Degree distributions in networks: Beyond the power law

The power law is useful in describing count phenomena such as network degrees and word frequencies. With a single parameter, it captures the main feature that the frequencies are linear on the log-log scale. Nevertheless, there have been criticisms of the power law, for example, that a threshold needs to be preselected without its uncertainty quantified, that the power law is simply inadequate, and that subsequent hypothesis tests are required to determine whether the data could have come from the power law. We propose a modeling framework that combines two different generalizations of the power law, namely the generalized Pareto distribution and the Zipf-polylog distribution, to resolve these issues. The proposed mixture distributions are shown to fit the data well and quantify the threshold uncertainty in a natural way. A model selection step embedded in the Bayesian inference algorithm further answers the question whether the power law is adequate

On the Estimation of Bivariate Return Curves for Extreme Values

In the multivariate setting, defining extremal risk measures is important in many contexts, such as finance, environmental planning and structural engineering. In this paper, we review the literature on extremal bivariate return curves, a risk measure that is the natural bivariate extension to a return level, and propose new estimation methods based on multivariate extreme value models that can account for both asymptotic dependence and asymptotic independence. We identify gaps in the existing literature and propose novel tools for testing and validating return curves and comparing estimates from a range of multivariate models. These tools are then used to compare a selection of models through simulation and case studies. We conclude with a discussion and list some of the challenges.Comment: 41 pages (without supplementary), 11 figures, 2 table

Improving estimation for asymptotically independent bivariate extremes via global estimators for the angular dependence function

Modelling the extremal dependence of bivariate variables is important in a wide variety of practical applications, including environmental planning, catastrophe modelling and hydrology. The majority of these approaches are based on the framework of bivariate regular variation, and a wide range of literature is available for estimating the dependence structure in this setting. However, this framework is only applicable to variables exhibiting asymptotic dependence, even though asymptotic independence is often observed in practice. In this paper, we consider the so-called `angular dependence function'; this quantity summarises the extremal dependence structure for asymptotically independent variables. Until recently, only pointwise estimators of the angular dependence function have been available. We introduce a range of global estimators and compare them to another recently introduced technique for global estimation through a systematic simulation study, and a case study on river flow data from the north of England, UK

Sulfosuccinate and Sulfocarballylate Surfactants As Charge Control Additives in Nonpolar Solvents

A series of eight sodium sulfonic acid surfactants with differently branched tails (four double-chain sulfosuccinates and four triple-chain sulfocarballylates) were studied as charging agents for sterically stabilized poly­(methyl methacrylate) (PMMA) latexes in dodecane. Tail branching was found to have no significant effect on the electrophoretic mobility of the latexes, but the number of tails was found to influence the electrophoretic mobility. Triple-chain, sulfocarballylate surfactants were found to be more effective. Several possible origins of this observation were explored by comparing sodium dioctylsulfosuccinate (AOT1) and sodium trioctylsulfocarballylate (TC1) using identical approaches: the inverse micelle size, the propensity for ion dissociation, the electrical conductivity, the electrokinetic or ζ potential, and contrast-variation small-angle neutron scattering. The most likely origin of the increased ability of TC1 to charge PMMA latexes is a larger number of inverse micelles. These experiments demonstrate a small molecular variation that can be made to influence the ability of surfactants to charge particles in nonpolar solvents, and modifying molecular structure is a promising approach to developing more effective charging agents

A penalised piecewise-linear model for non-stationary extreme value analysis of peaks over threshold

This is the final version. Available on open access from Elsevier via the DOI in this recordData availability: Data will be made available on request.Metocean extremes often vary systematically with covariates such as direction and season. In this work, we present non-stationary models for the size and rate of occurrence of peaks over threshold of metocean variables with respect to one- or two-dimensional covariates. The variation of model parameters with covariate is described using a piecewise-linear function in one or two dimensions, defined with respect to pre-specified node locations on the covariate domain. Parameter roughness is regulated to provide optimal predictive performance, assessed using cross-validation, within a penalised likelihood framework for inference. Parameter uncertainty is quantified using bootstrap resampling. The models are used to estimate extremes of storm-peak significant wave height with respect to direction and season for a site in the northern North Sea. A covariate representation based on a triangulation of the direction-season domain with six nodes gives good predictive performance. The penalised piecewise-linear framework provides a flexible representation of covariate effects at reasonable computational cost.Engineering and Physical Sciences Research Council (EPSRC

