Mean Cluster Size Research Articles

Digoxin for reduction of circulating tumor cell cluster size in metastatic breast cancer: a proof-of-concept trial.

The presence of circulating tumor cell (CTC) clusters is associated with disease progression and reduced survival in a variety of cancer types. In breast cancer, preclinical studies showed that inhibitors of the Na+/K+ ATPase suppress CTC clusters and block metastasis. Here we conducted a prospective, open-label, proof-of-concept study in women with metastatic breast cancer, where the primary objective was to determine whether treatment with the Na+/K+ ATPase inhibitor digoxin could reduce mean CTC cluster size. An analysis of nine patients treated daily with a maintenance digoxin dose (0.7-1.4 ng ml-1 serum level) revealed a mean cluster size reduction of -2.2 cells per cluster upon treatment (P = 0.003), meeting the primary endpoint of the study. Mechanistically, transcriptome profiling of CTCs highlighted downregulation of cell-cell adhesion and cell-cycle-related genes upon treatment with digoxin, in line with its cluster-dissolution activity. No treatment-related adverse events occurred. Thus, our data provide a first-in-human proof of principle that digoxin treatment leads to a partial CTC cluster dissolution, encouraging larger follow-up studies with refined Na+/K+ ATPase inhibitors and that include clinical outcome endpoints. ClinicalTrials.gov identifier: NCT03928210 .

Associations between deep category fluency phenotyping and early tau aggregation in the medial temporal lobe

AbstractBackgroundSemantic processing relies on temporal brain regions, including medial temporal lobe (MTL) structures, that are the first to be affected by tau pathology in Alzheimer’s disease (AD). A widely used task to assess semantic memory is the category fluency. Performance on this task was demonstrated to be impaired since the prodromal stage of AD and associated to the structural integrity of the MTL. However, the associations between category fluency measures and MTL tau burden have been rarely explored at the early stages of the disease.MethodSeventy‐five participants underwent [18F]MK6240 tau‐PET, magnetic resonance imaging and cognitive assessment including category fluency (animals, 2 minutes). Amyloid‐b (Ab) status was determined with lumbar punction or [18F]Flutemetamol Aβ‐PET (Ab+ for cerebrospinal fluid Ab level<437pg/ml or Centiloid≥20). Participants included 33 Ab‐ cognitively normal (CN), 15 Ab+ CN and 27 Ab+ MCI individuals (Table 1). In addition to the category fluency total score, the mean cluster size (cluster = group of words that are sequentially produced and all contained within a subcategory such as birds), the number of subcategories evoked (aggregating semantically related clusters), the mean size of subcategories and the number of switches between clusters were calculated. Associations between these metrics and MTL tau burden were assessed using Spearman‐rank coefficients and generalized linear models adjusting for age, sex and education.ResultOver the entire sample, associations were found between the MTL tau burden and the total score (rs = ‐0.44, p<.001, Figure 1), the mean cluster size (rs = ‐0.29, p = .047), and the mean size of subcategories (rs = ‐0.40, p = .002), even when controlling for age, sex and education (b = ‐5.06, SE = 1.62, p = .003; b = ‐0.33, SE = 0.16, p = .039; b = ‐0.46, SE = 0.15, p = .003, respectively). The number of switches (rs = ‐0.13, p = 1.0) and the number of subcategories (rs = ‐0.13, p = 1.0) were not associated to the MTL tau burden.ConclusionMTL tau burden was equivalently associated to the category fluency total score and two metrics relying more purely on semantic memory (mean size of clusters and subcategories). Given its critical role in conceptual knowledge and its involvement in the earliest stage of tauopathy, future work will analyze the associations between tau burden in the (peri)rhinal cortex and the category fluency metrics.

Estimating an adjusted risk difference in a cluster randomized trial with individual-level analyses.

