Cluster Size Determination Research Articles

Power calculation for detecting interaction effect in cross-sectional stepped-wedge cluster randomized trials: an important tool for disparity research

BackgroundThe stepped-wedge cluster randomized trial (SW-CRT) design has become popular in healthcare research. It is an appealing alternative to traditional cluster randomized trials (CRTs) since the burden of logistical issues and ethical problems can be reduced. Several approaches for sample size determination for the overall treatment effect in the SW-CRT have been proposed. However, in certain situations we are interested in examining the heterogeneity in treatment effect (HTE) between groups instead. This is equivalent to testing the interaction effect. An important example includes the aim to reduce racial disparities through healthcare delivery interventions, where the focus is the interaction between the intervention and race. Sample size determination and power calculation for detecting an interaction effect between the intervention status variable and a key covariate in the SW-CRT study has not been proposed yet for binary outcomes.MethodsWe utilize the generalized estimating equation (GEE) method for detecting the heterogeneity in treatment effect (HTE). The variance of the estimated interaction effect is approximated based on the GEE method for the marginal models. The power is calculated based on the two-sided Wald test. The Kauermann and Carroll (KC) and the Mancl and DeRouen (MD) methods along with GEE (GEE-KC and GEE-MD) are considered as bias-correction methods.ResultsAmong three approaches, GEE has the largest simulated power and GEE-MD has the smallest simulated power. Given cluster size of 120, GEE has over 80% statistical power. When we have a balanced binary covariate (50%), simulated power increases compared to an unbalanced binary covariate (30%). With intermediate effect size of HTE, only cluster sizes of 100 and 120 have more than 80% power using GEE for both correlation structures. With large effect size of HTE, when cluster size is at least 60, all three approaches have more than 80% power. When we compare an increase in cluster size and increase in the number of clusters based on simulated power, the latter has a slight gain in power. When the cluster size changes from 20 to 40 with 20 clusters, power increases from 53.1% to 82.1% for GEE; 50.6% to 79.7% for GEE-KC; and 48.1% to 77.1% for GEE-MD. When the number of clusters changes from 20 to 40 with cluster size of 20, power increases from 53.1% to 82.1% for GEE; 50.6% to 81% for GEE-KC; and 48.1% to 79.8% for GEE-MD.ConclusionsWe propose three approaches for cluster size determination given the number of clusters for detecting the interaction effect in SW-CRT. GEE and GEE-KC have reasonable operating characteristics for both intermediate and large effect size of HTE.

Leveraging Metaheuristic Unequal Clustering for Hotspot Elimination in Energy-Aware Wireless Sensor Networks

Wireless sensor networks (WSNs) are becoming a significant technology for ubiquitous living and continue to be involved in active research because of their varied applications. Energy awareness will be a critical design problem in WSNs. Clustering is a widespread energy-efficient method and grants several benefits such as scalability, energy efficiency, less delay, and lifetime, but it results in hotspot issues. To solve this, unequal clustering (UC) has been presented. In UC, the size of the cluster differs with the distance to the base station (BS). This paper devises an improved tuna-swarm-algorithm-based unequal clustering for hotspot elimination (ITSA-UCHSE) technique in an energy-aware WSN. The ITSA-UCHSE technique intends to resolve the hotspot problem and uneven energy dissipation in the WSN. In this study, the ITSA is derived from the use of a tent chaotic map with the traditional TSA. In addition, the ITSA-UCHSE technique computes a fitness value based on energy and distance metrics. Moreover, the cluster size determination via the ITSA-UCHSE technique helps to address the hotspot issue. To demonstrate the enhanced performance of the ITSA-UCHSE approach, a series of simulation analyses were conducted. The simulation values stated that the ITSA-UCHSE algorithm has reached improved results over other models.

