Percolation Analysis Research Articles

Nucleation scaling in jigsaw percolation

Jigsaw percolation is a nonlocal process that iteratively merges connected clusters in a deterministic \puzzle by using connectivity properties of a random \people on the same set of vertices. We presume the Erd} os-R enyi people graph with edge probability p and investigate the probability that the puzzle is solved, that is, that the process eventually produces a single cluster. In some generality, for puzzle graphs with N vertices of degrees about D (in the appropriate sense), this probability is close to 1 or small depending on whether pD logN is large or small. The one dimensional ring and two dimensional torus puzzles are studied in more detail and in many cases the exact scaling of the critical probability is obtained. Main tools come from analysis of bootstrap percolation and other local nucleation-and-growth models. The paper settles several conjectures posed by Brummitt, Chatterjee, Dey, and Sivako who

Propagation control of data forwarding in opportunistic underwater sensor networks

Opportunistic underwater sensor networks (OUSNs) are developed for a set of underwater applications, including the tracking of underwater creatures and tactical surveillance. The data forwarding objectives of OUSNs differ significantly from those of wireless sensor networks or delay-tolerant networks due to their large energy consumption and large propagation delay underwater. This paper begins with a description of the underwater movement, which consists of the regular movement impelled by external force and the autonomous movement controlled by nodes. Then, a topology determined model is provided to generate a power-law distribution structure, where the communication links that are overlong or are close to the space boundary can be avoided. Finally, a proactive opportunistic forwarding mechanism (POFM) is proposed to minimize the energy consumption from data forwarding. In POFM, at the start of each time slot, each node without data decides whether to request for data or not independently. In particular, the probabilities of nodes requesting for data are calculated according to a dynamic percolation analysis, which suggests the nodes with larger degrees or at earlier time slots should be given larger probabilities. The performance of POFM is analyzed through simulation experiments that produce preferable tradeoff results, indicating that POFM has a minor energy consumption with a guaranteed delivery ratio and a limited propagation delay.

Analysis of the Spatial Organization of Pastures as a Contact Network, Implications for Potential Disease Spread and Biosecurity in Livestock, France, 2010.

The use of pastures is part of common herd management practices for livestock animals, but contagion between animals located on neighbouring pastures is one of the major modes of infectious disease transmission between herds. At the population level, this transmission is strongly constrained by the spatial organization of pastures. The aim of this study was to answer two questions: (i) is the spatial configuration of pastures favourable to the spread of infectious diseases in France? (ii) would biosecurity measures allow decreasing this vulnerability? Based on GIS data, the spatial organization of pastures was represented using networks. Nodes were the 3,159,787 pastures reported in 2010 by the French breeders to claim the Common Agricultural Policy subsidies. Links connected pastures when the distance between them was below a predefined threshold. Premises networks were obtained by aggregating into a single node all the pastures under the same ownership. Although the pastures network was very fragmented when the distance threshold was short (1.5 meters, relevant for a directly-transmitted disease), it was not the case when the distance threshold was larger (500 m, relevant for a vector-borne disease: 97% of the nodes in the largest connected component). The premises network was highly connected as the largest connected component always included more than 83% of the nodes, whatever the distance threshold. Percolation analyses were performed to model the population-level efficacy of biosecurity measures. Percolation thresholds varied according to the modelled biosecurity measures and to the distance threshold. They were globally high (e.g. >17% of nodes had to be removed, mimicking the confinement of animals inside farm buildings, to obtain the disappearance of the large connected component). The network of pastures thus appeared vulnerable to the spread of diseases in France. Only a large acceptance of biosecurity measures by breeders would allow reducing this structural risk.

Network-based modelling and percolation analysis of conformational dynamics and activation in the CDK2 and CDK4 proteins: dynamic and energetic polarization of the kinase lobes may determine divergence of the regulatory mechanisms.

The overarching goal of delineating molecular principles underlying differentiation of the activation mechanisms in cyclin-dependent kinases (CDKs) is important for understanding regulatory divergences among closely related kinases which can be exploited in drug discovery of targeted and allosteric inhibitors. To systematically characterize dynamic, energetic and network signatures of the activation mechanisms, we combined atomistic simulations and elastic network modeling with the analysis of the residue interaction networks and rigidity decomposition of the CDK2-cyclin A and CDK4-cyclin D1/D3 complexes. The results of this study show that divergences in the activation mechanisms of CDK2 and CDK4 may be determined by differences in stabilization and allosteric cooperativity of the regulatory regions. We show that differential stabilization of the kinase lobes in the CDK4-cyclin D complexes caused by the elevated mobility of the N-lobe residues can weaken allosteric interactions between regulatory regions and compromise cooperativity of the inter-lobe motions that is required to trigger activating transitions. Network modelling and percolation analysis were used to emulate thermal unfolding and perform decomposition of rigid and flexible regions in the CDK2 and CDK4 complexes. These simulations showed that the percolation phase transition in the CDK2-cyclin A complexes is highly cooperative and driven by allosteric coupling between functional regions from both kinase lobes. In contrast, the imbalances in the distribution of rigid and flexible regions for the CDK4-cyclin D complexes, which are manifested by the intrinsic instability of the N-lobe, may weaken allosteric interactions and preclude productive activation. The results of this integrative computational study offer a simple and robust network-based model that explains regulatory divergences between CDK2 and CDK4 kinases.

