Strichartz estimates for the Schr\"odinger equation on polygonal domains

We prove Strichartz estimates with a loss of derivatives for the Schr\"odinger equation on polygonal domains with either Dirichlet or Neumann homogeneous boundary conditions. Using a standard doubling procedure, estimates the on polygon follow from those on Euclidean surfaces with conical singularities. We develop a Littlewood-Paley squarefunction estimate with respect to the spectrum of the Laplacian on these spaces. This allows us to reduce matters to proving estimates at each frequency scale. The problem can be localized in space provided the time intervals are sufficiently small. Strichartz estimates then follow from a result of the second author regarding the Schr\"odinger equation on the Euclidean cone.Comment: 12 page

Mode spectrum and temporal soliton formation in optical microresonators

The formation of temporal dissipative solitons in optical microresonators enables compact, high repetition rate sources of ultra-short pulses as well as low noise, broadband optical frequency combs with smooth spectral envelopes. Here we study the influence of the resonator mode spectrum on temporal soliton formation. Using frequency comb assisted diode laser spectroscopy, the measured mode structure of crystalline MgF2 resonators are correlated with temporal soliton formation. While an overal general anomalous dispersion is required, it is found that higher order dispersion can be tolerated as long as it does not dominate the resonator's mode structure. Mode coupling induced avoided crossings in the resonator mode spectrum are found to prevent soliton formation, when affecting resonator modes close to the pump laser. The experimental observations are in excellent agreement with numerical simulations based on the nonlinear coupled mode equations, which reveal the rich interplay of mode crossings and soliton formation

A para-differential renormalization technique for nonlinear dispersive equations

For \alpha \in (1,2) we prove that the initial-value problem \partial_t u+D^\alpha\partial_x u+\partial_x(u^2/2)=0 on \mathbb{R}_x\times\mathbb{R}_t; u(0)=\phi, is globally well-posed in the space of real-valued L^2-functions. We use a frequency dependent renormalization method to control the strong low-high frequency interactions.Comment: 42 pages, no figure

miR-29b and miR-198 overexpression in CD8⁺ T cells of renal cell carcinoma patients down-modulates JAK3 and MCL-1 leading to immune dysfunction

Background: Mammalian microRNAs (miR) regulate the expression of genes relevant for the development of adaptive and innate immunity against cancer. Since T cell dysfunction has previously been reported in patients with renal cell carcinoma (RCC; clear cell type), we aimed to analyze these immune cells for genetic and protein differences when compared to normal donor T cells freshly after isolation and 35 days after in vitro stimulation (IVS) with HLA-matched RCC tumor cells. Methods: We investigated gene expression profiles of tumor-reactive CD8+ T cells obtained from RCC patient and compared with their HLA-matched healthy sibling donors using a microarray approach. In addition, miRNAs analysis was performed in a validation cohort of peripheral blood CD8+ T cells from 25 RCC patients compared to 15 healthy volunteers. Results: We observed that CD8+ T cells from RCC patients expressed reduced levels of anti-apoptotic and proliferation-associated gene products when compared with normal donor T cells both pre- and post-IVS. In particular, JAK3 and MCL-1 were down-regulated in patient CD8+ T cells versus their normal counterparts, likely due to defective suppressor activity of miR-29b and miR-198 in RCC CD8+ T cells. Indeed, specific inhibition of miR-29b or miR-198 in peripheral blood mononuclear cells (PBMCs) isolated from RCC patients, resulted in the up-regulation of JAK3 and MCL-1 proteins and significant improvement of cell survival in vitro. Conclusions: Our results suggest that miR-29b and miR-198 dysregulation in RCC patient CD8+ T cells is associated with dysfunctional immunity and foreshadow the development of miR-targeted therapeutics to correct such T cell defects in vivo