Cluster size determination using shadowgraphy measurements

Cluster-jet beams offer a wide variety of possible applications. The advantages of an internal and windowless cluster-jet target make it suitable for many experiments. It is important to know all the properties of the cluster-jet to prepare it for the desired conditions of the respective experiments. An essential property is the size of the clusters and their size distribution. To investigate the size of the clusters shadowgraphy measurements are performed. This article provides an overview of the shadowgraphy method and presents first results of these analyses using hydrogen clusters. These show an average cluster size of a few micrometers, which will also be of high interest, besides the here shown laser cluster interaction, for other installations using cluster beams.

Concentration dependence of As2S3 chalcogenide glass cluster size in amine solution.

Solution processing chalcogenide glasses is a common and effective first step in optoelectronic device fabrication. Arsenic(iii) sulfide (As2S3) is believed to take on a nanoscale cluster structure in n-propylamine and n-butylamine, which affects the morphology and properties of the deposited material; however, the size of these clusters and the mechanism of size determination are poorly understood. We combine experimental and analytical techniques to investigate As2S3 cluster size in n-propylamine and its dependence on solution concentration. We find that the cluster size increases with concentration and show that this trend is consistent across independent experimental techniques. We then explain these results by proposing a simplified dissolution mechanism and deriving cluster size through a free energy argument. Our findings enable informed control of chalcogenide glass cluster size during solution processing and improved property control in optoelectronic device fabrication.

Mean Gas Cluster Size Determination from Cluster Beam Cross-Section

This paper describes the simple experimental method of size determination of gas clusters in molecular beams formed from supersonic jets. Mean cluster size N is calculated from broadening of the transverse profile of beam intensity at a fixed distance behind the skimmer. The described method allows determining the mean sizes of the clusters of any pure gases. It does not require the building of some special models, or determination of empirical constants. Due to the high intensity of the supersonic beams, the measurements do not require any complex highly sensitive equipment. The effectiveness of the present method is validated by measurements in a cluster beams of test gases (easily condensable CO2, Ar, and weakly condensable N2) and the beam of C2H4 (ethylene), formed from a supersonic jet behind conical nozzles. The certainty of measured characteristics is confirmed by the results of numerical simulations. By using the described method the mean cluster sizes from 50 to 2000 molecules per cluster were determined. The correctness of the obtained cluster sizes of CO2 and Ar is proved by comparison with results of other authors, obtained by other experimental methods, and estimations according to the empirical correlations using condensation scaling parameter Г*.

Simple method to gas cluster size determination based on molecular beam cross-section

A new experimental method of gas cluster size determination based on measuring the transverse profile of the total intensity of a molecular beam was developed. Since the supersonic beam has a high intensity, the proposed method not requires high-sensitivity detecting equipment. By using this method it can determine the mean cluster size in situ not only of any pure gases, but in gas mixtures under certain conditions as well. Experimental measurements were carried out in jets of pure gases (Ar, CO2, N2) and gas mixture (10% С2Н4 + 90% Не) expansions through supersonic conical nozzles. The Hagena scaling parameter of the source conditions Г* varied from 102 to 2 × 104. The mean cluster sizes defined by new method were in the range of 50–1500 molecules/cluster. Comparison of the experimental data to the results of numerical simulations and estimates using the empirical formulae developed elsewhere shows a satisfactory agreement.

A Practical Method for Determining the Cluster Model Size and the Estimation of the Energy Barrier on Heterogeneous Catalysts

A practical method for determining the cluster model size and the estimation of the energy barrier on heterogeneous catalyst, In2O3(111) cluster, on which acetaldehyde is successively converted acetic acid and acetoacetic acid, has been proposed. The cluster size determination is executed as follows; 1) we determine the optimized adsorption structure of reactant, 2) we divide the structure into the reactant fragment and the cluster fragment, and calculate "Paired interacting orbitals (PIO)," 3) we determine the cluster size by using the atomic composition of the PIO of cluster fragment. The estimation of energy barrier is executed as follows; 1) we suppose a transition state, and assume a reactant side intermediate state (RTint), and a product side intermediate state (PDint), 2) we calculate PIOs of the RTint and those of the PDint and compare them, 3) we change the structures of RTint and PDint until the similarities of the PIOs are almost equal, 4) we calculate the total energies of both final intermediates, then, 5) we define an estimated barrier (Ebarriar) according to the following equation;Ebarrier = (ERTint.final +EPDint.final)/2 –Ereactant.

