Singularities of moduli spaces of sheaves on K3 surfaces and Nakajima quiver varieties

The aim of this paper is to study the singularities of certain moduli spaces of sheaves on K3 surfaces by means of Nakajima quiver varieties. The singularities in question arise from the choice of a non--generic polarization, with respect to which we consider stability, and admit natural symplectic resolutions corresponding to choices of general polarizations. For sheaves that are pure of dimension one, we show that these moduli spaces are, locally around a singular point, isomorphic to a quiver variety and that, via this isomorphism, the natural symplectic resolutions correspond to variations of GIT quotients of the quiver variety.Comment: 40 pages; final version; As pointed out to us by Z. Zhang, we prove quadraticity and not formality of the Kuranishi family. Quadraticity is all we need for our main theorem. The current version reflects this correction. A few other improvements in exposition and correction of typo

The Hodge numbers of O'Grady 10 via Ng\^o strings

We determine the Hodge numbers of the hyper-K\"ahler manifold known as O'Grady 10 by studying some related modular Lagrangian fibrations by means of a refinement of the Ng\^o Support Theorem.Comment: Revised and final version to appear in Jour. Math. Pur. et App

The geometry of antisymplectic involutions, I

We study fixed loci of antisymplectic involutions on projective hyperk\"ahler manifolds. When the involution is induced by an ample class of square 2 in the Beauville-Bogomolov-Fujiki lattice, we show that the number of connected components of the fixed locus is equal to the divisibility of the class, which is either 1 or 2.Comment: 45 page

Rationale and protocol of a double-blind, randomized, placebo-controlled trial to test the efficacy, safety, and tolerability of dimethyl fumarate in Friedreich Ataxia (DMF-FA-201)

IntroductionFriedreich Ataxia (FRDA) is an autosomal recessive neurodegenerative disorder that causes gait and limb ataxia, dysarthria, and impaired vibratory sense, with cardiomyopathy being the predominant cause of death. There is no approved therapy, which results in the use of symptomatic treatments and the chronic support of physiotherapy. Dimethyl fumarate (DMF) is a fumaric acid ester used for the treatment of psoriasis and Multiple Sclerosis (MS). It induces Nrf2 in vitro and in vivo, and it increases frataxin in FRDA patient lymphoblasts, in mouse models, and in MS treated patients.MethodsThe aim of our study is to investigate if DMF can increase the expression of the FXN gene and frataxin protein and ameliorate in-vivo detectable measures of mitochondrial dysfunction in FRDA. The study is composed of a screening visit and two sequential 12-week phases: a core phase and an extension phase. During the first phase (core), patients will be randomly assigned to either the DMF or a placebo group in a 1:1 ratio. During the first week, patients will receive a total daily dose of 240 mg of DMF or placebo; from the second week of treatment, the dose will be increased to two 120 mg tablets BID for a total daily dose of 480 mg. During the second phase (extension), all patients will be treated with DMF. EudraCT number 2021-006274-23.EndpointsThe primary endpoint will be a change in FXN gene expression level after 12 weeks of treatment. Secondary endpoints will be frataxin protein level, cardiopulmonary exercise test outputs, echocardiographic measures, Nrf2 pathway and mitochondrial biogenesis gene expression, safety, clinical scales, and quality of life scales.ConclusionsThis is the first study aimed at exploring the ability of DMF, an already available treatment for MS and psoriasis, to correct the biological deficits of FRDA and potentially improve mitochondrial respiration in-vivo

A retrospective multicentric observational study of trastuzumab emtansine in HER2 positive metastatic breast cancer: a real- world experience

We addressed trastuzumab emtansine (T-DM1) e cacy in HER2+ metastatic breast cancer patients treated in real-world practice, and its activity in pertuzumab- pretreated patients. We conducted a retrospective, observational study involving 23 cancer centres, and 250 patients. Survival data were analyzed by Kaplan Meier curves and log rank test. Factors testing signi cant in univariate analysis were tested in multivariate models. Median follow-up was 15 months and median T-DM1 treatment-length 4 months. Response rate was 41.6%, clinical bene t 60.9%. Median progression-free and median overall survival were 6 and 20 months, respectively. Overall, no di erences emerged by pertuzumab pretreatment, with median progression-free and median overall survival of 4 and 17 months in pertuzumab- pretreated (p=0.13), and 6 and 22 months in pertuzumab-naïve patients (p=0.27). Patients who received second-line T-DM1 had median progression-free and median overall survival of 3 and 12 months (p=0.0001) if pertuzumab-pretreated, and 8 and 26 months if pertuzumab-naïve (p=0.06). In contrast, in third-line and beyond, median progression-free and median overall survival were 16 and 18 months in pertuzumab- pretreated (p=0.05) and 6 and 17 months in pertuzumab-naïve patients (p=0.30). In multivariate analysis, lower ECOG performance status was associated with progression-free survival bene t (p<0.0001), while overall survival was positively a ected by lower ECOG PS (p<0.0001), absence of brain metastases (p 0.05), and clinical bene t (p<0.0001). Our results are comparable with those from randomized trials. Further studies are warranted to con rm and interpret our data on apparently lower T-DM1 e cacy when given as second-line treatment after pertuzumab, and on the optimal sequence order