Odd annular Bar-Natan Category and Gl(1|1)

We introduce two monoidal supercategories: the odd dotted Temperley-Lieb category TLo,•(δ), which is a generalization of the odd Temperley-Lieb category studied by Brun-dan and Ellis in [5], and the odd annular Bar-Natan category BNo(A), which generalizes the odd Bar-Natan category studied by Putyra in [16]. We then show there is an equivalence of categories between them if δ=0. We use this equivalence to better understand the action of the Lie superalgebra gl(1|1) on the odd Khovanov homology of a knot in a thickened annulus found by Grigsby and Wehrli in [7]

Comparison of Intermediate-Dose Methotrexate with Cranial Irradiation for the Post-Induction Treatment of Acute Lymphocytic Leukemia in Children

Abstract We compared two regimens with respect to their ability to prolong disease-free survival in 506 children and adolescents with acute lymphocytic leukemia. All responders to induction therapy were randomized to treatment with 2400 rad of cranial irradiation plus intrathecal methotrexate or to treatment with intermediate-dose methotrexate plus intrathecal methotrexate, as prophylaxis for involvement of the central nervous system and other sanctuary areas. Patients were then treated with a standard maintenance regimen. Complete responders were stratified into either standard-risk or increased-risk groups on the basis of age and white-cell count at presentation. Among patients with standard risk, hematologic relapses occurred in 9 of 117 given methotrexate and 24 of 120 given irradiation (P\u3c0.01). The rate of Central-nervous-system relapse was higher in the methotrexate group (23 of 117) than in the irradiation group (8 of 120) (P = 0.01). Among patients with increased risk, radiation offered greater protection to the central nervous system than methotrexate (P = 0.03); there was no difference in the rate of hematologic relapse. In both risk strata the frequency of testicular relapse was significantly lower in the methotrexate group (1 patient) than the radiation group (10 patients) (P = 0.01). Methotrexate offered better protection against systemic relapse in standard-risk patients and better protection against testicular relapse overall, but it offered less protection against relapses in the central nervous system than cranial irradiation. (N Engl J Med. 1983; 308:477–84.