Michele Bellingeri

Efficiency of attack strategies on complex model and real-world networks

We investigated the efficiency of attack strategies to network nodes when targeting several complex model and real-world networks. We tested 5 attack strategies, 3 of which were introduced in this work for the first time, to attack 3 model networks (Erdos and Renyi, Barabasi and Albert preferential attachment network, and scale-free network configuration models) and 3 real networks (Gnutella peer-to-peer network, email network of the University of Rovira i Virgili, and immunoglobulin interaction network). Nodes were removed sequentially according to the importance criterion defined by the attack strategy, and we used the size of the largest connected component (LCC) as a measure of network damage. We found that the efficiency of attack strategies (fraction of nodes to be deleted for a given reduction of LCC size) depends on the topology of the network, although attacks based on either the number of connections of a node or betweenness centrality were often the most efficient strategies. Sequential deletion of nodes in decreasing order of betweenness centrality was the most efficient attack strategy when targeting real-world networks. The relative efficiency of attack strategies often changed during the sequential removal of nodes, especially for networks with power-law degree distribution.

Using food web dominator trees to catch secondary extinctions in action

In ecosystems, a single extinction event can give rise to multiple ‘secondary’ extinctions. Conservation effort would benefit from tools that help forecast the consequences of species removal. One such tool is the dominator tree, a graph-theoretic algorithm that when applied to food webs unfolds their complex architecture, yielding a simpler topology made of linear pathways that are essential for energy delivery. Each species along these chains is responsible for passing energy to the taxa that follow it and, as such, it is indispensable for their survival. To assess the predictive potential of the dominator tree, we compare its predictions with the effects that followed the collapse of the capelin (Mallotus villosus) in the Barents Sea ecosystem. To this end, we first compiled a food web for this ecosystem, then we built the corresponding dominator tree and, finally, we observed whether model predictions matched the empirical observations. This analysis shows the potential and the drawbacks of the dominator trees as a tool for understanding the causes and consequences of extinctions in food webs.

Threshold extinction in food webs

Food web response to species loss has been investigated in several ways in the previous years. In binary food webs, species go secondarily extinct if no resource item remains to be exploited. In this work, we considered that species can go extinct before the complete loss of their resources and we introduced thresholds of minimum energy requirement for species survival. According to this approach, extinction of a node occurs whenever an initial extinction event eliminates its incoming links so it is left with an overall energy intake lower than the threshold value. We tested the robustness of 18 real food webs by removing species from most to least connected and considering different scenarios defined by increasing the extinction threshold. Increasing energy requirement threshold negatively affects food web robustness. We found that a very small increase of the energy requirement substantially increases system fragility. In addition, above a certain value of energy requirement threshold we found no relationship between the robustness and the connectance of the web. Further, food webs with more species showed higher fragility with increasing energy threshold. This suggests that the shape of the robustness–complexity relationship of a food web depends on the sensitivity of consumers to loss of prey.

Optimization strategies with resource scarcity: From immunization of networks to the traveling salesman problem

The best strategy to immunize a complex network is usually evaluated in terms of the percolation threshold, i.e. the number of vaccine doses which make the largest connected cluster (LCC) vanish. The strategy inducing the minimum percolation threshold represents the optimal way to immunize the network. Here we show that the efficacy of the immunization strategies can change during the immunization process. This means that, if the number of doses is limited, the best strategy is not necessarily the one leading to the smallest percolation threshold. This outcome should warn about the adoption of global measures in order to evaluate the best immunization strategy.

Light transmission behaviour as a function of the homogeneity in one dimensional photonic crystals

Abstract The average light transmission of one-dimensional photonic media has been studied as a function of the medium homogeneity, quantified by the Shannon–Wiener index. We have found a decrease in the average light transmission by increasing the Shannon–Wiener index up to minimum (corresponding to H ′xa0=xa00.9375): from this point, the transmission increases following the Shannon–Wiener index. The behaviour has been confirmed for different pairs of materials forming the photonic structure. Nevertheless, we have observed that the trend slope is proportional to the refractive index ratio between the two materials ( n hi / n low ).

Light Transmission Properties and Shannon Index in One-Dimensional Photonic Media With Disorder Introduced by Permuting the Refractive Index Layers

In this paper, we have studied, with a numerical method, how introducing disorder affects the light transmission properties of 1-D photonic structures over a wide range of wavelengths. A new type of disorder is introduced by permuting the refractive index layers in the optical medium. We compared the light transmission properties of ideal photonic crystals and of disordered media with the same kind and number of scattering elements for different sample lengths. We have calculated the transmission properties, by the transfer matrix method, of thousands of different disordered structures in order to perform a statistical analysis. We found that, below a certain sample length, disorder induces less average light reflection than ordered structures, whereas above the threshold length, disordered structures show more average reflection. Moreover, we have quantified the disorder of the structures with the Shannon index. We have found a decrease in the average light transmission as a function of the Shannon index. Furthermore, the sample length affects the trend of the average transmission as a function of the Shannon index.

