The Octonions

The octonions are the largest of the four normed division algebras. While somewhat neglected due to their nonassociativity, they stand at the crossroads of many interesting fields of mathematics. Here we describe them and their relation to Clifford algebras and spinors, Bott periodicity, projective and Lorentzian geometry, Jordan algebras, and the exceptional Lie groups. We also touch upon their applications in quantum logic, special relativity and supersymmetry.Comment: 56 pages LaTeX, 11 Postscript Figures, some small correction

Improved Regret Bounds of (Multinomial) Logistic Bandits via Regret-to-Confidence-Set Conversion

Logistic bandit is a ubiquitous framework of modeling users' choices, e.g., click vs. no click for advertisement recommender system. We observe that the prior works overlook or neglect dependencies in $S \geq \lVert \theta_\star \rVert_2$, where $\theta_\star \in \mathbb{R}^d$ is the unknown parameter vector, which is particularly problematic when $S$ is large, e.g., $S \geq d$. In this work, we improve the dependency on $S$ via a novel approach called {\it regret-to-confidence set conversion (R2CS)}, which allows us to construct a convex confidence set based on only the \textit{existence} of an online learning algorithm with a regret guarantee. Using R2CS, we obtain a strict improvement in the regret bound w.r.t. $S$ in logistic bandits while retaining computational feasibility and the dependence on other factors such as $d$ and $T$. We apply our new confidence set to the regret analyses of logistic bandits with a new martingale concentration step that circumvents an additional factor of $S$. We then extend this analysis to multinomial logistic bandits and obtain similar improvements in the regret, showing the efficacy of R2CS. While we applied R2CS to the (multinomial) logistic model, R2CS is a generic approach for developing confidence sets that can be used for various models, which can be of independent interest.Comment: 32 pages, 2 figures, 1 tabl

TESTING OF ROTATIONAL EXERCISE EQUIPMENT TO IMPROVE THE VESTIBULAR SYSTEM

The primary purpose of this study was to test the effect of training using the rotational exercise equipment developed in this study on the improvement of the vestibular system. In order to test the rotational exercise equipment developed in this study, 15 ordinary college students had trainings for 8 weeks and their nystagmus intensity was analyzed. The findings showed that the rotational training using the rotational exercise equipment affected vestibular balance, as it significantly decreased the slow phase velocity (SPV) immediately after rotational stimulation and reduced the recovery time of nystagmus to normal

BIOMECHANICAL ANALYSIS A SEQENCE OF ANGULAR VELOCITY AND COORDINATED MUSCLES ACTIVITY DURING BASEBALL HITTING

The purpose of this study was to analyse a sequence of rotations and coordinated muscles activities of upper body. Using kinematic and EMG data from 3 recreational university baseball players participating in this study, we computed the angular velocity of trunk, pelvis, bat and trunk-pelvis rotation angle and PMT of upper body muscles. Trunkpelvis rotation angle was 22 ° before the bat-ball contact. The pelvis, trunk, and bat showed a sequence of angular velocity beginning with the hip, followed by the trunk, and end tip of the bat. Additionally, PMT of upper body muscles generated right pectoralis major(1.03 sec.), right external oblique(1.11 sec.), left thoracloumbar fasci(1.12 sec.), left external oblique(1.13 sec.), right latissimus dorsi(1.15 sec.), left latissimus dorsi(1.16 sec.), right thoracloumbar fascia(1.16 sec.), left pectoralis major(1.25 sec.), on at a time during baseball hitting motion. PMT of upper body muscles were related to the shifting and rotating of body segment and this action can be considered the coordinated muscle activities of upper body

Massive transfusion protocol: the reason it is necessary

Objective. The purpose of this study is to identify problems of emergency transfusion at the bedside and to determine need for massive transfusion protocol. Methods. We included patients who met the criteria for “trauma team activation” and were admitted to division of trauma. The amount of blood product transfused in each unit was investigated for balanced transfusion. We also investigated the compliance with assessment of blood consumption score. The correlation between the time elapsed from patient visit to first transfusion order and time elapsed from first transfusion order to transfusion start was analyzed. Finally, we investigated various factors which serve to influence the decision-making process regarding early transfusion order. Results. Ratio of packed Red blood cells (pRBC): Fresh frozen plasma (FFP) was well-balanced, but platelet transfusion done was much lower than pRBC and FFP in emergency room. The application of emergency blood release did not match the criteria of assessment of blood consumption (ABC) score. The time from the first transfusion order to the transfusion start was found to be constant irrespective of time from patient visit to first transfusion order. And, the time from the first transfusion order to transfusion start did not differ significantly among patients with early transfusion order and delayed transfusion order. Only systolic blood pressure of < 90 mmHg was identified as a major predictor for early transfusion order. Conclusion. Balanced transfusion is not easy and emergency transfusion could be delayed at the bedside. Integrated and systematic structures for massive transfusion protocol would be invaluable and indispensable

Relationship between Bone-Specific Physical Activity Scores and Measures for Body Composition and Bone Mineral Density in Healthy Young College Women.

OBJECTIVE: The purpose of this cross-sectional study was to investigate the relationship between bone-specific physical activity (BPAQ) scores, body composition, and bone mineral density (BMD) in healthy young college women. METHODS: Seventy-three college women (21.7 ± 1.8 years; 162.1 ± 4.6 cm; 53.9 ± 5.8 kg) between the ages of 19 and 26 years were recruited from the universities in Seoul and Gyeonggi province, South Korea. We used dual energy X-ray absorptiometry to measure the lumbar spine (L2-L4) and proximal femur BMD (left side; total hip, femoral neck). The BPAQ scores (past, pBPAQ; current, cBPAQ; total, tBPAQ) were used to obtain a comprehensive account of lifetime physical activity related to bone health. We used X-scan plus II instrumentation to measure height (cm), weight (kg), fat free mass (FFM, kg), percent body fat (%), and body mass index (BMI). Participants were asked to record their 24-hour food intake in a questionnaire. RESULTS: There were positive correlations between BPAQ scores and total hip (pBPAQ r = 0.308, p = 0.008; tBPAQ, r = 0.286, p = 0.014) and FN BMD (pBPAQ r = 0.309, p = 0.008; tBPAQ, r = 0.311, p = 0.007), while no significant relationships were found in cBPAQ (p \u3e 0.05). When FFM, Vitamin D intake, cBPAQ, pBPAQ, and tBPAQ were included in a stepwise multiple linear regression analysis, FFM and pBPAQ were predictors of total hip, accounting for 16% (p = 0.024), while FFM and tBPAQ predicted 14% of the variance in FN (p = 0.015). Only FFM predicted 15% of the variance in L2-L4 (p = 0.004). There was a positive correlation between Vitamin D intake and L2-L4 (p = 0.025), but other dietary intakes variables were not significant (p \u3e 0.05). CONCLUSIONS: BPAQ-derived physical activity scores and FFM were positively associated with total hip and FN BMD in healthy young college women. Our study suggests that osteoporosis awareness and effective bone healthy behaviors for college women are required to prevent serious bone diseases later in life