FLUCTUATIONS OF CLUSTER NUMBERS IN PERCOLATION

2002 ◽  
Vol 13 (06) ◽  
pp. 777-781
Author(s):  
DANIEL TIGGEMANN
Keyword(s):  
Power Law ◽  
Higher Moments ◽  
The Mean ◽  
Large Clusters ◽  
Small Clusters ◽  
Skewness And Kurtosis

In order to study fluctuations in percolating systems, lattices for sizes up to L = 100 000 have been simulated several thousand times using the Hoshen–Kopelman algorithm. Distributions of cluster numbers are Gaussians for small clusters and half-sided quasi-Gaussians for large clusters. The variance of cluster numbers is proportional to the mean, with power-law deviations for small clusters. Higher moments like skewness and kurtosis were also studied.

scholarly journals Abnormal Portfolio Asset Allocation Model: Review

2020 ◽  
Vol 1 (1) ◽  
pp. 46-54
Author(s):  
Nurfadhlina Bt Abdul Halima ◽  
Dwi Susanti ◽  
Alit Kartiwa ◽  
Endang Soeryana Hasbullah
Keyword(s):  
Asset Allocation ◽  
Asset Returns ◽  
Higher Moments ◽  
Investment Portfolio ◽  
Allocation Model ◽  
Model Review ◽  
The Mean ◽  
Mean Variance ◽  
Skewness And Kurtosis ◽  
Normally Distributed

It has been widely studied how investors will allocate their assets to an investment when the return of assets is normally distributed. In this context usually, the problem of portfolio optimization is analyzed using mean-variance. When asset returns are not normally distributed, the mean-variance analysis may not be appropriate for selecting the optimum portfolio. This paper will examine the consequences of abnormalities in the process of allocating investment portfolio assets. Here will be shown how to adjust the mean-variance standard as a basic framework for asset allocation in cases where asset returns are not normally distributed. We will also discuss the application of the optimum strategies for this problem. Based on the results of literature studies, it can be concluded that the expected utility approximation involves averages, variances, skewness, and kurtosis, and can be extended to even higher moments.

scholarly journals Blood Oxygenation Level Dependent Magnetic Resonance Imaging (MRI), Dynamic Contrast Enhanced MRI and Diffusion Weighted MRI for Benign and Malignant Breast Cancer Discrimination: A Preliminary Experience

Cancers ◽  
2021 ◽  
Vol 13 (10) ◽  
pp. 2421
Author(s):  
Roberta Fusco ◽  
Vincenza Granata ◽  
Mauro Mattace Raso ◽  
Paolo Vallone ◽  
Alessandro Pasquale De Rosa ◽  
...  
Keyword(s):  
Standard Deviation ◽  
Univariate Analysis ◽  
Mean Value ◽  
Blood Oxygenation ◽  
Breast Lesions ◽  
Dce Mri ◽  
Malignant Lesions ◽  
The Mean ◽  
And Diffusion ◽  
Skewness And Kurtosis

