Competitive analysis of interrelated price online inventory problems with demands

This paper investigates the interrelated price online inventory problems in which decisions as to when and how much to replenish must be made in an online fashion to meet some demand even without concrete knowledge of future prices. The objective of the decision maker is to minimize the total cost with the demands met. Two different types of demand are considered carefully, which are linearly related demand to price and exponentially related demand to price. In this paper, the prices are online with only the price range variation known in advance, which are interrelated with the preceding price. Two models of price correla- tions are investigated. Namely an exponential model and a logarithmic model. The corresponding algorithms of the problems are developed and the competitive ratio of the algorithms are also derived by the solutions of linear programming

Non-Euclidean statistics for covariance matrices with applications to diffusion tensor imaging

The statistical analysis of covariance matrix data is considered and, in particular, methodology is discussed which takes into account the nonEuclidean nature of the space of positive semi-definite symmetric matrices. The main motivation for the work is the analysis of diffusion tensors in medical image analysis. The primary focus is on estimation of a mean covariance matrix and, in particular, on the use of Procrustes size-and-shape space. Comparisons are made with other estimation techniques, including using the matrix logarithm, matrix square root and Cholesky decomposition. Applications to diffusion tensor imaging are considered and, in particular, a new measure of fractional anisotropy called Procrustes Anisotropy is discussed

Procrustes analysis for diffusion tensor image processing

There is an increasing need to develop processing tools for diffusion tensor image data with the consideration of the non-Euclidean nature of the tensor space. In this paper Procrustes analysis, a non-Euclidean shape analysis tool under similarity transformations (rotation, scaling and translation), is proposed to redefine sample statistics of diffusion tensors. A new anisotropy measure Procrustes Anisotropy (PA) is defined with the full ordinary Procrustes analysis. Comparisons are made with other anisotropy measures including Fractional Anisotropy and Geodesic Anisotropy. The partial generalized Procrustes analysis is extended to a weighted generalized Procrustes framework for averaging sample tensors with different fractions of contributions to the mean tensor. Applications of Procrustes methods to diffusion tensor interpolation and smoothing are compared with Euclidean, Log-Euclidean and Riemannian methods

Effect of football boot upper padding on shooting accuracy and velocity performance

Football boots are marketed with a specific performance feature focus, for example, power boots are marketed for optimal shooting performance. However, little evidence exists on the impact of boot design on shooting performance. This study assessed the effect of upper padding on shooting velocity and accuracy using a test–retest reliable test setup. Nine university level football players performed a protocol of shooting to: (1) maximise velocity; and (2) maximise accuracy in football boots with and without upper padding (Poron Memory foam). The protocol was completed twice; the non-padded boot results were used for test–retest validation, while the non-padded versus padding results were used to investigate the effect of padding. Velocity was assessed through actual ball velocity, percentage of maximum velocity and perceived velocity. Accuracy was assessed through radial offset, vertical offset, horizontal offset, success (goal/no goal), zonal offset and perceived accuracy. No significant differences between boots were observed in the velocity measures for either velocity or accuracy focused shots. Significant differences between boots were observed in vertical offset for both accuracy (without padding mean ± standard deviation − 0.02 ± 1.05 m, with padding 0.28 ± 0.87 m, P = 0.029) and velocity (without padding 0.04 ± 1.33 m, with padding 0.38 ± 0.86 m, P = 0.042) focused shots resulting in more missed shots above the goal for the padded boot (without padding 41–43% missed, with padding 56–72% missed). These findings suggest the addition of upper padding has a negative impact on shooting accuracy while not impacting shooting velocity.</div

Weighted generalised Procrustes analysis of diffusion tensors

Weighted generalised Procrustes analysis of diffusion tensor

Bayesian multi-tensor diffusion MRI and tractography

Bayesian multi-tensor diffusion MRI and tractograph

The effect of football boot upper padding on dribbling and passing performance using a test–retest validated protocol

Touch/control football boots are reportedly designed for optimal passing and dribbling. Little research exists on the effect of boot design on touch/control performance and no validated protocol has been developed for assessing passing and dribbling from an equipment focus. This study aimed to assess the effect of upper padding on dribbling and passing performance using a test–retest reliable test setup. Eight university players performed a protocol of dribbling, short and long passing in football boots with 0 and 6 mm of upper padding (Poron foam). The protocol was completed twice; the 0-mm padding results were used for test–retest validation, while the 0-mm versus 6-mm padding results were used to investigate the effect of padding. Dribbling performance was assessed though completion time, number of touches applied and lateral deviation from cones and passing performance through ball velocity and offset from target. The protocol demonstrated good test–retest reliability and indicated no significant differences in any of the 12 performance variables between the 0- and 6-mm padded boots. These findings suggest an element of design freedom in the use of padding within football boot uppers without affecting dribbling or passing performance

Modeling diffusion directions of Corpus Callosum

Diffusion Tensor Imaging (DTI) has been used to study the characteristics of Multiple Sclerosis (MS) in the brain. The von Mises- Fisher distribution (vmf) is a probability distribution for modeling directional data on the unit hypersphere. In this paper we modeled the diffusion directions of the Corpus Callosum (CC) as a mixture of vmf distributions for both MS subjects and healthy controls. Higher diffusion concentration around the mean directions and smaller sum of angles between the mean directions are observed on the normal-appearing CC of the MS subjects as compared to the healthy controls

Competitive analysis of online inventory problem with interrelated prices

This paper investigates the online inventory problem with interrelated prices in which a decision of when and how much to replenish must be made in an online fashion even without concrete knowledge of future prices. Four new online models with different price correlations are proposed in this paper, which are the linear-decrease model, the log-decrease model, the logarithmic model and the exponential model. For the first two models, the online algorithms are developed, and as the performance measure of online algorithm, the upper and lower bounds of competitive ratios of the algorithms are derived respectively. For the exponential and logarithmic models, the online algorithms are proposed by the solution of linear programming and the corresponding competitive ratios are analyzed, respectively. Additionally, the algorithm designed for the exponential model is optimal, and the algorithm for the logarithmic model is optimal only under some certain conditions. Moreover, some numerical examples illustrate that the algorithms based on the dprice-conservative strategy are more suitable when the purchase price fluctuates relatively flat

Core-shell NaHoF4@TiO2 NPs: A labelling method to trace engineered nanomaterials of ubiquitous elements in the environment

Understanding the fate and behavior of nanoparticles (NPs) in the natural environment is important to assess their potential risk. Single particle inductively coupled plasma mass spectrometry (spICP-MS) allows for the detection of NPs at extremely low concentrations, but the high natural background of the constituents of many of the most widely utilized nanoscale materials makes accurate quantification of engineered particles challenging. Chemical doping, with a less naturally abundant element, is one approach to address this; however, certain materials with high natural abundance, such as TiO2 NPs, are notoriously difficult to label and differentiate from natural NPs. Using the low abundance rare earth element Ho as a marker, Ho-bearing core -TiO2 shell (NaHoF4@TiO2) NPs were designed to enable the quantification of engineered TiO2 NPs in real environmental samples. The NaHoF4@TiO2 NPs were synthesized on a large scale (gram), at relatively low temperatures, using a sacrificial Al(OH)3 template that confines the hydrolysis of TiF4 within the space surrounding the NaHoF4 NPs. The resulting NPs consist of a 60 nm NaHoF4 core and a 5 nm anatase TiO2 shell, as determined by TEM, STEM-EDX mapping, and spICPMS. The NPs exhibit excellent detectability by spICP-MS at extremely low concentrations (down to 1 × 10−3 ng/L) even in complex natural environments with high Ti background