Disorder, three body interaction and Bose glass phase in a spinor atomic gas in an optical lattice

We study the effects of disorder on the spin dependent interaction term of a spinor Bose Hubbard model with a three body interaction potential. The signature of the Bose glass (BG) phase is observed by computing the fraction of the lattice sites having finite superfluid (SF) order parameter and non integer occupation densities. We obtain the phase diagram both for the antiferromagnetic (AF) and ferromagnetic (F) cases via a percolation analysis. In the AF case, the BG phase intervenes between the odd-even Mott insulating (MI) lobes (for example, the lobes corresponding to occupation densities, n=1 and (n=2) but not between the even-odd MI lobes. In the ferromagnetic case, the presence of the BG phase is observed between all the MI lobes irrespective of them being even or odd. The BG phase almost destroys the first MI lobe while the MI phase looks more stable than the SF phase both in the AF and F cases due to the presence of the three body interactions.

Hierarchical organization of functional connectivity in the mouse brain: a complex network approach.

This paper represents a contribution to the study of the brain functional connectivity from the perspective of complex networks theory. More specifically, we apply graph theoretical analyses to provide evidence of the modular structure of the mouse brain and to shed light on its hierarchical organization. We propose a novel percolation analysis and we apply our approach to the analysis of a resting-state functional MRI data set from 41 mice. This approach reveals a robust hierarchical structure of modules persistent across different subjects. Importantly, we test this approach against a statistical benchmark (or null model) which constrains only the distributions of empirical correlations. Our results unambiguously show that the hierarchical character of the mouse brain modular structure is not trivially encoded into this lower-order constraint. Finally, we investigate the modular structure of the mouse brain by computing the Minimal Spanning Forest, a technique that identifies subnetworks characterized by the strongest internal correlations. This approach represents a faster alternative to other community detection methods and provides a means to rank modules on the basis of the strength of their internal edges.

Complexity and robustness in hypernetwork models of metabolism

Metabolic reaction data is commonly modelled using a complex network approach, whereby nodes represent the chemical species present within the organism of interest, and connections are formed between those nodes participating in the same chemical reaction. Unfortunately, such an approach provides an inadequate description of the metabolic process in general, as a typical chemical reaction will involve more than two nodes, thus risking oversimplification of the system of interest in a potentially significant way. In this paper, we employ a complex hypernetwork formalism to investigate the robustness of bacterial metabolic hypernetworks by extending the concept of a percolation process to hypernetworks. Importantly, this provides a novel method for determining the robustness of these systems and thus for quantifying their resilience to random attacks/errors. Moreover, we performed a site percolation analysis on a large cohort of bacterial metabolic networks and found that hypernetworks that evolved in more variable environments displayed increased levels of robustness and topological complexity.

The XXL Survey

X-ray extragalactic surveys are ideal laboratories for the study of the evolution and clustering of active galactic nuclei (AGN). The XXL Survey spans two fields of a combined 50 $deg^2$ observed for more than 6Ms with XMM-Newton, occupying the parameter space between deep surveys and very wide area surveys; at the same time it benefits from a wealth of ancillary data. This paper marks the first release of the XXL point source catalogue selected in the 2-10 keV energy band with limiting flux $F_{2-10keV}=4.8\cdot10^{-14}\rm{erg\,s^{-1}\,cm^{-2}}$. We use both public and proprietary data sets to identify the counterparts of the X-ray point-like sources and improved upon the photometric redshift determination for AGN by applying a Random Forest classification trained to identify for each object the optimal photometric redshift model library. We also assign a probability to each source to be a star or an outlier. We model with Bayesian analysis the X-ray spectra assuming a power-law model with the presence of an absorbing medium. We find an average unabsorbed photon index of $\Gamma=1.85$ and average hydrogen column density $\log{N_{H}}=21.07 cm^{-2}$. We find no trend of $\Gamma$ or $N_H$ with redshift and a fraction of 26% absorbed sources ($\log N_{H}>22$). We show that the XXL-1000-AGN number counts extended the number counts of the COSMOS survey to higher fluxes and are fully consistent with the Euclidean expectation. We constrain the intrinsic luminosity function of AGN in the 2-10 keV energy band where the unabsorbed X-ray flux is estimated from the X-ray spectral fit up to z=3. Finally, we demonstrate the presence of a supercluster size structure at redshift 0.14, identified by means of percolation analysis of the XXL-1000-AGN sample. The XXL survey, reaching a medium flux limit and covering a wide area is a stepping stone between current deep fields and planned wide area surveys.

