Mean Cluster Size Research Articles

Assessment of accuracy of the structure-factor-size-estimator method in determining red blood cell aggregate size from ultrasound spectral backscatter coefficient

A computer simulation study to produce ultrasonic backscatter coefficients (BSCs) from red blood cell (RBC) clusters is discussed. The simulation algorithm is suitable for generating non-overlapping, isotropic, and fairly identical RBC clusters. RBCs were stacked following the hexagonal close packing (HCP) structure to form a compact spherical aggregate. Such an aggregate was repeated and placed randomly under non-overlapping condition in the three-dimensional space to mimic an aggregated blood sample. BSCs were computed between 750 KHz and 200 MHz for samples of various cluster sizes at different hematocrits. Magnitudes of BSCs increased with mean aggregate sizes at low frequencies (<20 MHz). The accuracy of the structure-factor-size-estimator (SFSE) method in determining mean aggregate size and packing factor was also examined. A good correlation (R(2) ≥ 0.94) between the mean size of aggregates predicted by the SFSE and true size was found for each hematocrit. This study shows that for spherical aggregates there exists a region for each hematocrit where SFSE works most accurately. Typically, error of SFSE in estimating mean cluster size was <20% for dimensions between 14 and 17 μm at 40% hematocrit. This study suggests that the theoretical framework of SFSE is valid under the assumption of isotropic aggregates.

Tannic acid cross-linked gelatin–gum arabic coacervate microspheres for sustained release of allyl isothiocyanate: Characterization and in vitro release study

Tannic acid cross-linked gelatin–gum arabic coacervate microspheres, capable of sustained release of allyl isothiocyanate (AITC) with high encapsulation efficiency, were developed for safe and efficient oral delivery of AITC. The microspheres were spherical in shape and clustered. Statistical screening and optimization studies revealed that a maximum AITC encapsulation efficiency could be obtained when the microspheres were prepared with 4.5% total biopolymer, 6.5% oil, and 5.9% AITC in oil phase. Release studies showed that the sustained release performance of the optimized microspheres was greatly enhanced by using more tannic acid without loss in the encapsulation efficiency. The microspheres optimized with 1.5% tannic acid, having an encapsulation efficiency of 83.75% and a mean cluster size of 116.80 μm, released 46% of encapsulated AITC after 2 h in pepsin-containing simulated gastric fluid (pH 1.2), followed by releasing additional 48% in 6 h after being transferred to pancreatin-containing simulated intestinal fluid (pH 7.5).

Connectivity percolation of polydisperse anisotropic nanofillers

We present a generalized connectedness percolation theory reduced to a compact form for a large class of anisotropic particle mixtures with variable degrees of connectivity. Even though allowing for an infinite number of components, we derive a compact yet exact expression for the mean cluster size of connected particles. We apply our theory to rodlike particles taken as a model for carbon nanotubes and find that the percolation threshold is sensitive to polydispersity in length, diameter, and the level of connectivity, which may explain large variations in the experimental values for the electrical percolation threshold in carbon-nanotube composites. The calculated connectedness percolation threshold depends only on a few moments of the full distribution function. If the distribution function factorizes, then the percolation threshold is raised by the presence of thicker rods, whereas it is lowered by any length polydispersity relative to the one with the same average length and diameter. We show that for a given average length, a length distribution that is strongly skewed to shorter lengths produces the lowest threshold relative to the equivalent monodisperse one. However, if the lengths and diameters of the particles are linearly correlated, polydispersity raises the percolation threshold and more so for a more skewed distribution toward smaller lengths. The effect of connectivity polydispersity is studied by considering nonadditive mixtures of conductive and insulating particles, and we present tentative predictions for the percolation threshold of graphene sheets modeled as perfectly rigid, disklike particles.

