In type A we find equivalences of geometries arising in three settings: Nakajima's (“framed”) quiver varieties, conjugacy classes of matrices and loop Grassmannians. These are all given by explicit ...formulas. In particular, we embedd the framed quiver varieties into Beilinson-Drinfeld Grassmannians. This provides a compactification of Nakajima varieties and a decomposition of affine Grassmannians into Nakajima varieties. As an application we provide a geometric version of symmetric and skew (GL(m),GL(n)) dualities.
Let G be a reductive complex algebraic group. We fix a pair of opposite Borel subgroups and consider the corresponding semi‐infinite orbits in the affine Grassmannian GrG. We prove Simon Schieder's ...conjecture identifying his bialgebra formed by the top compactly supported cohomology of the intersections of opposite semi‐infinite orbits with U(n∨) (the universal enveloping algebra of the positive nilpotent subalgebra of the Langlands dual Lie algebra g∨). To this end we construct an action of Schieder bialgebra on the geometric Satake fiber functor. We propose a conjectural construction of Schieder bialgebra for an arbitrary symmetric Kac–Moody Lie algebra in terms of Coulomb branch of the corresponding quiver gauge theory.
This review is focused on the healing of fistulas and stable gastric pentadecapeptide BPC 157. Assuming that the healing of the various wounds is essential also for the gastrointestinal fistulas ...healing, the healing effect on fistulas in rats, consistently noted with the stable gastric pentadecapeptide BPC 157, may raise several interesting possibilities. BPC 157 is originally an anti-ulcer agent, native to and stable in human gastric juice (for more than 24 h). Likely, it is a novel mediator of Robert's cytoprotection maintaining gastrointestinal mucosal integrity. Namely, it is effective in the whole gastrointestinal tract, and heals various wounds (i.e., skin, muscle, tendon, ligament, bone; ulcers in the entire gastrointestinal tract; corneal ulcer); LD1 is not achieved. It is used in ulcerative colitis clinical trials, and now in multiple sclerosis, and addressed in several reviews. Therefore, it is not surprising that BPC 157 has documented consistent healing of the various gastrointestinal fistulas, external (esophagocutaneous, gastrocutaneous, duodenocutaneous, colocutaneous) and internal (colovesical, rectovaginal). Taking fistulas as a pathological connection, this rescue is verified with the beneficial effects in rats with the various gastrointestinal anastomoses, esophagogastric, jejunoileal, colo-colonic, ileoileal, esophagojejunal, esophagoduodenal, and gastrojejunal. This beneficial effect occurs equally when the gastrointestinal anastomoses are impaired with the application of NSAIDs, cysteamine, large bowel resection, as well as concomitant esophageal, gastric, and duodenal lesions and/or ulcerative colitis presentation, short bowel syndrome progression, liver and brain disturbances presentation. Particular aspects of the BPC 157 healing of the fistulas are especially emphasized.
For an integral symmetric matrix
κ
we construct a new “nonabelian homology localization” of the lattice vertex algebra
L
κ
on the corresponding loop Grassmannian space 𝒢
κ
. We attempt to motivate ...our construction by presenting related topics in the language of “interaction of particles over algebraic curves”.
We prove most of Lusztig's conjectures on the canonical basis in homology of a Springer fiber. The conjectures predict that this basis controls numerics of representations of the Lie algebra of ...semisimple algebraic group over an algebraically closed field of positive characteristic. We check this for almost all characteristics. To this end we construct a noncommutative resolution of the nilpotent cone which is derived equivalent to the Springer resolution. On the one hand, this noncommutative resolution is closely related to the positive characteristic derived localization equivalences obtained earlier by the present authors and Rumynin. On the other hand, it is compatible with the t-structure arising from an equivalence with the derived category of perverse sheaves on the affine flag variety of the Langlands dual group. This equivalence established by Arkhipov and the first author fits the framework of local geometric Landlands duality. The latter compatibility allows one to apply Frobenius purity theorem to deduce the desired properties of the basis. We expect the noncommutative counterpart of the Springer resolution to be of independent interest from the perspectives of algebraic geometry and geometric Langlands duality.
In this paper we prove, for G a connected reductive algebraic group satisfying a technical assumption, that the Satake category of G (with coefficients in a finite field, a finite extension of Q_l, ...or the ring of integers of such a field) can be described via Iwahori-Whittaker perverse sheaves on the affine Grassmannian. As an application, we confirm a conjecture of Juteau-Mautner-Williamson describing the tilting objects in the Satake category.
