Two-body quantum mechanical problem on spheres

The quantum mechanical two-body problem with a central interaction on the sphere ${\bf S}^{n}$ is considered. Using recent results in representation theory an ordinary differential equation for some energy levels is found. For several interactive potentials these energy levels are calculated in explicit form.Comment: 41 pages, no figures, typos corrected; appendix D was adde

ROCK-Isoform-Specific Polarization of Macrophages Associated with Age-Related Macular Degeneration

Age is a major risk factor in age-related macular degeneration (AMD), but the underlying cause is unknown. We find increased Rho-associated kinase (ROCK) signaling and M2 characteristics in eyes of aged mice, revealing immune changes in aging. ROCK isoforms determine macrophage polarization into M1 and M2 subtypes. M2-like macrophages accumulated in AMD, but not in normal eyes, suggesting that these macrophages may be linked to macular degeneration. M2 macrophages injected into the mouse eye exacerbated choroidal neovascular lesions, while M1 macrophages ameliorated them, supporting a causal role for macrophage subtypes in AMD. Selective ROCK2 inhibition with a small molecule decreased M2-like macrophages and choroidal neovascularization. ROCK2 inhibition upregulated M1 markers without affecting macrophage recruitment, underlining the plasticity of these macrophages. These results reveal age-induced innate immune imbalance as underlying AMD pathogenesis. Targeting macrophage plasticity opens up new possibilities for more effective AMD treatment

Relationship between the Clinical Frailty Scale and short-term mortality in patients ≥ 80 years old acutely admitted to the ICU: a prospective cohort study.

BACKGROUND: The Clinical Frailty Scale (CFS) is frequently used to measure frailty in critically ill adults. There is wide variation in the approach to analysing the relationship between the CFS score and mortality after admission to the ICU. This study aimed to evaluate the influence of modelling approach on the association between the CFS score and short-term mortality and quantify the prognostic value of frailty in this context. METHODS: We analysed data from two multicentre prospective cohort studies which enrolled intensive care unit patients ≥ 80 years old in 26 countries. The primary outcome was mortality within 30-days from admission to the ICU. Logistic regression models for both ICU and 30-day mortality included the CFS score as either a categorical, continuous or dichotomous variable and were adjusted for patient's age, sex, reason for admission to the ICU, and admission Sequential Organ Failure Assessment score. RESULTS: The median age in the sample of 7487 consecutive patients was 84 years (IQR 81-87). The highest fraction of new prognostic information from frailty in the context of 30-day mortality was observed when the CFS score was treated as either a categorical variable using all original levels of frailty or a nonlinear continuous variable and was equal to 9% using these modelling approaches (p < 0.001). The relationship between the CFS score and mortality was nonlinear (p < 0.01). CONCLUSION: Knowledge about a patient's frailty status adds a substantial amount of new prognostic information at the moment of admission to the ICU. Arbitrary simplification of the CFS score into fewer groups than originally intended leads to a loss of information and should be avoided. Trial registration NCT03134807 (VIP1), NCT03370692 (VIP2)