Optimal Control Architecture Selection for Thermal Control of Buildings

AbstractThe problem of partitioning a building into clusters is considered in this paper, with reference to its decentralized thermal control. Optimal control schemes for these systems are often centralized and address both the thermal comfort and energy efficiency requirements. However, due to robustness considerations, a decentralized architecture may be preferred for large scale systems, which is at best sub-optimal. Therefore, the ‘degree of decentralization’ governs the tradeoff between optimality and robustness. This paper proposes a combinatorial optimization based systematic methodology for obtaining an optimal degree of decentralization on the basis of two metrics – one for optimality (defined as Coupling Loss Factor) and one for robustness (defined as Mean Cluster Size). The methodology was evaluated on a detailed building case study to obtain the decentralized control architectures for different values of wall insulation parameters. The results are found to be in agreement with the physics of the underlying thermal interactions.

Qualitative Analysis of Semantic Clustering in Early and Mid Adolescence

Background: Semantic fluency tasks are used in evaluating word retrieval in children. In addition to examining overall word output, semantic clustering is used to assess the strategic retrieval process involved during searching and retrieving exemplars from specified category. Limited research on analysis of word retrieval strategies in adolescents exists with respect to Indian context. Therefore, present study is an attempt to conduct qualitative analysis of semantic clustering in early and mid adolescence. Method: 30 early and mid adolescent children aged 12 – 15 years were assessed on semantic fluency with participants instructed to generate as many words as possible belonging to specific semantic categories (animal, food & vehicle) in one minute for each category. Offline analysis of responses was done on total word output, semantic clusters and mean cluster size. Mean & Standard deviation were obtained for the measures for each semantic category. Results: Total word output produced by adolescents for the animal, food and vehicle fluency tasks were 13.13, 12.4 & 10.2 respectively. Detailed qualitative analysis on clustering revealed specific & common rules of organization pattern in terms of clustering the word output under semantic sub categories for each task. The average number of clusters and mean cluster size produced by adolescent children were approximately 3.47 & 2.12 respectively. Conclusion: The present study revealed specific clustering pattern on specific semantic categories which does not reach adult like pattern of word retrieval. Routine evaluation of semantic clustering can provide additional insight into word retrieval strategies in adolescents with developmental neurological conditions.

Relative efficiency and sample size for cluster randomized trials with variable cluster sizes

The statistical power of cluster randomized trials depends on two sample size components, the number of clusters per group and the numbers of individuals within clusters (cluster size). Variable cluster sizes are common and this variation alone may have significant impact on study power. Previous approaches have taken this into account by either adjusting total sample size using a designated design effect or adjusting the number of clusters according to an assessment of the relative efficiency of unequal versus equal cluster sizes. This article defines a relative efficiency of unequal versus equal cluster sizes using noncentrality parameters, investigates properties of this measure, and proposes an approach for adjusting the required sample size accordingly. We focus on comparing two groups with normally distributed outcomes using t-test, and use the noncentrality parameter to define the relative efficiency of unequal versus equal cluster sizes and show that statistical power depends only on this parameter for a given number of clusters. We calculate the sample size required for an unequal cluster sizes trial to have the same power as one with equal cluster sizes. Relative efficiency based on the noncentrality parameter is straightforward to calculate and easy to interpret. It connects the required mean cluster size directly to the required sample size with equal cluster sizes. Consequently, our approach first determines the sample size requirements with equal cluster sizes for a pre-specified study power and then calculates the required mean cluster size while keeping the number of clusters unchanged. Our approach allows adjustment in mean cluster size alone or simultaneous adjustment in mean cluster size and number of clusters, and is a flexible alternative to and a useful complement to existing methods. Comparison indicated that we have defined a relative efficiency that is greater than the relative efficiency in the literature under some conditions. Our measure of relative efficiency might be less than the measure in the literature under some conditions, underestimating the relative efficiency. The relative efficiency of unequal versus equal cluster sizes defined using the noncentrality parameter suggests a sample size approach that is a flexible alternative and a useful complement to existing methods.

Which verbal fluency measure is most useful in demonstrating executive deficits after traumatic brain injury?