Electrolyte-induced Instability of Colloidal Dispersions in Nonpolar Solvents

Dispersions of poly(methyl methacrylate) (PMMA) latexes were prepared in a low dielectric, nonpolar solvent (dodecane) both with and without the oil-soluble electrolyte, tetradodecylammonium-tetrakis(3,5-bis(trifluoromethyl)phenyl)borate. For dispersions with a high concentration of background electrolyte, the latexes become colloidally unstable and sediment in a short period of time (<1 h). This is completely reversible upon dilution. Instability of the dispersions is due to an apparent attraction between the colloids, directly observed using optical tweezers by bringing optically trapped particles into close proximity. Simple explanations generally used by colloid scientists to explain loss of stability (charge screening or stabilizer collapse) are insufficient to explain this observation. This unexpected interaction seems, therefore, to be a consequence of the materials that can be dispersed in low dielectric media and is expected to have ramifications for studying colloids in such solvents

The effect of solvent and counterion variation on inverse micelle CMCs in hydrocarbon solvents

Critical micelle concentrations (CMCs) for the formation of inverse micelles have been determined for anionic surfactants in nonpolar, hydrocarbon solvents. Sodium dioctylsulfosuccinate (Aerosol OT or AOT) was chosen as the model surfactant, with systematic variations in both the solvent (benzene, cyclohexane, and dodecane) and the surfactant counterion (sodium and tetrapropylammonium). Recent work (Langmuir 29 (2013) 3352–3258) has shown that high-resolution small-angle neutron scattering (SANS) measurements can be used to directly determine the presence or absence of aggregates in solution. No variation in the value of the CMC was found within the resolution of the measurements for changing either solvent or counterion; some effects on the structure of inverse micelles were observed. This lack of a significant difference in the onset of inverse micellization with changes to the molecular species is surprising, and the implications on the solvophobic effect in nonpolar solvents are discussed

Spin State As a Probe of Vesicle Self-Assembly

International audienceA novel system of paramagnetic vesicles was designed using ion pairs of iron-containing surfactants. Unilamellar vesicles (diameter approximate to 200 nm) formed spontaneously and were characterized by cryogenic transmission electron microscopy, nanoparticle tracking, analysis, and light and small-angle neutron scattering. Moreover, for the first time, it is shown that magnetization measurements can be used to investigate self-assembly of such functionalized systems, giving information on the vesicle compositions and distribution Of surfactants between the bilayers and the aqueous bulk

Celebrating Soft Matter's 10th Anniversary: influencing the charge of poly(methyl methacrylate) latexes in nonpolar solvents

Sterically-stabilized poly(methyl methacrylate) (PMMA) latexes dispersed in nonpolar solvents are a classic, well-studied system in colloid science. This is because they can easily be synthesized with a narrow size distribution and because they interact essentially as hard spheres. These PMMA latexes can be charged using several methods (by adding surfactants, incorporating ionizable groups, or dispersing in autoionizable solvents), and due to the low relative permittivity of the solvents (εr ≈ 2 for alkanes to εr ≈ 8 for halogenated solvents), the charges have long-range interactions. The number of studies of these PMMA particles as charged species has increased over the past ten years, after few studies immediately following their discovery. A large number of variations in both the physical and chemical properties of the system (size, concentration, surfactant type, or solvent, as a few examples) have been studied by many groups. By considering the literature on these particles as a whole, it is possible to determine the variables that have an effect on the charge of particles. An understanding of the process of charge formation will add to understanding how to control charge in nonaqueous solvents as well as make it possible to develop improved technologically relevant applications for charged polymer nanoparticles