Eta Products, BPS States and K3 Surfaces

Inspired by the multiplicative nature of the Ramanujan modular discriminant, Δ, we consider physical realizations of certain multiplicative products over the Dedekind eta-function in two parallel directions: the generating function of BPS states in certain heterotic orbifolds and elliptic K3 surfaces associated to congruence subgroups of the modular group. We show that they are, after string duality to type II, the same K3 surfaces admitting Nikulin automorphisms. In due course, we will present identities arising from q-expansions as well as relations to the sporadic Mathieu group M 24

N=2 Gauge Theories: Congruence Subgroups, Coset Graphs and Modular Surfaces

We establish a correspondence between generalized quiver gauge theories in four dimensions and congruence subgroups of the modular group, hinging upon the trivalent graphs which arise in both. The gauge theories and the graphs are enumerated and their numbers are compared. The correspondence is particularly striking for genus zero torsion-free congruence subgroups as exemplified by those which arise in Moonshine. We analyze in detail the case of index 24, where modular elliptic K3 surfaces emerge: here, the elliptic j-invariants can be recast as dessins d'enfant which dictate the Seiberg-Witten curves.Comment: 42+1 pages, 5 figures; various helpful comments incorporate

Moonshine and the Meaning of Life

With a jocund air, we present an observation on the first 24 coefficients of the modular invariant and of the modular discriminant. The observation is purely for the sake of entertainment and could be of some diversion to a mathematical audience.Comment: 1 pag

Anisotropic pair-superfluidity of trapped two-component Bose gases

We theoretically investigate the pair-superfluid phase of two-component ultracold gases with negative inter-species interactions in an optical lattice. We establish the phase diagram for filling $n=1$ at zero and finite temperature, by applying Bosonic Dynamical Mean-Field Theory, and confirm the stability of pair-superfluidity for asymmetric hopping of the two species. While the pair superfluid is found to be robust in the presence of a harmonic trap, we observe that it is destroyed already by a small population imbalance of the two species.Comment: 7 pages, 11 figure

Association between early treatment of multiple sclerosis and patient-reported outcomes: a nationwide observational cohort study

Background Timing of disease-modifying therapy affects clinical disability in multiple sclerosis, but it is not known whether patient reported outcomes are also affected. This study investigates the relationship between treatment timing and patient-reported symptoms and health-related quality of life. Methods This was a nationwide observational cohort study of adults with relapsing multiple sclerosis, with disease onset between 2001 and 2016, and commenced on disease-modifying treatment within 4 years from disease onset. Patients commencing treatment within 0–2 years were compared with patients commencing treatment at 2–4 years. Indication bias was mitigated by propensity matching. Outcomes were patient-reported symptoms and health-related quality of life as measured by the Multiple Sclerosis Impact Scale (MSIS-29) and EuroQol-5 Dimensions-3 Level (EQ-5D). The follow-up period was 4–10 years from disease onset. Results There were 2648 patients (69% female, median age 32.8) eligible for matching. Mean follow-up time was 3.7 years. Based on 780 matched patients, each year of treatment delay was associated with a worse MSIS physical score by 2.75 points (95% CI 1.29 to 4.20), and worse MSIS psychological score by 2.02 points (95% CI 0.03 to 3.78), in the adjusted models. Among 690 matched patients, earlier treatment start was not associated with EQ-5D score during the follow-up. Conclusions Earlier commencement of disease-modifying treatment was associated with better patient-reported physical symptoms when measured using a disease-specific metric; however, general quality of life was not affected. This indicates that other factors may inform patients’ overall quality of life

Premorbid Sociodemographic Status and Multiple Sclerosis Outcomes in a Universal Health Care Context