This paper examines switching and clustering in phonemic and semantic fluency tasks in individuals with traumatic brain injury (TBI). Fluency tasks were administered to 30 Hebrew-speaking patients with TBI and 30 age-matched control participants. Significant group differences were found in total output, number of switches, and number of clusters on both tasks, but not in mean cluster size. Unlike prediction, z scores of the number of semantic switches and clusters were lower than the equivalent z scores on the phonemic test. Results highlight the executive component of semantic fluency and the importance of using this task when assessing cognitive functioning after TBI.

Observation of electronic energy bands in argon clusters

The $3p$ valence region of argon clusters has been investigated with photoemission near the photoionization threshold. A strong feature between 14.6 and 15.3 eV binding energy shows a photon-energy dependence indicative of electronic-energy band dispersion. A similar feature at approximately the same binding energy and with a similar dispersion occurs in photoemission spectra of both the ordered and disordered solids. The effect is already fully developed for scaling-law mean cluster sizes $⟨N⟩$ of approximately 200 atoms, thus showing an early onset of bulklike electronic properties.

Nucleation theory models for describing kinetics of cluster growth in C60/NMP solutions

AbstractSlow growth of C60 fullerene clusters (size up to 500 nm after about one month) in polar N‐methyl‐2‐pyrrolidone (NMP) solutions is considered from the viewpoint of the nucleation theory. It is shown that the limited growth model used previously for qualitative description of C60 clusters in solutions with low polarity is inapplicable in this case. Two simple modifications of the general approach are proposed taking into account possible limitations of cluster growth in the given class of solutions. The time evolution of the main parameters of cluster state (mean cluster size and free monomer concentration) is compared with respect to the better consistency with available experimental data for C60/NMP.

Energy band dispersion in photoemission spectra of argon clusters

Using photoemission we have investigated free argon clusters from a supersonic nozzle expansion in the photon energy range from threshold up to 28 eV. Measurements were performed both at high resolution with a hemispherical electrostatic energy analyser and at lower resolution with a magnetic bottle device. The latter experiments were performed for various mean cluster sizes. In addition to the ≈1.5 eV broad 3p-derived valence band seen in previous work, there is a sharper feature at ≈15 eV binding energy. Surprisingly for non-oriented clusters, this peak shifts smoothly in binding energy over the narrow photon energy range 15.5–17.7 eV, indicating energy band dispersion. The onset of this bulk band-like behaviour could be determined from the cluster size dependence.

Cluster–cluster aggregation with particle replication and chemotaxy: a simple model for thegrowth of animal cells in culture

Aggregation of animal cells in culture comprises a series of motility, collision and adhesionprocesses of basic relevance for tissue engineering, bioseparations, oncology researchand in vitro drug testing. In the present paper, a cluster–cluster aggregationmodel with stochastic particle replication and chemotactically driven motility isinvestigated as a model for the growth of animal cells in culture. The focus ison the scaling laws governing the aggregation kinetics. Our simulations revealthat in the absence of chemotaxy the mean cluster size and the total number ofclusters scale in time as stretched exponentials dependent on the particle replicationrate. Also, the dynamical cluster size distribution functions are represented by ascaling relation in which the scaling function involves a stretched exponentialof the time. The introduction of chemoattraction among the particles leads todistribution functions decaying as power laws with exponents that decrease in time. Thefractal dimensions and size distributions of the simulated clusters are qualitativelydiscussed in terms of those determined experimentally for several normal and tumoralcell lines growing in culture. It is shown that particle replication and chemotaxyaccount for the simplest cluster size distributions of cellular aggregates observed inculture.

Understanding on the residue contact network using the log‐normal cluster model and the multilevel wheel diagram

Residue clusters play essential role in stabilizing protein structures in the form of complex networks. We show that the cluster sizes in a native protein follow the log-normal distribution for a dataset consisting of 424 proteins. To our knowledge, this is the first time of such fitting for the native structures. Based on log-normal model, the asymptotically increasing mean cluster sizes produce a critical protein chain length of about 200 amino acids, beyond which length most globular proteins have nearly the same mean cluster sizes. This suggests that the larger proteins use a different packing mechanism than the smaller proteins. We confirmed the scale-free property of the residue contact network for most of the protein structures in the dataset, although the violations were observed for the tightly packed proteins. Residue cluster network wheel (RCNW) is proposed to visualize the relationship between the multiple properties of the residue network such as the cluster size, the residue types and contacts, and the flexibility of the residue. We noticed that the residues with large cluster size have smaller Calpha displacement measured using the normal mode analysis.