Purpose. To combine blood oxygenation level dependent magnetic resonance imaging (BOLD-MRI), dynamic contrast enhanced MRI (DCE-MRI), and diffusion weighted MRI (DW-MRI) in differentiation of benign and malignant breast lesions. Methods. Thirty-seven breast lesions (11 benign and 21 malignant lesions) pathologically proven were included in this retrospective preliminary study. Pharmaco-kinetic parameters including Ktrans, kep, ve, and vp were extracted by DCE-MRI; BOLD parameters were estimated by basal signal S0 and the relaxation rate R2*; and diffusion and perfusion parameters were derived by DW-MRI (pseudo-diffusion coefficient (Dp), perfusion fraction (fp), and tissue diffusivity (Dt)). The correlation coefficient, Wilcoxon-Mann-Whitney U-test, and receiver operating characteristic (ROC) analysis were calculated and area under the ROC curve (AUC) was obtained. Moreover, pattern recognition approaches (linear discrimination analysis and decision tree) with balancing technique and leave one out cross validation approach were considered. Results. R2* and D had a significant negative correlation (−0.57). The mean value, standard deviation, Skewness and Kurtosis values of R2* did not show a statistical significance between benign and malignant lesions (p > 0.05) confirmed by the ‘poor’ diagnostic value of ROC analysis. For DW-MRI derived parameters, the univariate analysis, standard deviation of D, Skewness and Kurtosis values of D* had a significant result to discriminate benign and malignant lesions and the best result at the univariate analysis in the discrimination of benign and malignant lesions was obtained by the Skewness of D* with an AUC of 82.9% (p-value = 0.02). Significant results for the mean value of Ktrans, mean value, standard deviation value and Skewness of kep, mean value, Skewness and Kurtosis of ve were obtained and the best AUC among DCE-MRI extracted parameters was reached by the mean value of kep and was equal to 80.0%. The best diagnostic performance in the discrimination of benign and malignant lesions was obtained at the multivariate analysis considering the DCE-MRI parameters alone with an AUC = 0.91 when the balancing technique was considered. Conclusions. Our results suggest that the combined use of DCE-MRI, DW-MRI and/or BOLD-MRI does not provide a dramatic improvement compared to the use of DCE-MRI features alone, in the classification of breast lesions. However, an interesting result was the negative correlation between R2* and D.

scholarly journals On the scaling of fragmentation and energy dissipation in collisions of dust aggregates

2021 ◽  
Vol 23 (2) ◽  
Author(s):  
Philipp Umstätter ◽  
Herbert M. Urbassek
Keyword(s):  
Energy Dissipation ◽  
Collision Energy ◽  
Velocity Range ◽  
Collision Velocity ◽  
Granular Mechanics ◽  
Extra Factor ◽  
Cluster Fragmentation ◽  
Silica Clusters ◽  
Large Clusters ◽  
Small Clusters

Abstract Fragmentation of granular clusters may be studied by experiments and by granular mechanics simulation. When comparing results, it is often assumed that results can be compared when scaled to the same value of $$E/E_{\mathrm{sep}}$$ E / E sep , where E denotes the collision energy and $$E_{\mathrm{sep}}$$ E sep is the energy needed to break every contact in the granular clusters. The ratio $$E/E_{\mathrm{sep}}\propto v^2$$ E / E sep ∝ v 2 depends on the collision velocity v but not on the number of grains per cluster, N. We test this hypothesis using granular-mechanics simulations on silica clusters containing a few thousand grains in the velocity range where fragmentation starts. We find that a good parameter to compare different systems is given by $$E/(N^{\alpha }E_{\mathrm{sep}})$$ E / ( N α E sep ) , where $$\alpha \sim 2/3$$ α ∼ 2 / 3 . The occurrence of the extra factor $$N^{\alpha }$$ N α is caused by energy dissipation during the collision such that large clusters request a higher impact energy for reaching the same level of fragmentation than small clusters. Energy is dissipated during the collision mainly by normal and tangential (sliding) forces between grains. For large values of the viscoelastic friction parameter, we find smaller cluster fragmentation, since fragment velocities are smaller and allow for fragment recombination. Graphic abstract

scholarly journals A novel bidirectional clustering algorithm based on local density

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Baicheng Lyu ◽  
Wenhua Wu ◽  
Zhiqiang Hu
Keyword(s):  
Clustering Algorithm ◽  
Local Density ◽  
Clustering Algorithms ◽  
Cluster Number ◽  
Denoising Method ◽  
Number Of Clusters ◽  
Data Points ◽  
Cutoff Distance ◽  
Large Clusters ◽  
Small Clusters

AbstractWith the widely application of cluster analysis, the number of clusters is gradually increasing, as is the difficulty in selecting the judgment indicators of cluster numbers. Also, small clusters are crucial to discovering the extreme characteristics of data samples, but current clustering algorithms focus mainly on analyzing large clusters. In this paper, a bidirectional clustering algorithm based on local density (BCALoD) is proposed. BCALoD establishes the connection between data points based on local density, can automatically determine the number of clusters, is more sensitive to small clusters, and can reduce the adjusted parameters to a minimum. On the basis of the robustness of cluster number to noise, a denoising method suitable for BCALoD is proposed. Different cutoff distance and cutoff density are assigned to each data cluster, which results in improved clustering performance. Clustering ability of BCALoD is verified by randomly generated datasets and city light satellite images.

