Howe Pairs in the Theory of Vertex Algebras

For any vertex algebra V and any subalgebra A of V, there is a new subalgebra of V known as the commutant of A in V. This construction was introduced by Frenkel-Zhu, and is a generalization of an earlier construction due to Kac-Peterson and Goddard-Kent-Olive known as the coset construction. In this paper, we interpret the commutant as a vertex algebra notion of invariant theory. We present an approach to describing commutant algebras in an appropriate category of vertex algebras by reducing the problem to a question in commutative algebra. We give an interesting example of a Howe pair (ie, a pair of mutual commutants) in the vertex algebra setting.Comment: A few typos corrected, final versio

A commutant realization of W^(2)_n at critical level

For n\geq 2, there is a free field realization of the affine vertex superalgebra A associated to psl(n|n) at critical level inside the bc\beta\gamma system W of rank n^2. We show that the commutant C=Com(A,W) is purely bosonic and is freely generated by n+1 fields. We identify the Zhu algebra of C with the ring of invariant differential operators on the space of n\times n matrices under SL_n \times SL_n, and we classify the irreducible, admissible C-modules with finite dimensional graded pieces. For n\leq 4, C is isomorphic to the W_n^{(2)}-algebra at critical level, and we conjecture that this holds for all n.Comment: Some corrections and expository improvements, references added, final version. arXiv admin note: text overlap with arXiv:1201.016

Invariant chiral differential operators and the W_3 algebra

Attached to a vector space V is a vertex algebra S(V) known as the beta-gamma system or algebra of chiral differential operators on V. It is analogous to the Weyl algebra D(V), and is related to D(V) via the Zhu functor. If G is a connected Lie group with Lie algebra g, and V is a linear G-representation, there is an action of the corresponding affine algebra on S(V). The invariant space S(V)^{g[t]} is a commutant subalgebra of S(V), and plays the role of the classical invariant ring D(V)^G. When G is an abelian Lie group acting diagonally on V, we find a finite set of generators for S(V)^{g[t]}, and show that S(V)^{g[t]} is a simple vertex algebra and a member of a Howe pair. The Zamolodchikov W_3 algebra with c=-2 plays a fundamental role in the structure of S(V)^{g[t]}.Comment: a few typos corrected, final versio

Efficient Online Surface Correction for Real-time Large-Scale 3D Reconstruction

State-of-the-art methods for large-scale 3D reconstruction from RGB-D sensors usually reduce drift in camera tracking by globally optimizing the estimated camera poses in real-time without simultaneously updating the reconstructed surface on pose changes. We propose an efficient on-the-fly surface correction method for globally consistent dense 3D reconstruction of large-scale scenes. Our approach uses a dense Visual RGB-D SLAM system that estimates the camera motion in real-time on a CPU and refines it in a global pose graph optimization. Consecutive RGB-D frames are locally fused into keyframes, which are incorporated into a sparse voxel hashed Signed Distance Field (SDF) on the GPU. On pose graph updates, the SDF volume is corrected on-the-fly using a novel keyframe re-integration strategy with reduced GPU-host streaming. We demonstrate in an extensive quantitative evaluation that our method is up to 93% more runtime efficient compared to the state-of-the-art and requires significantly less memory, with only negligible loss of surface quality. Overall, our system requires only a single GPU and allows for real-time surface correction of large environments.Comment: British Machine Vision Conference (BMVC), London, September 201

Pioglitazone in early Parkinson\u27s disease: a phase 2, multicentre, double-blind, randomised trial

Background A systematic assessment of potential disease-modifying compounds for Parkinson\u27s disease concluded that pioglitazone could hold promise for the treatment of patients with this disease. We assessed the effect of pioglitazone on the progression of Parkinson\u27s disease in a multicentre, double-blind, placebo-controlled, futility clinical trial. Methods Participants with the diagnosis of early Parkinson\u27s disease on a stable regimen of 1 mg/day rasagiline or 10 mg/day selegiline were randomly assigned (1:1:1) to 15 mg/day pioglitazone, 45 mg/day pioglitazone, or placebo. Investigators were masked to the treatment assignment. Only the statistical centre and the central pharmacy knew the treatment name associated with the randomisation number. The primary outcome was the change in the total Unified Parkinson\u27s Disease Rating Scale (UPDRS) score between the baseline and 44 weeks, analysed by intention to treat. The primary null hypothesis for each dose group was that the mean change in UPDRS was 3 points less than the mean change in the placebo group. The alternative hypothesis (of futility) was that pioglitazone is not meaningfully different from placebo. We rejected the null if there was significant evidence of futility at the one-sided alpha level of 0.10. The study is registered at ClinicalTrials.gov, number NCT01280123. Findings 210 patients from 35 sites in the USA were enrolled between May 10, 2011, and July 31, 2013. The primary analysis included 72 patients in the 15 mg group, 67 in the 45 mg group, and 71 in the placebo group. The mean total UPDRS change at 44 weeks was 4.42 (95% CI 2.55-6.28) for 15 mg pioglitazone, 5.13 (95% CI 3.17-7.08) for 45 mg pioglitazone, and 6.25 (95% CI 4.35-8.15) for placebo (higher change scores are worse). The mean difference between the 15 mg and placebo groups was -1.83 (80% CI -3.56 to -0.10) and the null hypothesis could not be rejected (p=0.19). The mean difference between the 45 mg and placebo groups was -1.12 (80% CI -2.93 to 0.69)and the null hypothesis was rejected in favour of futility (p=0.09). Planned sensitivity analyses of the primary outcome, using last value carried forward (LVCF) to handle missing data and using the completers\u27 only sample, suggested that the 15 mg dose is also futile (p=0.09 for LVCF, p= 0.09 for completers) but failed to reject the null hypothesis for the 45 mg dose (p=0.12 for LVCF, p=0.19 for completers). Six serious adverse events occurred in the 15 mg group, nine in the 45 mg group, and three in the placebo group; none were thought to be definitely or probably related to the study interventions. Interpretation These findings suggest that pioglitazone at the doses studied here is unlikely to modify progression in early Parkinson\u27s disease. Further study of pioglitazone in a larger trial in patients with Parkinson\u27s disease is not recommended