Mercaptosilane-Assisted Synthesis of Metal Clusters within Zeolites and Catalytic Consequences of Encapsulation

We report here a general synthetic strategy to encapsulate metal clusters within zeolites during their hydrothermal crystallization. Precursors to metal clusters are stabilized against their premature colloidal precipitation as hydroxides during zeolite crystallization using bifunctional (3-mercaptopropyl)trimethoxysilane ligands. Mercapto (-SH) groups in these ligands interact with cationic metal centers, while alkoxysilane moieties form covalent Si-O-Si or Si-O-Al linkages that promote zeolite nucleation around ligated metal precursors. These protocols led to the successful encapsulation of Pt, Pd, Ir, Rh, and Ag clusters within the NaA zeolite, for which small channel apertures (0.41 nm) preclude postsynthesis deposition of metal clusters. Sequential treatments in O(2) and H(2) formed small (approximately 1 nm) clusters with uniform diameter. Titration of exposed atoms with H(2) or O(2) gave metal dispersions that agree well with mean cluster sizes measured from electron microscopy and X-ray absorption spectroscopy, consistent with accessible cluster surfaces free of mercaptosilane residues. NaA micropore apertures restrict access to encapsulated clusters by reactants based on their molecular size. The ratio of the rates of hydrogenation of ethene and isobutene is much higher on clusters encapsulated within NaA than those dispersed on SiO(2), as also found for the relative rates of methanol and isobutanol oxidation. These data confirm the high encapsulation selectivity achieved by these synthetic protocols and the ability of NaA micropores to sieve reactants based on molecular size. Containment within small micropores also protects clusters against thermal sintering and prevents poisoning of active sites by organosulfur species, thus allowing alkene hydrogenation to persist even in the presence of thiophene. The bifunctional nature and remarkable specificity of the mercapto and alkoxysilane functions for metal and zeolite precursors, respectively, render these protocols extendable to diverse metal-zeolite systems useful as shape-selective catalysts in demanding chemical environments.

Modeling of colloid agglomeration inhibition inside a slitlike pore

An extended particle agglomeration control model and Monte Carlo simulation methodology were used to describe the behavior of the colloidal aggregation process in presence of inhibitor as a confined fluid. In this work results about the mean cluster size, Z, with respect to different variables, temperature, inhibitor concentration and pore size, are presented and showed that Z strongly depends on the slitlike pore size. In addition, a temperature interval where the heating of the system leads to the particle clustering was found.

Developmental Changes in Semantic Verbal Fluency: Analyses of Word Productivity as a Function of Time, Clustering, and Switching

We investigated age-related improvement in semantic category verbal fluency (VF) in 309 Dutch schoolchildren attending first to ninth grade. Quantitative analyses of number of correct responses as a function of time as well as qualitative analyses of clustering and switching were conducted. Overall, Dutch VF task performance, i.e., number of correct responses over 60 seconds, was not established before mid-adolescence. This is in line with previously published studies, using VF number of correct responses over 60 seconds as the main outcome measure and examining VF task performance across other cultures and languages (e.g., Italian, French, Hebrew). Next, mean cluster size, a measure of lexico-semantic knowledge, was not established until at least grade 3. In contrast, performance on the VF outcome measures “number of switches/clusters” was established at least 4 years later. Qualitative and quantitative Design Fluency (DF) outcome measures support the notion that the numbers of switches/clusters are valid measures of higher order cognitive functions, such as strategy use and cognitive flexibility. In line of this, VF number of correct responses during 16–60 seconds, a measure of controlled information processing, is established at least 2 years later (i.e., grades 7–8) than number of correct responses during the first 15 seconds time slide, a measure of automatic processing. Finally, environment, i.e., the level of parental education, primarily affected automatic and lexico-semantic knowledge. No effects of sex on VF performance were found. These data suggest that the alternative scoring methods of VF tasks can be used to acquire knowledge on development of lower and higher order cognitive functions in healthy children and the influence of the environment on it.