Percolation analysis of a disordered spinor Bose gas

We study the effects of an on-site disorder potential in a gas of spinor (spin-1) ultracold atoms loaded in an optical lattice corresponding to both ferromagnetic and antiferromagnetic spin-dependent interactions. Starting with a disordered spinor Bose–Hubbard model (SBHM) on a two-dimensional square lattice, we observe the appearance of a Bose glass phase using the fraction of the lattice sites having finite superfluid order parameter and non integer local densities as an indicator. A precise distinction between three different types of phases namely, superfluid, Mott insulator and Bose glass is done via a percolation analysis thereby demonstrating that a reliable enumeration of phases is possible at particular values of the parameters of the SBHM. Finally, we present the phase diagram based on the above information for both antiferromagnetic and ferromagnetic interactions.

Market analyses of livestock trade networks to inform the prevention of joint economic and epidemiological risks.

Conventional epidemiological studies of infections spreading through trade networks, e.g. via livestock movements, generally show that central large-size holdings (hubs) should be preferentially surveyed and controlled in order to reduce epidemic spread. However, epidemiological strategies alone may not be economically optimal when costs of control are factored in together with risks of market disruption from targeting core holdings in a supply chain. Using extensive data on animal movements in supply chains for cattle and swine in France, we introduce a method to identify effective strategies for preventing outbreaks with limited budgets while minimizing the risk of market disruptions. Our method involves the categorization of holdings based on position along the supply chain and degree of market share. Our analyses suggest that trade has a higher risk of propagating epidemics through cattle networks, which are dominated by exchanges involving wholesalers, than for swine. We assess the effectiveness of contrasting interventions from the perspectives of regulators and the market, using percolation analysis. We show that preferentially targeting minor, non-central agents can outperform targeting of hubs when the costs to stakeholders and the risks of market disturbance are considered. Our study highlights the importance of assessing joint economic–epidemiological risks in networks underlying pathogen propagation and trade.

Analysis of Percolation of the Stabilized Suspensions of TiO2 and SiO2 Nanoparticles in Soil Columns Simulating Landfill Layers

Analysis of Percolation of the Stabilized Suspensions of TiO2 and SiO2 Nanoparticles in Soil Columns Simulating Landfill Layers

Effect of the terminal group of phosphonate self-assembled films formed on Ti surfaces on the biomimetic layer formation and cell adhesion

ObjectivesTo evaluate the effect of different Self-Assembled Films (SAFs) on the development of calcium-phosphate (Ca/P) biomimetic layers on commercially pure titanium (cpTi) and the final cell adhesion on these coatings. Materials and methodsA total of five different surfaces were evaluated. Alkyl phosphonate Self-Assembled Films (SAFs) with three different ending groups (methyl [–CH3], carboxyl [–COOH], and phosphonate [–PO(OH)2]) were used to cover ultra-polished cpTi surfaces. These functionalized surfaces were compared with a hydroxylated ultra-polished cpTi surface. A biomimetic Ca/P layer was deposited on each surface by precipitation. A control cpTi sample with no precipitates was introduced in the study. Topography (AFM), morphology (ESEM), chemistry (XPS, EDX), crystallography (XRD), wettability (dynamic contact angle), layer thickness (WLCM), percolation (fluid retention) and cell response analysis were used for surface characterization. ResultsXRD showed the formation of hydroxyapatite (HA) in the four biomimetic coatings. The Ca/P ratios obtained by XPS in the four biomimetic coatings showed similar values (≈1.40) corresponding to amorphous hydroxyapatite. The water wettability of the biomimetic coatings was similar but the surface morphology was different. The thickest biomimetic coating with lower percolation threshold and greater cell adhesion was obtained on the carboxyl-terminated SAF. The biomimetic coatings improved the cell adhesion but it was further improved by the presence of underlying SAFs that bond the coating to cpTi surface. ConclusionsThe use of SAFs chemically stabilizes the biomimetic precipitates and guarantees higher cell adhesion than in absence of SAFs. The apatite nucleation and growth depended on the underlying SAF. Biomimetic coatings on hydroxylated surface increases cell adhesion but on SAFs functionalized surfaces achieve higher cell response. The SAFs with carboxyl ending group promoted the formation of thick and interconnected biomimetic coatings, with low fluid retention and a very significant cell response.

