2-Vector Spaces and Groupoids

This paper describes a relationship between essentially finite groupoids and 2-vector spaces. In particular, we show to construct 2-vector spaces of Vect-valued presheaves on such groupoids. We define 2-linear maps corresponding to functors between groupoids in both a covariant and contravariant way, which are ambidextrous adjoints. This is used to construct a representation--a weak functor--from Span(Gpd) (the bicategory of groupoids and spans of groupoids) into 2Vect. In this paper we prove this and give the construction in detail.Comment: 44 pages, 5 figures - v2 adds new theorem, significant changes to proofs, new sectio

The sl_3 web algebra

In this paper we use Kuperberg’s sl3-webs and Khovanov’s sl3-foams to define a new algebra KS, which we call the sl3-web algebra. It is the sl3 analogue of Khovanov’s arc algebra. We prove that KS is a graded symmetric Frobenius algebra. Furthermore, we categorify an instance of q-skew Howe duality, which allows us to prove that KS is Morita equivalent to a certain cyclotomic KLR-algebra of level 3. This allows us to determine the split Grothendieck group K0 (WS )Q(q) , to show that its center is isomorphic to the cohomology ring of a certain Spaltenstein variety, and to prove that KS is a graded cellular algebra.info:eu-repo/semantics/publishedVersio

Epstein-Barr-negative MS: a true phenomenon?

This work was supported by institutional funding and in part by the BMBF grant KKNMS (Competence Net Multiple Sclerosis) to H Tumani

Conversion from clinically isolated syndrome to multiple sclerosis: A large multicentre study

International audienceWe explored which clinical and biochemical variables predict conversion from clinically isolated syndrome (CIS) to clinically definite multiple sclerosis (CDMS) in a large international cohort. Thirty-three centres provided serum samples from 1047 CIS cases with at least two years' follow-up. Age, sex, clinical presentation, T2-hyperintense lesions, cerebrospinal fluid (CSF) oligoclonal bands (OCBs), CSF IgG index, CSF cell count, serum 25-hydroxyvitamin D3 (25-OH-D), cotinine and IgG titres against Epstein-Barr nuclear antigen 1 (EBNA-1) and cytomegalovirus were tested for association with risk of CDMS. At median follow-up of 4.31 years, 623 CIS cases converted to CDMS. Predictors of conversion in multivariable analyses were OCB (HR = 2.18, 95% CI = 1.71-2.77, p 9 lesions vs 0/1 lesions: HR = 2.74, 95% CI = 2.04-3.68, p < 0.001) and age at CIS (HR per year inversely increase = 0.98, 95% CI = 0.98-0.99, p < 0.001). Lower 25-OH-D levels were associated with CDMS in univariable analysis, but this was attenuated in the multivariable model. OCB positivity was associated with higher EBNA-1 IgG titres. We validated MRI lesion load, OCB and age at CIS as the strongest independent predictors of conversion to CDMS in this multicentre setting. A role for vitamin D is suggested but requires further investigation