In cluster randomized trials (CRTs) with a binary outcome, intervention effects are usually reported as odds ratios, but the CONSORT statement advocates reporting both a relative and an absolute intervention effect. With a simulation study, we assessed several methods to estimate a risk difference (RD) in the framework of a CRT with adjustment on both individual- and cluster-level covariates. We considered both a conditional approach (with the generalized linear mixed model [GLMM]) and a marginal approach (with the generalized estimating equation [GEE]). For both approaches, we considered the Gaussian, binomial, and Poisson distributions. When considering the binomial or Poisson distribution, we used the g-computation method to estimate the RD. Convergence problems were observed with the GEE approach, especially with low intra-cluster coefficient correlation values, small number of clusters, small mean cluster size, high number of covariates, and prevalences close to 0. All methods reported no bias. The Gaussian distribution with both approaches and binomial and Poisson distributions with the GEE approach had satisfactory results in estimating the standard error. Results for type I error and coverage rates were better with the GEE than GLMM approach. We recommend using the Gaussian distribution because of its ease of use (the RD is estimated in one step only). The GEE approach should be preferred and replaced with the GLMM approach in cases of convergence problems.

New Approaches to Extremal Index Estimation

The extremal index is a parameter associated with the extreme value distributions of dependent stationary sequences. Under certain local dependence conditions, exceedances above a specified threshold tend to occur in isolated clusters. The reciprocal of the extremal index can be interpreted as the limiting size of these clusters. Accurately estimating the size of such clusters is crucial for analyzing real data and can significantly influence decision making processes that impact population well being. The paper presents a recent method for the estimation of the extremal index which starts by the estimation of the parameter itself and, only then, to use that estimate in the cluster mean size estimation. The procedure starts with the estimation of a specific proportion by the corresponding relative frequency. Thus, it is very simple, intuitive, it has good statistical properties, and it does not depend on the method used for the mean cluster estimation. The interpretation of the extremal index as a proportion is known, but it has not been used directly as an estimation method. In recent years, various authors have proposed different estimators for the extremal index. This paper applies some of the latest estimation methods for the extremal index to real data and analyses their performance using training and test samples. The results are compared with other well known estimators, for which R packages are available. The results show a better performance of the Proportion estimator, followed by the Gaps estimator, when compared to the other considered index estimators.

Characteristics of Clustering and Switching in Verbal Fluency in Mild Cognitive Impairment and Dementia of Alzheimer’s Type

Objectives: The purpose of this study was to compare the performance on a verbal fluency task, clustering and switching characteristics, and proportion by error type between healthy elderly, Mild Cognitive Impairment (MCI) and Dementia of Alzheimer’s Type (DAT) group. Methods: Thirty healthy elderly, 30 MCI and 29 DAT individuals were asked to produce words in the category of ‘supermarket items’ for semantic fluency and ‘ㄱ’, ‘ㅇ’, and ‘ㅅ’ Korean letter categories for phonemic fluency with one minute allotted per category. Results: First, the number of correct responses in the verbal fluency task was significantly different between groups, with post hoc analyses showing significant differences between the healthy elderly and DAT groups and between the MCI and DAT groups. Second, the mean cluster size was not significant between groups in the semantic fluency task. However, it was significant between the healthy elderly and DAT groups, and between MCI and DAT groups in the phonemic fluency task. Third, the number of switches was significant between the healthy elderly and DAT elderly. Finally, the three groups had the highest proportion of perseverative errors in the semantic fluency task and the highest proportion of other errors in the phonemic fluency task. Conclusion: This study has clinical significance in that it examined the number of correct responses and characteristics of clustering and switching on verbal fluency tasks in the healthy elderly, MCI and DAT groups.

Exact analysis of generalized degree-based percolation without memory

We study the problem of generalized degree-based percolation without memory, where the probability of node removal depends on a non-negative function of node degree within the remaining network. We derive a set of nonlinear ordinary differential equations describing the evolution of the degree distribution during the percolation process. Employing generating function methods, we calculate various quantities of interest such as the probability of a randomly selected node belonging to the giant component, the mean cluster size, and the critical point at which a network transitions from connected to fragmented. Validation of our approach is achieved through extensive Monte Carlo simulations and numerical solutions. Our results indicate that removing highly connected nodes with small preference probabilities significantly lowers the critical point compared to random removal. Moreover, our analytical framework is applicable to random networks generated by the configuration model with any bounded degree distribution. It provides a comprehensive and systematic approach to analyze network robustness against various degree-based attack strategies, offering valuable insights into network design and protection.