For an almost simple complex algebraic group G with affine Grassmannian $\text{Gr}_G=G(\mathbb{C}(({\rm t})))/G(\mathbb{C}{\rm t})$, we consider the equivariant homology $H^{G(\mathbb{C}{\rm ...t})}(\text{Gr}_G)$ and K-theory $K^{G(\mathbb{C}{\rm t})}(\text{Gr}_G)$. They both have a commutative ring structure with respect to convolution. We identify the spectrum of homology ring with the universal group-algebra centralizer of the Langlands dual group $\check G$, and we relate the spectrum of K-homology ring to the universal group-group centralizer of G and of $\check G$. If we add the loop-rotation equivariance, we obtain a noncommutative deformation of the (K-)homology ring, and thus a Poisson structure on its spectrum. We relate this structure to the standard one on the universal centralizer. The commutative subring of $G(\mathbb{C}{\rm t})$-equivariant homology of the point gives rise to a polarization which is related to Kostant's Toda lattice integrable system. We also compute the equivariant K-ring of the affine Grassmannian Steinberg variety. The equivariant K-homology of GrG is equipped with a canonical basis formed by the classes of simple equivariant perverse coherent sheaves. Their convolution is again perverse and is related to the Feigin–Loktev fusion product of $G(\mathbb{C}{\rm t})$-modules.
Despite widespread use of noninvasive ventilation (NIV) in some coronavirus disease 2019 (COVID-19) hypoxemic patients, its clinical application is still subject of debate.
This is a retrospective, ...observational study with data collected from 91 consecutive patients treated in COVID intensive care unit (ICU) in our institution between October 2020 and February 2021. Outcomes were represented as ventilation hours, ICU and hospital length of stay, and ICU and hospital mortality.
Patients' mean age was 66 ± 11 y and severe COVID-19 pneumonia with mean paO
/FiO
137 ± 57 was observed in 90% of the patients. High positive end-expiratory pressure (PEEP) NIV by means of total face mask was initially applied in 58 (64%) patients, high flow oxygen therapy (HFOT) in 25 (27%) patients, whilst invasive mechanical ventilation (IMV) started at the moment of admission in 8 (9%) patients. NIV and high flow oxygen therapy (HFOT) have been kept on throughout ICU stay in 50 (55%) patients, while 41 (45%) patients were put on IMV. Overall ICU mortality was 41%, while ICU mortality of patients on NIV was 14%.
High PEEP NIV was convenient and safe as initial respiratory support and in some COVID-19 ARDS patients remained an optimal respiratory support throughout their disease.
Recently, the pentadecapeptide BPC 157-induced counteraction of bupivacaine cardiotoxicity has been reported. Medication includes (i) lidocaine-induced local anesthesia via intraplantar application ...and axillary and spinal (L4-L5) intrathecal block, (ii) lidocaine-induced arrhythmias, (iii) convulsions, and (iv) lidocaine-induced HEK293 cell depolarisation. BPC 157 applications (intraplantar, intraperitoneal, and intragastric) were given (i) immediately after lidocaine, (ii) 10 min after, or (iii) 5 min before. The BPC 157/NO-system relationship was verified with NO-agents, the NOS-blocker L-NAME and the NOS-substrate L-arginine, given alone and/or together, in axillary and spinal intrathecal blocks. BPC 157 applied immediately after lidocaine or 5 min before the application of lidocaine considerably ameliorated plantar presentation. BPC 157 medication considerably counteracted lidocaine-induced limb function failure; L-NAME was counteracted; L-arginine exhibited counteraction when given immediately after lidocaine, but prolongation was seen when given later. Given together, prophylactically or therapeutically, L-NAME and L-arginine (L-NAME + L-arginine) counteracted the other’s response. BPC 157 maintained its original response when given together with L-NAME or L-arginine. When BPC 157 was given together with L-NAME and L-arginine, its original response reappeared. BPC 157 antagonised the lidocaine-induced bradycardia and eliminated tonic-clonic convulsions. Also, BPC 157 counteracted the lidocaine-induced depolarisation of HEK293 cells. Thus, BPC 157 has antidote activity in its own right against lidocaine and local anesthetics.
PDF
