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## Diffusion kurtosis imaging of the healthy human brain

Henriques, Rafael Neto
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## Diffusional kurtosis imaging using a fast heuristic constrained linear least squares algorithm: a plugin for OsiriX

Mesquita, Nuno Maria Sampaio
Relevância na Pesquisa
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Diffusion Kurtosis Imaging (DKI) is a fairly new magnetic resonance imag-ing (MRI) technique that tackles the non-gaussian motion of water in biological tissues by taking into account the restrictions imposed by tissue microstructure, which are not considered in Diffusion Tensor Imaging (DTI), where the water diffusion is considered purely gaussian. As a result DKI provides more accurate information on biological structures and is able to detect important abnormalities which are not visible in standard DTI analysis. This work regards the development of a tool for DKI computation to be implemented as an OsiriX plugin. Thus, as OsiriX runs under Mac OS X, the pro-gram is written in Objective-C and also makes use of Apple’s Cocoa framework. The whole program is developed in the Xcode integrated development environ-ment (IDE). The plugin implements a fast heuristic constrained linear least squares al-gorithm (CLLS-H) for estimating the diffusion and kurtosis tensors, and offers the user the possibility to choose which maps are to be generated for not only standard DTI quantities such as Mean Diffusion (MD), Radial Diffusion (RD), Axial Diffusion (AD) and Fractional Anisotropy (FA), but also DKI metrics, Mean Kurtosis (MK), Radial Kurtosis (RK) and Axial Kurtosis (AK).The plugin was subjected to both a qualitative and a semi-quantitative analysis which yielded convincing results. A more accurate validation pro-cess is still being developed...

## Parametric Mapping of Brain Tissues from Diffusion Kurtosis Tensor

Chen, Yuanyuan; Zhao, Xin; Ni, Hongyan; Feng, Jie; Ding, Hao; Qi, Hongzhi; Wan, Baikun; Ming, Dong
Fonte: Hindawi Publishing Corporation Publicador: Hindawi Publishing Corporation
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
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Diffusion kurtosis imaging (DKI) is a new diffusion magnetic resonance imaging (MRI) technique to go beyond the shortages of conventional diffusion tensor imaging (DTI) from the assumption that water diffuse in biological tissue is Gaussian. Kurtosis is used to measure the deviation of water diffusion from Gaussian model, which is called non-Gaussian, in DKI. However, the high-order kurtosis tensor in the model brings great difficulties in feature extraction. In this study, parameters like fractional anisotropy of kurtosis eigenvalues (FAek) and mean values of kurtosis eigenvalues (Mek) were proposed, and regional analysis was performed for 4 different tissues: corpus callosum, crossing fibers, thalamus, and cerebral cortex, compared with other parameters. Scatterplot analysis and Gaussian mixture decomposition of different parametric maps are used for tissues identification. Diffusion kurtosis information extracted from kurtosis tensor presented a more detailed classification of tissues actually as well as clinical significance, and the FAek of D-eigenvalues showed good sensitivity of tissues complexity which is important for further study of DKI.

## Flow Cytometric Assessment of Erythrocyte Shape through Analysis of FSC Histograms: Use of Kurtosis and Implications for Longitudinal Evaluation

Ahlgrim, Christoph; Pottgiesser, Torben; Sander, Thomas; Schumacher, Yorck Olaf; Baumstark, Manfred W.
Fonte: Public Library of Science Publicador: Public Library of Science
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
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Sphericity of erythrocytes can be estimated from analysis of FSC signal distribution in flow cytometry. Previously, Pearson’s coefficient of dissymmetry (PCD) and spherical index (SphI) were applied to determine erythrocyte sphericity from the FSC histogram. The aim of the present study is to illustrate the application of kurtosis as an indicator of erythrocyte sphericity in flow cytometry in a broad range of FSC distributions. Moreover, the possibility of longitudinal evaluation of erythrocyte sphericity is studied. Change of erythrocyte sphericity of 10 healthy subjects was induced by variation of buffer osmolarity to validate applicability of sphericity measures. Agreement between the sphericity indicators was then studied in samples from 20 healthy donors taken at three time points, which were processed through density gradient centrifugation and incubated with FITC-labelled antibodies to induce a broad variation of erythrocyte form (1086 samples). SphI, PCD and kurtosis of FSC distribution were calculated. Correlation of the respective measures, standard error of measurement (SEM) and r ratio (intra- to interindividual variance) were determined to illustrate agreement between the sphericity indicators. In the first study part...

