The odd nilHecke algebra and its diagrammatics

We introduce an odd version of the nilHecke algebra and develop an odd analogue of the thick diagrammatic calculus for nilHecke algebras. We graphically describe idempotents which give a Morita equivalence between odd nilHecke algebras and the rings of odd symmetric functions in finitely many variables. Cyclotomic quotients of odd nilHecke algebras are Morita equivalent to rings which are odd analogues of the cohomology rings of Grassmannians. Like their even counterparts, odd nilHecke algebras categorify the positive half of quantum sl(2).Comment: 48 pages, eps and xypic diagram

Nilpotency in type A cyclotomic quotients

We prove a conjecture made by Brundan and Kleshchev on the nilpotency degree of cyclotomic quotients of rings that categorify one-half of quantum sl(k).Comment: 19 pages, 39 eps files. v3 simplifies antigravity moves and corrects typo

Inferior Cerebellar Hypoplasia Resembling a Dandy-Walker-Like Malformation in Purebred Eurasier Dogs with Familial Non-Progressive Ataxia: A Retrospective and Prospective Clinical Cohort Study

Cerebellar malformations can be inherited or caused by insults during cerebellar development. To date, only sporadic cases of cerebellar malformations have been reported in dogs, and the genetic background has remained obscure. Therefore, this study's objective was to describe the clinical characteristics, imaging features and pedigree data of a familial cerebellar hypoplasia in purebred Eurasier dogs. A uniform cerebellar malformation characterized by consistent absence of the caudal portions of the cerebellar vermis and, to a lesser degree, the caudal portions of the cerebellar hemispheres in association with large retrocerebellar fluid accumulations was recognized in 14 closely related Eurasier dogs. Hydrocephalus was an additional feature in some dogs. All dogs displayed non-progressive ataxia, which had already been noted when the dogs were 5 - 6 weeks old. The severity of the ataxia varied between dogs, from mild truncal sway, subtle dysmetric gait, dysequilibrium and pelvic limb ataxia to severe cerebellar ataxia in puppies and episodic falling or rolling. Follow-up examinations in adult dogs showed improvement of the cerebellar ataxia and a still absent menace response. Epileptic seizures occurred in some dogs. The association of partial vermis agenesis with an enlarged fourth ventricle and an enlarged caudal (posterior) fossa resembled a Dandy-Walker-like malformation in some dogs. Pedigree analyses were consistent with autosomal recessive inheritance

Caudal Fossa Ratio in Norma Dogs and Eurasier Dogs with VLDLR-Associated Genetic Cerebellar Hypoplasia

Cerebellar and hindbrain malformations, such as cerebellar hypoplasia (CH), vermis hypoplasia, and Dandy-Walker malformation, occur in dogs as well as in humans. Neuroimaging is essential for a precise description of these malformations and defining translational animal models. Neuroimaging is increasingly performed in puppies, but there is a lack of data on developmental changes in the caudal fossa, which can impair assessment of caudal fossa size in this age group. The purpose of this study was to validate caudal fossa ratio (CFR) in dogs and to explore CFR in Eurasier dogs with genetic CH. CFR was calculated from midsagittal brain images of 130 dogs as caudal fossa area/total cranial cavity area. In addition, the volume of the caudal fossa was measured in 64 randomly selected dogs from this group. Repeated measurements were used to investigate inter- and intra-rater variability and influence of imaging modality. Furthermore, the influence of age, weight, and breed was explored. The CFR was a reliable parameter with negligible influence from the examiners, imaging modality, and weight of the dog. The midsagittal area of the caudal fossa and the volume of the caudal fossa correlated closely with each other. In this study, we observed a smaller CFR in puppies. The CFR in adult dogs lies within 0.255 and 0.330, while CFR is smaller in puppies up to 4 months of age. Besides age, there was also an effect of breed, which should be explored in larger data sets. Measurements of CFR in Eurasier dogs with genetic CH caused by a mutation in the very-low-density-lipoprotein-receptor gene revealed the presence of two variants, one with an enlarged caudal fossa and one with a normal to small caudal fossa. This observation indicates that there is phenotypic heterogeneity and interaction between the developing cerebellum and the surrounding mesenchyme in this animal model

Influence of female sex and fertile age on neuromyelitis optica spectrum disorders

Background: Gender and age at onset are important epidemiological factors influencing prevalence, clinical presentation, and treatment response in autoimmune diseases. Objective: To evaluate the impact of female sex and fertile age on aquaporin-4-antibody (AQP4-ab) status, attack localization, and response to attack treatment in patients with neuromyelitis optica (NMO) and its spectrum disorders (neuromyelitis optica spectrum disorder (NMOSD)). Methods: Female-to-male ratios, diagnosis at last visit (NMO vs NMOSD), attack localization, attack treatment, and outcome were compared according to sex and age at disease or attack onset. Results: A total of 186 NMO/SD patients (82% female) were included. In AQP4-ab-positive patients, female predominance was most pronounced during fertile age (female-to-male ratio 23:1). Female patients were more likely to be positive for AQP4-abs (92% vs 55%;p40years. Conclusion: Our data suggest an influence of sex and age on susceptibility to AQP4-ab-positive NMO/SD. Genetic and hormonal factors might contribute to pathophysiology of NMO/SD

Contrasting disease patterns in seropositive and seronegative neuromyelitis optica: A multicentre study of 175 patients

BACKGROUND: The diagnostic and pathophysiological relevance of antibodies to aquaporin-4 (AQP4-Ab) in patients with neuromyelitis optica spectrum disorders (NMOSD) has been intensively studied. However, little is known so far about the clinical impact of AQP4-Ab seropositivity. OBJECTIVE: To analyse systematically the clinical and paraclinical features associated with NMO spectrum disorders in Caucasians in a stratified fashion according to the patients' AQP4-Ab serostatus. METHODS: Retrospective study of 175 Caucasian patients (AQP4-Ab positive in 78.3%). RESULTS: Seropositive patients were found to be predominantly female (p 1 myelitis attacks in the first year were identified as possible predictors of a worse outcome. CONCLUSION: This study provides an overview of the clinical and paraclinical features of NMOSD in Caucasians and demonstrates a number of distinct disease characteristics in seropositive and seronegative patients

Raw image data

Raw image data from dog 4 and all prospectively examined dogs (dogs 6 - 11) from the publication Bernardino et al. (Plos One)