Faltings heights of abelian varieties with complex multiplication

Let M be the Shimura variety associated with the group of spinor similitudes of a rational quadratic space over of signature (n,2). We prove a conjecture of Bruinier-Kudla-Yang, relating the arithmetic intersection multiplicities of special divisors and big CM points on M to the central derivatives of certain $L$-functions. As an application of this result, we prove an averaged version of Colmez's conjecture on the Faltings heights of CM abelian varieties.Comment: Final version. To appear in Annals of Mat

Extraction of the beam elastic shape from uncertain FBG strain measurement points

Aim of the present paper is the analysis of the strain along the beam that is equipped with Glass Fibers Reinforced Polymers (GFRP) with an embedded set of optical Fiber Bragg Grating sensors (FBG), in the context of a project to equip with these new structural elements an Italian train bridge. Different problems are attacked, and namely: (i)during the production process [1] it is difficult to locate precisely the FBG along the reinforcement bar, therefore the following question appears: How can we associate the strain measurements to the points along the bar? Is it possible to create a signal analysis procedure such that this correspondence is found?(ii)the beam can be inflected and besides the strain at some points, we would like to recover the elastic shape of the deformed beam that is equipped with the reinforcement bars. Which signal processing do we use to determine the shape of the deformed beam in its inflection plane?(iii)if the beam is spatially inflected, in two orthogonal planes, is it possible to recover the beam spatial elastic shape? Object of the paper is to answer to these questions

Soft SUSY breaking contributions to proton decay

We show that in supersymmetric grand unified theories new effective D=4 and D=5 operators for proton decay are induced by soft SUSY-breaking terms, when heavy GUT gauge bosons are integrated out, in addition to the standard D=6 ones. As a result, the proton lifetime in gauge mediated channels can be enhanced or even suppressed depending on the size of the heavy Higgses soft terms.Comment: 16 pages, 2 figures, LaTeX, JHEP3 class, axodra

Nonperturbative study of the two-frequency sine-Gordon model

The two-frequency sine-Gordon model is examined. The focus is mainly on the case when the ratio of the frequencies is 1/2, given the recent interest in the literature. We discuss the model both in a perturbative (form factor perturbation theory) and a nonperturbative (truncated conformal space approach) framework, and give particular attention to a phase transition conjectured earlier by Delfino and Mussardo. We give substantial evidence that the transition is of second order and that it is in the Ising universality class. Furthermore, we check the UV-IR operator correspondence and conjecture the phase diagram of the theory.Comment: Minor corrections, LaTeX2e, 39 pages, 26 figures (4 pslatex, 1 postscript and 21 eps

Gravitational Waves from Domain Walls in Pulsar Timing Array Datasets

We present a model-independent search for the gravitational wave background from cosmic domain walls (DWs) in the NANOGrav 12.5 years dataset and International PTA Data Release 2. DWs that annihilate at temperatures $\sim 20-50~\text{MeV}$ with tensions $\sim (40-100~\text{TeV})^3$ provide as good a fit to both datasets as the astrophysical background from supermassive black hole mergers. DWs may decay into the Standard Model (SM) or a dark sector. In the latter case we predict an abundance $\Delta N_{\text{eff}}$ of dark radiation well within the reach of upcoming CMB surveys. Complementary signatures at colliders and laboratories can arise if couplings to the SM are present. As an example, we discuss heavy axion scenarios, where DW annihilation may interestingly be induced by QCD confinement.Comment: 5+7 pages, 8 figure

Prevalence of established and emerging biomarkers of immune checkpoint inhibitor response in advanced hepatocellular carcinoma.

The clinical deployment of immune checkpoint inhibitors (ICIs) has created a tandem drive for the identification of biomarkers linked to benefit. Comprehensive genomic profiling was performed to evaluate the frequency of genomic biomarkers of ICI response in 755 patients with advanced hepatocellular carcinoma (HCC). Median age was 62 years' old, 73% were male, 46% had extrahepatic disease, 107 had documented hepatitis C, 96 had hepatitis B and 4 patients were coinfected. Median tumor mutation burden (TMB) was 4 mutations/Mb and only 6 tumors (0.8%) were TMB-high. Out of 542 cases assessed for microsatellite instability (MSI), one (0.2%) was MSI-high and TMB-high. Twenty-seven (4%) patients had POLE/D alterations. One patient had a pathogenic POLE R762W mutation but TMB was 4 mutations/Mb. Forty percent had DNA damage response gene alterations. In a small case series (N=17) exploring the relationship between biomarkers and ICI response, one patient (TMB 15 mutations/Mb, MSI-low) had a sustained complete response to nivolumab lasting > 2 years. Otherwise there were no significant genomic or TMB differences between responders, progressors, and those with stable disease. Overall, markers of genomic instability were infrequent in this cohort. Larger clinically annotated datasets are needed to explore genomic and non-genomic determinants of ICI response in HCC

Phase-change chalcogenide glass metamaterial

Combining metamaterials with functional media brings a new dimension to their performance. Here we demonstrate substantial resonance frequency tuning in a photonic metamaterial hybridized with an electrically/optically switchable chalcogenide glass. The transition between amorphous and crystalline forms brings about a 10% shift in the near-infrared resonance wavelength of an asymmetric split-ring array, providing transmission modulation functionality with a contrast ratio of 4:1 in a device of sub-wavelength thickness.Comment: 3 pages, 3 figure