Invariance properties of limiting point processes and applications to clusters of extremes

Abstract Motivated by examples from extreme value theory, but without using the theory of regularly varying time series or any assumptions about the marginal distribution, we introduce the general notion of a cluster process as a limiting point process of returns of a certain event in a time series. We explore general invariance properties of cluster processes that are implied by stationarity of the underlying time series. Of particular interest in applications are the cluster size distributions, and we derive general properties and interconnections between the size of an inspected and a typical cluster. While the extremal index commonly used in extreme value theory is often interpreted as the inverse of a “mean cluster size”, we point out that this only holds true for the expected value of the typical cluster size, caused by an effect very similar to the inspection paradox in renewal theory.

Norms, convergent validity, test–retest reliability, and practice effects for verbal fluency overall performance, clustering, and switching in Spanish-speaking children

Objective We conducted two empirical studies (in a cross-sectional and a longitudinal design) with the aim at establishing normative data (including norms for strategy use [i.e., clustering and switching strategies] and performance over time), and examining the convergent validity, the test–retest reliability (3–4 wks interval) and the changes in performance with practice (1 year interval) of the different verbal fluency (VF) quantitative and qualitative scores in Spanish-speaking children and adolescents. Method In S1 (n = 620 6- to 15-year-old Spanish-speaking children and adolescents), MANCOVA and Pearson’s correlations were employed. In S2 (n = 148 6- to 12-year-old Spanish-speaking children), intraclass correlation coefficient (ICC), paired t-tests, and Confirmatory Factor Analysis (CFA) were used. Results S1 results showed an age effect on all VF measures (quantitative and qualitative). The number of switches/clusters was more related to total word productivity and to executive functions (EF) than the mean cluster size. In S2, a significant increase in phonological VF performance was observed on number of switches and word productivity scores from baseline (Time 1) to repeat testing at Time 2. Practice effects were observed at Time 3 on all measures except for semantic and phonological mean cluster size. Test–retest reliability coefficients at Time 2 for number of clusters and switches, but not for mean cluster size, fell in the moderate range, ranging from ICCs .61 to ICCs .81. Test–retest reliability coefficients for total word productivity were higher (ICCs above .80) and stronger when testing as a unity with CFA methods (ϕ=.94, p < .001). Conclusions These data may be relevant for informing the neuropsychological assessment of spontaneous cognitive flexibility in children with typical development (TD) and those with developmental or acquired disorders.

Quasi-two-dimensional dispersions of Brownian particles with competitive interactions: phase behavior and structural properties.

Competing short-range attractive (SA) and long range repulsive (LR) particle interactions can be used to describe three-dimensional charge-stabilized colloid or protein dispersions at low added salt concentrations, as well as membrane proteins with interaction contributions mediated by lipid molecules. Using Langevin dynamics (LD) simulations, we determine the generalized phase diagram, cluster shapes and size distributions of a generic quasi-two-dimensional (Q2D) dispersion of spherical SALR particles confined to in-plane motion inside a bulk fluid. The SA and LR interaction parts are modelled by a generalized Lennard-Jones potential and a screened Coulomb potential, respectively. The microstructures of the detected equilibrium and non-equilibrium Q2D phases are distinctly different from those observed in three-dimensional (3D) SALR systems, by exhibiting different levels of hexagonal ordering. We discuss a thermodynamic perturbation theory prediction for the metastable binodal line of a reference system of particles with SA interactions only, which in the explored Q2D-SALR phase diagram region separates cluster from non-clustered phases. The transition from the high-temperature (small SA) dispersed fluid (DF) phase to the lower-temperature equilibrium cluster (EC) fluid phase is characterised by a low-wavenumber peak height of the static structure factor (corresponding to a thermal correlation length of about twice the particle diameter) featuring a distinctly smaller value (≈1.4) than in 3D SALR systems. With decreasing temperature (increasing SA), the cluster morphology changes from disk-like shapes in the equilibrium cluster phase, to double-stranded anisotropic hexagonal cluster segments formed in a cluster-percolated (CP) gel-like phase. This transition can be quantified by a hexagonal order parameter distribution function. The mean cluster size and coordination number of particles in the CP phase are insensitive to changes in the attraction strength.

