It is widely believed that the median is “usually” between the mean and the mode for skewed unimodal distributions. However, this inequality is not always true, especially with grouped data. Unavailability of complete raw data further necessitates the importance of evaluating this characteristic in grouped data. There is a gap in the current statistical literature on assessing mean–median–mode inequality for grouped data. The study aims to evaluate the relationship between the mean, median, and mode with unimodal grouped data; derive conditions for their inequalities; and present their application.

Background: Individuals with cerebral palsy (CP) are prone to sedentary life with limited recreational- and physical activity. RaceRunning (RR) is a sport for individuals with disabilities such as motor impairment that allow them to move independently and enjoy physical activity. The aim of the study was to investigate muscle fatigue of RR athletes with different classiffcation of CP during six minuteRaceRunning test (6MRRT). The Cerebral Palsy International Sports and RecreationAssociation has the goal to make RR a Paralympic sport. For a sport to be included in the Paralympics a classiffcation system has to be made. Information about muscle function during RR could give vital physical information about athletes with CP and contribute to the development of such classiffcation system. Method: Median frequency of the power spectrum from surface electromyography(sEMG) of four muscles (vastus lateralis, biceps femoris, gluteus medius, gastrocnemius lateralis) was computed along with amplitude changes (root mean square) in order to assess muscle fatigue. Results: Indications of muscle fatigue were observed from one out of five athletes for athlete's less affected side. Further sEMG studies with more subjects have to be conducted on CP RR athletes to give more conclusive results of muscle fatigue.

Many epidemiological studies have named pinching, deviated wrist postures, and repetitive motion as ergonomic risk factors in the development of carpal tunnel syndrome (CTS). Evidence suggests that hypervascularization of the median nerve and increased intraneural blood flow proximal to the carpal tunnel result in response to ergonomic risk factors (finger pressing and deviated wrist postures). The purposes of this study were to 1) determine the effect of a pinch posture, with and without force exerted by the finger, thumb, or both and 2) determine the effect of repetitive wrist flexion and extension on intraneural blood flow velocity in the median nerve proximal to the carpal tunnel. Eleven healthy and eleven CTS symptomatic individuals participated in this study and completed three components: 15 pinch posture force trials, 3 repetitive wrist motion trials, and 3 static wrist posture trials. Intraneural blood flow was measured using pulse wave Doppler during each trial. Main effects of pinch posture force (F4,80 = 21.397, p < 0.001) and wrist posture (F2,40 = 14.545, p < 0.001) were observed. Trials where force was applied by the finger (2.21 cm/s), thumb (2.22 cm/s) or both (2.34 cm/s) produced higher intraneural blood flow velocities than trials with no force (1.79 cm/s) or relaxed hand (1.89 cm/s). Trials performed in flexion (2.24 cm/s) were greater than neutral (2.06 cm/s) and extension (1.97 cm/s). No interactions or main effects of time were found in response to repetitive wrist motion. These results suggest that at low force levels (6 N) it’s not how the force is applied but rather that the force is being applied that has an effect on the median nerve. Additionally these results suggest that the contribution of repetitive motion to the development of CTS may not be directly to the median nerve. / Thesis / Master of Science (MSc)

京都大学 / 新制・論文博士 / 博士(医学) / 乙第13587号 / 論医博第2307号 / 新制||医||1070(附属図書館) / 京都大学大学院医学研究科医学専攻 / (主査)教授 安達 泰治, 教授 森本 尚樹, 教授 伊達 洋至 / 学位規則第4条第2項該当 / Doctor of Medical Science / Kyoto University / DFAM

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In recent years there has been a trend towards large-scale logistics for individual members of the public, such as ride-sharing services and drone package delivery. Efficient coordination of pickups and deliveries is essential in order to keep costs and wait times down. In this thesis we present these types of problems in a more general framework, expanding applicability of our discussion to an even wider domain of problems. We present fast new al- gorithms with supporting theoretical and experimental analysis, providing certain guarantees about how close our algorithms compare to a theoretically optimal approach. / Master of Science / In recent years there has been a trend towards large-scale logistics for individual members of the public, such as ride-sharing services and drone package delivery. Efficient coordination of pickups and deliveries is essential in order to keep costs and wait times down. In this thesis we present these types of problems in a more general framework, expanding applicability of our discussion to an even wider domain of problems. We present fast new algorithms with supporting theoretical and experimental analysis, providing certain guarantees about how close our algorithms compare to a theoretically optimal approach.

