On combinatorial expansion of the conformal blocks arising from AGT conjecture

In their recent paper \cite{Alday:2009aq} Alday, Gaiotto and Tachikawa proposed a relation between $\mathcal{N}=2$ four-dimensional supersymmetric gauge theories and two-dimensional conformal field theories. As part of their conjecture they gave an explicit combinatorial formula for the expansion of the conformal blocks inspired from the exact form of instanton part of the Nekrasov partition function. In this paper we study the origin of such an expansion from a CFT point of view. We consider the algebra $\mathcal{A}=\text{\sf Vir}\otimes\mathcal{H}$ which is the tensor product of mutually commuting Virasoro and Heisenberg algebras and discover the special orthogonal basis of states in the highest weight representations of $\mathcal{A}$. The matrix elements of primary fields in this basis have a very simple factorized form and coincide with the function called $Z_{\text{\sf{bif}}}$ appearing in the instanton counting literature. Having such a simple basis, the problem of computation of the conformal blocks simplifies drastically and can be shown to lead to the expansion proposed in \cite{Alday:2009aq}. We found that this basis diagonalizes an infinite system of commuting Integrals of Motion related to Benjamin-Ono integrable hierarchy.Comment: References added, misprints corrected, the exposition has been substantially improve

The effect of endurance exercise on both skeletal muscle and systemic oxidative stress in previously sedentary obese men

Background: Obesity is associated with low-grade systemic inflammation, in part because of secretion of proinflammatory cytokines, resulting into peripheral insulin resistance (IR). Increased oxidative stress is proposed to link adiposity and chronic inflammation. The effects of endurance exercise in modulating these outcomes in insulin-resistant obese adults remain unclear. We investigated the effect of endurance exercise on markers of oxidative damage (4-hydroxy-2-nonenal (4-HNE), protein carbonyls (PCs)) and antioxidant enzymes (superoxide dismutase (SOD), catalase) in skeletal muscle; urinary markers of oxidative stress (8-hydroxy-2-deoxyguanosine (8-OHdG), 8-isoprostane); and plasma cytokines (C-reactive protein (CRP), interleukin-6 (IL-6), leptin, adiponectin). Methods: Age- and fitness-matched sedentary obese and lean men (n=9 per group) underwent 3 months of moderate-intensity endurance cycling training with a vastus lateralis biopsy, 24-h urine sample and venous blood samples taken before and after the intervention. Results: Obese subjects had increased levels of oxidative damage: 4-HNE (+37% P⩽0.03) and PC (+63% P⩽0.02); evidence of increased adaptive response to oxidative stress because of elevated levels of copper/zinc SOD (Cu/ZnSOD) protein content (+84% P⩽0.01); increased markers of inflammation: CRP (+737% P⩽0.0001) and IL-6 (+85% P⩽0.03), and these correlated with increased markers of obesity; and increased leptin (+262% P⩽0.0001) with lower adiponectin (−27% P⩽0.01) levels vs lean controls. Training reduced 4-HNE (−10% P⩽0.04), PC (−21% P⩽0.05), 8-isoprostane (−26% P⩽0.02) and leptin levels (−33% P⩽0.01); had a tendency to decrease IL-6 levels (−21% P=0.07) and IR (−17% P=0.10); and increased manganese SOD (MnSOD) levels (+47% P⩽0.01). Conclusion: Endurance exercise reduced skeletal muscle-specific and systemic oxidative damage while improving IR and cytokine profile associated with obesity, independent of weight loss. Hence, exercise is a useful therapeutic modality to reduce risk factors associated with the pathogenesis of IR in obesity

A remark on the three approaches to 2D Quantum gravity

The one-matrix model is considered. The generating function of the correlation numbers is defined in such a way that this function coincide with the generating function of the Liouville gravity. Using the Kontsevich theorem we explain that this generating function is an analytic continuation of the generating function of the Topological gravity. We check the topological recursion relations for the correlation functions in the $p$-critical Matrix model.Comment: 11 pages. Title changed, presentation improve