Constrained spanning tree algorithms for irregularly-shaped spatial clustering

Spatial clustering methodologies that are capable of detecting and delineating irregular clusters can provide information about the geographical spread of various diseases under surveillance. This paper proposes and compares three spatial scan statistics designed to detect clusters with irregular shapes. The proposed methods use geographical boundary information to construct a graph in which a cluster growing process is performed based on likelihood function maximization. Constraints on cluster shape are imposed through early stopping, a double connection requirement and a maximum linkage criteria. The methods are evaluated using simulated data sets with either circular or irregular clusters, and compared to the circular and elliptic scan statistics. Results show that for circular clusters, the standard circular scan statistic is optimal, as expected. The double connection, elliptic maximum linkage scan statistics also achieve good results. For irregularly-shaped clusters, the elliptic, maximum linkage and double connected scan statistics are optimal for different cluster models and by different evaluation criteria, but the circular scan statistic also performs well. If the emphasis is on statistical power for cluster detection, the simple circular scan statistic is attractive across the board choice. If the emphasis is on the accurate determination of cluster size, shape and boundaries, the double connected, maximum linkage and elliptical scan statistics are often more suitable choices. All methods perform well though, with the exception of the unrestricted dynamic minimum spanning tree scan statistic and the early stopping scan statistic, which we do not recommend.

Polarization bremsstrahlung in a backward direction for medium structure diagnostics

Possibilities to elaborate the new energy dispersive methods of the diagnostics of a medium atomic structure based on the polarization bremsstrahlung from relativistic electrons moving in a sample are analyzed in the paper. The method of radial density of atoms measuring in a weakly ordered medium is proposed in the paper as well as the method of cluster size determination in small grained medium.

Bias enhanced nucleation of diamond thin films in a modified HFCVD reactor

In this study we investigated the nucleation of synthetic diamond thin films on Si substrates by double bias enhanced Hot Filament Chemical Vapour Deposition (HFCVD) method. First, we investigated the influence of the bias voltage and secondly the influence of the nucleation time under different bias voltages. The bias voltage was varied from −120 V up to −220 V as well as the nucleation time was changed from 30 up to 120 min in order to obtain the optimized nucleation conditions for following growth of continuous diamond layer. Samples were analyzed by Scanning Electron Microscopy (SEM) and Raman Spectroscopy. SEM was used for determination of cluster sizes and their distribution on the Si surface, while Raman Spectroscopy for determination and analysis of carbon phases.

Kinetic Model of Condensation in a Free Argon Expanding Jet

The direct-simulation Monte Carlo (DSMC) method has recently been developed to simulate homogeneous condensation in a free-expansion rocket plume. However, cluster‐monomer and cluster‐cluster collision models as well as the determination of cluster size were simplified in the previous work, and the effect on the accuracy of the numerical simulation results was not quantified. In this work, the molecular-dynamics (MD) method is used to simulate collision and sticking probabilities for argon clusters and the results are compared with the hard-sphere model. These improved models are then integrated into a DSMC code to predict the Rayleigh scattering intensity in a free-expanding argon condensation plume, and numerical results are compared with experimental data along the plume centerline. Nomenclature A = constant B = constant b = impact parameter c =v elocity d = diameter E = evaporation rate or energy I = intensity i = number of atoms J = nucleation rate K = intensity constant k B = Boltzmann’s constant L = specific latent heat M = cluster mass m = molecular mass N = number density nc = number of simulated nuclei particles ps = saturation pressure q = sticking coefficient R = ideal gas constant r = distance or radius T = temperature V = interaction potential or specific volume α = species polarizability � t = time step � V = cell volume � = potential constant λ0 =w avelength ρ = density σ = surface tension or potential constant Subscripts

