Percolation on random networks with arbitrary k-core structure

The k-core decomposition of a network has thus far mainly served as a powerful tool for the empirical study of complex networks. We now propose its explicit integration in a theoretical model. We introduce a Hard-core Random Network model that generates maximally random networks with arbitrary degree distribution and arbitrary k-core structure. We then solve exactly the bond percolation problem on the HRN model and produce fast and precise analytical estimates for the corresponding real networks. Extensive comparison with selected databases reveals that our approach performs better than existing models, while requiring less input information.Comment: 9 pages, 5 figure

Growing networks of overlapping communities with internal structure

We introduce an intuitive model that describes both the emergence of community structure and the evolution of the internal structure of communities in growing social networks. The model comprises two complementary mechanisms: One mechanism accounts for the evolution of the internal link structure of a single community, and the second mechanism coordinates the growth of multiple overlapping communities. The first mechanism is based on the assumption that each node establishes links with its neighbors and introduces new nodes to the community at different rates. We demonstrate that this simple mechanism gives rise to an effective maximal degree within communities. This observation is related to the anthropological theory known as Dunbar's number, i.e., the empirical observation of a maximal number of ties which an average individual can sustain within its social groups. The second mechanism is based on a recently proposed generalization of preferential attachment to community structure, appropriately called structural preferential attachment (SPA). The combination of these two mechanisms into a single model (SPA+) allows us to reproduce a number of the global statistics of real networks: The distribution of community sizes, of node memberships and of degrees. The SPA+ model also predicts (a) three qualitative regimes for the degree distribution within overlapping communities and (b) strong correlations between the number of communities to which a node belongs and its number of connections within each community. We present empirical evidence that support our findings in real complex networks.Comment: 14 pages, 8 figures, 2 table

PPARs, Cardiovascular Metabolism, and Function: Near- or Far-from-Equilibrium Pathways

Peroxisome proliferator-activated receptors (PPAR α, β/δ and γ) play a key role in metabolic regulatory processes and gene regulation of cellular metabolism, particularly in the cardiovascular system. Moreover, PPARs have various extra metabolic roles, in circadian rhythms, inflammation and oxidative stress. In this review, we focus mainly on the effects of PPARs on some thermodynamic processes, which can behave either near equilibrium, or far-from-equilibrium. New functions of PPARs are reported in the arrhythmogenic right ventricular cardiomyopathy, a human genetic heart disease. It is now possible to link the genetic desmosomal abnormalitiy to the presence of fat in the right ventricle, partly due to an overexpression of PPARγ. Moreover, PPARs are directly or indirectly involved in cellular oscillatory processes such as the Wnt-b-catenin pathway, circadian rhythms of arterial blood pressure and cardiac frequency and glycolysis metabolic pathway. Dysfunction of clock genes and PPARγ may lead to hyperphagia, obesity, metabolic syndrome, myocardial infarction and sudden cardiac death, In pathological conditions, regulatory processes of the cardiovascular system may bifurcate towards new states, such as those encountered in hypertension, type 2 diabetes, and heart failure. Numerous of these oscillatory mechanisms, organized in time and space, behave far from equilibrium and are “dissipative structures”

Complex networks as an emerging property of hierarchical preferential attachment

Real complex systems are not rigidly structured; no clear rules or blueprints exist for their construction. Yet, amidst their apparent randomness, complex structural properties universally emerge. We propose that an important class of complex systems can be modeled as an organization of many embedded levels (potentially infinite in number), all of them following the same universal growth principle known as preferential attachment. We give examples of such hierarchy in real systems, for instance in the pyramid of production entities of the film industry. More importantly, we show how real complex networks can be interpreted as a projection of our model, from which their scale independence, their clustering, their hierarchy, their fractality and their navigability naturally emerge. Our results suggest that complex networks, viewed as growing systems, can be quite simple, and that the apparent complexity of their structure is largely a reflection of their unobserved hierarchical nature.Comment: 12 pages, 7 figure

Interactions between PPAR Gamma and the Canonical Wnt/Beta-Catenin Pathway in Type 2 Diabetes and Colon Cancer

In both colon cancer and type 2 diabetes, metabolic changes induced by upregulation of the Wnt/beta-catenin signaling and downregulation of peroxisome proliferator-activated receptor gamma (PPAR gamma) may help account for the frequent association of these two diseases. In both diseases, PPAR gamma is downregulated while the canonical Wnt/beta-catenin pathway is upregulated. In colon cancer, upregulation of the canonical Wnt system induces activation of pyruvate dehydrogenase kinase and deactivation of the pyruvate dehydrogenase complex. As a result, a large part of cytosolic pyruvate is converted into lactate through activation of lactate dehydrogenase. Lactate is extruded out of the cell by means of activation of monocarboxylate lactate transporter-1. This phenomenon is called Warburg effect. PPAR gamma agonists induce beta-catenin inhibition, while inhibition of the canonical Wnt/beta-catenin pathway activates PPAR gamma

Coexistence of phases and the observability of random graphs

In a recent Letter, Yang et al. [Phys. Rev. Lett. 109, 258701 (2012)] introduced the concept of observability transitions: the percolationlike emergence of a macroscopic observable component in graphs in which the state of a fraction of the nodes, and of their first neighbors, is monitored. We show how their concept of depth- L percolation—where the state of nodes up to a distance L of monitored nodes is known—can be mapped onto multitype random graphs, and use this mapping to exactly solve the observability problem for arbitrary L. We then demonstrate a nontrivial coexistence of an observable and of a nonobservable extensive component. This coexistence suggests that monitoring a macroscopic portion of a graph does not prevent a macroscopic event to occur unbeknown to the observer. We also show that real complex systems behave quite differently with regard to observability depending on whether they are geographically constrained or not

General and exact approach to percolation on random graphs

We present a comprehensive and versatile theoretical framework to study site and bond percolation on clustered and correlated random graphs. Our contribution can be summarized in three main points. (i) We introduce a set of iterative equations that solve the exact distribution of the size and composition of components in finite-size quenched or random multitype graphs. (ii) We define a very general random graph ensemble that encompasses most of the models published to this day and also makes it possible to model structural properties not yet included in a theoretical framework. Site and bond percolation on this ensemble is solved exactly in the infinite-size limit using probability generating functions [i.e., the percolation threshold, the size, and the composition of the giant (extensive) and small components]. Several examples and applications are also provided. (iii) Our approach can be adapted to model interdependent graphs—whose most striking feature is the emergence of an extensive component via a discontinuous phase transition—in an equally general fashion. We show how a graph can successively undergo a continuous then a discontinuous phase transition, and preliminary results suggest that clustering increases the amplitude of the discontinuity at the transition

Efficient sampling of spreading processes on complex networks using a composition and rejection algorithm

Efficient stochastic simulation algorithms are of paramount importance to the study of spreading phenomena on complex networks. Using insights and analytical results from network science, we discuss how the structure of contacts affects the efficiency of current algorithms. We show that algorithms believed to require $\mathcal{O}(\log N)$ or even $\mathcal{O}(1)$ operations per update---where $N$ is the number of nodes---display instead a polynomial scaling for networks that are either dense or sparse and heterogeneous. This significantly affects the required computation time for simulations on large networks. To circumvent the issue, we propose a node-based method combined with a composition and rejection algorithm, a sampling scheme that has an average-case complexity of $\mathcal{O} [\log(\log N)]$ per update for general networks. This systematic approach is first set-up for Markovian dynamics, but can also be adapted to a number of non-Markovian processes and can enhance considerably the study of a wide range of dynamics on networks.Comment: 12 pages, 7 figure