Cluster Size Distribution Research Articles

Power and sample size calculations for cluster randomized trials with binary outcomes when intracluster correlation coefficients vary by treatment arm.

Generalized estimating equations are commonly used to fit logistic regression models to clustered binary data from cluster randomized trials. A commonly used correlation structure assumes that the intracluster correlation coefficient does not vary by treatment arm or other covariates, but the consequences of this assumption are understudied. We aim to evaluate the effect of allowing variation of the intracluster correlation coefficient by treatment or other covariates on the efficiency of analysis and show how to account for such variation in sample size calculations. We develop formulae for the asymptotic variance of the estimated difference in outcome between treatment arms obtained when the true exchangeable correlation structure depends on the treatment arm and the working correlation structure used in the generalized estimating equations analysis is: (i) correctly specified, (ii) independent, or (iii) exchangeable with no dependence on treatment arm. These formulae require a known distribution of cluster sizes; we also develop simplifications for the case when cluster sizes do not vary and approximations that can be used when the first two moments of the cluster size distribution are known. We then extend the results to settings with adjustment for a second binary cluster-level covariate. We provide formulae to calculate the required sample size for cluster randomized trials using these variances. We show that the asymptotic variance of the estimated difference in outcome between treatment arms using these three working correlation structures is the same if all clusters have the same size, and this asymptotic variance is approximately the same when intracluster correlation coefficient values are small. We illustrate these results using data from a recent cluster randomized trial for infectious disease prevention in which the clusters are groups of households and modest in size (mean 9.6 individuals), with intracluster correlation coefficient values of 0.078 in the control arm and 0.057 in an intervention arm. In this application, we found a negligible difference between the variances calculated using structures (i) and (iii) and only a small increase (typically ) for the independent correlation structure (ii), and hence minimal effect on power or sample size requirements. The impact may be larger in other applications if there is greater variation in the ICC between treatment arms or with an additional covariate. The common approach of fitting generalized estimating equations with an exchangeable working correlation structure with a common intracluster correlation coefficient across arms likely does not substantially reduce the power or efficiency of the analysis in the setting of a large number of small or modest-sized clusters, even if the intracluster correlation coefficient varies by treatment arm. Our formulae, however, allow formal evaluation of this and may identify situations in which variation in intracluster correlation coefficient by treatment arm or another binary covariate may have a more substantial impact on power and hence sample size requirements.

A Cluster-based Method to Quantify Individual Heterogeneity in Tuberculosis Transmission.

Recent evidence suggests transmission of Mycobacterium tuberculosis (Mtb) may be characterized by extreme individual heterogeneity in secondary cases (i.e., few cases account for the majority of transmission). Such heterogeneity implies outbreaks are rarer but more extensive and has profound implications in infectious disease control. However, discrete person-to-person transmission events in tuberculosis (TB) are often unobserved, precluding our ability to directly quantify individual heterogeneity in TB epidemiology. We used a modified negative binomial branching process model to quantify the extent of individual heterogeneity using only observed transmission cluster size distribution data (i.e., the simple sum of all cases in a transmission chain) without knowledge of individual-level transmission events. The negative binomial parameter k quantifies the extent of individual heterogeneity (generally, indicates extensive heterogeneity, and as transmission becomes more homogenous). We validated the robustness of the inference procedure considering common limitations affecting cluster size data. Finally, we demonstrate the epidemiologic utility of this method by applying it to aggregate US molecular surveillance data from the US Centers for Disease Control and Prevention. The cluster-based method reliably inferred k using TB transmission cluster data despite a high degree of bias introduced into the model. We found that the TB transmission in the United States was characterized by a high propensity for extensive outbreaks (; 95% confidence interval = 0.09, 0.10). The proposed method can accurately quantify critical parameters that govern TB transmission using simple, more easily obtainable cluster data to improve our understanding of TB epidemiology.