Fluorescence Microscopy Visualization of Single-Walled Carbon Nanotubes Using Semiconductor Nanocrystals

Carbon nanotube (CNT) based electronic, optical, chemical, and biological devices are in dire need of simple optical microscopy solutions, which can be utilized to image and manipulate CNTs in solution state, many times in biologically relevant aqueous environments. Here, we demonstrate fluorescence visualization of single-walled carbon nanotubes (SWNT) in aqueous solutions using simple light microscopes. For this purpose, stable SWNT dispersions of sodium-dodecyl-sulfonate (SDS) were prepared and mixed with CdSe−ZnS core−shell nanocrystals (quantum-dots (QDs)) functionalized by mercaptoacetic acid. QDs arrange themselves on the sidewalls of SWNTs by virtue of electrostatic interaction between zinc ions in their shell and electronegative oxygen atoms/anions in the sulfonate group of the surfactant, embodying the fluorescence visualization of SWNTs. Transmitted brightfield, SEM, and TEM images also provide clear indication of SWNT sidewalls decorated with these QDs. This visualization technique will facilitate simple optical determination of cluster sizes of CNTs and their manipulation for fabrication of CNT-based devices.

붓스트랩 기법과 유전자 알고리즘을 이용한 최적 군집 수 결정

Optimal determination of cluster size has an effect on the result of clustering. In K-means algorithm, the difference of clustering performance is large by initial K. But the initial cluster size is determined by prior knowledge or subjectivity in most clustering process. This subjective determination may not be optimal. In this Paper, the genetic algorithm based optimal determination approach of cluster size is proposed for automatic determination of cluster size and performance upgrading of its result. The initial population based on attribution is generated for searching optimal cluster size. The fitness value is defined the inverse of dissimilarity summation. So this is converged to upgraded total performance. The mutation operation is used for local minima problem. Finally, the re-sampling of bootstrapping is used for computational time cost.

Resolving Globular Clusters in the Fornax Cluster and Beyond

We describe an ongoing program to measure structural parameters for globular clusters with a range of ages in early-type galaxies. Using deep, optimally-dithered HST WFPC2 observations of NGC 3597, NGC 1316, and NGC 1399, we apply a χ2 minimization method to the determination of cluster sizes. The goals include studying the structure spectrum of stellar clusters at birth, and determining the rate at which tidal and evaporative destruction mechanisms operate to alter luminosity functions and specific frequencies to what we see in ellipticals today.

Cluster size determination from diffractive He atom scattering

In a crossed molecular beam arrangement helium atoms are scattered from argon clusters which are produced in an averaged size range of n̄=6 to n̄=90 by adiabatic expansion through sonic and conical nozzles. The diffraction oscillations in the total differential cross section are used to derive information on the size distribution of the clusters by comparison with quantum mechanical calculations based on a model potential. In the size range covered by the measurements, the average cluster size is given by n̄=38.4(Γ*/1000)1.64, where Γ* is the scaling parameter of the source conditions introduced by Hagena [Z. Phys. D 4, 291 (1987)]. The results are in agreement with recent measurements of corrected mass spectra but disagree with the results obtained from electron diffraction. General relations are recommended which connect the scaling parameter with the averaged size.

Average cluster size determination in supersonic beams from angular distribution measurements after scattering by a buffer gas

A method for the determination of average cluster size in supersonic beams is presented. Based on angular distribution broadening of the beams caused by passing through a buffer gas, this method is well suited for in situ determination of the mean cluster size when the apparatus contains a movable detector with sufficient spatial resolution. The shape and width of the beam profile after scattering by a buffer gas are evaluated theoretically as functions of buffer gas pressure and atom-cluster collision cross-section. Experimental results are presented for an argon beam, yielding average cluster sizes between 300 and 7000 atoms depending on the stagnation pressure. Simple criteria to assess the applicability of the method to a given experimental situation are discussed. The average cluster sizes determined in this work agree quite satisfactorily with previously published values for similar beam generation conditions.