During the acquisition and transmission of images, it is important that the information is retained with the highest quality. Occasionally noise from various sources can corrupt an image. In this case, various image processing filtering techniques that are effective in removing noise can be used. Noise removal filters are designed to remove specific types of noise. However, they also degrade the image and detail is lost. This is particularly troublesome in cases where there is very little noise. A number of detail preserving filters have been proposed in the past, but most of the work was focused on monochrome images. With today's technological advancements, most of the images used are in full color, and detail preserving filters that have been designed for monochrome, cannot be directly applied for color. In this work, several detail preserving filters that have been designed to remove impulsive noise from color images are first surveyed and compared. We then consider the extension of detail preserving median filters to color images. At the end, we propose new filters that are capable of removing colored impulsive noise with minimum image degradation. Two user adjustable parameters can vary the strength of the filter for best results. Several comparisons with other previously proposed filters will be presented. Finally, in order to make the filter user friendly, an Adobe Photoshop plug-in is to be developed.

This study analyzes the market share of the top 10 home builders in nine Metropolitan Statistical Areas, along with fourteen other independent variables, to find a statistical relationship with median home sales price. Through a stepwise regression of the independent variables it is determined that there is no correlation between median home sale price and market share of the top 10 home builders. In the stepwise regression two variables are found to be correlated to median homes sales price: Owner Occupancy Percentage and Residential Construction Wages, a data point compiled for this study. A linear regression is run between market share of the top 10 and median home sale price and no correlation is found. / Master of Science / This study observes changes in median home sale price and changes in the market concentration of the top 10 home builders. Data from nine cities was analyzed. Using linear regression with the two previously mentioned variables along with fourteen other variables the study finds no relationship between the two variables. Among the variables the two that had the highest statistical relationship are Owner Occupancy Percentage and Residential Construction Wages. This study is relevant to the on-going discussion about concentration in the housing market.

This dissertation presents algorithms for restoring some of the major corruptions observed in archived film or video material. The two principal problems of impulsive distortion (Dirt and Sparkle or Blotches) and noise degradation are considered. There is also an algorithm for suppressing the inter-line jitter common in images decoded from noisy video signals. In the case of noise reduction and Blotch removal the thesis considers image sequences to be three dimensional signals involving evolution of features in time and space. This is necessary if any process presented is to show an improvement over standard two-dimensional techniques. It is important to recognize that consideration of image sequences must involve an appreciation of the problems incurred by the motion of objects in the scene. The most obvious implication is that due to motion, useful three dimensional processing does not necessarily proceed in a direction 'orthogonal' to the image frames. Therefore, attention is given to discussing motion estimation as it is used for image sequence processing. Some discussion is given to image sequence models and the 3D Autoregressive model is investigated. A multiresolution BM scheme is used for motion estimation throughout the major part of the thesis. Impulsive noise removal in image processing has been traditionally achieved by the use of median filter structures. A new three dimensional multilevel median structure is presented in this work with the additional use of a detector which limits the distortion caused by the filters . This technique is found to be extremely effective in practice and is an alternative to the traditional global median operation. The new median filter is shown to be superior to those previously presented with respect to the ability to reject the kind of distortion found in practice. A model based technique using the 3D AR model is also developed for detecting and removing Blotches. This technique achieves better fidelity at the expense of heavier computational load. Motion compensated 3D IIR and FIR Wiener filters are investigated with respect to their ability to reject noise in an image sequence. They are compared to several algorithms previously presented which are purely temporal in nature. The filters presented are found to be effective and compare favourably to the other algorithms. The 3D filtering process is superior to the purely temporal process as expected. The algorithm that is presented for suppressing inter-line jitter uses a 2D AR model to estimate and correct the relative displacements between the lines. The output image is much more satisfactory to the observer although in a severe case some drift of image features is to be expected. A suggestion for removing this drift is presented in the conclusions. There are several remaining problems in moving video. In particular, line scratches and picture shake/roll. Line scratches cannot be detected successfully by the detectors presented and so cannot be removed efficiently. Suppressing shake and roll involves compensating the entire frame for motion and there is a need to separate global from local motion. These difficulties provide ample opportunity for further research.

In a single capture-recapture problem, two new Wilson methods for interval estimation of population size are derived. Classical Chapman interval, Wilson and Wilson-cc intervals are examined and compared in terms of their expected interval width and exact coverage properties in two models. The new approach performs better than the Chapman in each model. Bayesian analysis also gives a different way to estimate population size.