We introduce a principal support vector machine (PSVM) approach that can be used for both linear and nonlinear sufficient dimension reduction. The basic idea is to divide the response variables into slices and use a modified form of support vector machine to find the optimal hyperplanes that separate them. These optimal hyperplanes are then aligned by the principal components of their normal vectors. It is proved that the aligned normal vectors provide an unbiased, √ n-consistent, and asymptotically normal estimator of the sufficient dimension reduction space. The method is then generalized to nonlinear sufficient dimension reduction using the reproducing kernel Hilbert space. In that context, the aligned normal vectors become functions and it is proved that they are unbiased in the sense that they are functions of the true nonlinear sufficient predictors. We compare PSVM with other sufficient dimension reduction methods by simulation and in real data analysis, and through both comparisons firmly establish its practical advantages.

A microfluidic platform developed for quantifying the dependence of erythrocyte (red blood cell, RBC) responses by ABO-Rh blood type via direct current insulator dielectrophoresis (DC-iDEP) is presented. The PDMS DC-iDEP device utilized a 400 x 170 μm² rectangular insulating obstacle embedded in a 1.46-cm long, 200-μm wide inlet channel to create spatial non-uniformities in direct current (DC) electric field density realized by separation into four outlet channels. The DC-iDEP flow behaviors were investigated for all eight blood types (A+, A-, B+, B-, AB+, AB-, O+, O-) in the human ABO-Rh blood typing system. Three independent donors of each blood type, same donor reproducibility, different conductivity buffers (0.52-9.1 mS/cm), and DC electric fields (17.1-68.5 V/cm) were tested to investigate separation dependencies. The data analysis was conducted from image intensity profiles across inlet and outlet channels in the device. Individual channel fractions suggest that the dielectrophoretic force experienced by the cells is dependent on erythrocyte antigen expression. Two different statistical analysis methods were conducted to determine how distinguishable a single blood type was from the others. Results indicate that channel fraction distributions differ by ABO-Rh blood types suggesting that antigens present on the erythrocyte membrane polarize differently in DC-iDEP fields. Under optimized conductivity and field conditions, certain blind blood samples could be sorted with low misclassification rates.

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1Purpose: The volleyball attack is the action winning the majority of points during a game and 2 attack effectiveness (AE) is therefore one of the most important predictors of victory. 3Traditionally, greater vertical jump heights (VJH) and higher spike speeds (SS) have been 4 thought to increase AE, however relevant research is limited. Our aim was to assess the 5 relationship of VJH and SS with AE as well as identify possible associations of demographic 6 and anthropometric factors, including common volleyball injuries, with VJH, SS and AE. Methods: Twenty two male volleyball players from two teams in the top division of the 8 Cypriot championship were included in the study. VJH was measured with the "jump-and-9 reach" test, SS was tested with a sports speed radar and AE was calculated from performance 10 sheets of four games between the two teams. 11Results: Significant results included strong, positive correlations between VJH and SS, %lean 12 mass and SS, body-bone% and SS, height and SS, and frequency of resistance training and SS. 13AE was found to increase with increasing age, while SS over 90km·h -1 appeared to have a 14 negative effect on AE. History of pain in the dominant shoulder and in the ankles/knees was 15 associated with lower SS and higher VJH respectively. 95Athletes who had at least one positive test on their dominant side were included in the 'shoulder 96 impingement' group. 97For an illustration and explanation of these tests the reader is referred to our previous article 12 . 98After a volleyball-specific 15-minute warm-up, each player was instructed to perform a vertical as an attack that won a point without the opposing team setting the ball for a counter-attack. 118'Tips' and 'roll shots' were included in the analysis. Videos of two matches were subsequently 119 watched and AE of each spiking player was calculated manually to confirm the accuracy of the 120 data of the team performance reports. 121The data for each team was collected before (interview and examination), during (SS) and after RESULTS 138The demographics and anthropometrics of the sample are shown in table 1. 139Pain history (shoulder and ankle/knee) and characteristics (mean±sd and range) of SS, AE and 140VJH are presented in table 2. 141Of the 10 athletes with ankle/knee pain history, 4 had knee pain history (2 past, 2 present) and 142 6 ankle pain history (4 past, 2 present). Two players had both ankle/knee pain history (one right 143 ankle -past, and the other left knee -past) and dominant shoulder pain history (both present). 187We believe that the most striking finding of the present study is the significantly lower AE with 188SS>90 km·h -1 compared with speeds<90 km·h -1 . Our assumption is that greater SS may be the 197The positive correlation between age and AE may be attributed to one of the following two not compromised compared to those without history of ankle/knee pain, it was in fact greater. 213We speculate that lower limb pain/injury in this group of players may be a consequence of their 21...

A major controversy in psychiatric genetics is whether nonadditive genetic interaction effects contribute to the risk of highly polygenic disorders. We applied a support vector machines (SVMs) approach, which is capable of building linear and nonlinear models using kernel methods, to classify cases from controls in a large schizophrenia case–control sample of 11,853 subjects (5,554 cases and 6,299 controls) and compared its prediction accuracy with the polygenic risk score (PRS) approach. We also investigated whether SVMs are a suitable approach to detecting nonlinear genetic effects, that is, interactions. We found that PRS provided more accurate case/control classification than either linear or nonlinear SVMs, and give a tentative explanation why PRS outperforms both multivariate regression and linear kernel SVMs. In addition, we observe that nonlinear kernel SVMs showed higher classification accuracy than linear SVMs when a large number of SNPs are entered into the model. We conclude that SVMs are a potential tool for assessing the presence of interactions, prior to searching for them explicitly.