## Performances of diffusion kurtosis imaging and diffusion tensor imaging in detecting white matter abnormality in schizophrenia

Zhu, Jiajia; Zhuo, Chuanjun; Qin, Wen; Wang, Di; Ma, Xiaomei; Zhou, Yujing; Yu, Chunshui
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
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Diffusion kurtosis imaging (DKI) is an extension of diffusion tensor imaging (DTI), exhibiting improved sensitivity and specificity in detecting developmental and pathological changes in neural tissues. However, little attention was paid to the performances of DKI and DTI in detecting white matter abnormality in schizophrenia. In this study, DKI and DTI were performed in 94 schizophrenia patients and 91 sex- and age-matched healthy controls. White matter integrity was assessed by fractional anisotropy (FA), mean diffusivity (MD), axial diffusivity (AD), radial diffusivity (RD), mean kurtosis (MK), axial kurtosis (AK) and radial kurtosis (RK) of DKI and FA, MD, AD and RD of DTI. Group differences in these parameters were compared using tract-based spatial statistics (TBSS) (P < 0.01, corrected). The sensitivities in detecting white matter abnormality in schizophrenia were MK (34%) > AK (20%) > RK (3%) and RD (37%) > FA (24%) > MD (21%) for DKI, and RD (43%) > FA (30%) > MD (21%) for DTI. DKI-derived diffusion parameters (RD, FA and MD) were sensitive to detect abnormality in white matter regions (the corpus callosum and anterior limb of internal capsule) with coherent fiber arrangement; however, the kurtosis parameters (MK and AK) were sensitive to reveal abnormality in white matter regions (the juxtacortical white matter and corona radiata) with complex fiber arrangement. In schizophrenia...

## Are Idiosyncratic Skewness and Idiosyncratic Kurtosis Priced?

Cao, Xu
Fonte: Brock University Publicador: Brock University
Tipo: Electronic Thesis or Dissertation
Português
Relevância na Pesquisa
27.403179%
This thesis investigates the pricing effects of idiosyncratic moments. We document that idiosyncratic moments, namely idiosyncratic skewness and idiosyncratic kurtosis vary over time. If a factor/characteristic is priced, it must show minimum variation to be correlated with stock returns. Moreover, we can identify two structural breaks in the time series of idiosyncratic kurtosis. Using a sample of US stocks traded on NYSE, AMEX and NASDAQ markets from January 1970 to December 2013, we run Fama-MacBeth test at the individual stock level. We document a negative and significant pricing effect of idiosyncratic skewness, consistent with the finding of Boyer et al. (2010). We also report that neither idiosyncratic volatility nor idiosyncratic kurtosis are consistently priced. We run robustness tests using different model specifications and period sub-samples. Our results are robust to the different factors and characteristics usually included in the Fama-MacBeth pricing tests. We also split first our sample using endogenously determined structural breaks. Second, we divide our sample into three equal sub-periods. The results are consistent with our main findings suggesting that expected returns of individual stocks are explained by idiosyncratic skewness. Both idiosyncratic volatility and idiosyncratic kurtosis are irrelevant to asset prices at the individual stock level. As an alternative method...

## Sample Kurtosis, GARCH-t and the Degrees of Freedom Issue

HERACLEOUS, Maria S.
Fonte: European University Institute Publicador: European University Institute
Tipo: Trabalho em Andamento Formato: application/pdf; digital
Português
Relevância na Pesquisa
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Econometric modeling based on the Student’s t distribution introduces an additional parameter — the degree of freedom. In this paper we use a simulation study to investigate the ability of (i) the GARCH-t model (Bollerslev, 1987) to estimate the true degree of freedom parameter and (ii) the sample kurtosis coefficient to accurately determine the implied degrees of freedom. Simulation results reveal that the GARCH-t model and the sample kurtosis coefficient provide biased and inconsistent estimates of the degree of freedom parameter. Moreover, by varying σ2, we find that only the constant term in the conditional variance equation is affected, while the other parameters remain unaffected.

