Loop Groups and QNEC

We construct and study solitonic representations of the conformal net associated to some vacuum Positive Energy Representation (PER) of a loop group LG. For the corresponding solitonic states, we prove the Quantum Null Energy Condition (QNEC) and the Bekenstein Bound. As an intermediate result, we show that a Positive Energy Representation of a loop group LG can be extended to a PER of $$H^{s}(S^1,G)$$ H s ( S 1 , G ) for $$s>3/2$$ s > 3 / 2 , where G is any compact, simple and simply connected Lie group. We also show the existence of the exponential map of the semidirect product $$LG \rtimes R$$ L G ⋊ R , with R a one-parameter subgroup of $$\mathrm{Diff}_+(S^1)$$ Diff + ( S 1 ) , and we compute the adjoint action of $$H^{s+1}(S^1,G)$$ H s + 1 ( S 1 , G ) on the stress energy tensor.

BRAFnon-V600E more frequently co-occurs with IDH1/2 mutations in adult patients with gliomas than in patients harboring BRAFV600E but without a survival advantage

Background The effects of BRAFnon-V600E and BRAFV600E on the outcomes and the molecular characteristics of adult glioma patients are unknown and need to be explored, although BRAFV600E has been extensively studied in pediatric glioma. Methods Co-occurring mutations and copy number alterations of associated genes in the MAPK and p53 pathways were investigated using data from The Cancer Genome Atlas (TCGA) public database retrieved by cBioPortal. The prognosis of available adult glioma cohorts with BRAFV600E and BRAFnon-V600E mutations were also investigated. Results Ninety patients with BRAFV600E or BRAFnon-V600E were enrolled in this study, and data from 52 nonredundant patients were investigated. Glioblastoma multiform was the most common cancer type, with BRAFnon-V600E and BRAFV600E. TP53 (56.00% vs. 7.41%), IDH1/2 (36.00% vs. 3.70%), and ATRX (32.00% vs. 7.41%) exhibited more mutations in BRAFnon-V600E than in BRAFV600E, and TP53 was an independent risk factor (56.00% vs. 7.41%). Both BRAFnon-V600E and BRAFV600E frequently overlapped with CDKN2A/2B homozygous deletions (HDs), but there was no significant difference. Survival analysis showed no difference between the BRAFnon-V600E and BRAFV600E cohorts, even after excluding the survival benefit of IDH1/2 mutations and considering the BRAFnon-V600E mutations in the glycine-rich loop (G-loop) and in the activation segment. The estimated mean survival of patients with BRAFnon-V600E & IDH1/2WT with mutations in the G-loop groups was the shortest. Conclusions BRAFnon-V600E exhibited a stronger association with IDH1/2 mutations than BRAFV600E, but no survival advantage was found.

BRAFnon-V600E more frequently co-occurs with IDH1/2 mutation in adult patients with gliomas than patients harboring BRAFV600E, but without survival advantage

Background The effect of BRAFnon−V600E and BRAFV600E on the outcome and the molecular characteristics in adult glioma patients is unknown and needs to be explored, although BRAFV600E has been extensively studied in pediatric glioma. Methods Co-occurring mutations and copy number alterations of associated genes in the MAPK and p53 pathways were retrieved and investigated using the cBioPortal. The prognosis of available adult glioma cohorts with BRAFV600E and BRAFnon−V600E mutations was also investigated. Results Glioblastoma multiform was the most common cancer type with BRAF non−V600E and BRAFV600E. TP53 (56.00% vs. 7.41%), IDH1/2 (36.00% vs. 3.70%), and ATRX (32.00% vs. 7.41%) exhibited more mutations in BRAFnon−V600E than in BRAFV600E, and TP53 was the independent risk factor (56.00% vs. 7.41%). Both BRAFnon−V600E and BRAFV600E frequently overlapped with CDKN2A/2B homozygous deletions (HD), whereas there was no significant difference. Survival analysis showed no difference between BRAF non−V600E and BRAFV600E cohorts, even excluded the effects of IDH1/2 mutations, and concerned the BRAFnon−V600E mutations in the glycine-rich loop (G-loop) and in the activation segment. The estimated mean survival of BRAFnon−V600E and IDH1/2WT with mutations in the G-loop groups was the shortest. Conclusions BRAF non−V600E exhibited a higher association with IDH1/2 mutation than BRAFV600E, but no survival advantage was found.

