This note gives a central limit theorem for the length of the longest subsequence of a random permutation which follows some repeating pattern. This includes the case of any fixed pattern of ups and downs which has at least one of each, such as the alternating case considered by Stanley in [2] and Widom in [3]. In every case considered the convergence in the limit of long permutations is to normal with mean and variance linear in the length of the permutations.

BACKGROUND: Myelin oligodendrocyte glycoprotein (MOG)-IgG is increasingly detected in children with CNS demyelinating diseases. Due to the clinical overlap in children with CNS demyelination with and without MOG-IgG positivity, identifying distinct characteristics would help early diagnosis. OBJECTIVE: To compare the specific features that may help differentiate MOG-IgG positive from negative children with CNS demyelinating diseases. To compare characteristics of patients with high and low MOG-IgG titers. METHODS: Children with CNS demyelinating disorders with onset before 18 years of age who were tested for MOG-IgG at the University of California San Francisco were included. This retrospective study collected the following by chart review: demographic, clinical, MRI, CSF, and treatment data. Serum was tested for MOG-IgG at Mayo Clinic by live cell-based fluorescent activated cell sorting assay with titer ≥1:20 confirming positivity. RESULTS: We assessed 65 Mog-IgG positive and 65 MOG-IgG negative patients. Median (IQR) age of onset was 7.6 (6.6) years for MOG-IgG positive and 13.8 (5.8) years for MOG-IgG negative (p<0.001). The female to male ratio was approximately 1:1 for the MOG-IgG positive group and 3:1 for the negative group (p=0.042). The most common initial diagnosis was demyelinating disease not otherwise specified (52.3%) in the positive group, compared to relapsing-remitting multiple sclerosis (41.5%) in the negative group (p<0.01). Optic nerve involvement (52.3%) was the most common clinical localization at onset for the MOG-IgG positive group, while brainstem/cerebellar (49.2%) localization predominated in the MOG-IgG negative group. The positive group also presented more often with a severe event at disease onset than the negative group (81.5% vs 60.3%; p< 0.002). MOG-IgG positive children had a lower frequency of oligoclonal bands (15.8% vs 57.4%; p<0.001). The frequency of baseline brain and spinal cord MRI abnormalities were similar in both groups; however, MOG-IgG positive patients more often had T2 hyperintense lesions in the optic nerves (26/43 vs 10/41; p<0.001). Disease-modifying medications were used in 64.6% of MOG-IgG positive patients versus 80% of negative children. Of the 32 positive patients with follow-up titers, seven reverted to negative while two who tested negative initially converted to positive. Positive titers greater than 1:160 were only observed within four months of a clinical event (disease onset or relapse). Patients with high and low MOG-IgG titers were comparable in demographic and clinical characteristics. CONCLUSION: Despite some clinical overlap, we report notable demographic, MRI and CSF differences between MOG-IgG positive and negative children with CNS demyelinating disorders at disease onset. High MOG-IgG titers were only observed close to a clinical event.

BACKGROUND: Understanding nutritions role in multiple sclerosis (MS) can guide recommendations and intervention-based studies. OBJECTIVE: Evaluate the association between nutrition and pediatric-onset MS outcomes. METHODS: Prospective longitudinal multicenter study conducted as part of the US Network of Pediatric MS centers. Predictors were collected using a food screener estimating intake of various dietary food groups (e.g. dairy and fruits) and additional calculated indices (e.g. Healthy Eating Index (HEI)). Outcomes included time-from-enrollment to clinical relapse, new magnetic resonance imaging (MRI) T2 lesions, and Expanded Disability Status Scale (EDSS) increase. RESULTS: 353 children with MS were enrolled (mean ± SD age 15.4 ± 2.9, follow-up 3.9 ± 2.6 years). Multivariable analysis demonstrated that increased dairy by 50% of recommended intake was associated with increased relapse risk by 41% (adjusted hazard ratio (HR) 1.41, 95% CI 1.07-1.86), and risk of T2 progression by 40% (1.40, 1.12-1.74). Increased intake of fruit or vegetable above recommended, and every five-point HEI increase decreased relapse risk by 25% (0.75, 0.60-0.95), 45% (0.55, 0.32-0.96), and 15% (0.84, 0.74-0.96), respectively. No associations were found with EDSS. CONCLUSION: This work supports the influence of dietary intake on MS course, particularly with dairy intake. Future prospective study is required to establish causation.