Wintertime subarctic new particle formation from Kola Peninsula sulfur emissions

Abstract. The metallurgical industry in the Kola Peninsula, north-west Russia, form, after Norilsk, Siberia, the second largest source of air pollution in the Arctic and subarctic domain. Sulfur dioxide (SO2) emissions from the ore smelters are transported to wide areas, including Finnish Lapland. We performed investigations on concentrations of SO2, aerosol precursor vapours, aerosol and ion cluster size distributions together with chemical composition measurements of freshly formed clusters at the SMEAR I station in Finnish Lapland relatively close (∼ 300 km) to the Kola Peninsula industrial sites during the winter 2019–2020. We show that highly concentrated SO2 from smelter emissions is converted to sulfuric acid (H2SO4) in sufficient concentrations to drive new particle formation hundreds of kilometres downwind from the emission sources, even at very low solar radiation intensities. Observed new particle formation is primarily initiated by H2SO4–ammonia (negative-)ion-induced nucleation. Particle growth to cloud condensation nuclei (CCN) sizes was concluded to result from sulfuric acid condensation. However, air mass advection had a large role in modifying aerosol size distributions, and other growth mechanisms and condensation of other compounds cannot be fully excluded. Our results demonstrate the dominance of SO2 emissions in controlling wintertime aerosol and CCN concentrations in the subarctic region with a heavily polluting industry.

Thermodynamic analysis of Al clusters formation over aluminum melt

The formation of the aluminum nanoparticles with the size of up to 60 atoms in a gas phase is theoretically studied. Thermodynamic modeling has been applied to investigate the effect of the synthesis conditions on the distribution of the nanoparticles. The magic numbers of the particles have been estimated and found to be consistent with the available data. Furthermore, the simulations showed that higher amounts of larger nanoparticles are obtained during condensation from the supercooled aluminum vapor. In contrast, lower amounts of smaller clusters may be formed in a gas phase over the aluminum melt. Varying the temperature and concentration of supercooled aluminum vapor in a broad range results in no significant change in cluster size distribution. This effect is governed by the equilibrium shift.

A non-absorbing SIR stochastic lattice gas model on hybrid lattices

In this paper, we perform Monte Carlo calculations to study the critical behavior of the spread of infectious diseases through a novel approach to the SIR epidemiological model. A stochastic lattice gas version of the model was applied on hybrid lattices which, in turn, are generated from typical square lattices when inserting a connection probability p that a given lattice site has both first- and second-nearest neighbor interactions. By combining percolation theory and finite-size scaling analysis, we estimate both the critical threshold and leading critical exponent ratios of the non-absorbing SIR model in different cases of hybrid lattices. An analysis of the average size of the percolating cluster and the size distribution of non-percolating clusters of recovered individuals was carried out to determine the universality class of the model.

Generating functions for message passing on weighted networks: Directed bond percolation and susceptible, infected, recovered epidemics.

We study the SIR (susceptible, infected, removed/recovered) model on directed graphs with heterogeneous transmission probabilities within the message-passing approximation. We characterize the percolation transition, predict cluster size distributions, and suggest vaccination strategies. All predictions are compared to numerical simulations on real networks. The percolation threshold that we predict is a rigorous lower bound to the threshold on real networks. For large, locally treelike networks, our predictions agree very well with the numerical data.

Geant4-DNA modeling of nanodosimetric quantities in the Jet Counter for alpha particles

The purpose of this work was to validate the calculation accuracy of nanodosimetric quantities in Geant4-DNA track structure simulation code. We implemented the Jet Counter (JC) nanodosimeter geometry in the simulation platform and quantified the impact of the Geant4-DNA physics models and JC detector performance on the ionization cluster size distributions (ICSD). ICSD parameters characterize the quality of radiation field and are supposed to be correlated to the complexity of the initial DNA damage in nanoscale and eventually the response of biological systems to radiation. We compared Monte Carlo simulations of ICSD in JC geometry performed using Geant4-DNA and PTra codes with experimental data collected for alpha particles at 3.8 MeV. We investigated the impact of simulation and experimental settings, i.e., three Geant4-DNA physics models, three sizes of a nanometer sensitive volume, gas to water density scaling procedure, JC ion extraction efficiency and the presence of passive components of the detector on the ICSD and their parameters. We found that ICSD in JC geometry obtained from Geant4-DNA simulations in water correspond well to ICSD measurements in nitrogen gas for all investigated settings, while the best agreement is for Geant4-DNA physics option 4. This work also discusses the accuracy and robustness of ICSD parameters in the context of the application of track structure simulation methods for treatment planning in particle therapy.

