predicting how environmental change will impact species diversity and ecosystem productivity. Here, we developed a computer simulation utilizing the individual-based model approach to investigate genome size evolution of a haploid, clonal and free-living prokaryotic population across different levels of environmental perturbations. Our results showthat a greater variability of the environment resulted in genomes with a larger number of genes. Environmental perturbations were more effectively buffered by populations of individuals with relatively large genomes. Unpredictable changes of the environment led to a series of population bottlenecks followed by adaptive radiations. Our model shows that the evolution of genome size is indirectly driven by the temporal variability of the environment. This complements the effects of natural selection directly acting on genome optimization. Furthermore, species that have evolved in relatively stable environments may face the greatest risk of extinction under global change as genome streamlining genetically constrains their ability to acclimatize to the new environmental conditions, unless mechanisms of genetic diversification such as horizontal gene transfer will enrich their gene pool and therefore their potential to adapt

Spatially-constrained clustering of ecological networks

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 biological entities are firstly identified and the spatial information is used afterwards to improve the ecological interpretation. We develop an integrative approach to retrieve groups of nodes that are geographically close and ecologically similar. Our model-based spatially-constrained method embeds the geographical information within a regularization framework by adding some constraints to the maximum likelihood estimation of parameters. A simulation study and the analysis of real data demonstrate that our approach is able to detect complex spatial patterns that are ecologically meaningful. The model-based framework allows us to consider external information (e.g., geographic proximities, covariates) in the analysis of ecological networks and appears to be an appealing alternative to consider such data