## Enhanced contrast detection of subsurface defects by pulsed infrared thermography based on the fourth order statistic moment, kurtosis

Madruga Saavedra, Francisco Javier; Ibarra Castanedo, Clemente; Conde Portilla, Olga María; Maldague, Xavier P. V.; López Higuera, José Miguel
Fonte: SPIE Society of Photo-Optical Instrumentation Engineers Publicador: SPIE Society of Photo-Optical Instrumentation Engineers
Tipo: info:eu-repo/semantics/conferenceObject; publishedVersion
Português
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The automatic detection of subsurface defects has become a desired goal in the application of non-destructive testing and evaluation techniques. In this paper, an algorithm based on the fourth order standardised statistic moment, i.e. kurtosis, is proposed for detection and/or characterization of subsurface defects having a thermal diffusivity either higher or lower than the host material. The analysis of thermographic data for the detection of defects can be reduced to the temporal statistics of the thermographic sequence. The final result provided by this algorithm is an image showing the different defects without the necessity of establishing other evaluating parameters such as the delayed time of the first image or the acquisition frequency in the analysis, which are required in other processing techniques. All the information is contained in a single image allowing to discriminate between the defect types (high o low thermal diffusivity). Synthetic data from ThermocalcÃ Â® and experimental works using a PlexiglasTM specimen were performed showing good agreement. Processed results using synthetic and experimental data with other methods used in the field of thermography for defect detection and/or characterization are provided as well for comparison.

## The kurtosis coeficient and the linear discriminant function

Peña, Daniel; Prieto, Francisco J.
Tipo: Trabalho em Andamento Formato: application/pdf
Relevância na Pesquisa
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In this note we analyze the relationship between the direction obtained from the minimization of the kurtosis coefficient of the projections of a mixture of multivariate normal distributions and the linear discriminant function. We show that both directions are closely related, and in particular that given two vector random variables having symmetric distributions with unknown means and the same covariance matrix,the direction which minimizes the kurtosis coefficient of the projection is the linear discriminant function. This result provides a way to compute the discriminant function between two normal populations in the case in which the means and the common covariance matrix are unknown.

## The kurtosis coefficient and the linear discriminant function

Peña, Daniel; Prieto, Francisco J.
Tipo: info:eu-repo/semantics/acceptedVersion; info:eu-repo/semantics/article Formato: application/pdf
Relevância na Pesquisa
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In this note we analyze the relationship between the direction obtained from the minimization of the kurtosis coeiiicient of the projections of a mixture of multivariate normal distributions and the linear discriminant function. We show that both directions are closely related and, in particular, that given two vector random variables having symmetric distributions with unknown means and the same covariance matrix, the direction which minimizes the kurtosis coefficient of the projection is the linear discriminant function. This result provides a way to compute the discriminant function between two normal populations in the case in which means and common covariance matrix are unknown; This research has been sponsored by the Catedra BBV of Quality and by DGES Grant PB96-0111

## Independent components techniques based on kurtosis for functional data analysis

Peña, Daniel; Prieto, Francisco J.; Rendón, Carolina
Tipo: info:eu-repo/semantics/draft; info:eu-repo/semantics/workingPaper
Relevância na Pesquisa
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The motivation for this paper arises from an article written by Peña et al. [40] in 2010,where they propose the eigenvectors associated with the extreme values of a kurtosismatrix as interesting directions to reveal the possible cluster structure of a dataset. In recent years many research papers have proposed generalizations of multivariatetechniques to the functional data case. In this paper we introduce an extension of themultivariate kurtosis for functional data, and we analyze some of its properties. Inparticular, we explore if our proposal preserves some of the properties of the kurtosisprocedures applied to the multivariate case, regarding the identification of outliers andcluster structures. This analysis is conducted considering both theoretical andexperimental properties of our proposal