Cluster size distribution of cells disseminating from a primary tumor.

The first stage of the metastatic cascade often involves motile cells emerging from a primary tumor either as single cells or as clusters. These cells enter the circulation, transit to other parts of the body and finally are responsible for growth of secondary tumors in distant organs. The mode of dissemination is believed to depend on the EMT nature (epithelial, hybrid or mesenchymal) of the cells. Here, we calculate the cluster size distribution of these migrating cells, using a mechanistic computational model, in presence of different degree of EMT-ness of the cells; EMT is treated as given rise to changes in their active motile forces (μ) and cell-medium surface tension (Γ). We find that, for (μ > μmin, Γ > 1), when the cells are hybrid in nature, the mean cluster size, [Formula: see text], where μmin increases with increase in Γ. For Γ ≤ 0, [Formula: see text], the cells behave as completely mesenchymal. In presence of spectrum of hybrid states with different degree of EMT-ness (motility) in primary tumor, the cells which are relatively more mesenchymal (higher μ) in nature, form larger clusters, whereas the smaller clusters are relatively more epithelial (lower μ). Moreover, the heterogeneity in μ is comparatively higher for smaller clusters with respect to that for larger clusters. We also observe that more extended cell shapes promote the formation of smaller clusters. Overall, this study establishes a framework which connects the nature and size of migrating clusters disseminating from a primary tumor with the phenotypic composition of the tumor, and can lead to the better understanding of metastasis.

Radiation-resistant binary solid solutions via vacancy trapping on solute clusters

Additions of solute that trap vacancies slow down vacancy diffusion and promote point-defect recombination in alloys subjected to irradiation. Such selective alloying can thus help to minimize the detrimental consequences resulting from point defect fluxes. The current work investigates the effect of solute additions on the recombination rate using kinetic Monte Carlo simulations for a model alloy system, which was parametrized to Cu-Ag in the dilute limit, but with an increased solubility limit, ≈ 0.86 at.% at 300 K. As the solute concentration was increased above 0.1 at.%, solute clustering was observed and led to a strong increase in recombination rate. The beneficial effects of solute clustering on reducing vacancy mobility, and reducing solute drag, were analyzed by calculating relevant transport coefficients using the KineCluE code (Schuler et al., Computational Materials Science (2020) 172,109,191). Moreover, it was observed in the KMC simulations that large recombination rates resulted in a shift of steady-state distributions of solute cluster sizes to smaller clusters compared to equilibrium distributions in the solid solution. This shift is rationalized as resulting from the irreversible character of the interstitial-vacancy recombination reaction. These results suggest a novel irradiation effect on phase stability where a high recombination rate increases the solubility limit of a solute at steady state over its equilibrium value.

Performance of a triple-GEM demonstrator in pp collisions at the CMS detector

After the Phase-2 high-luminosity upgrade to the Large Hadron Collider (LHC), the collision rate and therefore the background rate will significantly increase, particularly in the high η region. To improve both the tracking and triggering of muons, the Compact Muon Solenoid (CMS) Collaboration plans to install triple-layer Gas Electron Multiplier (GEM) detectors in the CMS muon endcaps. Demonstrator GEM detectors were installed in CMS during 2017 to gain operational experience and perform a preliminary investigation of detector performance. We present the results of triple-GEM detector performance studies performed in situ during normal CMS and LHC operations in 2018. The distribution of cluster size and the efficiency to reconstruct high pT muons in proton-proton collisions are presented as well as the measurement of the environmental backgroundrate to produce hits in the GEM detector.