A molecular beam study of CO oxidation on Pd clusters supported on alumina: the effect of cluster size.

The activity in CO oxidation of regular arrays of Pd clusters, in the size range of 5-180 atoms, supported on alumina has been studied by using a molecular beam method. The Pd clusters are grown on a nanostructured ultrathin alumina film on Ni3Al(111) providing a hexagonal array of clusters with a narrow size distribution. The steady state turnover frequency (TOF) is measured as a function of the mean cluster size. On average the TOF increases with size. Below about 20 atoms, the TOF increases rapidly and for larger clusters it grows slowly and reaches a value close to those obtained on bulk single crystals at 180 atoms. The size effect is explained by the smaller activity of Pd atoms in contact with the alumina support.

Comparison of verbal fluency performance in Kannada-speaking adults with and without euthymic bipolar disorder type 1

Individuals with euthymic bipolar disorder (BD) type I exhibit deficits in executive functions. Although less explored in the BD population, the tasks of verbal fluency (VF) have shown great potential in understanding semantic organization. This study provides an extensive exploration across the letter and semantic VF tasks in 27 demographically matched euthymic BD-I and healthy controls (HC). The groups were compared on measures of the total number of correct words (TNCW), temporal pattern analysis, number of clusters (NC), mean cluster size (MCS), number of switches (NS), and error pattern. An overall reduction in letter fluency scores (the TNCW, number of switches, and NC) as compared to semantic fluency scores was noted for both groups, with a significantly greater decrease in the BD-1 group. The MCS and temporal pattern were relatively similar across the two groups. The influence of education with no gender difference was observed between groups with error types prevalent in both groups. The study findings call attention toward assessing the VF performance in persons with BD in terms of error production and the strategies employed (clustering–switching).

Altered cerebrovascular reactivity along functional networks in older adults with long COVID

AbstractBackgroundCerebrovascular reactivity (CVR), an indicator of neurovascular function associated with cognitive decline, relies on vascular and inflammatory processes, making it a potential mechanism of interest driving neurological changes in long COVID among older adults. Given the variability in symptoms associated with long COVID, distribution corrected z‐scores (DisCo‐Z), a subject‐specific abnormalities (SSA) approach more suited for heterogenous conditions, was employed to examine CVR and long COVID in older adults. Relationships between CVR, post‐COVID subjective cognitive decline (pcSCD), and cognitive function were examined.Methods15 older adults with long COVID (M age = 63.9, 6 males) and 24 healthy older adults (M age = 66.7, 6 males) performed a breath‐holding task while in the MR scanner to examine CVR. DisCo‐Z was used to examine the presence and size of extreme clusters of increased or decreased CVR (&gt;100 voxels) within the 7 Yeo functional networks. Non‐parametric tests were used to examine group differences in presence and mean size of extreme clusters. Finally, relationships between: 1) extent of pcSCD and extreme cluster values in long COVID, and 2) cognitive testing scores and global “burden” (cluster size mean and sum) were examined.ResultsGroups did not differ significantly on gender (p = .323) or age (p = .324). Greater incidence of positive extreme clusters within Ventral Attention (p = .028) and Limbic (p = .049) networks were observed in long COVID (with minimal incidences of negative extreme clusters across networks). Group differences were observed for mean cluster size in the Ventral Attention network (p = .016), as well. Extent of pcSCD was positively correlated with DisCo‐Z values for the Ventral Attention network (p = .021) with a trending level of significance for the Limbic network (p = 0.053). Finally, within the full sample, global CVR burden was negatively correlated with memory test scores (p = 0.014).ConclusionsUsing the SSA approach, group differences in CVR were observed in older adults experiencing long COVID. In particular, differences were observed within functional networks thought to drive attention, executive function, and emotional control, which was correlated with pcSCD. Finally, global CVR burden was negatively correlated with memory. These findings, though preliminary, suggest CVR may represent a potential neurobiological mechanism driving pcSCD in older adults.