scholarly journals Structural Changes in Israeli Family Farms: Long-Run Trends in the Farm Size Distribution and the Role of Part-Time Farming

Agriculture ◽  
2021 ◽  
Vol 11 (6) ◽  
pp. 518
Author(s):  
Ayal Kimhi ◽  
Nitzan Tzur-Ilan
Keyword(s):  
Size Distribution ◽  
Structural Changes ◽  
Farm Size ◽  
Farm Income ◽  
Higher Moments ◽  
Full Time ◽  
Family Farms ◽  
Income Sources ◽  
Part Time ◽  
The Mean

Israeli agriculture has experienced rapid structural changes in recent decades, including the massive exit of farmers, a resulting increase in average farm size, a higher farm specialization and a higher reliance on non-farm income sources. The higher farm heterogeneity makes it necessary to examine changes in the entire farm size distribution rather than the common practice of analyzing changes in the average farm size alone. This article proposes a nonparametric analysis in which the change in the distribution of farm sizes between two periods is decomposed into several components, and the contributions of subgroups of farms to this change are analyzed. Using data on Israeli family farms, we analyze the changes in the farm size distribution in two separate time periods that are characterized by very different economic environments, focusing on the different contributions of full-time farms and part-time farms to the overall distributional changes. We found that between 1971 and 1981, a period characterized by stability and prosperity, the farm size distribution has shifted to the right with relatively minor changes in higher moments of the distribution. On the other hand, between 1981 and 1995, a largely unfavorable period to Israeli farmers, the change in the distribution was much more complex. While the overall change in the size distribution of farms was smaller in magnitude than in the earlier period, higher moments of the distribution were not less important than the increase in the mean and led to higher dispersion of farm sizes. Between 1971 and 1981, the contributions of full- and part-time farms to the change in the size distribution were quite similar. Between 1981 and 1995, however, full-time farms contributed mostly to the growth in the average farm size, while the average farm size among part-time farms actually decreased, and their contribution to the higher dispersion of farm sizes was quantitatively larger. This highlights the need to analyze the changes in the entire farm size distribution rather than focusing on the mean alone, and to allow for differences between types of farms.

scholarly journals Characterization of maturity and quality of Brazilian apirenic grapes in the São Francisco river Valley

2012 ◽  
Vol 32 (1) ◽  
pp. 26-33 ◽  
Author(s):  
Robson de Jesus Mascarenhas ◽  
Silvanda de Melo Silva ◽  
Maria Auxiliadora Coêlho de Lima ◽  
Rejane Maria Nunes Mendonça ◽  
Heinz Johann Holschuh
Keyword(s):  
Titratable Acidity ◽  
Soluble Solids ◽  
Minimum Diameter ◽  
Red Grapes ◽  
Berry Size ◽  
Large Clusters ◽  
Small Clusters ◽  
Light Green

The objective of this study was to characterize and correlate maturity and quality of the first varieties of Brazilian seedless grapes 'BRS Clara', 'BRS Linda', 'BRS Morena', and 'Advanced Selection 8' compared with the American variety 'Crimson Seedless' in compliance with the Brazilian Normative/2002 and export standards Advanced Selection 8' is dark reddish, has large clusters, and is a very large ellipsoid berry; 'BRS Morena' is black with medium sized clusters and large berry shaped as ellipsoid to globoid; 'BRS Linda' is light green and has large sized clusters; 'Crimson' is pink and has small clusters with berries varying from medium to large sizes and ellipsoid shaped; and 'BRS Clara' is green yellowish has medium sized clusters and small berry of elongated ellipsoid shape. All varieties evaluated meet the standard for domestic market established as berry size minimum diameter 12 mm. 'BRS Clara' does not meet the export requirements of diameter. Berries of the red grapes 'BRS Morena' and 'Crimson Seedless' are firmer. The pH, titratable acidity, and soluble solids meet the official standards. Larger clusters are less acidic and present higher soluble solids/titratable acidity ratios implying that they are the sweetest type when ripe.