## Are Idiosyncratic Skewness and Idiosyncratic Kurtosis Priced?

Cao, Xu
Fonte: Brock University Publicador: Brock University
Tipo: Electronic Thesis or Dissertation
Português
Relevância na Pesquisa
37.461792%
This thesis investigates the pricing effects of idiosyncratic moments. We document that idiosyncratic moments, namely idiosyncratic skewness and idiosyncratic kurtosis vary over time. If a factor/characteristic is priced, it must show minimum variation to be correlated with stock returns. Moreover, we can identify two structural breaks in the time series of idiosyncratic kurtosis. Using a sample of US stocks traded on NYSE, AMEX and NASDAQ markets from January 1970 to December 2013, we run Fama-MacBeth test at the individual stock level. We document a negative and significant pricing effect of idiosyncratic skewness, consistent with the finding of Boyer et al. (2010). We also report that neither idiosyncratic volatility nor idiosyncratic kurtosis are consistently priced. We run robustness tests using different model specifications and period sub-samples. Our results are robust to the different factors and characteristics usually included in the Fama-MacBeth pricing tests. We also split first our sample using endogenously determined structural breaks. Second, we divide our sample into three equal sub-periods. The results are consistent with our main findings suggesting that expected returns of individual stocks are explained by idiosyncratic skewness. Both idiosyncratic volatility and idiosyncratic kurtosis are irrelevant to asset prices at the individual stock level. As an alternative method...

## Eigenvectors of a kurtosis matrix as interesting directions to reveal cluster structure

Peña, Daniel; Prieto, Francisco J.; Viladomat, Júlia
Tipo: info:eu-repo/semantics/acceptedVersion; info:eu-repo/semantics/article Formato: application/pdf
Relevância na Pesquisa
37.325657%
In this paper we study the properties of a kurtosis matrix and propose its eigenvectors as interesting directions to reveal the possible cluster structure of a data set. Under a mixture of elliptical distributions with proportional scatter matrix, it is shown that a subset of the eigenvectors of the fourth-order moment matrix corresponds to Fisher's linear discriminant subspace. The eigenvectors of the estimated kurtosis matrix are consistent estimators of this subspace and its calculation is easy to implement and computationally efficient, which is particularly favourable when the ratio n/p is large.

## Sample Kurtosis, GARCH-t and the Degrees of Freedom Issue

HERACLEOUS, Maria S.
Fonte: European University Institute Publicador: European University Institute
Tipo: Trabalho em Andamento Formato: application/pdf
Português
Relevância na Pesquisa
37.218318%
Econometric modeling based on the Student's t distribution introduces an additional parameter -- the degree of freedom. In this paper we use a simulation study to investigate the ability of (i) the GARCH-t model (Bollerslev, 1987) to estimate the true degree of freedom parameter and (ii) the sample kurtosis coefficient to accurately determine the implied degrees of freedom. Simulation results reveal that the GARCH-t model and the sample kurtosis coefficient provide biased and inconsistent estimates of the degree of freedom parameter. Moreover, by varying σ², we find that only the constant term in the conditional variance equation is affected, while the other parameters remain unaffected.

## Quantificação da difusão na ressonância magnética da mama: ADC e Kurtosis

Borlinhas, Filipa
Fonte: Escola Superior de Tecnologia da Saúde de Lisboa Publicador: Escola Superior de Tecnologia da Saúde de Lisboa
Relevância na Pesquisa
37.54454%

## On the kurtosis of deep-water gravity waves

Fedele, Francesco
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
27.403179%
In this paper, we revisit Janssen's (2003) formulation for the dynamic excess kurtosis of weakly nonlinear gravity waves at deep water. For narrowband directional spectra, the formulation is given by a sixfold integral that depends upon the Benjamin-Feir index and the parameter $R=\sigma_{\theta}^{2}/2\nu^{2}$, a measure of short-crestedness for the dominant waves with $\nu$ and $\sigma_{\theta}$} denoting spectral bandwidth and angular spreading. Our refinement leads to a new analytical solution for the dynamic kurtosis of narrowband directional waves described with a Gaussian type spectrum. For multidirectional or short-crested seas initially homogenous and Gaussian, in a focusing (defocusing) regime dynamic kurtosis grows initially, attaining a positive maximum (negative minimum) at the intrinsic time scale $\tau_{c}=\nu^{2}\omega_{0}t_{c}=1/\sqrt{3R},\qquad\mathrm{or}\qquad t_{c}/T_{0}\approx0.13/\nu\sigma_{\theta},$ where $\omega_{0}=2\pi/T_{0}$ denotes the dominant angular frequency. Eventually the dynamic excess kurtosis tends monotonically to zero as the wave field reaches a quasi-equilibrium state characterized with nonlinearities mainly due to bound harmonics. Quasi-resonant interactions are dominant only in unidirectional or long-crested seas where the longer-time dynamic kurtosis can be larger than that induced by bound harmonics...

