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The local dependence function is important in many applications of probability and statistics. We extend the bivariate local dependence function introduced by Bairamov and Kotz (2000) and further developed by Bairamov et al. (2003) to three-variate and multivariate local dependence function characterizing the dependency between three and more random variables in a given specific point. The definition and properties of the three-variate local dependence function are discussed. An example of a three-variate local dependence function for underlying three-variate normal distribution is presented. The graphs and tables with numerical values are provided. The multivariate extension of the local dependence function that can characterize the dependency between multiple random variables at a specific point is also discussed., Comment: 29 pages 13 Figures

In this study, we propose a novel framework that utilizes deep learning (DL) and attention mechanisms to predict the radiographic progression of patellofemoral osteoarthritis (PFOA) over a period of seven years. This study included subjects (1832 subjects, 3276 knees) from the baseline of the MOST study. PF joint regions-of-interest were identified using an automated landmark detection tool (BoneFinder) on lateral knee X-rays. An end-to-end DL method was developed for predicting PFOA progression based on imaging data in a 5-fold cross-validation setting. A set of baselines based on known risk factors were developed and analyzed using gradient boosting machine (GBM). Risk factors included age, sex, BMI and WOMAC score, and the radiographic osteoarthritis stage of the tibiofemoral joint (KL score). Finally, we trained an ensemble model using both imaging and clinical data. Among the individual models, the performance of our deep convolutional neural network attention model achieved the best performance with an AUC of 0.856 and AP of 0.431; slightly outperforming the deep learning approach without attention (AUC=0.832, AP= 0.4) and the best performing reference GBM model (AUC=0.767, AP= 0.334). The inclusion of imaging data and clinical variables in an ensemble model allowed statistically more powerful prediction of PFOA progression (AUC = 0.865, AP=0.447), although the clinical significance of this minor performance gain remains unknown. This study demonstrated the potential of machine learning models to predict the progression of PFOA using imaging and clinical variables. These models could be used to identify patients who are at high risk of progression and prioritize them for new treatments. However, even though the accuracy of the models were excellent in this study using the MOST dataset, they should be still validated using external patient cohorts in the future.

Over the course of the COVID-19 pandemic, existing conspiracy theories were refreshed and new ones were created, often interwoven with antisemitic narratives, stereotypes and codes. The sheer volume of antisemitic and conspiracy theory content on the Internet makes data-driven algorithmic approaches essential for anti-discrimination organizations and researchers alike. However, the manifestation and dissemination of these two interrelated phenomena is still quite under-researched in scholarly empirical research of large text corpora. Algorithmic approaches for the detection and classification of specific contents usually require labeled datasets, annotated based on conceptually sound guidelines. While there is a growing number of datasets for the more general phenomenon of hate speech, the development of corpora and annotation guidelines for antisemitic and conspiracy content is still in its infancy, especially for languages other than English. We contribute to closing this gap by developing an annotation guide for antisemitic and conspiracy theory online content in the context of the COVID-19 pandemic. We provide working definitions, including specific forms of antisemitism such as encoded and post-Holocaust antisemitism. We use these to annotate a German-language dataset consisting of ~3,700 Telegram messages sent between 03/2020 and 12/2021., Comment: Link to the data sheet of the dataset: https://doi.org/10.5281/zenodo.6412114

The concept of conditional expectation is important in applications of probability and statistics in many areas such as reliability engineering, economy, finance, and actuarial sciences due to its property of being the best predictor of a random variable as a function of another random variable. This concept also is essential in the martingale theory and theory of Markov processes. Even though, there has been studied and published many interesting properties of conditional expectations with respect to a sigma-algebra generated by a random variable it remains an attractive subject having interesting applications in many fields. In this paper, we present some new properties of the conditional expectation of a random variable given another random variable and describe useful applications in problems of per-share-price of stock markets. The copula and dependence properties of conditional expectations as random variables are also studied. We present also some new equalities having interesting applications and results in martingale theory and Markov processes. Keywords: Conditional expectation, sigma algebra, per-share price, order statistics, prediction Conflicts of interest statement: We declare that have no conflicts of interest., Comment: The paper contains theoretical results on new properties of conditional expectations with applications in finance