Model misspecification in peaks over threshold analysis

Classical peaks over threshold analysis is widely used for statistical modeling of sample extremes, and can be supplemented by a model for the sizes of clusters of exceedances. Under mild conditions a compound Poisson process model allows the estimation of the marginal distribution of threshold exceedances and of the mean cluster size, but requires the choice of a threshold and of a run parameter, $K$, that determines how exceedances are declustered. We extend a class of estimators of the reciprocal mean cluster size, known as the extremal index, establish consistency and asymptotic normality, and use the compound Poisson process to derive misspecification tests of model validity and of the choice of run parameter and threshold. Simulated examples and real data on temperatures and rainfall illustrate the ideas, both for estimating the extremal index in nonstandard situations and for assessing the validity of extremal models.

Structural properties of the synchronized cluster on complex networks

We investigate how the largest synchronized connected component (LSCC) is formed and evolves to achieve a global synchronization on complex networks using Kuramoto model. In this study we use two different networks, Erdösi-Rényi network and Barabási-Albert network. From the finite-size scaling analysis, we find that the scaling exponents for the percolation order parameter and mean cluster size on both networks agree with the mean-field percolation theory, beta=gamma=1. We also find that the finite-size scaling exponent, nu, also agrees with the mean-field percolation result, nu=3. Moreover, we also show that the cluster size distributions are identical with the mean-field percolation distribution on both networks. Combining with the analysis for the merging clusters, we directly show that the LSCC on both networks evolves by merging clusters of various sizes.

Susceptibility of random graphs with given vertex degrees

We study the susceptibility, i.e., the mean cluster size, in random graphs with given vertex degrees. We show, under weak as- sumptions, that the susceptibility converges to the expected cluster size in the corresponding branching process. In the supercritical case, a cor- responding result holds for the modied susceptibility ignoring the giant component and the expected size of a nite cluster in the branching pro- cess; this is proved using a duality theorem. The critical behaviour is studied. Examples are given where the critical exponents dier on the subcritical and supercritical sides.

Determining cluster size through Rayleigh scattering and interferometry of argon clusters formed in a planar expansion

Rayleigh scattering and interferometry are used to determine the mean cluster size of argon clusters formed in a planar supersonic expansion. An axisymmetric expansion is examined for comparison. The results indicate that a planar expansion produces mean cluster sizes that are larger than those formed in an axisymmetric expansion at equivalent stagnation pressures. The mean cluster size of clusters formed in a planar expansion depends more strongly on stagnation pressure than does the axisymmetric expansion.

Mesoscale Convective Systems and Critical Clusters

AbstractSize distributions and other geometric properties of mesoscale convective systems (MCSs), identified as clusters of adjacent pixels exceeding a precipitation threshold in satellite radar images, are examined with respect to a recently identified critical range of water vapor. Satellite microwave estimates of column water vapor and precipitation show that the onset of convection and precipitation in the tropics can be described as a phase transition, where the rain rate and likelihood of rainfall suddenly increase as a function of water vapor. This is confirmed in Tropical Rainfall Measuring Mission radar data used here. Percolation theory suggests that cluster properties should be highly sensitive to changes in the density of occupied pixels, which here translates into a rainfall probability, which in turn sensitively depends on the water vapor. To confirm this, clusters are categorized by their prevalent water vapor. As expected, mean cluster size and radius of gyration strongly increase as the critical water vapor is approached from below. In the critical region one finds scale-free size distributions spanning several orders of magnitude. Large clusters are typically from the critical region: at low water vapor most clusters are small, and supercritical water vapor values are too rare to contribute much. The perimeter of the clusters confirms previous observations in satellite, field, and model data of robust nontrivial scaling. The well-known area–perimeter scaling is fully compatible with the quantitative prediction from the plausible null model of gradient percolation, where the accessible hull is a fractal object with dimension 4/3.