## The Kurtosis of the Cosmic Shear Field

Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
27.403179%
We study the fourth-order moment of the cosmic shear field using the dark matter halo approach to describe the nonlinear gravitational evolution of structure in the universe. Since the third-order moment of the shear field vanishes because of symmetry, non-Gaussian signatures in its one-point statistics emerge at the fourth-order level. We argue that the shear kurtosis parameter S_4 = /^3 may be more directly applicable to realistic data than the well-studied higher-order statistics of the convergence field, since obtaining the convergence requires a non-local reconstruction from the measured shear field. We compare our halo model predictions for the variance, skewness and kurtosis of lensing fields with ray-tracing simulations of cold dark matter models and find good agreement. The shear kurtosis calculation is made tractable by developing approximations for fast and accurate evaluations of the 8-dimensional integrals needed to obtain the kurtosis. We show that on small scales it is dominated by correlations within halos more massive than 10^14 solar masses. The shear kurtosis is sensitive to the mass density parameter of the universe, Omega, and has relatively weak dependences on other parameters. The approximations we develop for the third- and fourth-order moments allow for accurate halo model predictions for the 3-dimensional mass distribution as well. We demonstrate their accuracy in the small scale regime...

## Kurtosis of Large-Scale Cosmic Fields

Lokas, Ewa Luiza; Juszkiewicz, Roman; Weinberg, David; Bouchet, Francois
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
27.403179%
An attractive and simple hypothesis for the formation of large-scale structure is that it developed by gravitational instability from primordial fluctuations with an initially Gaussian probability distribution. Non-linear gravitational evolution drives the distribution away from the Gaussian form, generating measurable skewness and kurtosis even when the variance of the fluctuations is much smaller than unity. We use perturbation theory to compute the kurtosis of the mass density field and the velocity divergence field that arises during the weakly non-linear evolution of initially Gaussian fluctuations. We adopt an Einstein--de~Sitter universe for the perturbative calculations, and we discuss the generalization to a universe of arbitrary $\Omega$. We obtain semi-analytic results for the case of scale-free, power-law spectra of the initial fluctuations and final smoothing of cosmic fields with a Gaussian filter. We also give an exact analytical formula for the dependence of the skewness of these fields on the power spectrum index. We show that the kurtosis decreases with the power spectrum index, and we compare our more accurate results for the kurtosis to previous estimates from Monte Carlo integrations. We also compare our results to values obtained from cosmological N-body simulations with power-law initial spectra. Measurements of the skewness and kurtosis parameters can be used to test the hypothesis that structure in the universe formed by gravitational instability from Gaussian initial conditions.; Comment: 29 pp incl. 8 figs...

## Skewness and kurtosis analysis for non-Gaussian distributions

Celikoglu, Ahmet; Tirnakli, Ugur
Tipo: Artigo de Revista Científica
In a recent paper [\textit{M. Cristelli, A. Zaccaria and L. Pietronero, Phys. Rev. E 85, 066108 (2012)}], Cristelli \textit{et al.} analysed relation between skewness and kurtosis for complex dynamical systems and identified two power-law regimes of non-Gaussianity, one of which scales with an exponent of 2 and the other is with $4/3$. Finally the authors concluded that the observed relation is a universal fact in complex dynamical systems. Here, we test the proposed universal relation between skewness and kurtosis with large number of synthetic data and show that in fact it is not universal and originates only due to the small number of data points in the data sets considered. The proposed relation is tested using two different non-Gaussian distributions, namely $q$-Gaussian and Levy distributions. We clearly show that this relation disappears for sufficiently large data sets provided that the second moment of the distribution is finite. We find that, contrary to the claims of Cristelli \textit{et al.} regarding a power-law scaling regime, kurtosis saturates to a single value, which is of course different from the Gaussian case ($K=3$), as the number of data is increased. On the other hand, if the second moment of the distribution is infinite...