Objective is to assess the ability of texture features for detecting radiographic patellofemoral osteoarthritis (PFOA) from knee lateral view radiographs. We used lateral view knee radiographs from MOST public use datasets (n = 5507 knees). Patellar region-of-interest (ROI) was automatically detected using landmark detection tool (BoneFinder). Hand-crafted features, based on LocalBinary Patterns (LBP), were then extracted to describe the patellar texture. First, a machine learning model (Gradient Boosting Machine) was trained to detect radiographic PFOA from the LBP features. Furthermore, we used end-to-end trained deep convolutional neural networks (CNNs) directly on the texture patches for detecting the PFOA. The proposed classification models were eventually compared with more conventional reference models that use clinical assessments and participant characteristics such as age, sex, body mass index(BMI), the total WOMAC score, and tibiofemoral Kellgren-Lawrence (KL) grade. Atlas-guided visual assessment of PFOA status by expert readers provided in the MOST public use datasets was used as a classification outcome for the models. Performance of prediction models was assessed using the area under the receiver operating characteristic curve (ROC AUC), the area under the precision-recall (PR) curve-average precision (AP)-, and Brier score in the stratified 5-fold cross validation setting.Of the 5507 knees, 953 (17.3%) had PFOA. AUC and AP for the strongest reference model including age, sex, BMI, WOMAC score, and tibiofemoral KL grade to predict PFOA were 0.817 and 0.487, respectively. Textural ROI classification using CNN significantly improved the prediction performance (ROC AUC= 0.889, AP= 0.714). We present the first study that analyses patellar bone texture for diagnosing PFOA. Our results demonstrates the potential of using texture features of patella to predict PFOA.

Objective: To assess the ability of imaging-based deep learning to predict radiographic patellofemoral osteoarthritis (PFOA) from knee lateral view radiographs. Design: Knee lateral view radiographs were extracted from The Multicenter Osteoarthritis Study (MOST) (n = 18,436 knees). Patellar region-of-interest (ROI) was first automatically detected, and subsequently, end-to-end deep convolutional neural networks (CNNs) were trained and validated to detect the status of patellofemoral OA. Patellar ROI was detected using deep-learning-based object detection method. Manual PFOA status assessment provided in the MOST dataset was used as a classification outcome for the CNNs. Performance of prediction models was assessed using the area under the receiver operating characteristic curve (ROC AUC) and the average precision (AP) obtained from the precision-recall (PR) curve in the stratified 5-fold cross validation setting. Results: Of the 18,436 knees, 3,425 (19%) had PFOA. AUC and AP for the reference model including age, sex, body mass index (BMI), the total Western Ontario and McMaster Universities Arthritis Index (WOMAC) score, and tibiofemoral Kellgren-Lawrence (KL) grade to predict PFOA were 0.806 and 0.478, respectively. The CNN model that used only image data significantly improved the prediction of PFOA status (ROC AUC= 0.958, AP= 0.862). Conclusion: We present the first machine learning based automatic PFOA detection method. Furthermore, our deep learning based model trained on patella region from knee lateral view radiographs performs better at predicting PFOA than models based on patient characteristics and clinical assessments., Comment: 24 pages, preprint, Submitted to Osteoarthritis and Cartilage

Knee osteoarthritis (OA) is very common progressive and degenerative musculoskeletal disease worldwide creates a heavy burden on patients with reduced quality of life and also on society due to financial impact. Therefore, any attempt to reduce the burden of the disease could help both patients and society. In this study, we propose a fully automated novel method, based on combination of joint shape and convolutional neural network (CNN) based bone texture features, to distinguish between the knee radiographs with and without radiographic osteoarthritis. Moreover, we report the first attempt at describing the bone texture using CNN. Knee radiographs from Osteoarthritis Initiative (OAI) and Multicenter Osteoarthritis (MOST) studies were used in the experiments. Our models were trained on 8953 knee radiographs from OAI and evaluated on 3445 knee radiographs from MOST. Our results demonstrate that fusing the proposed shape and texture parameters achieves the state-of-the art performance in radiographic OA detection yielding area under the ROC curve (AUC) of 95.21%, Comment: MIUA2020