Consequences of extreme events on population persistence and evolution of a quantitative trait

Abstract The intensification and increased frequency of weather and climate extremes are emerging as one of the most important aspects of climate change. Using a quantitative genetic model, we explore the effects of increasing environmental stochasticity and its interplay with genetic variation and selection pressure on population dynamics and evolution of a fitness-related trait. We use simulations with variations in trend (i.e., directional change) and stochasticity (i.e., increase in variance) of a climate variable defining a phenotypic optimum, and various hypotheses on mutational variance and strength of selection on a phenotypic trait. We let the population reach mutation–selection balance and then we linearly increase over simulation time both the mean and the variance of the statistical distribution of the climate variable. Higher variance of climate variables increases the probability of extreme climatic events, i.e. events that are both statistically rare and with potentially high ecological impact, that is, causing episodes of massive mortality in the population. Our analysis shows that the population is able to track the directional component of the optimum for low increases of variability, while for high increases the tracking is reduced. Persistence of the population depends quite strongly on the selection pressure and decreases with increasing variance of the climate variable. Higher mutational variance does not substantially decrease the risk of extinction of a population.

Robustness of empirical food webs with varying consumer's sensitivities to loss of resources

Food web responses to species loss have been mostly studied in binary food webs, thus without accounting for the amount of energy transferred in consumer-resource interactions. We introduce an energetic criterion, called extinction threshold, for which a species goes secondarily extinct when a certain fraction of its incoming energy is lost. We study the robustness to random node loss of 10 food webs based on empirically-derived weightings. We use different extinction scenarios (random removal and from most- to least-connected species), and we simulate 10(5) replicates for each extinction threshold to account for stochasticity of extinction dynamics. We quantified robustness on the basis of how many additional species (i.e. secondary extinctions) were lost after the direct removal of species (i.e. primary extinctions). For all food webs, the expected robustness linearly decreases with extinction threshold, although a large variance in robustness is observed. The sensitivity of robustness to variations in extinction threshold increases with food web species richness and quantitative unweighted link density, while we observed a nonlinear relationship when the predictor is food web connectance and no relationship with the proportion of autotrophs.

Optical properties of one-dimensional disordered multilayer photonic structures

The investigation of the differences between ordered and disordered materials (in the hundreds of nanometer lengthscale) is a crucial topic for a better understanding of light transport in photonic media. Here we study the light transmission properties of 1D photonic structures in which disorder is introduced in two different ways. In the first study, we have grouped the high refractive index layers in layer clusters, randomly distributed among layers of low refractive index. We have controlled the maximum size of such clusters and the ratio of the high-low refractive index layers (here called dilution). We studied the total transmission of the disordered structure within the photonic band gap of the ordered structure as a function of the maximum cluster size, and we have observed a valley in trend of the total transmission for a specific maximum cluster size. This value increases with increasing dilution. Furthermore, within one dilution we observe oscillations of the total transmission with increasing cluster size. In the second study, we have realized photonic structures with a random variation of the layer thickness. The structures were fabricated by radio-frequency (RF) sputtering technique. The transmission spectrum of the disordered structure was simulated by taking into account the refractive index dispersion of the materials, resulting in a good agreement between the experimental data and the simulations. We found that the transmission of the photonic structure in the range 300– 1200 nm is lower with respect the corresponding periodic photonic crystal. The studied disordered 1D photonic structures are very interesting for the modelization and realization of broad band filters and light harvesting devices.

The Influence of a Power Law Distribution of Cluster Size on the Light Transmission of Disordered 1-D Photonic Structures

A better understanding of the optical properties of random photonic structures is beneficial for many applications, such as random lasing, optical imaging and photovoltaics. Here, we investigate the light transmission properties of disordered photonic structures in which the high refractive index layers are aggregated in clusters. The size of the clusters follows a power law distribution described by an exponential parameter a. The sorted high refractive layer clusters are randomly distributed within the low refractive index layers. We study the total light transmission within the photonic band gap of the corresponding periodic crystal as a function of the exponent in the distribution. We observe that, for 0 ≤ a ≤ 3.5, the trend can be fitted with a sigmoidal function.