Space–time percolation and detection by mobile nodes

Consider the model where nodes are initially distributed as a Poisson point process with intensity $\lambda$ over $\mathbb{R}^d$ and are moving in continuous time according to independent Brownian motions. We assume that nodes are capable of detecting all points within distance $r$ of their location and study the problem of determining the first time at which a target particle, which is initially placed at the origin of $\mathbb{R}^d$, is detected by at least one node. We consider the case where the target particle can move according to any continuous function and can adapt its motion based on the location of the nodes. We show that there exists a sufficiently large value of $\lambda$ so that the target will eventually be detected almost surely. This means that the target cannot evade detection even if it has full information about the past, present and future locations of the nodes. Also, this establishes a phase transition for $\lambda$ since, for small enough $\lambda$, with positive probability the target can avoid detection forever. A key ingredient of our proof is to use fractal percolation and multi-scale analysis to show that cells with a small density of nodes do not percolate in space and time.

Influence of starch content on the properties of low-cost microfiltration ceramic membranes

The use of starch as pore former is frequent in the fabrication of porous ceramic membranes, since starches are cheap, innocuous and environmentally friendly. A study has been conducted to evaluate the influence of potato starch content (0–30wt%) and sintering temperature (1100 and 1400°C) on low-cost ceramic microfiltration membranes. The raw materials were a mixture of kaolin, alumina and starch, from which membrane specimens were shaped by uniaxial dry pressing.The results indicated that the percentage of potato starch did affect the properties of the membrane. Thus, an increase of starch content provoked a reduction of bulk density (an increase of porosity) a rise of water permeability and a substantial modification (coarsening) of the pore size distribution. This effect deals with the role as pore former of starch, which burns out when fired. More interestingly, it was experimentally observed that the effect of starch was particularly effective for starch percentages higher than 10wt% once a connected coarse pore network is developed. On the other hand, an increase in sintering temperature from 1100 to 1400°C also influenced membranes׳ characteristics but the effect was much less significant than that of starch content.A percolation analysis based on the Effective Medium Approximation (EMA) contact model allowed to conclude that the critical porosity calculated corresponds to a starch content of 10.2wt%, which agrees quite well with the estimation from experimental results. Finally, tortuosity was calculated with a simple model derived from the Hagen–Poiseuille equation. The obtained data showed that tortuosity factor decreased as the starch content or sintering temperature increased. These findings are consistent with SEM analysis and pore size determination.

Highly conducting composite hydrogels from gellan gum, PEDOT:PSS and carbon nanofibres

Conducting filler composite hydrogels were prepared by first dispersing vapour grown carbon nanofibers (VGCNF) in a dispersion of poly(3,4-ethylenedioxythiophene) polystyrene sulfonate (PEDOT:PSS), followed by mixing with a gellan gum (GG) solution prior to cross-linking with CaCl2. The gel transition temperature of GG was largely unaffected by the inclusion of PEDOT:PSS and/or VGCNFs. We demonstrate that electrical impedance spectroscopy coupled with percolation analysis can be used to identify the water content threshold at which the electrical behaviour of hydrogels becomes dominated by conducting fillers (rather then the cationic cross-linkers). These studies suggested that the electrical behaviour transfers from dominated by Ca2+ cross-liners to dominated by electrons (from the conducting fillers) at a water content of 87.2±1.2%. The composite hydrogels exhibited conductivity values of up to 107±6mS/cm for gels containing 81% water.

