Explosive Percolation in the Human Protein Homology Network

We study the explosive character of the percolation transition in a real-world network. We show that the emergence of a spanning cluster in the Human Protein Homology Network (H-PHN) exhibits similar features to an Achlioptas-type process and is markedly different from regular random percolation. The underlying mechanism of this transition can be described by slow-growing clusters that remain isolated until the later stages of the process, when the addition of a small number of links leads to the rapid interconnection of these modules into a giant cluster. Our results indicate that the evolutionary-based process that shapes the topology of the H-PHN through duplication-divergence events may occur in sudden steps, similarly to what is seen in first-order phase transitions.Comment: 13 pages, 6 figure

Stochastic synchronization in globally coupled phase oscillators

Cooperative effects of periodic force and noise in globally Cooperative effects of periodic force and noise in globally coupled systems are studied using a nonlinear diffusion equation for the number density. The amplitude of the order parameter oscillation is enhanced in an intermediate range of noise strength for a globally coupled bistable system, and the order parameter oscillation is entrained to the external periodic force in an intermediate range of noise strength. These enhancement phenomena of the response of the order parameter in the deterministic equations are interpreted as stochastic resonance and stochastic synchronization in globally coupled systems.Comment: 5 figure

A Hebbian approach to complex network generation

Through a redefinition of patterns in an Hopfield-like model, we introduce and develop an approach to model discrete systems made up of many, interacting components with inner degrees of freedom. Our approach clarifies the intrinsic connection between the kind of interactions among components and the emergent topology describing the system itself; also, it allows to effectively address the statistical mechanics on the resulting networks. Indeed, a wide class of analytically treatable, weighted random graphs with a tunable level of correlation can be recovered and controlled. We especially focus on the case of imitative couplings among components endowed with similar patterns (i.e. attributes), which, as we show, naturally and without any a-priori assumption, gives rise to small-world effects. We also solve the thermodynamics (at a replica symmetric level) by extending the double stochastic stability technique: free energy, self consistency relations and fluctuation analysis for a picture of criticality are obtained

High Dimensional Apollonian Networks

We propose a simple algorithm which produces high dimensional Apollonian networks with both small-world and scale-free characteristics. We derive analytical expressions for the degree distribution, the clustering coefficient and the diameter of the networks, which are determined by their dimension

Patient centered guidelines for the laboratory diagnosis of Gaucher disease type 1

Gaucher disease (GD) is an autosomal recessive lysosomal storage disorder due to the deficient activity of the acid beta-glucosidase (GCase) enzyme, resulting in the progressive lysosomal accumulation of glucosylceramide (GlcCer) and its deacylated derivate, glucosylsphingosine (GlcSph). GCase is encoded by the GBA1 gene, located on chromosome 1q21 16 kb upstream from a highly homologous pseudogene. To date, more than 400 GBA1 pathogenic variants have been reported, many of them derived from recombination events between the gene and the pseudogene. In the last years, the increased access to new technologies has led to an exponential growth in the number of diagnostic laboratories offering GD testing. However, both biochemical and genetic diagnosis of GD are challenging and to date no specific evidence-based guidelines for the laboratory diagnosis of GD have been published. The objective of the guidelines presented here is to provide evidence-based recommendations for the technical implementation and interpretation of biochemical and genetic testing for the diagnosis of GD to ensure a timely and accurate diagnosis for patients with GD worldwide. The guidelines have been developed by members of the Diagnostic Working group of the International Working Group of Gaucher Disease (IWGGD), a non-profit network established to promote clinical and basic research into GD for the ultimate purpose of improving the lives of patients with this disease. One of the goals of the IWGGD is to support equitable access to diagnosis of GD and to standardize procedures to ensure an accurate diagnosis. Therefore, a guideline development group consisting of biochemists and geneticists working in the field of GD diagnosis was established and a list of topics to be discussed was selected. In these guidelines, twenty recommendations are provided based on information gathered through a systematic review of the literature and two different diagnostic algorithms are presented, considering the geographical differences in the access to diagnostic services. Besides, several gaps in the current diagnostic workflow were identified and actions to fulfill them were taken within the IWGGD. We believe that the implementation of recommendations provided in these guidelines will promote an equitable, timely and accurate diagnosis for patients with GD worldwide

