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

Metasql: A Generate-then-Rank Framework for Natural Language to SQL Translation

The Natural Language Interface to Databases (NLIDB) empowers non-technical users with database access through intuitive natural language (NL) interactions. Advanced approaches, utilizing neural sequence-to-sequence models or large-scale language models, typically employ auto-regressive decoding to generate unique SQL queries sequentially. While these translation models have greatly improved the overall translation accuracy, surpassing 70% on NLIDB benchmarks, the use of auto-regressive decoding to generate single SQL queries may result in sub-optimal outputs, potentially leading to erroneous translations. In this paper, we propose Metasql, a unified generate-then-rank framework that can be flexibly incorporated with existing NLIDBs to consistently improve their translation accuracy. Metasql introduces query metadata to control the generation of better SQL query candidates and uses learning-to-rank algorithms to retrieve globally optimized queries. Specifically, Metasql first breaks down the meaning of the given NL query into a set of possible query metadata, representing the basic concepts of the semantics. These metadata are then used as language constraints to steer the underlying translation model toward generating a set of candidate SQL queries. Finally, Metasql ranks the candidates to identify the best matching one for the given NL query. Extensive experiments are performed to study Metasql on two public NLIDB benchmarks. The results show that the performance of the translation models can be effectively improved using Metasql

Identification method for inter-turn faults in transformers based on digital twin concept

A transformer inter-turn fault identification method is proposed based on the digital twin concept to tackle the challenges of high operational complexity and low accuracy associated with traditional transformer fault identification methods. Initially, the Bald Eagle Search algorithm is employed to optimize the critical parameters of the Extreme Learning Machine (ELM), determining the optimal input layer weight and hidden layer threshold of the Extreme Learning Machine. Subsequently, leveraging the digital twin concept, a digital replica of the physical transformer is established, enabling multi-physical field coupling simulation encompassing electrical, thermal, and acoustic domains to elucidate the variation patterns of various physical parameters across different operational scenarios and fault scenarios. Furthermore, key physical characteristic parameters such as sound pressure and winding hot spot temperature are carefully selected to drive a fault identification model tailored to inter-turn faults within the framework of the digital twin concept. Through a detailed investigation using 630 kV A/10 kV transformers as a case study, the results exhibit an impressive fault identification accuracy of 95.24% for the proposed method. Comparative analysis reveals notable enhancements in fault identification accuracy of 12.22%, 7.85%, and 3.73% for ELM, Support Vector Machine and Tuna Swarm Optimization—ELM models, respectively. These findings underscore the effectiveness and practicality of the transformer inter-turn fault identification method based on the digital twin concept, offering valuable insights for the real-time monitoring and diagnosis of inter-turn faults in transformers

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

Influence of coal seam bedding on the effect of fracturing coal and enhancing permeability by microwave

As a typical structural weak surface, bedding is ubiquitous in coal seams. The relative mechanical properties between coal seam bedding and coal matrix are the key to determining the effect of enhancing permeability by microwave in coal seams with bedding development. To this end, a self-developed microwave irradiation (MI) test device was used to carry out microwave fracturing coal experiments on coal samples with an angle of 0°, 30°, 45°, 60° and 90° between the bedding plane and the loading direction. The evolution characteristics of microscopic pore structure and microscopic cracks of coal samples with different bedding directions were explored, and the influence of bedding structure on the number, scale, and connectivity of coal pores and fractures under MI was revealed. The gas permeability characteristics of coal in different bedding directions before and after MI were compared and analyzed. The variation law of coal permeability under the influence of coal seam bedding and fracturing coal by microwave was clarified, and the influence mechanism of coal seam bedding on fracturing coal and enhancing permeability by microwave was revealed. The results show that the coal seam bedding has a significant effect on the effect of fracturing coal and enhancing permeability by microwave. The larger the angle between the bedding plane and the loading direction, the greater the reduction of the bound pores and the growth of the connected fractures of the coal under MI. Compared with the original coal samples, the order of magnitude difference between the permeability of coal samples in different bedding directions after MI is effectively reduced, and the permeability anisotropy is obviously weakened. The development of meso-cracks in coal under MI has a significant bedding effect. The specific evolution process is first to expand the original cracks along the bedding plane, followed by the initiation of new cracks along the bedding plane, and finally to expand the cracks intersecting with the bedding plane. The difference of dielectric loss and heat transfer properties between coal matrix and bedding plane makes the thermal stress distribution of coal subject to the bedding plane. When the bedding plane is perpendicular or parallel to the loading direction, the coal body is dominated by tensile failure. When the bedding plane is oblique to the loading direction, the coal body is dominated by shear slip failure