Perspectives on Exertional Rhabdomyolysis

© 2017, The Author(s). Exertional (exercise-induced) rhabdomyolysis is a potentially life threatening condition that has been the subject of research, intense discussion, and media attention. The causes of rhabdomyolysis are numerous and can include direct muscle injury, unaccustomed exercise, ischemia, extreme temperatures, electrolyte abnormalities, endocrinologic conditions, genetic disorders, autoimmune disorders, infections, drugs, toxins, and venoms. The objective of this article is to review the literature on exertional rhabdomyolysis, identify precipitating factors, and examine the role of the dietary supplement creatine monohydrate. PubMed and SPORTDiscus databases were searched using the terms rhabdomyolysis, muscle damage, creatine, creatine supplementation, creatine monohydrate, and phosphocreatine. Additionally, the references of papers identified through this search were examined for relevant studies. A meta-analysis was not performed. Although the prevalence of rhabdomyolysis is low, instances still occur where exercise is improperly prescribed or used as punishment, or incomplete medical history is taken, and exertional rhabdomyolysis occurs. Creatine monohydrate does not appear to be a precipitating factor for exertional rhabdomyolysis. Healthcare professionals should be able to recognize the basic signs of exertional rhabdomyolysis so prompt treatment can be administered. For the risk of rhabdomyolysis to remain low, exercise testing and prescription must be properly conducted based on professional standards

Sex differences in exercise-induced diaphragmatic fatigue in endurance-trained athletes

There is evidence that female athletes may be more susceptible to exercise-induced arterial hypoxemia and expiratory flow limitation and have greater increases in operational lung volumes during exercise relative to men. These pulmonary limitations may ultimately lead to greater levels of diaphragmatic fatigue in women. Accordingly, the purpose of this study was to determine whether there are sex differences in the prevalence and severity of exercise-induced diaphragmatic fatigue in 38 healthy endurance-trained men (n = 19; maximal aerobic capacity = 64.0 ± 1.9 ml·kg–1·min–1) and women (n = 19; maximal aerobic capacity = 57.1 ± 1.5 ml·kg–1·min–1). Transdiaphragmatic pressure (Pdi) was calculated as the difference between gastric and esophageal pressures. Inspiratory pressure-time products of the diaphragm and esophagus were calculated as the product of breathing frequency and the Pdi and esophageal pressure time integrals, respectively. Cervical magnetic stimulation was used to measure potentiated Pdi twitches (Pdi,tw) before and 10, 30, and 60 min after a constant-load cycling test performed at 90% of peak work rate until exhaustion. Diaphragm fatigue was considered present if there was a 15% reduction in Pdi,tw after exercise. Diaphragm fatigue occurred in 11 of 19 men (58%) and 8 of 19 women (42%). The percent drop in Pdi,tw at 10, 30, and 60 min after exercise in men (n = 11) was 30.6 ± 2.3, 20.7 ± 3.2, and 13.3 ± 4.5%, respectively, whereas results in women (n = 8) were 21.0 ± 2.1, 11.6 ± 2.9, and 9.7 ± 4.2%, respectively, with sex differences occurring at 10 and 30 min (P < 0.05). Men continued to have a reduced contribution of the diaphragm to total inspiratory force output (pressure-time product of the diaphragm/pressure-time product of the esophagus) during exercise, whereas diaphragmatic contribution in women changed very little over time. The findings from this study point to a female diaphragm that is more resistant to fatigue relative to their male counterparts

Safety and physiological effects of two different doses of elosulfase alfa in patients with morquio a syndrome: A randomized, double-blind, pilot study.

The primary treatment outcomes of a phase 2, randomized, double-blind, pilot study evaluating safety, physiological, and pharmacological effects of elosulfase alfa in patients with Morquio A syndrome are herewith presented. Patients aged ≥7 years and able to walk ≥200 m in the 6-min walk test (6MWT) were randomized to elosulfase alfa 2.0 or 4.0 mg/kg/week for 27 weeks. The primary objective was to evaluate the safety of both doses. Secondary objectives were to evaluate effects on endurance (6MWT and 3-min stair climb test [3MSCT]), exercise capacity (cardio-pulmonary exercise test [CPET]), respiratory function, muscle strength, cardiac function, pain, and urine keratan sulfate (uKS) levels, and to determine pharmacokinetic parameters. Twenty-five patients were enrolled (15 randomized to 2.0 mg/kg/week and 10 to 4.0 mg/kg/week). No new or unexpected safety signals were observed. After 24 weeks, there were no improvements versus baseline in the 6MWT, yet numerical improvements were seen in the 3MSCT with 4.0 mg/kg/week. uKS and pharmacokinetic data suggested no linear relationship over the 2.0-4.0 mg/kg dose range. Overall, an abnormal exercise capacity (evaluated in 10 and 5 patients in the 2.0 and 4.0 mg/kg/week groups, respectively), impaired muscle strength, and considerable pain were observed at baseline, and there were trends towards improvements in all domains after treatment. In conclusion, preliminary data of this small study in a Morquio A population with relatively good endurance confirmed the acceptable safety profile of elosulfase alfa and showed a trend of increased exercise capacity and muscle strength and decreased pain

Performance of ab initio and density functional methods for conformational equilibria of CnH2n+2 alkane isomers (n=2-8)

