On cross-ratio distortion and Schwarz derivative

We prove asymptotic estimates for the cross-ratio distortion with respect to a smooth or holomorphic function in terms of its Schwarz derivative.Comment: the spelling of the name `Schwarz' correcte

Herman's Theory Revisited

We prove that a $C^{2+\alpha}$-smooth orientation-preserving circle diffeomorphism with rotation number in Diophantine class $D_\delta$, $0<\delta<\alpha\le1$, is $C^{1+\alpha-\delta}$-smoothly conjugate to a rigid rotation. We also derive the most precise version of Denjoy's inequality for such diffeomorphisms.Comment: 10 page

Frequency locking of modulated waves

We consider the behavior of a modulated wave solution to an $\mathbb{S}^1$-equivariant autonomous system of differential equations under an external forcing of modulated wave type. The modulation frequency of the forcing is assumed to be close to the modulation frequency of the modulated wave solution, while the wave frequency of the forcing is supposed to be far from that of the modulated wave solution. We describe the domain in the three-dimensional control parameter space (of frequencies and amplitude of the forcing) where stable locking of the modulation frequencies of the forcing and the modulated wave solution occurs. Our system is a simplest case scenario for the behavior of self-pulsating lasers under the influence of external periodically modulated optical signals

Durvalumab Plus Carboplatin/Paclitaxel Followed by Maintenance Durvalumab With or Without Olaparib as First-Line Treatment for Advanced Endometrial Cancer: The Phase III DUO-E Trial

PURPOSE Immunotherapy and chemotherapy combinations have shown activity in endometrial cancer, with greater benefit in mismatch repair (MMR)-deficient (dMMR) than MMR-proficient (pMMR) disease. Adding a poly(ADP-ribose) polymerase inhibitor may improve outcomes, especially in pMMR disease. METHODS This phase III, global, double-blind, placebo-controlled trial randomly assigned eligible patients with newly diagnosed advanced or recurrent endometrial cancer 1:1:1 to: carboplatin/paclitaxel plus durvalumab placebo followed by placebo maintenance (control arm); carboplatin/paclitaxel plus durvalumab followed by maintenance durvalumab plus olaparib placebo (durvalumab arm); or carboplatin/paclitaxel plus durvalumab followed by maintenance durvalumab plus olaparib (durvalumab + olaparib arm). The primary end points were progression-free survival (PFS) in the durvalumab arm versus control and the durvalumab + olaparib arm versus control. RESULTS Seven hundred eighteen patients were randomly assigned. In the intention-to-treat population, statistically significant PFS benefit was observed in the durvalumab (hazard ratio [HR], 0.71 [95% CI, 0.57 to 0.89]; P = .003) and durvalumab + olaparib arms (HR, 0.55 [95% CI, 0.43 to 0.69]; P < .0001) versus control. Prespecified, exploratory subgroup analyses showed PFS benefit in dMMR (HR [durvalumab v control], 0.42 [95% CI, 0.22 to 0.80]; HR [durvalumab + olaparib v control], 0.41 [95% CI, 0.21 to 0.75]) and pMMR subgroups (HR [durvalumab v control], 0.77 [95% CI, 0.60 to 0.97]; HR [durvalumab + olaparib v control] 0.57; [95% CI, 0.44 to 0.73]); and in PD-L1-positive subgroups (HR [durvalumab v control], 0.63 [95% CI, 0.48 to 0.83]; HR [durvalumab + olaparib v control], 0.42 [95% CI, 0.31 to 0.57]). Interim overall survival results (maturity approximately 28%) were supportive of the primary outcomes (durvalumab v control: HR, 0.77 [95% CI, 0.56 to 1.07]; P = .120; durvalumab + olaparib v control: HR, 0.59 [95% CI, 0.42 to 0.83]; P = .003). The safety profiles of the experimental arms were generally consistent with individual agents. CONCLUSION Carboplatin/paclitaxel plus durvalumab followed by maintenance durvalumab with or without olaparib demonstrated a statistically significant and clinically meaningful PFS benefit in patients with advanced or recurrent endometrial cancer