Altered cerebrovascular reactivity along functional networks in older adults with long COVID

AbstractBackgroundCerebrovascular reactivity (CVR), an indicator of neurovascular function associated with cognitive decline, relies on vascular and inflammatory processes, making it a potential mechanism of interest driving neurological changes in long COVID among older adults. Given the variability in symptoms associated with long COVID, distribution corrected z‐scores (DisCo‐Z), a subject‐specific abnormalities (SSA) approach more suited for heterogenous conditions, was employed to examine CVR and long COVID in older adults. Relationships between CVR, post‐COVID subjective cognitive decline (pcSCD), and cognitive function were examined.Method15 older adults with long COVID (M age = 63.9, 6 males) and 24 healthy older adults (M age = 66.7, 6 males) performed a breath‐holding task while in the MR scanner to examine CVR. DisCo‐Z was used to examine the presence and size of extreme clusters of increased or decreased CVR (&gt;100 voxels) within the 7 Yeo functional networks. Non‐parametric tests were used to examine group differences in presence and mean size of extreme clusters. Finally, relationships between: 1) extent of pcSCD and extreme cluster values in long COVID, and 2) cognitive testing scores and global “burden” (cluster size mean and sum) were examined.ResultGroups did not differ significantly on gender (p = .323) or age (p = .324). Greater incidence of positive extreme clusters within Ventral Attention (p = .028) and Limbic (p = .049) networks were observed in long COVID (with minimal incidences of negative extreme clusters across networks). Group differences were observed for mean cluster size in the Ventral Attention network (p = .016), as well. Extent of pcSCD was positively correlated with DisCo‐Z values for the Ventral Attention network (p = .021) with a trending level of significance for the Limbic network (p = 0.053). Finally, within the full sample, global CVR burden was negatively correlated with memory test scores (p = 0.014).ConclusionUsing the SSA approach, group differences in CVR were observed in older adults experiencing long COVID. In particular, differences were observed within functional networks thought to drive attention, executive function, and emotional control, which was correlated with pcSCD. Finally, global CVR burden was negatively correlated with memory. These findings, though preliminary, suggest CVR may represent a potential neurobiological mechanism driving pcSCD in older adults.

Clustering and Switching in Semantic Verbal Fluency: Their Development and Relationship with Word Productivity in Typically Developing Greek-Speaking Children and Adolescents.

Performance in semantic verbal fluency (SVF) tasks, mainly measured by the number of words of a particular semantic category produced within a limited time, is a widely accepted measure of cognitive functioning used in the neuropsychological assessment of children and adults. Two strategic processes, Clustering and Switching (C&S) have been proposed to underlie fluency processes and affect performance in the task. However, few studies have reported on the development of those cognitive strategies and their relationship with word productivity in typically developing children. Even fewer studies have covered a broad developmental period from preschool to adolescence or measured the effect of contextual factors in this relationship. Based on a sample of 472 typically developing Greek-speaking children aged 4;0 to 16;11 years, we investigated the development of SVF performance and reported on the degree to which it is affected by C&S strategies, children's sex, and level of parental education. Results revealed a large effect of age on word productivity and on the use of C&S strategies. Two switching factors (number of clusters and number of switches) and two clustering factors (mean cluster size and a novel measure, maximum cluster size), appeared to be significantly associated with word productivity, with the largest effect being attributed to the two switching factors. C&S factors, together with children's age and parental education, predicted 91.7% of the variance in the SVF score. Children's sex was not found to have a significant effect on either word productivity or C&S strategies. Results are discussed for their theoretical implications on the strategic processes underlying word production in typically developing children.

Inhomogeneous percolation on the Bethe lattice with critical exponents and its application

This manuscript explores the critical exponents for three-dimensional irregular Bethe lattice (TDIBL) and their closer association with real-life applications. In the current investigation, we evaluate the CEs for TDIBL using several percolating variables, including the cluster size distribution (CSD), percolating probability (PP), mean cluster size (MCS), characteristic cluster size (CCS), and characteristic generation size (CGS). The CEs for TDIBL findings illustrate that the percolation model accomplishes enormous universal classes and is connected with a complicated fractal and resizing structure of underlying geometric characteristics, which will contribute to the system’s mean degree in the percolating method. Additionally, sensitivity analysis and numerical simulation will further enhance our appraisal of the percolating procedure graphically. Furthermore, we address the novel coronavirus 2019 (COVID-19) transmission behavior in the database using our methodology. Utilizing this data type to develop predictions by conveying policy-using courtesy groups with varying infection and recovery probabilities is also feasible. We acknowledge that our revolutionary endeavor will be intriguing, and we will inquire about scientific researchers collaborating with various percolation methods of investigation.

