Search

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

The purposes of this study were to investigate: 1) the effect of placement of region-of-interest (ROI) for texture analysis of subchondral bone in knee radiographs, and 2) the ability of several texture descriptors to distinguish between the knees with and without radiographic osteoarthritis (OA). Bilateral posterior-anterior knee radiographs were analyzed from the baseline of OAI and MOST datasets. A fully automatic method to locate the most informative region from subchondral bone using adaptive segmentation was developed. We used an oversegmentation strategy for partitioning knee images into the compact regions that follow natural texture boundaries. LBP, Fractal Dimension (FD), Haralick features, Shannon entropy, and HOG methods were computed within the standard ROI and within the proposed adaptive ROIs. Subsequently, we built logistic regression models to identify and compare the performances of each texture descriptor and each ROI placement method using 5-fold cross validation setting. Importantly, we also investigated the generalizability of our approach by training the models on OAI and testing them on MOST dataset.We used area under the receiver operating characteristic (ROC) curve (AUC) and average precision (AP) obtained from the precision-recall (PR) curve to compare the results. We found that the adaptive ROI improves the classification performance (OA vs. non-OA) over the commonly used standard ROI (up to 9% percent increase in AUC). We also observed that, from all texture parameters, LBP yielded the best performance in all settings with the best AUC of 0.840 [0.825, 0.852] and associated AP of 0.804 [0.786, 0.820]. Compared to the current state-of-the-art approaches, our results suggest that the proposed adaptive ROI approach in texture analysis of subchondral bone can increase the diagnostic performance for detecting the presence of radiographic OA.

The focus of this paper is the random sequences in the form $\{X_{0},X_{1},$ $X_{n}=X_{n-2}+X_{n-1},n=2,3,..\dot{\}},$ referred to as Fibonacci Random Sequence (FRS). The initial random variables $X_{0}$ and $X_{1}$ are assumed to be absolutely continuous with joint probability density function (pdf) $f_{X_{0},X_{1}}.$ The FRS is completely determined by $X_{0}$ and $X_{1}$ and the members of Fibonacci sequence $\digamma \equiv\{0,1,1,2,3,5,8,13,21,34,55,89,144,...\}.$ We examine the distributional and limit properties of the random sequence $X_{n},n=0,1,2,...$ .

The Hilbert space of probability mass functions (pmf) is introduced in this thesis. A factorization method for multivariate pmfs is proposed by using the tools provided by the Hilbert space of pmfs. The resulting factorization is special for two reasons. First, it reveals the algebraic relations between the involved random variables. Second, it determines the conditional independence relations between the random variables. Due to the first property of the resulting factorization, it can be shown that channel decoders can be employed in the solution of probabilistic inference problems other than decoding. This approach might lead to new probabilistic inference algorithms and new hardware options for the implementation of these algorithms. An example of new inference algorithms inspired by the idea of using channel decoder for other inference tasks is a multiple-input multiple-output (MIMO) detection algorithm which has a complexity of the square-root of the optimum MIMO detection algorithm., Comment: PhD Dissertation, 123 pages

This paper summarizes the design of a programmable processor with transport triggered architecture (TTA) for decoding LDPC and turbo codes. The processor architecture is designed in such a manner that it can be programmed for LDPC or turbo decoding for the purpose of internetworking and roaming between different networks. The standard trellis based maximum a posteriori (MAP) algorithm is used for turbo decoding. Unlike most other implementations, a supercode based sum-product algorithm is used for the check node message computation for LDPC decoding. This approach ensures the highest hardware utilization of the processor architecture for the two different algorithms. Up to our knowledge, this is the first attempt to design a TTA processor for the LDPC decoder. The processor is programmed with a high level language to meet the time-to-market requirement. The optimization techniques and the usage of the function units for both algorithms are explained in detail. The processor achieves 22.64 Mbps throughput for turbo decoding with a single iteration and 10.12 Mbps throughput for LDPC decoding with five iterations for a clock frequency of 200 MHz., Comment: 8 pages, 7 figures, conference

Baker (2008) introduced a new class of bivariate distributions based on distributions of order statistics from two independent samples of size n. Lin-Huang (2010) discovered an important property of Baker's distribution and showed that the Pearson's correlation coefficient for this distribution converges to maximum attainable value, i.e. the correlation coefficient of the Frech\'et upper bound, as n increases to infinity. Bairamov and Bayramoglu (2011) investigated a new class of bivariate distributions constructed by using Baker's model and distributions of order statistics from dependent random variables, allowing high correlation than that of Baker's distribution. In this paper a new class of Baker's type bivariate distributions with high correlation are constructed on the base of distributions of order statistics by using an arbitrary continuous copula instead of the product copula. Keywords: Bivariate distribution function, FGM distributions, copula, positive quadrant dependent, negative quadrant dependent, order statistics, Pearson's correlation coefficient.

We propose an Euclidean geometric representation for the classical detection theory. The proposed representation is so generic that can be employed to almost all communication problems. The hypotheses and observations are mapped into R^N in such a way that a posteriori probability of an hypothesis given an observation decreases exponentially with the square of the Euclidean distance between the vectors corresponding to the hypothesis and the observation., Comment: 5 pages, 3 figures, submitted to ISIT 2010

We show that any joint probability mass function (PMF) can be expressed as a product of parity check factors and factors of degree one with the help of some auxiliary variables, if the alphabet size is appropriate for defining a parity check equation. In other words, marginalization of a joint PMF is equivalent to a soft decoding task as long as a finite field can be constructed over the alphabet of the PMF. In factor graph terminology this claim means that a factor graph representing such a joint PMF always has an equivalent Tanner graph. We provide a systematic method based on the Hilbert space of PMFs and orthogonal projections for obtaining this factorization., Comment: 5 pages, 1 figures, appeared in the proceedings of ISIT 2009; Changed content, more recent version than as appeared in the proceedings