Characterization of in-situ ion irradiated Fe-21Cr-32Ni austenitic model alloy and alloy 800H at low doses

The microstructural evolution of ternary Fe-21Cr-32Ni (21Cr32Ni) model alloy and of alloy 800H was investigated with a series of in-situ ion irradiation experiments performed using the Intermediate Voltage Electron Microscope (IVEM)-Tandem Facility at Argonne National Laboratory (ANL). Samples were irradiated in-situ with 1 MeV Kr++ ions in the temperature range of 50K to 713K to doses up to 2 dpa. The size distribution of defect clusters, average defect cluster diameter, and defect cluster density were measured and compared. Results showed that the evolution of defects (i.e. the average defect cluster size and number density) in 21Cr32Ni model alloy and alloy 800H with dose were similar at irradiation temperatures up to 300K where they initially increased with dose up to 0.1 dpa after which no significant changes in defect size and density were observed with further irradiation. In addition, both alloys exhibited ordered defect structures along the <100> direction at relatively low temperatures, up to 300K, which remained stable throughout post-irradiation in-situ thermal annealing up to a temperature of 773K. During irradiation at 713K, small defect clusters were observed at low doses (<0.1 dpa) in both alloys. However, at this irradiation temperature, the clusters in 21Cr32Ni grew with a faster rate than those formed in alloy 800H, causing the microstructure in the former to be dominated by numerous large dislocation loops having both {111}- and {110}-type habit planes, and in the latter to be dominated by small defect clusters and small {111}-type dislocation loops. This may indicate that defect trapping by the solute atoms in alloy 800H at 713K can slow point defect migration to defect clusters and limit their growth.

Characterisation of the PTB ion counter nanodosimeter's target volume and its equivalent size in terms of liquid H2O

The pattern of inelastic interactions in subcellular targets, especially in DNA, is largely responsible for radiation-induced damage to tissue. The track structure of ionising particles is therefore of particular importance in view of the biological effectiveness of ionising radiation.In approaches to model radiation effects to DNA, track structure details on the nanometre scale and the specifics of the target geometry play an important role. Hence, reliable experimental benchmark data for these models require detailed knowledge on the size and shape of the target volume of the devices used to measure quantities related to track structure in simulated nanometric target volumes.A dedicated investigation of the target size of a nanodosimeter device has been carried out in order to investigate to what extent measured ionisation cluster size distributions can serve as benchmark data for modelling approaches, for the first time with particular focus on the equivalent target size in terms of liquid H2O. To this end, measurements with alpha particles from a241Am source were carried out using three different target gases, H2O, C3H8 and C4H8O. For each of the three target gases, three different drift-time windows were applied to realise three different target sizes.A method has been developed to determine the dimensions of the simulated nanometric target volume in liquid H2O for cylindrical and spherical shape, as often used in approaches to model radiation effects to DNA. Simulations with nanometric targets of dimensions determined with this method agree very well with the corresponding measurements.Scaling of the spatial distribution of the extraction efficiency for different target gases and drift-time windows, which corresponds to the nanodosimeter's target volume, in terms of liquid H2O using (ρλion)-ratios has also been investigated and proved to yield an estimate of the target volume in liquid H2O.Thus, it can be concluded that ionisation cluster size distributions measured with a nanodosimeter device are suited as benchmark data for approaches that model radiation induced damage to DNA in nanometric volumes of liquid H2O in simple geometries such as cylinders or spheres, provided that the nanodosimeter's target volume is characterised accordingly. By proper selection of drift-time window length as well as target gas and density a wide range of target volume dimensions in terms of liquid H2O can be realised with the PTB Ion Counter nanodosimeter according to specific requirements of modelling approaches.

Bali's Ancient Rice Terraces: A Hamiltonian Approach.

We propose a Hamiltonian approach to reproduce the relevant elements of the centuries-old Subak irrigation system in Bali, showing a cluster-size distribution of rice-field patches that is a power-law with an exponent of ∼2. Besides this exponent, the resulting system presents two equilibria. The first originates from a balance between energy and entropy contributions. The second arises from the specific energy contribution through a local Potts-type interaction in combination with a long-range antiferromagnetic interaction without attenuation. Finite-size scaling analysis shows that, as a result of the second equilibrium, the critical transition balancing energy and entropy contributions at the Potts (local ferromagnetic) regime is absorbed by the transition driven by the global-antiferromagnetic interactions, as the system size increases. The phase transition balancing energy and entropy contributions at the global-antiferromagnetic regime also shows signs of criticality. Our study extends the Hamiltonian framework to a new domain of coupled human-environmental interactions.