Phonological and semantic verbal fluency test: Scoring criteria and normative data for clustering and switching strategies for Colombian children and adolescents.

Verbal fluency tests (VFT) are highly sensitive to cognitive deficits. Usually, the score on VFT is based on the number of correct words produced, yet it alone gives little information regarding underlying test performance. The implementation of different strategies (cluster and switching) to perform efficiently during the tasks provide more valuable information. However, normative data for clustering and switching strategies are scarce. Moreover, scoring criteria adapted to Colombian Spanish are missing. (1) To describe the Colombian adaptation of the scoring system guidelines for clustering and switching strategies in VFT; (2) to determine its reliability; and (3) to provide normative data for Colombian children and adolescents aged 6-17 years. A total of 691 children and adolescents from Colombia completed phonological (/f/, /a/, /s/, /m/, /r/ and /p/) and semantic (animals and fruits) VFT, and five scores were calculated: total score (TS), number of clusters (NC), cluster size (CS), mean cluster size (MCS) and number of switches (NS). The intraclass correlation coefficient was used for interrater reliability. Hierarchical multiple regressions were conducted to investigate which strategies were associated with VFT TS. Multiple regressions were conducted for each strategy, including as predictors age, age2 , sex, mean parents' education (MPE), MPE2 and type of school, to generate normative data. Reliability indexes were excellent. Age was associated with VFT TS, but weakly compared with strategies. For both VFT TS, NS was the strongest variable, followed by CS and NC. Regarding norms, age was the strongest predictor for all measures, while age2 was relevant for NC (/f/ phoneme) and NS (/m/ phoneme). Participants with higher MPE obtained more NC, and NS, and larger CS in several phonemes and categories. Children and adolescents from private school generated more NC, NS and larger CS in /s/ phoneme. This study provides new scoring guidelines and normative data for clustering and switching strategies for Colombian children and adolescents between 6 and 17 years old. Clinical neuropsychologists should include these measures as part of their everyday practice. What is already known on the subject VFT are widely used within the paediatric population due to its sensitivity to brain injury. Its score is based on the number of correct words produced; however, TS alone gives little information regarding underlying test performance. Several normative data for VFT TS in the paediatric population exist, but normative data for clustering and switching strategies are scarce. What this paper adds to existing knowledge The present study is the first to describe the Colombian adaptation of the scoring guidelines for clustering and switching strategies, and provided normative data for these strategies for children and adolescents between 6 and 17 years old. What are the potential or actual clinical implications of this work? Knowing VFT's performance, including strategy development and use in healthy children and adolescents, may be useful for clinical settings. We encourage clinicians to include not only TS, but also a careful analysis of strategies that may be more informative of the underlying cognitive processes failure than TS.

Interaction-Limited Aggregation: Fine-Tuning the Size of pNIPAM Particles by Association with Hydrophobic Ions.

We have investigated the formation of stable clusters of poly(N-isopropylacrylamide) (pNIPAM) chains in water at temperatures above the lower critical solution temperature (LCST), induced by the presence of sodium tetraphenylborate, NaPh4B. The hydrophobic Ph4B- ions interact strongly with the pNIPAM chains, providing them with a net effective negative charge, which leads to the stabilization of pNIPAM clusters for temperatures above the LCST, with a mean cluster size that depends non-monotonically on salt concentration. Combining experiments with physical modeling at the mesoscopic level and atomistic molecular dynamic simulations, we show that this effect is caused by the interplay between the hydrophobic attraction between pNIPAM chains and the electrostatic repulsion induced by the associated Ph4B- ions. These results provide insight on the significance of weak associative anion-polymer interaction driven by hydrophobic interaction and how this anionic binding can prevent macroscopic phase separation. Harvesting the competition between attractive hydrophobic and repulsive electrostatic interaction opens avenues for the dynamic control of the formation of well-calibrated polymer microparticles.