Patient centered guidelines for the laboratory diagnosis of Gaucher disease type 1

: Gaucher disease (GD) is an autosomal recessive lysosomal storage disorder due to the deficient activity of the acid beta-glucosidase (GCase) enzyme, resulting in the progressive lysosomal accumulation of glucosylceramide (GlcCer) and its deacylated derivate, glucosylsphingosine (GlcSph). GCase is encoded by the GBA1 gene, located on chromosome 1q21 16 kb upstream from a highly homologous pseudogene. To date, more than 400 GBA1 pathogenic variants have been reported, many of them derived from recombination events between the gene and the pseudogene. In the last years, the increased access to new technologies has led to an exponential growth in the number of diagnostic laboratories offering GD testing. However, both biochemical and genetic diagnosis of GD are challenging and to date no specific evidence-based guidelines for the laboratory diagnosis of GD have been published. The objective of the guidelines presented here is to provide evidence-based recommendations for the technical implementation and interpretation of biochemical and genetic testing for the diagnosis of GD to ensure a timely and accurate diagnosis for patients with GD worldwide. The guidelines have been developed by members of the Diagnostic Working group of the International Working Group of Gaucher Disease (IWGGD), a non-profit network established to promote clinical and basic research into GD for the ultimate purpose of improving the lives of patients with this disease. One of the goals of the IWGGD is to support equitable access to diagnosis of GD and to standardize procedures to ensure an accurate diagnosis. Therefore, a guideline development group consisting of biochemists and geneticists working in the field of GD diagnosis was established and a list of topics to be discussed was selected. In these guidelines, twenty recommendations are provided based on information gathered through a systematic review of the literature and two different diagnostic algorithms are presented, considering the geographical differences in the access to diagnostic services. Besides, several gaps in the current diagnostic workflow were identified and actions to fulfill them were taken within the IWGGD. We believe that the implementation of recommendations provided in these guidelines will promote an equitable, timely and accurate diagnosis for patients with GD worldwide

Segregation in the annihilation of two-species reaction-diffusion processes on fractal scale-free networks

In the reaction-diffusion process $A+B \to \varnothing$ on random scale-free (SF) networks with the degree exponent $\gamma$, the particle density decays with time in a power law with an exponent $\alpha$ when initial densities of each species are the same. The exponent $\alpha$ is $\alpha > 1$ for $2 < \gamma < 3$ and $\alpha=1$ for $\gamma \ge 3$. Here, we examine the reaction process on fractal SF networks, finding that $\alpha < 1$ even for $2 < \gamma < 3$. This slowly decaying behavior originates from the segregation effect: Fractal SF networks contain local hubs, which are repulsive to each other. Those hubs attract particles and accelerate the reaction, and then create domains containing the same species of particles. It follows that the reaction takes place at the non-hub boundaries between those domains and thus the particle density decays slowly. Since many real SF networks are fractal, the segregation effect has to be taken into account in the reaction kinetics among heterogeneous particles.Comment: 4 pages, 6 figure

An algorithm for counting circuits: application to real-world and random graphs

We introduce an algorithm which estimates the number of circuits in a graph as a function of their length. This approach provides analytical results for the typical entropy of circuits in sparse random graphs. When applied to real-world networks, it allows to estimate exponentially large numbers of circuits in polynomial time. We illustrate the method by studying a graph of the Internet structure.Comment: 7 pages, 3 figures, minor corrections, accepted versio

Phase Transitions and Oscillations in a Lattice Prey-Predator Model

A coarse grained description of a two-dimensional prey-predator system is given in terms of a 3-state lattice model containing two control parameters: the spreading rates of preys and predators. The properties of the model are investigated by dynamical mean-field approximations and extensive numerical simulations. It is shown that the stationary state phase diagram is divided into two phases: a pure prey phase and a coexistence phase of preys and predators in which temporal and spatial oscillations can be present. The different type of phase transitions occuring at the boundary of the prey absorbing phase, as well as the crossover phenomena occuring between the oscillatory and non-oscillatory domains of the coexistence phase are studied. The importance of finite size effects are discussed and scaling relations between different quantities are established. Finally, physical arguments, based on the spatial structure of the model, are given to explain the underlying mechanism leading to oscillations.Comment: 11 pages, 13 figure