Conformational energies of n-butane, n-pentane, and n-hexane have been calculated at the CCSD(T) level and at or near the basis set limit. Post-CCSD(T) contribution were considered and found to be unimportant. The data thus obtained were used to assess the performance of a variety of density functional methods. Double-hybrid functionals like B2GP-PLYP and B2K-PLYP, especially with a small Grimme-type empirical dispersion correction, are capable of rendering conformational energies of CCSD(T) quality. These were then used as a `secondary standard' for a larger sample of alkanes, including isopentane and the branched hexanes as well as key isomers of heptane and octane. Popular DFT functionals like B3LYP, B3PW91, BLYP, PBE, and PBE0 tend to overestimate conformer energies without dispersion correction, while the M06 family severely underestimates GG interaction energies. Grimme-type dispersion corrections for these overcorrect and lead to qualitatively wrong conformer orderings. All of these functionals also exhibit deficiencies in the conformer geometries, particularly the backbone torsion angles. The PW6B95 and, to a lesser extent, BMK functionals are relatively free of these deficiencies. Performance of these methods is further investigated to derive conformer ensemble corrections to the enthalpy function, $H_{298}-H_0$, and the Gibbs energy function, ${\rm gef}(T)\equiv - [G(T)-H_0]/T$, of these alkanes. While $H_{298}-H_0$ is only moderately sensitive to the level of theory, ${\rm gef}(T)$ exhibits more pronounced sensitivity. Once again, double hybrids acquit themselves very well.Comment: J. Phys. Chem. A, revised [Walter Thiel festschrift

Parafermionic Liouville field theory and instantons on ALE spaces

In this paper we study the correspondence between the $\hat{\textrm{su}}(n)_{k}\oplus \hat{\textrm{su}}(n)_{p}/\hat{\textrm{su}}(n)_{k+p}$ coset conformal field theories and $\mathcal{N}=2$ SU(n) gauge theories on $\mathbb{R}^{4}/\mathbb{Z}_{p}$. Namely we check the correspondence between the SU(2) Nekrasov partition function on $\mathbb{R}^{4}/\mathbb{Z}_{4}$ and the conformal blocks of the $S_{3}$ parafermion algebra (in $S$ and $D$ modules). We find that they are equal up to the U(1)-factor as it was in all cases of AGT-like relations. Studying the structure of the instanton partition function on $\mathbb{R}^4/\mathbb{Z}_p$ we also find some evidence that this correspondence with arbitrary $p$ takes place up to the U(1)-factor.Comment: 21 pages, 6 figures, misprints corrected, references added, version to appear in JHE

Effect of Galactose Ingestion Before and During Exercise on Substrate Oxidation, Postexercise Satiety, and Subsequent Energy Intake in Females.

OBJECTIVE: To examine the effects of consuming a galactose carbohydrate (CHO) drink on substrate oxidation, postexercise satiety, and subsequent energy intake. METHODS: Nine recreationally active eumenorrheic females undertook 3 trials, each consisting of running for 60 minutes at 65% VO2peak followed immediately by a 90-minute rest period. Prior to (300 ml) and at 15-minute intervals during exercise (150 ml), participants consumed either a glucose (GLU: GI 89) or galactose (GAL: GI 20) drink, each of which contained 45 g of CHO, or an artificially sweetened placebo (PLA). Following the rest period, participants were provided with an ad libitum test lunch and asked to record food intake for the remainder of the day. RESULTS: Plasma glucose was significantly greater throughout exercise and rest following the GLU trial compared with the GAL and PLA trials (P < 0.05); however there were no differences in CHO oxidation. Hunger was significantly lower (P < 0.05) throughout the GAL compared to the GLU and PLA trials. There were no significant differences between trials for energy intake during the postexercise meal. Overall net energy balance for the 24 hours was negative in both the GAL (-162 ± 115 kcal; P < 0.05 vs GLU) and PLA trials (-49 ± 160 kcal). CONCLUSIONS: Results demonstrate that ingesting a solution containing GAL before and during exercise can positively impact postexercise satiety and energy balance throughout the day, compared to a more readily available and widely consumed form of CHO. Despite this, there appears to be no apparent benefit in consuming a CHO beverage on fuel utilization for this moderate exercise intensity and duration

Vacuum decay in CFT and the Riemann-Hilbert problem

We study vacuum stability in 1 + 1 dimensional Conformal Field Theories with external background fields. We show that the vacuum decay rate is given by a non-local two-form. This two-form is a boundary term that must be added to the effective in/out Lagrangian. The two-form is expressed in terms of a Riemann-Hilbert decomposition for background gauge fields, and its novel "functional" version in the gravitational case