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

A semi-automatic deep learning model based on biparametric MRI scanning strategy to predict bone metastases in newly diagnosed prostate cancer patients

ObjectiveTo develop a semi-automatic model integrating radiomics, deep learning, and clinical features for Bone Metastasis (BM) prediction in prostate cancer (PCa) patients using Biparametric MRI (bpMRI) images.MethodsA retrospective study included 414 PCa patients (BM, n=136; NO-BM, n=278) from two institutions (Center 1, n=318; Center 2, n=96) between January 2016 and December 2022. MRI scans were confirmed with BM status via PET-CT or ECT pre-treatment. Tumor areas on bpMRI images were delineated as tumor’s region of interest (ROI) using auto-delineation tumor models, evaluated with Dice similarity coefficient (DSC). Samples were auto-sketched, refined, and used to train the ResNet BM prediction model. Clinical, radiomics, and deep learning data were synthesized into the ResNet-C model, evaluated using receiver operating characteristic (ROC).ResultsThe auto-segmentation model achieved a DSC of 0.607. Clinical BM prediction’s internal validation had an accuracy (ACC) of 0.650 and area under the curve (AUC) of 0.713; external cohort had an ACC of 0.668 and AUC of 0.757. The deep learning model yielded an ACC of 0.875 and AUC of 0.907 for the internal, and ACC of 0.833 and AUC of 0.862 for the external cohort. The Radiomics model registered an ACC of 0.819 and AUC of 0.852 internally, and ACC of 0.885 and AUC of 0.903 externally. ResNet-C demonstrated the highest ACC of 0.902 and AUC of 0.934 for the internal, and ACC of 0.885 and AUC of 0.903 for the external cohort.ConclusionThe ResNet-C model, utilizing bpMRI scanning strategy, accurately assesses bone metastasis (BM) status in newly diagnosed prostate cancer (PCa) patients, facilitating precise treatment planning and improving patient prognoses

Case report: Clinical features of pediatric acute myeloid leukemia presenting with cardiac tamponade: a case series study and literature review

ObjectiveThis study aims to elucidate the clinical features observed in cases of pediatric acute myeloid leukemia (AML) initially presenting with cardiac tamponade and to share treatment experiences.Materials and methodsFive pediatric patients were initially diagnosed with AML accompanied by cardiac myeloid sarcoma (MS). The diagnosis was established by examining our hospital records and reviewing pertinent literature from 1990 to July 2023, accessible through MEDLINE/PubMed. We comprehensively assessed the clinical characteristics and treatment modalities employed for these patients.ResultFive pediatric patients presented with acute symptoms, including shortness of breath, malaise, cough, and fever, leading to their hospitalization. Physical examination revealed irritability, hypoxia, tachypnea, tachycardia, and hypotension. Initial detection utilized chest X-ray or echocardiogram, leading to subsequent diagnoses based on pericardial effusion and/or bone marrow examination. Two patients received chemotherapy at the time of initial diagnosis, one with cytarabine and etoposide, and the other with cytarabine and cladribine. Post-treatment, their bone marrow achieved remission, and over a 2.5-year follow-up, their cardiac function remained favorable. Unfortunately, the remaining three patients succumbed within two weeks after diagnosis, either due to receiving alternative drugs or without undergoing chemotherapy.ConclusionThis is the first and largest case series of pediatric AML patients with cardiac MS, manifesting initially with cardiac tamponade. It highlights the rarity and high mortality associated with this condition. The critical factors for reducing mortality include identifying clinical manifestations, conducting thorough physical examinations, performing echocardiography promptly, initiating early and timely pericardial drainage, and avoiding cardiotoxic chemotherapy medications