Multivariate moments and Cochran theorems.

This thesis is divided into two related parts: (I) Moments. For a multivariate elliptically contoured random matrix Y\sim MEC\sb{n\times p}(\mu,\ \Sigma\sb{Y},\ \phi), formulae for finding the higher order moments of both Y and its quadratic forms are obtained in terms of \mu,\ \Sigma\sb{Y} and $\phi,$ where \Sigma\sb{Y} is not required to have the form $A\otimes\Sigma.$ These results are so general that they are new even for the normal setting. Specific worked out examples on moments are given for both normal and certain non-normal settings such as multivariate uniform distributions, symmetric multivariate Pearson Type VII distributions, generalized Wishart distributions, multivariate components of variance models and MANOVA models. The proofs involve linear operators in inner product spaces, Kronecker products, multilinear differential forms and adjoint operators of the linear functions. (II) Cochran theorems. For a family of quadratic forms, \{Q\sb{i}(Y)\}\sbsp{i=1}{\ell}, of Y with Q\sb{i}(Y)=Y\sp\prime W\sb{i}Y+B\sbsp{i}{\prime}Y+Y\sp\prime C\sb{i}+D\sb{i},\ W\sb{i} symmetric and Y\sim N\sb{n\times p}(\mu,\ \Sigma\sb{Y}), necessary and sufficient conditions are obtained under which \{Q\sb{i}(Y)\} is an independent family of Wishart W\sb{p}(m\sb{i},\Sigma,\lambda\sb{i}) random matrices, (*). Such a result is referred to as a Cochran theorem. The Cochran theorems just mentioned are general in that the covariance matrix \Sigma\sb{Y} need not take the form $A\otimes\Sigma$ and need not be positive definite. Some of these results are extended further to the case where either (i) W\sb{p}(m\sb{i},\Sigma,\lambda\sb{i}) in (*) is replaced by DW\sb{p} (m\sb{1i},m\sb{2i},\Sigma,\lambda\sb{1i},\lambda\sb{2i}), the distribution of the difference of two independent Wishart random matrices Q\sb{1i} and Q\sb{2i} with Q\sb{1i}\sim W\sb{p}(m\sb{1i},\Sigma,\lambda\sb{1i}) and Q\sb{2i}\sim W\sb{p}(m\sb{2i},\Sigma,\lambda\sb{2i}), or (ii) Y is multivariate elliptically contoured distributed. The proofs involve linear operators in inner product spaces, Moore-Penrose inverses, projections, inclusion maps, spectra, invariant measures and conditional expectations.Dept. of Mathematics and Statistics. Paper copy at Leddy Library: Theses & Major Papers - Basement, West Bldg. / Call Number: Thesis1993 .W358. Source: Dissertation Abstracts International, Volume: 54-09, Section: B, page: 4762. Adviser: Chi Song Wong. Thesis (Ph.D.)--University of Windsor (Canada), 1993

Distribution of quadratic forms under skew normal settings

AbstractFor a class of multivariate skew normal distributions, the noncentral skew chi-square distribution is studied. The necessary and sufficient conditions under which a sequence of quadratic forms is generalized noncentral skew chi-square distributed random variables are obtained. Several examples are given to illustrate the results

Aggregation‐induced emission luminogens for gas sensors

Luminescent chromophores armed with aggregation-induced emission (AIE) characteristics can switch their fluorescence sensing by manipulating the aggregation and disaggregation states, leading to high sensitivity and high signal-to-noise ratio sensors. Accordingly, aggregation-induced emission luminogens (AIEgens) have been widely applied to various biosensing, one of which is the gas sensors. Due to the weak signal, easy diffusion, difficult capture, and instability of gas molecules, electrochemical or infrared tests are generally used for detection. However, electrochemical tests have high power consumption, and the environment easily disturbs infrared tests. Fortunately, photochemical sensors utilizing AIE properties can effectively overcome these deficiencies. AIEgens usually exhibit large Stokes shift, good photostability, and low random blinking, suggesting excellent sensing reproducibility and many achievements have been obtained in AIEgens-based gas sensors. This review summarizes the gas detection mechanism of AIEgens, and enumerate the reported gas sensors based on AIEgens. Then a perspective on the field and challenges facing it are elaborated so that researchers can better understand the development status of this field and develop more AIE-type spectroscopic probes with gas-responsive functions. It is expected to greatly enrich the types of gas sensors and promote the development of the application of AIE properties

Predictive nomogram model for major adverse kidney events within 30 days in sepsis patients with type 2 diabetes mellitus