NEW AMY AND DELPHI MULTIPLICITY DATA AND THE LOGNORMAL DISTRIBUTION

1991 ◽  
Vol 06 (03) ◽  
pp. 245-257 ◽  
Author(s):  
R. SZWED ◽  
G. WROCHNA ◽  
A.K. WRÓBLEWSKI
Keyword(s):  
Energy Dependence ◽  
Lognormal Distribution ◽  
Scaling Function ◽  
Average Multiplicity ◽  
Linear Functions ◽  
The Mean ◽  
Multiplicity Distributions ◽  
The Scaling Function ◽  
Skewness And Kurtosis

Multiplicity distributions for e+e−→ hadrons recently reported by the AMY and DELPHI collaborations are compared with the data obtained at lower energies. It is proven that the new data obey the KNO-G scaling and the scaling function can be described by the lognormal distribution. The dispersions are linear functions of the mean as for the data measured at lower energies and the standardized moments (such as skewness and kurtosis) are independent of the energy. The energy dependence of the average multiplicity is described by <nch>=β sα−1.

Two-Dimensional Correlation Spectroscopy (2D-COS) of Gas-Phase Pyrrole Clusters in a Supersonic Jet: Treatment of Sharp Bands on a Broad Background

2020 ◽  
Vol 74 (4) ◽  
pp. 408-416
Author(s):  
Yoshiteru Matsumoto ◽  
Souichi Tezuka
Keyword(s):  
Ir Spectra ◽  
Gas Phase ◽  
Supersonic Jet ◽  
Correlation Spectroscopy ◽  
Cavity Ringdown Spectroscopy ◽  
Two Dimensional ◽  
Cavity Ringdown ◽  
Correlation Spectrum ◽  
Large Clusters ◽  
Small Clusters

Two-dimensional correlation spectroscopy (2D-COS) is a useful technique to analyze any intensity behavior of optical spectra that exhibit a complicated feature with overlapped bands. In this study, we apply 2D-COS to the infrared (IR) spectra of gas-phase pyrrole (Py) clusters. The NH stretching vibrations of the Py clusters are measured by cavity ringdown spectroscopy. The observed IR spectra of the Py clusters consist of sharp bands, full width half-maximum (FWHM) ∼1 cm−1, and a broad background (FWHM >50 cm−1). The 2D asynchronous correlation spectra reveal that the sharp bands and a broad background are assigned to small clusters of dimer to pentamer and large clusters with bulk-like structures, respectively, which support the results of our previous study. The sharp bands are also analyzed using another 2D asynchronous correlation spectrum, which is obtained by decomposing the observed IR spectra into sharp and broad components. Because the asynchronous signals are consistent with those obtained from the IR spectra without decomposition, the result would suggest that we need not to decompose the IR spectra into sharp and broad components before applying 2D-COS. However, our model simulations of 2D-COS showed a counterexample that gives an incorrect result without removing a broad background component from the IR spectra. This study strongly suggests that we need to undertake a careful treatment of the complicated IR spectrum with various widths of bands.

Inverting the statistics of the circle transform

1988 ◽  
Vol 25 (04) ◽  
pp. 708-716
Author(s):  
Peter Waksman
Keyword(s):  
Plane Domain ◽  
Higher Moments ◽  
Mean Square ◽  
Second Moment ◽  
The Mean ◽  
Geometric Content

For a plane domain the circle transform assigns to each circle its length of intersection with the domain. The problem is to determine the geometry of the domain given the mean of these intersection lengths as the circles' centers vary and given how that mean varies with circle radius. We also consider the mean square and higher moments of the intersection lengths — as a function of the circle radius. The discussion includes an identification of the geometric content of the mean when centers are inside of a disk and of the second moment when the centers are arbitrary points in the plane. The latter is equivalent to the distribution of distance between pairs of points of the domain.

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