Sums of magnetic eigenvalues are maximal on rotationally symmetric domains

The sum of the first n energy levels of the planar Laplacian with constant magnetic field of given total flux is shown to be maximal among triangles for the equilateral triangle, under normalization of the ratio (moment of inertia)/(area)^3 on the domain. The result holds for both Dirichlet and Neumann boundary conditions, with an analogue for Robin (or de Gennes) boundary conditions too. The square similarly maximizes the eigenvalue sum among parallelograms, and the disk maximizes among ellipses. More generally, a domain with rotational symmetry will maximize the magnetic eigenvalue sum among all linear images of that domain. These results are new even for the ground state energy (n=1).Comment: 19 pages, 1 figur

New insights into the genetic etiology of Alzheimer's disease and related dementias

Characterization of the genetic landscape of Alzheimer's disease (AD) and related dementias (ADD) provides a unique opportunity for a better understanding of the associated pathophysiological processes. We performed a two-stage genome-wide association study totaling 111,326 clinically diagnosed/'proxy' AD cases and 677,663 controls. We found 75 risk loci, of which 42 were new at the time of analysis. Pathway enrichment analyses confirmed the involvement of amyloid/tau pathways and highlighted microglia implication. Gene prioritization in the new loci identified 31 genes that were suggestive of new genetically associated processes, including the tumor necrosis factor alpha pathway through the linear ubiquitin chain assembly complex. We also built a new genetic risk score associated with the risk of future AD/dementia or progression from mild cognitive impairment to AD/dementia. The improvement in prediction led to a 1.6- to 1.9-fold increase in AD risk from the lowest to the highest decile, in addition to effects of age and the APOE ε4 allele

53BP1 as a potential predictor of response in PARP inhibitor-treated homologous recombination-deficient ovarian cancer

Contains fulltext : 202591.pdf (publisher's version ) (Closed access)OBJECTIVE: Poly(ADP-ribose) polymerase (PARP) inhibitors have shown substantial activity in homologous recombination- (HR-) deficient ovarian cancer and are undergoing testing in other HR-deficient tumors. For reasons that are incompletely understood, not all patients with HR-deficient cancers respond to these agents. Preclinical studies have demonstrated that changes in alternative DNA repair pathways affect PARP inhibitor (PARPi) sensitivity in ovarian cancer models. This has not previously been assessed in the clinical setting. METHODS: Clonogenic and plasmid-based HR repair assays were performed to compare BRCA1-mutant COV362 ovarian cancer cells with or without 53BP1 gene deletion. Archival biopsies from ovarian cancer patients in the phase I, open-label clinical trial of PARPi ABT-767 were stained for PARP1, RAD51, 53BP1 and multiple components of the nonhomologous end-joining (NHEJ) DNA repair pathway. Modified histochemistry- (H-) scores were determined for each repair protein in each sample. HRD score was determined from tumor DNA. RESULTS: 53BP1 deletion increased HR in BRCA1-mutant COV362 cells and decreased PARPi sensitivity in vitro. In 36 women with relapsed ovarian cancer, responses to the PARPi ABT-767 were observed exclusively in cancers with HR deficiency. In this subset, 7 of 18 patients (39%) had objective responses. The actual HRD score did not further correlate with change from baseline tumor volume (r=0.050; p=0.87). However, in the HR-deficient subset, decreased 53BP1 H-score was associated with decreased antitumor efficacy of ABT-767 (r=-0.69, p=0.004). CONCLUSION: Differences in complementary repair pathways, particularly 53BP1, correlate with PARPi response of HR-deficient ovarian cancers