A novel method for the 3D inhomogeneous percolation on the Lattice with its application

This article anticipates the puzzle of acquiring a three-dimensional inhomogeneous site percolation on an irregular Bethe Lattice (TDIBL). In this work, we explore a TDIBL with the intent to realize the right tradeoff among different percolating variates, namely, cluster size distribution (CSD), critical occupation probability (COP), percolating probability (PP), and mean cluster size (MCS). The variates results are acquired using the generating function (GF) and generalized recursive approaches (GRA). The findings revealed that, for inhomogeneous site percolation (ISP) on the proposed model, the high fraction of probabilities (occupation and distribution probabilities) boosts the intensity of the process, which will enlarge the mean degree of the system in the percolation process. Moreover, numerical simulation and sensitivity analysis will also enhance our understanding of the percolating process via 2D and 3D. Their corresponding shape profiles of earned findings are drawn to perceive their dynamics amongst the options of entailed parameters. Furthermore, exhausting the above scheme, we discuss the transmission behavior of the novel corona-virus 2019 (COVID-19) and present particular disease-control schemes courtesy of groups with numerous infection probabilities and find the effect according to the age distribution. We recognize that this endeavor is timely, that it will be about curiosity, and that it will include scientists working with diverse percolation approaches.

Southern Hemisphere Breeding Stock D humpback whale population estimates from North West Cape, Western Australia

Estimates of the abundance of Breeding Stock D humpback whales (Megaptera novaeangliae) are key to the conservation and management of what is thought to be one of the largest populations of the species. Five years (2000, 2001, 2006, 2007 and 2008) of aerial surveys carried out over an eight-year period at North West Cape (Western Australia) using line transect methodology allowed trends in whale numbers to be investigated, and provided a base for comparison with estimates made approximately 400km south at Shark Bay (Western Australia). A total of 3,127 whale detections were made during 74 surveys of the 7,043km2 study area west of NWC. Pod abundance for each flight was computed using a HorvitzThompson like estimator and converted to an absolute measure of abundance after corrections were made for estimated mean cluster size, unsurveyed time, swimming speed and animal availability. Resulting estimates from the migration model of best fit with the most credible assumptions were 7,276 (CI = 4,993–10,167) for 2000, 12,280 (CI = 6,830–49,434) for 2001, 18,692 (CI = 12,980–24,477) for 2006, 20,044 (CI = 13,815–31,646) for 2007, and 26,100 (CI = 20,152–33,272) for 2008. Based on these data, the trend model with the greatest r2 was exponential with an annual increase rate of 13% (CI = 5.6%–18.1%). While this value is above the species’ estimated maximum plausible growth rate of 11.8%, it is reasonably close to previous reports of between 10–12%. The coefficient of variation, however, was too large for a reliable trend estimate. Perception bias was also not accounted for in these calculations. Based on a crude appraisal which yielded an estimated p(0) of 0.783 (from independent observer effort, CV = 0.973), the 2008 humpback population size may be as large as 33,300. In conclusion, the work here provides evidence of an increasing Breeding Stock D population, but further surveys are necessary to confirm whether the population is indeed increasing at its maximum rate.

Forward–backward multiplicity distribution with the Chou–Yang model for pp collisions at s = 0.9, 7 and 8 TeV from the CMS experiment

In this paper, a Chou–Yang-type multiplicity distribution comprising a total multiplicity component and a binomial asymmetry component is used to describe charged hadron multiplicity data at [Formula: see text] = 0.9, 7 and 8 TeV from the CMS experiment at CERN. The data was obtained and processed from the CERN Open Data Portal. For the total multiplicity component, it was found that a weighted superposition of a Negative Binomial Distribution (NBD) and a Furry–Yule Distribution (FYD) is able to describe the shoulder-like structure characteristic of Koba–Nielsen–Olesen (KNO) scaling violation well. The mean cluster size produced from collisions was also found to increase with collision energy. A prediction is given for pp collisions at [Formula: see text] = 14 TeV.