BackgroundIn sepsis patients, Type 2 Diabetes Mellitus (T2DM) was associated with an increased risk of kidney injury. Furthermore, kidney damage is among the dangerous complications, with a high mortality rate in sepsis patients. However, the underlying predictive model on the prediction of major adverse kidney events within 30 days (MAKE30) in sepsis patients with T2DM has not been reported by any study.MethodsA total of 406 sepsis patients with T2DM were retrospectively enrolled and divided into a non-MAKE30 group (261 cases) and a MAKE30 group (145 cases). In sepsis patients with T2DM, univariate and multivariate logistic regression analyses were conducted to identify independent predictors of MAKE30. Based on the findings of multivariate logistic regression analysis, the corresponding nomogram was constructed. The nomogram was evaluated using the calibration curve, Receiver Operating Characteristic (ROC) curve, and decision curve analysis. A composite of death, new Renal Replacement Therapy (RRT), or Persistent Renal Dysfunction (PRD) comprised MAKE30. Finally, subgroup analyses of the nomogram for 30-day mortality, new RRT, and PRD were performed.ResultsIn sepsis patients with T2DM, Mean Arterial Pressure (MAP), Platelet (PLT), cystatin C, High-Density Lipoprotein (HDL), and apolipoprotein E (apoE) were independent predictors for MAKE30. According to the ROC curve, calibration curve, and decision curve analysis, the nomogram model based on those predictors had satisfactory discrimination (AUC = 0.916), good calibration, and clinical application. Additionally, in sepsis patients with T2DM, the nomogram model exhibited a high ability to predict the occurrence of 30-day mortality (AUC = 0.822), new RRT (AUC = 0.874), and PRD (AUC = 0.801).ConclusionThe nomogram model, which is available within 24 hours after admission, had a robust and accurate assessment for the MAKE30 occurrence, and it provided information to better manage sepsis patients with T2DM

Increased Formation of Follicular Antrum in Aquaporin-8-Deficient Mice Is Due to Defective Proliferation and Migration, and Not Steroidogenesis of Granulosa Cells

Aquaporin-8 (AQP8) is a water channel protein expressed exclusively in granulosa cells (GCs) in mouse ovary. Our previous studies of AQP8-deficient (AQP8-/-) mice demonstrated that AQP8 participates in folliculogenesis, including in the formation of follicles, ovulation, and atresia. However, its physiological function in formation of the antral follicle is still largely unknown. In the present study, we observed significantly increased numbers of antral follicles in AQP8-/- ovaries as well as significantly increased follicular antrum formation in in vitro 3D culture of AQP8-/- follicles. Functional detection of AQP8-/- GCs indicated that cell proliferation is impaired with FSH treatment, and wound healing and Transwell migration are also impaired with or without FSH treatment, compared with that in WT. However, the biosynthesis of estradiol and progesterone as well as the mRNA levels of key steroidogenic enzyme genes (CYP19A1 and StAR) in AQP8-/- GCs did not change, even with addition of FSH and/or testosterone. In order to estimate the influence of the impaired proliferation and migration on the density of GC mass, preantral follicles were injected with FITC-dextran, which distributes only in the intercellular space, and analyzed by confocal microscopy. The micrographs showed significantly higher transmission of fluorescence in AQP8-/- follicles, suggesting increased intercellular space of GCs. Based on this evidence, we concluded that AQP8 deficiency leads to increased formation of follicular antra in vivo and in vitro, and the mechanism may be associated with increased intercellular space of GCs, which may be caused by defective proliferation and migration of GCs. This study may offer new insight into the molecular mechanisms of the formation of follicular antrum

allodb: An R package for biomass estimation at globally distributed extratropical forest plots

Allometric equations for calculation of tree above-ground biomass (AGB) form the basis for estimates of forest carbon storage and exchange with the atmosphere. While standard models exist to calculate forest biomass across the tropics, we lack a standardized tool for computing AGB across boreal and temperate regions that comprise the global extratropics. Here we present an integrated R package, allodb, containing systematically selected published allometric equations and proposed functions to compute AGB. The data component of the package is based on 701 woody species identified at 24 large Forest Global Earth Observatory (ForestGEO) forest dynamics plots representing a wide diversity of extratropical forests. A total of 570 parsed allometric equations to estimate individual tree biomass were retrieved, checked and combined using a weighting function designed to ensure optimal equation selection over the full tree size range with smooth transitions across equations. The equation dataset can be customized with built-in functions that subset the original dataset and add new equations. Although equations were curated based on a limited set of forest communities and number of species, this resource is appropriate for large portions of the global extratropics and can easily be expanded to cover novel forest types

A Viable Approach to Mitigating Irreproducibility

In a recent article, Trafimow suggested the usefulness of imagining an ideal universe where the only difference between original and replication experiments is the operation of randomness. This contrasts with replication in the real universe where systematicity, as well as randomness, creates differences between original and replication experiments. Although Trafimow showed (a) that the probability of replication in the ideal universe places an upper bound on the probability of replication in the real universe, and (b) how to calculate the probability of replication in the ideal universe, the conception is afflicted with an important practical problem. Too many participants are needed to render the approach palatable to most researchers. The present aim is to address this problem. Embracing skewness is an important part of the solution

Evaluating the Precision of Published Research on Social Identity Theory

This data set is published on OSF as part of the requirements for publication listed by Taylor and Francis

A Parallel Splitting Augmented Lagrangian Method for Two-Block Separable Convex Programming with Application in Image Processing

The augmented Lagrangian method (ALM) is one of the most successful first-order methods for convex programming with linear equality constraints. To solve the two-block separable convex minimization problem, we always use the parallel splitting ALM method. In this paper, we will show that no matter how small the step size and the penalty parameter are, the convergence of the parallel splitting ALM is not guaranteed. We propose a new convergent parallel splitting ALM (PSALM), which is the regularizing ALM’s minimization subproblem by some simple proximal terms. In application this new PSALM is used to solve video background extraction problems and our numerical results indicate that this new PSALM is efficient