Dust in brown dwarfs and extra-solar planets

Context. Modelling the formation of cloud condensation nuclei (CCNs) is key for predicting cloud properties in planet and brown dwarf atmospheres. The large diversity of exoplanets (rocky planets, mini-Neptunes, giant gas planets) requires a fundamental approach to cloud formation modelling in order to allow a full analysis of observational data contributing to exoplanet characterisation. Aims. We aim to understand the onset of cloud formation and study the formation of TiO2-CCNs. The formation of (TiO2)N clusters as precursors to extrasolar cloud formation is modelled by two different methods in order to understand their potential, identify underlying shortcomings, and to validate our methods. We propose potential spectral tracers for TiO2-CCN formation. Methods. We applied three-dimensional Monte Carlo (3D MC) simulations to model the collision-induced growth of TiO2-molecules to (TiO2)N-clusters in the free molecular flow regime of an atmospheric gas. We derived individual, time-dependent (TiO2)N cluster number densities. For T = 1000 K, the results are compared to a kinetic approach that utilises thermodynamic data for individual (TiO2)N clusters. Results. The (TiO2)N cluster size distribution is temperature dependent and evolves in time until a steady state is reached. For T = 1000 K, the 3D MC and the kinetic approach agree well regarding the cluster number densities for N = 1 … 10, the vivid onset of cluster formation, and the long transition into a steady state. Collision-induced growth and evaporation simulated using a 3D MC approach enables a faster onset of cluster growth through nucleation bursts. Different size distributions develop for monomer-cluster and for cluster-cluster growth, with the largest clusters appearing for cluster-cluster growth. Conclusions. The (TiO2)N cluster growth efficiency has a sweet-spot temperature at ≈1000 K at which CCN formation is triggered. The combination of local thermodynamic conditions and chemical processes therefore determines CCN formation efficiency. The onset of cloud formation may be observable through the (TiO2)4, (TiO2)5, and (TiO2)6 vibrational lines, which may be detectable with the Mid-Infrared Instrument on the James Webb Space Telescope or the Extremely Large Telescope’s mid-IR imager, but more complete line-list data are desirable.

Impact of Wettability and Gravity on Fluid Displacement and Trapping in Representative 2D Micromodels of Porous Media (2D Sand Analogs)

AbstractThe combined effects of gravitational forces and wettability on displacement and trapping have not previously been investigated experimentally in realistic 2D porous media. Here we report the first use of representative 2D micromodels that accurately reproduce characteristic geometric, morphological, and topological properties of 3D sand packs. We use these representative micromodels to compare the wettability dependence of displacement front morphology and trapping processes using selected fluid pairs at capillary numbers between 10−6 and 10−5. The contact angles studied ranged from 30° (normal imbibition) to 150° (strong drainage). The impact of gravity was dramatic: In the horizontal flow case, only one finger developed, that is longitudinal displacement was always favored, whereas gravity created a more compact displacement front with broad lateral extension, and this lateral movement created loops, leading to by‐pass trapping. As a result, the trapping efficiency rose from 7% to 29%. We observed universal scaling of the cluster size distribution demonstrating that our micromodels are statistically representative. The universal 2D‐scaling exponent of 2.05 was obtained with an acceptable error smaller than 5%. Our experimental results obtained by fluorescence microscopy showed (a) precursor corner flow for weak imbibition at θ = 51°, that is above the critical contact angle of αc = 45° (Zhao et al., 2016, https://doi.org/10.1073/pnas.1603387113), and (b) a new wetting transition from corner flow to full duct flow under neutral wettability conditions, that is at θc ≈ 90°; and (c) above this second critical contact angle, that is under strong drainage conditions, we again observed corner flow (specifically, core‐annular flow).