Longitudinal Changes in the Motor Learning- Related Brain Activation Response in Presymptomatic Huntington\u27s Disease

Neurocognitive decline, including deficits in motor learning, occurs in the presymptomatic phase of Huntington’s disease (HD) and precedes the onset of motor symptoms. Findings from recent neuroimaging studies have linked these deficits to alterations in fronto-striatal and fronto-parietal brain networks. However, little is known about the temporal dynamics of these networks when subjects approach phenoconversion. Here, 10 subjects with presymptomatic HD were scanned with 15O-labeled water at baseline and again 1.5 years later while performing a motor sequence learning task and a kinematically matched control task. Spatial covariance analysis was utilized to characterize patterns of change in learningrelated neural activation occurring over time in these individuals. Pattern expression was compared to corresponding values in 10 age-matched healthy control subjects. Spatial covariance analysis revealed significant longitudinal changes in the expression of a specific learning-related activation pattern characterized by increasing activity in the right orbitofrontal cortex, with concurrent reductions in the right medial prefrontal and posterior cingulate regions, the left insula, left precuneus, and left cerebellum. Changes in the expression of this pattern over time correlated with baseline measurements of disease burden and learning performance. The network changes were accompanied by modest improvement in learning performance that took place concurrently in the gene carriers. The presence of increased network activity in the setting of stable task performance is consistent with a discrete compensatory mechanism. The findings suggest that this effect is most pronounced in the late presymptomatic phase of HD, as subjects approach clinical onset

Art therapy for Parkinson's disease.

Abstract Objective To explore the potential rehabilitative effect of art therapy and its underlying mechanisms in Parkinson's disease (PD). Methods Observational study of eighteen patients with PD, followed in a prospective, open-label, exploratory trial. Before and after twenty sessions of art therapy, PD patients were assessed with the UPDRS, Pegboard Test, Timed Up and Go Test (TUG), Beck Depression Inventory (BDI), Modified Fatigue Impact Scale and PROMIS-Self-Efficacy, Montreal Cognitive Assessment, Rey-Osterrieth Complex Figure Test (RCFT), Benton Visual Recognition Test (BVRT), Navon Test, Visual Search, and Stop Signal Task. Eye movements were recorded during the BVRT. Resting-state functional MRI (rs-fMRI) was also performed to assess functional connectivity (FC) changes within the dorsal attention (DAN), executive control (ECN), fronto-occipital (FOC), salience (SAL), primary and secondary visual (V1, V2) brain networks. We also tested fourteen age-matched healthy controls at baseline. Results At baseline, PD patients showed abnormal visual-cognitive functions and eye movements. Analyses of rs-fMRI showed increased functional connectivity within DAN and ECN in patients compared to controls. Following art therapy, performance improved on Navon test, eye tracking, and UPDRS scores. Rs-fMRI analysis revealed significantly increased FC levels in brain regions within V1 and V2 networks. Interpretation Art therapy improves overall visual-cognitive skills and visual exploration strategies as well as general motor function in patients with PD. The changes in brain connectivity highlight a functional reorganization of visual networks

Fermionic Coset, Critical Level W^(2)_4-Algebra and Higher Spins

The fermionic coset is a limit of the pure spinor formulation of the AdS5xS5 sigma model as well as a limit of a nonlinear topological A-model, introduced by Berkovits. We study the latter, especially its symmetries, and map them to higher spin algebras. We show the following. The linear A-model possesses affine \AKMSA{pgl}{4}{4}_0 symmetry at critical level and its \AKMSA{psl}{4}{4}_0 current-current perturbation is the nonlinear model. We find that the perturbation preserves $\mathcal{W}^{(2)}_4$-algebra symmetry at critical level. There is a topological algebra associated to \AKMSA{pgl}{4}{4}_0 with the properties that the perturbation is BRST-exact. Further, the BRST-cohomology contains world-sheet supersymmetric symplectic fermions and the non-trivial generators of the $\mathcal{W}^{(2)}_4$-algebra. The Zhu functor maps the linear model to a higher spin theory. We analyze its \SLSA{psl}{4}{4} action and find finite dimensional short multiplets.Comment: 25 page