Approaches to high-resolution 1H NMR in solids

Principles and selected applications of solid-state 1H NMR are reviewed, with emphasis on the role of local fields and particularly the magnetic dipole-dipole couplings. The strong dipolar fields of the hydrogen nuclei compound the usual difficulties of solid-state NMR, notably the line broadening due to spatial anisotropy, and largely determine what information can be obtained from a spectrum and how. Methods designed to defeat both the 1H- 1H interactions and the orientational broadening, such as a combination of multiple-pulse averaging and magic-angle spinning, may yield highly resolved spectra displaying the isotropic chemical shifts. Although still far from routine, techniques to eliminate homonuclear dipole-dipole couplings have been applied successfully to polymers, zeolites, coals, and surface systems, among others. Yet these same dipolar interactions, if used to advantage, have spectroscopic value as well precisely because they do establish definite relationships among the coupled nuclei according to a well-defined geometrical dependence. Potential uses include the determination of cluster sizes and the measurement of H-X internuclear distances in powders to high accuracy. Some examples of these techniques, plus related methods such as zero-field NMR and proton imaging, are mentioned to suggest the wide range of possible chemical applications.

Time-of-flight mass spectroscopy of ionized cluster beam in film deposition conditions

A time-of-flight mass spectroscopy technique was developed that enables continuous monitoring of ion mass distribution in the output of a typical ionized cluster beam (ICB) source with minimum modification of the setup and negligible disturbance of film growth. The low mass resolution of this spectrometer is sufficient for cluster size determination and is counterbalanced by a number of advantages promising a more general applicability of the technique. This spectrometer has been used to study germanium cluster formation in a commercially available ICB source. No clusters larger than a few atoms were observed during several deposition runs, under conditions relevant to practical applications. It is difficult to reconcile these findings with the original hypothesis of homogeneous nucleation and growth of large clusters by free jet expansion of metal vapor. Since the precise temperature gradient in the crucible could not be controlled in this type of source, it cannot be excluded that large clusters may be formed under very particular conditions. If this is the case, vapor condensation on the nozzle’s walls must play the key role in the formation of clusters, of germanium at least, making ICB less attractive as a semiconductor thin film growth technique.

Cluster size determination in amorphous structures using the Boson peak

The universal line-shape of the Boson peak in the low frequency region of the Raman spectra in different amorphous materials was successfully fitted by a lognormal curve. The lognormal size- distribution of clusters appears to be the medium range order of amorphous structures. This size-distribution of clusters was determined for a few samples.

Clustering in dilute, binary supercritical mixtures: A fluctuation analysis

Solute-solvent concentration fluctuation correlations at infinite dilution are a statistical measure of the excess number of solvent molecules surrounding a given solute molecule, with respect to a uniform distribution at the prevailing density. This leads to the concept of a cluster which, in dilute supercritical mixtures (trace solute(s) in the vicinity of a solvent's critical point) acquires mechanistic and not merely statistical significance. Experimental measurements of solute partial molar volumes at infinite dilution in such systems are shown to be equivalent, when analyzed in the light of fluctuation theory, to a cluster size determination. This quantity can be either positive or negative. Calculations based on experimental measurements of infinite dilution partial molar volumes of organic solids in supercritical fluids indicate the existence of clusters of ca 100 solvent molecules per solute molecule. The fluctuation approach cannot be used arbitrarily close to the solvent's critical point, since it is based on the assumption of a finite solvent compressibility. Asymptotic laws for the behavior of solute fluctuations in dilute mixtures within differently defined regions of space (constant volume; constant solvent mass) are derived. Finally, it is shown that there is a univocal relationship between cluster formation and the experimentally observed solubility enhancement in dilute mixtures of non-volatile solutes in supercritical solvents.