The asymptotic distribution of cluster sizes for supercritical percolation on random split trees

AbstractWe consider the model of random trees introduced by Devroye, the so‐called random split trees. The model encompasses many important randomized algorithms and data structures. We then perform supercritical Bernoulli bond‐percolation on those trees and obtain a precise weak limit theorem for the sizes of the largest clusters. We also show that the approach developed in this work may be useful for studying percolation on other classes of trees with logarithmic height, for instance, we also study the case of d‐regular trees.

Experimental nanodosimetry: Track structure of 80 MeV boron ions

The radiobiological effects of ionising radiations are strongly correlated to the local density of lesions produced in micrometre- and nanometre-sized subcellular structures, and thus to the track structure properties of interacting particles. These properties have been studied mainly by means of Monte Carlo simulations, however experimental methodologies and instruments have also been developed that allow to measure the stochastics of ionisations produced in a nanometric sensitive volume (SV) by charged particles crossing it or passing nearby at specified distances. The number ν of ionisations produced in SV by the passage of a single primary ionising particle is measured, and the measurement is repeated many times to produce a probability distribution P(ν), called ionisation cluster size distribution. Measurable quantities can be derived that correlate with the biological effectiveness of the specific radiation quality (ion type and velocity). In view of the emerging interest of carbon ions in radiotherapy, it is important to characterize not only the track structure of carbon ions but also that of other light ions that are produced in nuclear interactions. This work presents first experimental results for boron ions at 80 MeV. Ionisation cluster size distributions were measured with the Startrack-Counter installed at the TANDEM-ALPI accelerator complex at the Legnaro National Laboratories (LNL) of the Italian Istituto Nazionale di Fisica Nucleare (INFN) and simulated by means of a dedicated Monte Carlo code. Measurements and simulations were performed for particles that traverse directly the sensitive volume or pass nearby at specified impact parameters.

Gut bacterial aggregates as living gels

The spatial organization of gut microbiota influences both microbial abundances and host-microbe interactions, but the underlying rules relating bacterial dynamics to large-scale structure remain unclear. To this end, we studied experimentally and theoretically the formation of three-dimensional bacterial clusters, a key parameter controlling susceptibility to intestinal transport and access to the epithelium. Inspired by models of structure formation in soft materials, we sought to understand how the distribution of gut bacterial cluster sizes emerges from bacterial-scale kinetics. Analyzing imaging-derived data on cluster sizes for eight different bacterial strains in the larval zebrafish gut, we find a common family of size distributions that decay approximately as power laws with exponents close to -2, becoming shallower for large clusters in a strain-dependent manner. We show that this type of distribution arises naturally from a Yule-Simons-type process in which bacteria grow within clusters and can escape from them, coupled to an aggregation process that tends to condense the system toward a single massive cluster, reminiscent of gel formation. Together, these results point to the existence of general, biophysical principles governing the spatial organization of the gut microbiome that may be useful for inferring fast-timescale dynamics that are experimentally inaccessible.

Transient aggregation of particles at interfaces

The formation of an axisymmetric monolayer of dense particles at a liquid interface is explored in order to study the interaction between numerous objects of different sizes randomly distributed on a liquid surface. The individual motion of each bead cannot be solved but the overall clustering can be described statistically. The clustering dynamics of this system with a long-range interaction varies during the aggregation process. The cluster-size distribution evolves with a self-similar mechanism and we observe a well-defined transition between two aggregating regimes that we can characterize.

Roles of the Coupling Agent and Surfactant in Droplet Structure in Sizing Emulsions: A Molecular Dynamics Simulations Study

Sizing emulsions used as glass fiber surface treatments in composites manufacturing are aqueous suspensions of hydrophobic film formers, surface coupling agents, and surfactants. We employ all-atom molecular dynamics simulations to characterize droplet structures in several aqueous blends of the film-former diglycidyl ether of bisphenol A, coupling agent glycidoxypropyl trimethoxysilane, and a triblock copolymer surfactant (Pluronic L35 PEO/PPO copolymer). We show that the quasi-equilibrium states of emulsion droplets are invariant to different initial configurations. We examine the role of the surfactant in determining coupling agent partitioning between the droplet shell and corona and coupling agent cluster size distributions. This work takes a step toward systematic understanding of the sizing chemistry to optimize the interface between the glass and the resin in commercially relevant composites.