The lottery is a very lucrative industry. Popular fascination often focuses on the largest prizes. However, less attention has been paid to detecting unusual lottery buying behaviors at lower stakes. Our paper introduces a new model to detect illegal discounting in the North Carolina Education Lottery using statistical analysis of net gains and ticket buying habits. Nine outlying players are flagged and are further examined using a proposed stochastic model to calculate the range of their possible losses in the lottery. The unusual buying patterns of the players flagged as outliers are further confirmed using a K-means clustering analysis of lottery store visiting behaviors.

Data matrix centering is an ever-present yet under-examined aspect of data analysis. Functional data analysis (FDA) often operates with a default of centering such that the vectors in one dimension have mean zero. We find that centering along the other dimension identifies a novel useful mode of variation beyond those familiar in FDA. We explore ambiguities in both matrix orientation and nomenclature. Differences between centerings and their potential interaction can be easily misunderstood. We propose a unified framework and new terminology for centering operations. We clearly demonstrate the intuition behind and consequences of each centering choice with informative graphics. We also propose a new direction energy hypothesis test as part of a series of diagnostics for determining which choice of centering is best for a data set. We explore the application of these diagnostics in several FDA settings.

Shape analysis is an important and powerful tool in a wide variety of medical applications. Many shape analysis techniques require shape representations which are in correspondence. Unfortunately, popular techniques for generating shape representations do not handle objects with complex geometry or topology well, and those that do are not typically readily available for non-expert users. We describe a method for generating correspondences across a population of objects using a given template. We also describe its implementation and distribution via SlicerSALT, an open-source platform for making powerful shape analysis techniques more widely available and usable. Finally, we show results of this implementation on mouse femur data.

Temporomandibular Joint (TMJ) Osteoarthritis (OA) is associated with significant pain and disability. It is really hard to diagnose TMJ OA during early stages of the disease. Subchondral bone texture has been observed to change in the TMJ early during TMJ OA progression. We believe that raw probability-distribution matrices describing image texture encode important information that might aid diagnosing TMJ OA. In this paper we present novel statistical methods for High Dimensionality Low Sample Size Data (HDLSSD) to test the discriminatory power of probability-distribution matrices in computed from TMJ OA medical scans. Our results, and comparison with previous results obtained from the summary features obtained from them indicate that probability-distribution matrices are an important piece of information provided by texture analysis methods and should not be down sampled for analysis.

Computed tomography (CT) images can potentially provide insights into bone structure for diagnosis of disorders and diseases. However, evaluation of trabecular bone structure and whole bone shape is often qualitative or semiquantitative. This limits inter-study comparisons and the ability to detect subtle bone quality variations during early disease onset or in response to new treatments. In this work, we enable quantitative characterization of bone diseases through bone morphometry, texture analysis, and shape analysis methods. The potential of our analysis methods to identify the impact of hemophilia is validated in a mouse femur wound model. In our results, shape localizes and characterizes the formation of spurious bone, and our texture and bone morphometry analysis results provide extra information about the composition of that bone. Some of our one-dimensional (1D) textural features were able to significantly differentiate our injured femurs from our healthy femurs, even with this small sample size demonstrating the potential of the proposed analysis framework. While trabecular bone morphometrics have been a pillar in 3D microCT bone research for decades, the proposed analysis framework augments how we define and understand phenotypical presentation of bone disease. The contributed open source software is exposed to the medical image analysis community through 3D Slicer extensions to ensure both robustness and reproducibility.

To date, there is no single sign, symptom, or test that can clearly diagnose early stages of Temporomandibular Joint Osteoarthritis (TMJ OA). However, it has been observed that changes in the bone occur in early stages of this disease, involving structural changes both in the texture and morphometry of the bone marrow and the subchondral cortical plate. In this paper we present a tool to detect and highlight subtle variations in subchondral bone structure obtained from high resolution Cone Beam Computed Tomography (hr-CBCT) in order to help with detecting early TMJ OA. The proposed tool was developed in ITK and 3DSlicer and it has been disseminated as open-source software tools. We have validated both our texture analysis and morphometry analysis biomarkers for detection of TMJ OA comparing hr-CBCT to μCT. Our initial statistical results using the multidimensional features computed with our tool indicate that it is possible to classify areas of demonstrated loss of trabecular bone in both μCT and hr-CBCT. This paper describes the first steps to alleviate the current inability of radiological changes to diagnose TMJ OA before morphological changes are too advanced by quantifying subchondral bone biomarkers. This paper indicates that texture based and morphometry based biomarkers have the potential to identify OA patients at risk for further bone destruction.