On Strichartz estimates from decoupling and applications

Strichartz estimates are derived from $\ell^2$-decoupling for phase functions satisfying a curvature condition. Bilinear refinements without loss in the high frequency are discussed. Estimates are established from uniform curvature generalizing Galilean invariance or from transversality in one dimension. The bilinear refinements are utilized to prove local well-posedness for generalized cubic nonlinear Schr\"odinger equations

A Two-Sample Mendelian Randomization Analysis Investigates Associations Between Gut Microbiota and Celiac Disease

Celiac disease (CeD) is a complex immune-mediated inflammatory condition triggered by the ingestion of gluten in genetically predisposed individuals. Literature suggests that alterations in gut microbiota composition and function precede the onset of CeD. Considering that microbiota is partly determined by host genetics, we speculated that the genetic makeup of CeD patients could elicit disease development through alterations in the intestinal microbiota. To evaluate potential causal relationships between gut microbiota and CeD, we performed a two-sample Mendelian randomization analysis (2SMR). Exposure data were obtained from the raw results of a previous genome-wide association study (GWAS) of gut microbiota and outcome data from summary statistics of CeD GWAS and Immunochip studies. We identified a number of putative associations between gut microbiota single nucleotide polymorphisms (SNPs) associated with CeD. Regarding bacterial composition, most of the associated SNPs were related to Firmicutes phylum, whose relative abundance has been previously reported to be altered in CeD patients. In terms of functional units, we linked a number of SNPs to several bacterial metabolic pathways that seemed to be related to CeD. Overall, this study represented the first 2SMR approach to elucidate the relationship between microbiome and CeD.This research was funded by the Basque Department of Health, grant numbers GVSAN2018/111086 and GVSAN2019/111085 to J.R.B. and N.F.-J., respectively

Nonexistence of extremals for the adjoint restriction inequality on the hyperboloid

We study the problem of existence of extremizers for the $L^2$ to $L^p$ adjoint Fourier restriction inequalities on the hyperboloid in dimensions 3 and 4, in which cases $p$ is an even integer. We will use the method developed by Foschi to show that extremizers do not exist.Comment: 32 pages. Correction for Theorem 1.2 and Proposition 7.5 and addition of Remark 1.

Metal–Polymer Heterojunction in Colloidal-Phase Plasmonic Catalysis

[EN] Plasmonic catalysis in the colloidal phase requires robust surface ligands that prevent particles from aggregation in adverse chemical environments and allow carrier flow from reagents to nanoparticles. This work describes the use of a water-soluble conjugated polymer comprising a thiophene moiety as a surface ligand for gold nanoparticles to create a hybrid system that, under the action of visible light, drives the conversion of the biorelevant NAD+ to its highly energetic reduced form NADH. A combination of advanced microscopy techniques and numerical simulations revealed that the robust metal-polymer heterojunction, rich in sulfonate functional groups, directs the interaction of electron-donor molecules with the plasmonic photocatalyst. The tight binding of polymer to the gold surface precludes the need for conventional transition-metal surface cocatalysts, which were previously shown to be essential for photocatalytic NAD+ reduction but are known to hinder the optical properties of plasmonic nanocrystals. Moreover, computational studies indicated that the coating polymer fosters a closer interaction between the sacrificial electron-donor triethanolamine and the nanoparticles, thus enhancing the reactivity.This work was supported by grant PID2019-111772RB-I00 funded by MCIN/AEI/10.13039/501100011033 and grant IT 1254-19 funded by Basque Government. The authors acknowl- edge the financial support of the European Commission (EUSMI, Grant 731019). S.B. is grateful to the European Research Council (ERC-CoG-2019 815128). The authors acknowledge the contributions by Dr. Adrian Pedrazo Tardajos related to sample support and electron microscopy experiments

Weighted inequalities for square and maximal functions in the plane

We prove weighted inequalities for square functions of Littlewood-Paley type defined from a decomposition of the plane into sectors of lacunary aperture and for the maximal function over a lacunary set of directions. Some applications to multiplier theorems are also given