A Schröder Generalization of Haglund's Statistic on Catalan Paths

Garsia and Haiman (J. Algebraic. Combin. 5 (1996), 191-244) conjectured that a certain sum C_n(q, t) of rational functions in q, t reduces to a polynomial in q, t with nonnegative integral coefficients. Haglund later discovered (Adv. Math., in press), and with Garsia proved (Proc. Nat. Acad. Sci. 98 (2001), 4313-4316) the refined conjecture C_n(q, t) = . Here the sum is over all Catalan lattice paths and area and bounce have simple descriptions in terms of..

Incidence and prevalence of NMOSD in Australia and New Zealand

Objectives We have undertaken a clinic-based survey of neuromyelitis optica spectrum disorders (NMOSDs) in Australia and New Zealand to establish incidence and prevalence across the region and in populations of differing ancestry. Background NMOSD is a recently defined demyelinating disease of the central nervous system (CNS). The incidence and prevalence of NMOSD in Australia and New Zealand has not been established. Methods Centres managing patients with demyelinating disease of the CNS across Australia and New Zealand reported patients with clinical and laboratory features that were suspicious for NMOSD. Testing for aquaporin 4 antibodies was undertaken in all suspected cases. From this group, cases were identified who fulfilled the 2015 Wingerchuk diagnostic criteria for NMOSD. A capture–recapture methodology was used to estimate incidence and prevalence, based on additional laboratory identified cases. Results NMOSD was confirmed in 81/170 (48%) cases referred. Capture–recapture analysis gave an adjusted incidence estimate of 0.37 (95% CI 0.35 to 0.39) per million per year and a prevalence estimate for NMOSD of 0.70 (95% CI 0.61 to 0.78) per 100 000. NMOSD was three times more common in the Asian population (1.57 (95% CI 1.15 to 1.98) per 100 000) compared with the remainder of the population (0.57 (95% CI 0.50 to 0.65) per 100 000). The latitudinal gradient evident in multiple sclerosis was not seen in NMOSD. Conclusions NMOSD incidence and prevalence in Australia and New Zealand are comparable with figures from other populations of largely European ancestry. We found NMOSD to be more common in the population with Asian ancestry.</p

Incidence and prevalence of NMOSD in Australia and New Zealand

OBJECTIVES: We have undertaken a clinic-based survey of neuromyelitis optica spectrum disorders (NMOSDs) in Australia and New Zealand to establish incidence and prevalence across the region and in populations of differing ancestry. BACKGROUND: NMOSD is a recently defined demyelinating disease of the central nervous system (CNS). The incidence and prevalence of NMOSD in Australia and New Zealand has not been established. METHODS: Centres managing patients with demyelinating disease of the CNS across Australia and New Zealand reported patients with clinical and laboratory features that were suspicious for NMOSD. Testing for aquaporin 4 antibodies was undertaken in all suspected cases. From this group, cases were identified who fulfilled the 2015 Wingerchuk diagnostic criteria for NMOSD. A capture-recapture methodology was used to estimate incidence and prevalence, based on additional laboratory identified cases. RESULTS: NMOSD was confirmed in 81/170 (48%) cases referred. Capture-recapture analysis gave an adjusted incidence estimate of 0.37 (95% CI 0.35 to 0.39) per million per year and a prevalence estimate for NMOSD of 0.70 (95% CI 0.61 to 0.78) per 100 000. NMOSD was three times more common in the Asian population (1.57 (95% CI 1.15 to 1.98) per 100 000) compared with the remainder of the population (0.57 (95% CI 0.50 to 0.65) per 100 000). The latitudinal gradient evident in multiple sclerosis was not seen in NMOSD. CONCLUSIONS: NMOSD incidence and prevalence in Australia and New Zealand are comparable with figures from other populations of largely European ancestry. We found NMOSD to be more common in the population with Asian ancestry