Micro-Rheological Changes of Red Blood Cells in the Presence of an Arterio-Venous Fistula or a Loop-Shaped Venous Graft in the Rat

Introduction: In case of kidney failure, hemodialysis is the primary kidney replacement technique. Several vascular access methods used for the therapy, one of which is the arterio-venous fistula (AVF). In the AVF, the blood flow is altered, which can elevate the mechanical stress on the red blood cells (RBCs). This can affect the RBC hemorheological properties, and it can further cause systemic changes. To lower the turbulence and shear stress, we performed a loop-shaped arterio-arterial venous interposition graft (loop-shaped graft) to compare its effect to the conventional AVF.Materials and Methods: Thirty male Wistar were used (permission registration Nr.: 25/2016/UDCAW). The animals were randomly divided into sham-operated, AVF, and loop groups (n = 10/each). The superficial inferior epigastric vein (SIEV) was used to create the AVF and the loop-shaped graft. Blood samples were taken before/after the surgery and at the 1st, 3rd, and 5th postoperative weeks. We measured hemorhelogical, hematological, and blood gas parameters. The microcirculation of the hind limbs was also monitored using Laser Doppler fluxmetry.Results: Hematocrit, RBC count, and hemoglobin decreased by the 1st postoperative week. The erythrocyte aggregation values significantly increased in the fistula group by the 5th week (6.43 ± 2.31 vs. 13.60; p < 0.0001; vs. before operation). At the postoperative 1st week in the loop group, the values showed a significant decrease in RBC deformability. During the maturation period, dominantly at the 5th week, all values were normalized. The operated hind limb’s skin microcirculation significantly increased in the sham and loop group by the 1st week (39 ± 10.57 vs. 73.93 ± 1.97 BFU, p < 0.01). This increase wasn’t observed in the fistula group probably due to a steal-effect.Conclusion: Unlike in the loop group, in the presence of the fistula, several rheological parameters have changed. The loop-shaped graft had only minimal impact on micro-rheological parameters.

PROJECTIVE LOOPS GENERATE RATIONAL LOOP GROUPS

We generalize Uhlenbeck’s generator theorem of ${\mathcal{L}}^{-}\operatorname{U}_{n}$ to the full rational loop group ${\mathcal{L}}^{-}\operatorname{GL}_{n}\mathbb{C}$ and its subgroups ${\mathcal{L}}^{-}\operatorname{GL}_{n}\mathbb{R}$ , ${\mathcal{L}}^{-}\operatorname{U}_{p,q}$ : they are all generated by just simple projective loops. Recall that Terng–Uhlenbeck studied the dressing actions of such projective loops as generalized Bäcklund transformations for integrable systems. Our result makes a nice supplement: any rational dressing is the composition of these Bäcklund transformations. This conclusion is surprising in the sense that Lie theory suggests the indispensable role of nilpotent loops in the case of noncompact reality conditions, and nilpotent dressings appear quite complicated and mysterious. The sacrifice is to introduce some extra fake singularities. So we also propose a set of generators if fake singularities are forbidden. A very geometric and physical construction of $\operatorname{U}_{p,q}$ is obtained as a by-product, generalizing the classical construction of unitary groups.

The test function conjecture for local models of Weil-restricted groups

We prove the test function conjecture of Kottwitz and the first named author for local models of Shimura varieties with parahoric level structure attached to Weil-restricted groups, as defined by B. Levin. Our result covers the (modified) local models attached to all connected reductive groups over $p$-adic local fields with $p\geqslant 5$. In addition, we give a self-contained study of relative affine Grassmannians and loop groups formed using general relative effective Cartier divisors in a relative curve over an arbitrary Noetherian affine scheme.

A Tannakian Framework for G-displays and Rapoport–Zink Spaces

We develop a Tannakian framework for group-theoretic analogs of displays, originally introduced by Bültel and Pappas, and further studied by Lau. We use this framework to define Rapoport–Zink functors associated to triples $(G,\{\mu \},[b])$, where $G$ is a flat affine group scheme over ${\mathbb{Z}}_p$ and $\mu$ is a cocharacter of $G$ defined over a finite unramified extension of ${\mathbb{Z}}_p$. We prove these functors give a quotient stack presented by Witt vector loop groups, thereby showing our definition generalizes the group-theoretic definition of Rapoport–Zink spaces given by Bültel and Pappas. As an application, we prove a special case of a conjecture of Bültel and Pappas by showing their definition coincides with that of Rapoport and Zink in the case of unramified EL-type local Shimura data.