Automorphismes de certains complétés du corps de Weyl quantique

Let $k$ be a field and $\sigma$ the $k$-automorphism of $k((Y ))$ defined by: $\sigma(Y) = qY$, with $q\in k^\ast$. The purpose of this article is the description of the group Aut$_k(Lq)$ for the extension $Lq = k((Y ))((X;\sigma))$ of the quantum Weyl skewfield $D^q_1 = k(Y )(X;\sigma)$, when $q$ is not a root of one. The motivations of the main theorem (theorem 2.7) are detailed in the first part of the paper, devoted to the two-dimensional quantum Cremona transformations. Its proof is based on a general result (theorem 2.3) concerning the continuity of automorphisms in Laurent series skewfields, which also holds in the classical case (remark 2.10)

On Two Theorems About Symplectic Reflection Algebras

We give a new proof and an improvement of two Theorems of J. Alev, M.A. Farinati, T. Lambre and A.L. Solotar : the first one about Hochschild cohomology spaces of some twisted bimodules of the Weyl algebra W and the second one about Hochschild cohomology spaces of the smash product G * W (G a finite subgroup of SP(2n)), and as an application, we then give a new proof of a Theorem of P. Etingof and V. Ginzburg, which shows that the Symplectic Reflection Algebras are deformations of G * W (and, in fact, all possible ones).Comment: corrected typo

Modular Lie algebras and the Gelfand-Kirillov conjecture

Let g be a finite dimensional simple Lie algebra over an algebraically closed field of characteristic zero. We show that if the Gelfand-Kirillov conjecture holds for g, then g has type A_n, C_n or G_2.Comment: 20 page

Automorphisms of associative algebras and noncommutative geometry

A class of differential calculi is explored which is determined by a set of automorphisms of the underlying associative algebra. Several examples are presented. In particular, differential calculi on the quantum plane, the $h$-deformed plane and the quantum group GLpq(2) are recovered in this way. Geometric structures like metrics and compatible linear connections are introduced.Comment: 28 pages, some references added, several amendments of minor importance, remark on modular group in section 8 omitted, to appear in J. Phys.

Poisson-de Rham homology of hypertoric varieties and nilpotent cones

We prove a conjecture of Etingof and the second author for hypertoric varieties, that the Poisson-de Rham homology of a unimodular hypertoric cone is isomorphic to the de Rham cohomology of its hypertoric resolution. More generally, we prove that this conjecture holds for an arbitrary conical variety admitting a symplectic resolution if and only if it holds in degree zero for all normal slices to symplectic leaves. The Poisson-de Rham homology of a Poisson cone inherits a second grading. In the hypertoric case, we compute the resulting 2-variable Poisson-de Rham-Poincare polynomial, and prove that it is equal to a specialization of an enrichment of the Tutte polynomial of a matroid that was introduced by Denham. We also compute this polynomial for S3-varieties of type A in terms of Kostka polynomials, modulo a previous conjecture of the first author, and we give a conjectural answer for nilpotent cones in arbitrary type, which we prove in rank less than or equal to 2.Comment: 25 page

Nivolumab combined with brentuximab vedotin for R/R primary mediastinal large B-cell lymphoma: A 3-year follow-up

Patients with relapsed/refractory primary mediastinal large B-cell lymphoma (R/R PMBL) have poor responses to salvage therapy. Nivolumab and brentuximab vedotin (BV) showed promising early efficacy in patients with R/R PMBL in the phase 1/2 open-label, multicenter CheckMate 436 study; we report safety and efficacy findings from the 3-year follow-up. Patients who were eligible were aged ≥15 years with R/R PMBL previously treated with either high-dose chemotherapy plus autologous hematopoietic cell transplantation (HCT) or ≥2 prior multiagent chemotherapies, and had Eastern Cooperative Oncology Group performance status scores of 0 to 1 and CD30 expression of ≥1%. Patients were treated with nivolumab 240 mg and BV 1.8 mg/kg once every 3 weeks until disease progression or unacceptable toxicity. Primary end point was objective response rate (ORR); secondary end points included complete response rate, duration of response, progression-free survival (PFS), and overall survival (OS). Safety was monitored throughout. At final database lock (30 March 2022), 29 patients had received nivolumab plus BV; median follow-up was 39.6 months. Investigator-assessed ORR was 73.3%; median time to response was 1.3 months (range, 1.1-4.8). Median PFS was 26.0 months; median OS was not reached. PFS and OS rates at 24 months were 55.5% (95% confidence interval [CI], 32.0-73.8) and 75.5% (95% CI, 55.4-87.5), respectively. The most frequently occurring grade 3/4 treatment-related adverse event was neutropenia. Consolidative HCT was received by 12 patients, with a 100-day complete response rate of 100.0%. This 3-year follow-up showed long-term efficacy for nivolumab plus BV in R/R PMBL, with no new safety signals. This trial was registered at www.clinicaltrials.gov as #NCT02581631

A Novel and Selective Dopamine Transporter Inhibitor, (S)-MK-26, Promotes Hippocampal Synaptic Plasticity and Restores Effort-Related Motivational Dysfunctions