Importance: Multiple sclerosis (MS) severity may be informed by premorbid sociodemographic factors. Objective: To determine whether premorbid education, income, and marital status are associated with future MS disability and symptom severity, independent of treatment, in a universal health care context. Design, Setting, and Participants: This nationwide observational cohort study examined data from the Swedish MS Registry linked to national population registries from 2000 to 2020. Participants included people with MS onset from 2005 to 2015 and of working age (aged 23 to 59 years) 1 year and 5 years preceding disease onset. Exposures: Income quartile, educational attainment, and marital status measured at 1 and 5 years preceding disease onset. Main Outcome and Measures: Repeated measures of Expanded Disability Status Scale (EDSS) scores and patient-reported Multiple Sclerosis Impact Scale (MSIS-29) scores. Models were adjusted for age, sex, relapses, disease duration, and treatment exposure. Secondary analyses further adjusted for comorbidity. All analyses were stratified by disease course (relapse onset and progressive onset). Results: There were 4557 patients (mean [SD] age, 37.5 [9.3] years; 3136 [68.8%] female, 4195 [92.1%] relapse-onset MS) with sociodemographic data from 1-year preonset of MS. In relapse-onset MS, higher premorbid income and education correlated with lower disability (EDSS, -0.16 [95% CI, -0.12 to -0.20] points) per income quartile; EDSS, -0.47 [95% CI, -0.59 to -0.35] points if tertiary educated), physical symptoms (MSIS-29 physical subscore, -14% [95% CI, -11% to -18%] per income quartile; MSIS-29 physical subscore, -43% [95% CI, -35% to -50%] if tertiary educated), and psychological symptoms (MSIS-29 psychological subscore, -12% [95% CI, -9% to -16%] per income quartile; MSIS-29 psychological subscore, -25% [95% CI, -17% to -33%] if tertiary educated). Marital separation was associated with adverse outcomes (EDSS, 0.34 [95% CI, 0.18 to 0.51]; MSIS-29 physical subscore, 35% [95% CI, 12% to 62%]; MSIS-29 psychological subscore, 25% [95% CI, 8% to 46%]). In progressive-onset MS, higher income correlated with lower EDSS (-0.30 [95% CI, -0.48 to -0.11] points per income quartile) whereas education correlated with lower physical (-34% [95% CI, -53% to -7%]) and psychological symptoms (-33% [95% CI, -54% to -1%]). Estimates for 5-years preonset were comparable with 1-year preonset, as were the comorbidity-adjusted findings. Conclusions and relevance: In this cohort study of working-age adults with MS, premorbid income, education, and marital status correlated with disability and symptom severity in relapse-onset and progressive-onset MS, independent of treatment. These findings suggest that socioeconomic status may reflect both structural and individual determinants of health in MS

G(2) quivers

We present, in explicit matrix representation and a modernity befitting the community, the classification of the finite discrete subgroups of G2 and compute the McKay quivers arising therefrom. Of physical interest are the classes of Script N = 1 gauge theories descending from M-theory and of mathematical interest are possible steps toward a systematic study of crepant resolutions to smooth G2 manifolds as well as generalised McKay Correspondences. This writing is a companion monograph to hep-th/9811183 and hep-th/9905212, wherein the analogues for Calabi-Yau three- and four-folds were considered

Association between clinic-level quality of care and patient-level outcomes in multiple sclerosis

Background: Multiple sclerosis (MS) quality of care guidelines are consensus-based. The effectiveness of the recommendations is unknown.// Objective: To determine whether clinic-level quality of care affects clinical and patient-reported outcomes.// Methods: This nationwide observational cohort study included patients with adult-onset MS in the Swedish MS registry with disease onset 2005–2015. Clinic-level quality of care was measured by four indicators: visit density, magnetic resonance imaging (MRI) density, mean time to commencement of disease-modifying therapy, and data completeness. Outcomes were Expanded Disability Status Scale (EDSS) and patient-reported symptoms measured by the Multiple Sclerosis Impact Scale (MSIS-29). Analyses were adjusted for individual patient characteristics and disease-modifying therapy exposure.// Results: In relapsing MS, all quality indicators benefitted EDSS and physical symptoms. Faster treatment, frequent visits, and higher data completeness benefitted psychological symptoms. After controlling for all indicators and individual treatment exposures, faster treatment remained independently associated with lower EDSS (−0.06, 95% confidence interval (CI): −0.01, −0.10) and more frequent visits were associated with milder physical symptoms (MSIS-29 physical score: −16.2%, 95% CI: −1.8%, −29.5%). Clinic-level quality of care did not affect any outcomes in progressive-onset disease.// Conclusion: Certain quality of care indicators correlated to disability and patient-reported outcomes in relapse-onset but not progressive-onset disease. Future guidelines should consider recommendations specific to disease course..