Cohomology and Support Varieties for Lie Superalgebras II

In \cite{BKN} the authors initiated a study of the representation theory of classical Lie superalgebras via a cohomological approach. Detecting subalgebras were constructed and a theory of support varieties was developed. The dimension of a detecting subalgebra coincides with the defect of the Lie superalgebra and the dimension of the support variety for a simple supermodule was conjectured to equal the atypicality of the supermodule. In this paper the authors compute the support varieties for Kac supermodules for Type I Lie superalgebras and the simple supermodules for $\mathfrak{gl}(m|n)$. The latter result verifies our earlier conjecture for $\mathfrak{gl}(m|n)$. In our investigation we also delineate several of the major differences between Type I versus Type II classical Lie superalgebras. Finally, the connection between atypicality, defect and superdimension is made more precise by using the theory of support varieties and representations of Clifford superalgebras.Comment: 28 pages, the proof of Proposition 4.5.1 was corrected, several other small errors were fixe

Complexity for Modules Over the Classical Lie Superalgebra gl(m|n)

Let $\mathfrak{g}=\mathfrak{g}_{\bar{0}}\oplus \mathfrak{g}_{\bar{1}}$ be a classical Lie superalgebra and $\mathcal{F}$ be the category of finite dimensional $\mathfrak{g}$-supermodules which are completely reducible over the reductive Lie algebra $\mathfrak{g}_{\bar{0}}$. In an earlier paper the authors demonstrated that for any module $M$ in $\mathcal{F}$ the rate of growth of the minimal projective resolution (i.e., the complexity of $M$) is bounded by the dimension of $\mathfrak{g}_{\bar{1}}$. In this paper we compute the complexity of the simple modules and the Kac modules for the Lie superalgebra $\mathfrak{gl}(m|n)$. In both cases we show that the complexity is related to the atypicality of the block containing the module.Comment: 32 page

Neural correlates of explicit and implicit emotion processing in relation to treatment response in pediatric anxiety

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/136676/1/jcpp12658_am.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/136676/2/jcpp12658.pd

Additive effects of the dopamine D2 receptor and dopamine transporter genes on the error-related negativity in young children

The error-related negativity (ERN) is a negative deflection in the event-related potential that occurs approximately 50ms following the commission of an error at fronto-central electrode sites. Previous models suggest dopamine plays a role in the generation of the ERN. We recorded event-related potentials (ERPs) while 279 children aged 5-7 years completed a simple Go/No-Go task; the ERN was examined in relation to the dopamine D2 receptor (DRD2) and dopamine transporter (DAT1) genes. Results suggest an additive effect of the DRD2 and DAT1 genotype on ERN magnitude such that children with at least one DRD2 A1 allele and children with at least one DAT1 9 allele have an increased (i.e. more negative) ERN. These results provide further support for the involvement of dopamine in the generation of the ERN. © 2012 Blackwell Publishing Ltd and International Behavioural and Neural Genetics Society

Potential use of the organic fraction of municipal solid waste in anaerobic co-digestion with wastewater in submerged anaerobic membrane technology

Food waste was characterized for its potential use as substrate for anaerobic co-digestion in a submerged anaerobic membrane bioreactor pilot plant that treats urban wastewater (WW). 90% of the particles had sizes under 0.5 mm after grinding the food waste in a commercial food waste disposer. COD, nitrogen and phosphorus concentrations were 100, 2 and 20 times higher in food waste than their average concentrations in WW, but the relative flow contribution of both streams made COD the only pollutant that increased significantly when both substrates were mixed. As sulphate concentration in food waste was in the same range as WW, co-digestion of both substrates would increase the COD/SO4-S ratio and favour methanogenic activity in anaerobic treatments. The average methane potential of the food waste was 421 +/- 15 mL CH4 g(-1) VS, achieving 73% anaerobic biodegradability. The anaerobic co-digestion of food waste with WW is expected to increase methane production 2.9-fold. The settleable solids tests and the particle size distribution analyses confirmed that both treatment lines of a conventional WWTP (water and sludge lines) would be clearly impacted,by the incorporation of food waste into its influent. Anaerobic processes are therefore preferred over their aerobic counterparts due to their ability to valorise the high COD content to produce biogas (a renewable energy) instead of increasing the energetic costs associated with the aeration process for aerobic COD oxidation. (C) 2016 Elsevier Ltd. All rights reserved.This research work was possible thanks to financial support from the Generalitat Valenciana (project PROMETEO/2012/029) which is gratefully acknowledged.Moñino Amorós, P.; Jiménez Douglas, E.; Barat Baviera, R.; Aguado García, D.; Seco Torrecillas, A.; Ferrer, J. (2016). Potential use of the organic fraction of municipal solid waste in anaerobic co-digestion with wastewater in submerged anaerobic membrane technology. Waste Management. 56:158-165. https://doi.org/10.1016/j.wasman.2016.07.021S1581655

Impact of pubertal timing and depression on error‐related brain activity in anxious youth

Anxiety disorders are associated with enhanced error‐related negativity (ERN) across development but it remains unclear whether alterations in brain electrophysiology are linked to the timing of puberty. Pubertal timing and alterations of prefrontal and limbic development are implicated in risk for depression, but the interplay of these factors on the ERN–anxiety association has not been assessed. We examined the unique and interactive effects of pubertal timing and depression on the ERN in a sample of youth 10–19 years old with anxiety disorders (n = 30) or no history of psychopathology (n = 30). Earlier pubertal maturation was associated with an enhanced ERN. Among early, but not late maturing youth, higher depressive symptoms were associated with a reduced ERN. The magnitude of neural reactivity to errors is sensitive to anxiety, depression, and development. Early physical maturation and anxiety may heighten neural sensitivity to errors yet predict opposing effects in the context of depression.Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/146936/1/dev21763.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/146936/2/dev21763_am.pd

Segmentation of vestibular schwannoma from MRI, an open annotated dataset and baseline algorithm

Automatic segmentation of vestibular schwannomas (VS) from magnetic resonance imaging (MRI) could significantly improve clinical workflow and assist patient management. We have previously developed a novel artificial intelligence framework based on a 2.5D convolutional neural network achieving excellent results equivalent to those achieved by an independent human annotator. Here, we provide the first publicly-available annotated imaging dataset of VS by releasing the data and annotations used in our prior work. This collection contains a labelled dataset of 484 MR images collected on 242 consecutive patients with a VS undergoing Gamma Knife Stereotactic Radiosurgery at a single institution. Data includes all segmentations and contours used in treatment planning and details of the administered dose. Implementation of our automated segmentation algorithm uses MONAI, a freely-available open-source framework for deep learning in healthcare imaging. These data will facilitate the development and validation of automated segmentation frameworks for VS and may also be used to develop other multi-modal algorithmic models