Dopamine (DA), the most abundant human brain catecholaminergic neurotransmitter, modulates key behavioral and neurological processes in young and senescent brains, including motricity, sleep, attention, emotion, learning and memory, and social and reward-seeking behaviors. The DA transporter (DAT) regulates transsynaptic DA levels, influencing all these processes. Compounds targeting DAT (e.g., cocaine and amphetamines) were historically used to shape mood and cognition, but these substances typically lead to severe negative side effects (tolerance, abuse, addiction, and dependence). DA/DAT signaling dysfunctions are associated with neuropsychiatric and progressive brain disorders, including Parkinson's and Alzheimer diseases, drug addiction and dementia, resulting in devastating personal and familial concerns and high socioeconomic costs worldwide. The development of low-side-effect, new/selective medicaments with reduced abuse-liability and which ameliorate DA/DAT-related dysfunctions is therefore crucial in the fields of medicine and healthcare. Using the rat as experimental animal model, the present work describes the synthesis and pharmacological profile of (S)-MK-26, a new modafinil analogue with markedly improved potency and selectivity for DAT over parent drug. Ex vivo electrophysiology revealed significantly augmented hippocampal long-term synaptic potentiation upon acute, intraperitoneally delivered (S)-MK-26 treatment, whereas in vivo experiments in the hole-board test showed only lesser effects on reference memory performance in aged rats. However, in effort-related FR5/chow and PROG/chow feeding choice experiments, (S)-MK-26 treatment reversed the depression-like behavior induced by the dopamine-depleting drug tetrabenazine (TBZ) and increased the selection of high-effort alternatives. Moreover, in in vivo microdialysis experiments, (S)-MK-26 significantly increased extracellular DA levels in the prefrontal cortex and in nucleus accumbens core and shell. These studies highlight (S)-MK-26 as a potent enhancer of transsynaptic DA and promoter of synaptic plasticity, with predominant beneficial effects on effort-related behaviors, thus proposing therapeutic potentials for (S)-MK-26 in the treatment of low-effort exertion and motivational dysfunctions characteristic of depression and aging-related disorders

Hagfish genome elucidates vertebrate whole-genome duplication events and their evolutionary consequences.

Polyploidy or whole-genome duplication (WGD) is a major event that drastically reshapes genome architecture and is often assumed to be causally associated with organismal innovations and radiations. The 2R hypothesis suggests that two WGD events (1R and 2R) occurred during early vertebrate evolution. However, the timing of the 2R event relative to the divergence of gnathostomes (jawed vertebrates) and cyclostomes (jawless hagfishes and lampreys) is unresolved and whether these WGD events underlie vertebrate phenotypic diversification remains elusive. Here we present the genome of the inshore hagfish, Eptatretus burgeri. Through comparative analysis with lamprey and gnathostome genomes, we reconstruct the early events in cyclostome genome evolution, leveraging insights into the ancestral vertebrate genome. Genome-wide synteny and phylogenetic analyses support a scenario in which 1R occurred in the vertebrate stem-lineage during the early Cambrian, and 2R occurred in the gnathostome stem-lineage, maximally in the late Cambrian-earliest Ordovician, after its divergence from cyclostomes. We find that the genome of stem-cyclostomes experienced an additional independent genome triplication. Functional genomic and morphospace analyses demonstrate that WGD events generally contribute to developmental evolution with similar changes in the regulatory genome of both vertebrate groups. However, appreciable morphological diversification occurred only in the gnathostome but not in the cyclostome lineage, calling into question the general expectation that WGDs lead to leaps of bodyplan complexity

Improving a Natural CaMKII Inhibitor by Random and Rational Design

CaM-KIIN has evolved to inhibit stimulated and autonomous activity of the Ca(2+)/calmodulin (CaM)-dependent protein kinase II (CaMKII) efficiently, selectively, and potently (IC50 ∼100 nM). The CN class of peptides, derived from the inhibitory region of CaM-KIIN, provides powerful new tools to study CaMKII functions. The goal of this study was to identify the residues required for CaMKII inhibition, and to assess if artificial mutations could further improve the potency achieved during evolution.First, the minimal region with full inhibitory potency was identified (CN19) by determining the effect of truncated peptides on CaMKII activity in biochemical assays. Then, individual residues of CN19 were mutated. Most individual Ala substitutions decreased potency of CaMKII inhibition, however, P3A, K13A, and R14A increased potency. Importantly, this initial Ala scan suggested a specific interaction of the region around R11 with the CaMKII substrate binding site, which was exploited for further rational mutagenesis to generate an optimized pseudo-substrate sequence. Indeed, the potency of the optimized peptide CN19o was >250fold improved (IC50 <0.4 nM), and CN19o has characteristics of a tight-binding inhibitor. The selectivity for CaMKII versus CaMKI was similarly improved (to almost 100,000fold for CN19o). A phospho-mimetic S12D mutation decreased potency, indicating potential for regulation by cellular signaling. Consistent with importance of this residue in inhibition, most other S12 mutations also significantly decreased potency, however, mutation to V or Q did not.These results provide improved research tools for studying CaMKII function, and indicate that evolution fine-tuned CaM-KIIN not for maximal potency of CaMKII inhibition, but for lower potency that may be optimal for dynamic regulation of signal transduction