INVESTIGATION OF SCALE-INVARIANT PROPERTY OF ORGANIZATION SYSTEM OF TRAIN TRAFFIC VOLUME BASED ON THE PERCOLATION THEORY

Purpose. The work is devoted to the study the property of scaling invariance of the organization system of train traffic volume on Ukrainian railways. Methodology. To prove the real network origin of Trains Formation Plan (TFP) destination to the type of socalled scale-invariant networks it is proposed to generate scale-free networks with different dimensions, Barabási–Albert type with parameters that real networks of TFP destination has and to investigate their structure on survivability using the procedure of percolation nodes. Percolation process is proposed to be considered as a modified version of the spatial movement of cars on the network by increasing the number of railway stations, which have lost the ability to perform the basic function to pass cars on TFP destination in terms of adverse effects (an accident, overload). Findings. Comparative analysis of percolation at random and targeted destructive impact on network nodes has shown matching with the results of real network percolation of TFP destination, which proves the existence of self-similarity. Comparable figures in percolation were: percentage of remote stations in the network, in which the network fragmentation occurs, the average inverse path between network nodes, the diameter of the graph structure, the size meaning of the second largest cluster in the network from the steps of destruction. Originality. For the first time the hypothesis of the existence of scaling invariance properties of the graph TFP destinations on the railways of Ukraine, which can be attributed to a class of the graph scale-free networks was confirmed. Existing knowledge in the field theory of scale-free networks can be used to describe the survivability of system transportation on the railways of Ukraine. Practical value. Based on the identified properties of system directions of train traffic volumes, it is possible to create a mathematical model in the future that will predict the behavior of the transportation system with network structure. Properties analysis of system survivability of train traffic volumes will optimize the use of capital investments to increase network capacity by identifying the most critical lines and stations that systematically affect the efficiency of the network as a whole.

Adsorption of probe molecules in pillared interlayered clays: experiment and computer simulation.

In this paper we investigate the adsorption of various probe molecules in order to characterize the porous structure of a series of pillared interlayered clays (PILC). To that aim, volumetric and microcalorimetric adsorption experiments were performed on various Zr PILC samples using nitrogen, toluene, and mesitylene as probe molecules. For one of the samples, neutron scattering experiments were also performed using toluene as adsorbate. Various structural models are proposed and tested by means of a comprehensive computer simulation study, using both geometric and percolation analysis in combination with Grand Canonical Monte Carlo simulations in order to model the volumetric and microcalorimetric isotherms. On the basis of this analysis, we propose a series of structural models that aim at accounting for the adsorption experimental behavior, and make possible a microscopic interpretation of the role played by the different interactions and steric effects in the adsorption processes in these rather complex disordered microporous systems.

A Lattice-Based Approach to Percolation in Penetrable Sphere Systems

An heuristic mapping is presented that enables analysis of continuum percolation by penetrable spheres in terms of an analogous lattice model. The resulting framework is based upon the well-known Bethe lattice, which is modified by the inclusion of an adjustable proportion of fully connected subgraphs that provide a particularly simple, albeit operational, vehicle for modeling the effect of inter-particle clustering. The volume fraction at the percolation threshold is calculated as a function of (i) the degree of interpenetrability amongst the spheres, and: (ii) the extent of particle clustering, and the results are compared with findings from Monte Carlo (MC) simulations of this problem. It is found that a suitably chosen ansatz that reflects a monotonic increase in the degree of clustering with increasing inter-sphere penetrability leads to close agreement between percolation thresholds calculated using the present approach and the results of MC simulations.

Pore-Network Connectivity and Molecular Sieving of Normal and Isoalkanes in the Mesoporous Silica SBA-2

We have studied the adsorption of n-butane and isobutane in the mesoporous silica SBA-2. Our work has two purposes: (i) to better understand the structure of the material, and in particular the impact of calcination on the evolution of the pore network, and (ii) to investigate our ability to tune the structure of SBA-2 to separate normal and isoalkanes by molecular sieving. By a combination of experimental adsorption measurements, molecular simulation, and percolation analysis, we determined the evolution of the sizes of the pores and the connectivity of the pore network as the calcination temperature increases. For a certain range of calcination temperatures, the pore network drops below its percolation threshold for isobutane, while allowing the percolation of n-butane, giving an extremely high selectivity for n-butane over isobutane. This suggests that tuning the window size of SBA-2 and other structured mesoporous materials of this general type has the potential to generate optimized adsorbents for particular applications.

Conductive sol–gel films

We report that silver nanowires (AgNW) entrapped in a series of sol–gel thin films – zirconia, alumina, titania and silica – provide conductive, highly flexible, highly adhesive, transparent thin films with excellent thermal and electrical stability. These films were subjected to intensive study and characterization including resistance, percolation analysis, critical bending angle analysis, critical thermal stability, transparency, and more. Remarkably, when resistance is kept constant, all of the studied parameters follow the same order – either increasing or decreasing – of ZrO2, SiO2, Al2O3, and TiO2. A detailed interpretation, based on the particle-sizes of the elementary sol–gel building blocks, is provided. In particular we found that the AgNWs re-enforce the ceramic matrices, thus providing excellent electroconductive stability with low silver concentration and high degree of homogeneity of the dopant distribution. Having in mind that current materials for films with these properties are often accompanied by disadvantages (such as brittleness, scarcity and poor adhesion) we offer the new conductive films as an interesting alternative to be considered.