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

Post-intervention Status in Patients With Refractory Myasthenia Gravis Treated With Eculizumab During REGAIN and Its Open-Label Extension

OBJECTIVE: To evaluate whether eculizumab helps patients with anti-acetylcholine receptor-positive (AChR+) refractory generalized myasthenia gravis (gMG) achieve the Myasthenia Gravis Foundation of America (MGFA) post-intervention status of minimal manifestations (MM), we assessed patients' status throughout REGAIN (Safety and Efficacy of Eculizumab in AChR+ Refractory Generalized Myasthenia Gravis) and its open-label extension. METHODS: Patients who completed the REGAIN randomized controlled trial and continued into the open-label extension were included in this tertiary endpoint analysis. Patients were assessed for the MGFA post-intervention status of improved, unchanged, worse, MM, and pharmacologic remission at defined time points during REGAIN and through week 130 of the open-label study. RESULTS: A total of 117 patients completed REGAIN and continued into the open-label study (eculizumab/eculizumab: 56; placebo/eculizumab: 61). At week 26 of REGAIN, more eculizumab-treated patients than placebo-treated patients achieved a status of improved (60.7% vs 41.7%) or MM (25.0% vs 13.3%; common OR: 2.3; 95% CI: 1.1-4.5). After 130 weeks of eculizumab treatment, 88.0% of patients achieved improved status and 57.3% of patients achieved MM status. The safety profile of eculizumab was consistent with its known profile and no new safety signals were detected. CONCLUSION: Eculizumab led to rapid and sustained achievement of MM in patients with AChR+ refractory gMG. These findings support the use of eculizumab in this previously difficult-to-treat patient population. CLINICALTRIALSGOV IDENTIFIER: REGAIN, NCT01997229; REGAIN open-label extension, NCT02301624. CLASSIFICATION OF EVIDENCE: This study provides Class II evidence that, after 26 weeks of eculizumab treatment, 25.0% of adults with AChR+ refractory gMG achieved MM, compared with 13.3% who received placebo

Minimal Symptom Expression' in Patients With Acetylcholine Receptor Antibody-Positive Refractory Generalized Myasthenia Gravis Treated With Eculizumab

The efficacy and tolerability of eculizumab were assessed in REGAIN, a 26-week, phase 3, randomized, double-blind, placebo-controlled study in anti-acetylcholine receptor antibody-positive (AChR+) refractory generalized myasthenia gravis (gMG), and its open-label extension

Gosset polytopes in integral octonions

summary:We study the integral quaternions and the integral octonions along the combinatorics of the $24$-cell, a uniform polytope with the symmetry $D_{4}$, and the Gosset polytope $4_{21}$ with the symmetry $E_{8}$. We identify the set of the unit integral octonions or quaternions as a Gosset polytope $4_{21}$ or a $24$-cell and describe the subsets of integral numbers having small length as certain combinations of unit integral numbers according to the $E_{8}$ or $D_{4}$ actions on the $4_{21}$ or the $24$-cell, respectively. Moreover, we show that each level set in the unit integral numbers forms a uniform polytope, and we explain the dualities between them. In particular, the set of the pure unit integral octonions is identified as a uniform polytope $2_{31}$ with the symmetry $E_{7}$, and it is a dual polytope to a Gosset polytope $3_{21}$ with the symmetry $E_{7}$ which is the set of the unit integral octonions with $\operatorname {Re}=1/2$

Effects of Glucocorticoid Therapy on Sepsis Depend Both on the Dose of Steroids and on the Severity and Phase of the Animal Sepsis Model

Steroids are currently being used in sepsis, particularly in septic shock. However, clinical trials to date have shown contradictory results. This could be attributed to the different patient endotypes and steroid doses, which have also contributed to the inconclusive results. We investigated the effects of glucocorticoid therapy on sepsis in a polymicrobial sepsis model in a variety of settings, such as steroid dose, severity, and sepsis phase. We used a rat model of fecal slurry polymicrobial sepsis. First, we investigated the optimum dose of steroids in a sepsis model. We administered different doses of dexamethasone after sepsis induction (0.1DEX; 0.1 mg/kg, 0.2DEX; 0.2 mg/kg, 5DEX; 5 mg/kg). Second, we used two different severities of the fecal slurry polymicrobial sepsis rat model to examine the effects of the steroids. A moderate or severe model was defined as a survival rate of approximately 70% and 30%, respectively. Third, we administered steroids in an early (1 h after sepsis induction) or late phase (25 h after sepsis). In all the experiments, we investigated the survival rates. In the determined optimal model and settings, we measured serum lactate, alanine transferase (ALT), creatinine, tumor necrosis factor-α (TNF-α), interleukin (IL)-6, IL-10, and arterial blood gas. We evaluated the bacterial burden in the blood and spleen. Endotoxin tolerance of peripheral blood mononuclear cells (PBMCs) and splenocytes was also investigated to determine the level of immune suppression 24 h after sepsis by measuring TNF-α production after stimulation with lipopolysaccharide (LPS) in an ex vivo model. Early treatment of 0.2 mg/kg dexamethasone in a severe sepsis model showed the best beneficial effects. In moderate- or late-phase sepsis, there was no survival gain with steroid treatment. DEX0.2 group showed less acute kidney injury manifested by serum creatinine and blood urea nitrogen. DEX decreased the levels of cytokines, including IL-6, IL-10, and TNF-α. Colony-forming units were significantly decreased in the blood when administered with dexamethasone. Endotoxin tolerance was not significantly different between the DEX0.2 and control groups. In conclusion, early treatment of 0.2 mg/kg dexamethasone improved the outcomes of rats in a severe sepsis model

Serial Change of Endotoxin Tolerance in a Polymicrobial Sepsis Model

Immune suppression is known to occur during sepsis. Endotoxin tolerance is considered a mechanism of immune suppression in sepsis. However, the timing and serial changes in endotoxin tolerance have not been fully investigated. In this study, we investigated serial changes in endotoxin tolerance in a polymicrobial sepsis model. Herein, we used a rat model of fecal slurry polymicrobial sepsis. After induction of sepsis, endotoxin tolerance of peripheral blood mononuclear cells (PBMCs) and splenocytes was measured at various time points (6 h, 12 h, 24 h, 48 h, 72 h, 5 days, and 7 days), through the measurement of TNF-α production after stimulation with lipopolysaccharide (LPS) in an ex vivo model. At each time point, we checked for plasma tumor necrosis factor (TNF)-α, interleukin (IL)-6, and IL-10 levels. Moreover, we analyzed reactive oxygen species (ROS) as measured by 2′,7′-dichlorodihydrofluorescein, plasma lactate, serum alanine aminotransferase (ALT), and creatinine levels. Nuclear factor (NF)-κB, IL-1 receptor-associated kinase (IRAK)-M, and cleaved caspase 3 levels were measured in the spleen. Endotoxin tolerance, measured by TNF-α production stimulated through LPS in PBMCs and splenocytes, was induced early in the sepsis model, starting from 6 h after sepsis. It reached a nadir at 24 to 48 h after sepsis, and then started to recover. Endotoxin tolerance was more prominent in the severe sepsis model. Plasma cytokines peaked at time points ranging from 6 to 12 h after sepsis. ROS levels peaked at 12 h and then decreased. Lactate, ALT, and serum creatinine levels increased up to 24 to 48 h, and then decreased. Phosphorylated p65 and IRAK-M levels of spleen increased up to 12 to 24 h and then decreased. Apoptosis was prominent 48 h after sepsis, and then recovered. In the rat model of polymicrobial sepsis, endotoxin tolerance occurred earlier and started to recover from 24 to 48 h after sepsis