A Kerr Polarization Controller

Kerr-effect-induced changes of the polarization state of light are well known in pulsed laser systems. An example is nonlinear polarization rotation, which is critical to the operation of many types of mode-locked lasers. Here, we demonstrate that the Kerr effect in a high-finesse Fabry-Pérot resonator can be utilized to control the polarization of a continuous wave laser. It is shown that a linearly-polarized input field is converted into a left- or right-circularly-polarized field, controlled via the optical power. The observations are explained by Kerr-nonlinearity induced symmetry breaking, which splits the resonance frequencies of degenerate modes with opposite polarization handedness in an otherwise symmetric resonator. The all-optical polarization control is demonstrated at threshold powers down to 7 mW. The physical principle of such Kerr effect-based polarization controllers is generic to high-Q Kerr-nonlinear resonators and could also be implemented in photonic integrated circuits. Beyond polarization control, the spontaneous symmetry breaking of polarization states could be used for polarization filters or highly sensitive polarization sensors when operated close to the symmetry-breaking point

Introduced plants as novel Anthropocene habitats for insects

Major environmental changes in the history of life on Earth have given rise to novel habitats, which gradually accumulate species. Human‐induced change is no exception, yet the rules governing species accumulation in anthropogenic habitats are not fully developed. Here we propose that nonnative plants introduced to Great Britain may function as analogues of novel anthropogenic habitats for insects and mites, analysing a combination of local‐scale experimental plot data and geographic‐scale data contained within the Great Britain Database of Insects and their Food Plants. We find that novel plant habitats accumulate the greatest diversity of insect taxa when they are widespread and show some resemblance to plant habitats which have been present historically (based on the relatedness between native and nonnative plant species), with insect generalists colonizing from a wider range of sources. Despite reduced per‐plant diversity, nonnative plants can support distinctive insect communities, sometimes including insect taxa that are otherwise rare or absent. Thus, novel plant habitats may contribute to, and potentially maintain, broader‐scale (assemblage) diversity in regions that contain mixtures of long‐standing and novel plant habitats

Elevated HbA1c levels and the accumulation of differentiated T cells in CMV+ individuals

Aims/hypothesis Biological ageing of the immune system, or immunosenescence, predicts poor health and increased mortality. A hallmark of immunosenescence is the accumulation of differentiated cytotoxic T cells (CD27−CD45RA+/−; or dCTLs), partially driven by infection with the cytomegalovirus (CMV). Immune impairments reminiscent of immunosenescence are also observed in hyperglycaemia, and in vitro studies have illustrated mechanisms by which elevated glucose can lead to increased dCTLs. This study explored associations between glucose dysregulation and markers of immunosenescence in CMV+ and CMV− individuals. Methods A cross-sectional sample of participants from an occupational cohort study (n = 1,103, mean age 40 years, 88% male) were assessed for HbA1c and fasting glucose levels, diabetes, cardiovascular risk factors (e.g. lipids), numbers of circulating effector memory (EM; CD27−CD45RA−) and CD45RA re-expressing effector memory (EMRA; CD27−CD45RA+) T cells, and CMV infection status. Self-report and physical examination assessed anthropometric, sociodemographic and lifestyle factors. Results Among CMV+ individuals (n = 400), elevated HbA1c was associated with increased numbers of EM (B = 2.75, p \u3c 0.01) and EMRA (B = 2.90, p \u3c 0.01) T cells, which was robust to adjustment for age, sex, sociodemographic variables and lifestyle factors. Elevated EM T cells were also positively associated with total cholesterol (B = 0.04, p \u3c 0.05) after applying similar adjustments. No associations were observed in CMV− individuals. Conclusions/interpretation The present study identified consistent associations of unfavourable glucose and lipid profiles with accumulation of dCTLs in CMV+ individuals. These results provide evidence that the impact of metabolic risk factors on immunity and health can be co-determined by infectious factors, and provide a novel pathway linking metabolic risk factors with accelerated immunosenescence. Electronic supplementary material The online version of this article (doi:10.1007/s00125-015-3731-4) contains peer-reviewed but unedited supplementary material, which is available to authorised users