Complete Embedded Self-Translating Surfaces under Mean Curvature Flow

We describe a construction of complete embedded self-translating surfaces under mean curvature flow by desingularizing the intersection of a finite family of grim reapers in general position.Comment: 42 pages, 8 figures. v2: typos correcte

Stability of bicontinuous cubic phases in ternary amphiphilic systems with spontaneous curvature

We study the phase behavior of ternary amphiphilic systems in the framework of a curvature model with non-vanishing spontaneous curvature. The amphiphilic monolayers can arrange in different ways to form micellar, hexagonal, lamellar and various bicontinuous cubic phases. For the latter case we consider both single structures (one monolayer) and double structures (two monolayers). Their interfaces are modeled by the triply periodic surfaces of constant mean curvature of the families G, D, P, C(P), I-WP and F-RD. The stability of the different bicontinuous cubic phases can be explained by the way in which their universal geometrical properties conspire with the concentration constraints. For vanishing saddle-splay modulus $\bar \kappa$, almost every phase considered has some region of stability in the Gibbs triangle. Although bicontinuous cubic phases are suppressed by sufficiently negative values of the saddle-splay modulus $\bar \kappa$, we find that they can exist for considerably lower values than obtained previously. The most stable bicontinuous cubic phases with decreasing $\bar \kappa < 0$ are the single and double gyroid structures since they combine favorable topological properties with extreme volume fractions.Comment: Revtex, 23 pages with 10 Postscript files included, to appear in J. Chem. Phys. 112 (6) (February 2000

Probing Exfoliated Graphene Layers and Their Lithiation with Microfocused X-rays

X-ray diffraction is measured on individual bilayer and multilayer graphene single-crystals and combined with electrochemically induced lithium intercalation. In-plane Bragg peaks are observed by grazing incidence diffraction. Focusing the incident beam down to an area of about 10 μm × 10 μm, individual flakes are probed by specular X-ray reflectivity. By deploying a recursive Parratt algorithm to model the experimental data, we gain access to characteristic crystallographic parameters of the samples. Notably, it is possible to directly extract the bi/multilayer graphene c-axis lattice parameter. The latter is found to increase upon lithiation, which we control using an on-chip peripheral electrochemical cell layout. These experiments demonstrate the feasibility of in situ X-ray diffraction on individual, micron-sized single crystallites of few- and bilayer two-dimensional materials

Second-line cabozantinib versus nivolumab in advanced renal cell carcinoma: Systematic review and indirect treatment comparison

Background: Nivolumab and cabozantinib, two new treatment options for previously-treated advanced/metastatic renal cell carcinoma (aRCC), have recently been approved. Methods: Two independent reviewers performed study selection, data extraction, and risk of bias assessment. Indirect treatment comparisons were carried out by directly assessing HR differences and statistical modeling of Kaplan-Meier curves from these two trials. Results: Publications identified showed that no head-to-head comparisons had been carried out. Two indirect treatment comparisons used agreed that there was no significant difference in OS between cabozantinib and nivolumab and that cabozantinib significantly improved PFS compared to nivolumab. Conclusions: The field of aRCC treatments is evolving rapidly, creating opportunities for individualized treatments and challenges for clinicians to keep up with the evidence. In lieu of availability of direct comparisons of all options, advanced modeling results presented herein can help to inform and improve personalized treatments

Arctic Mission Benefit Analysis: impact of sea ice thickness, freeboard, and snow depth products on sea ice forecast performance

Assimilation of remote-sensing products of sea ice thickness (SIT) into sea ice–ocean models has been shown to improve the quality of sea ice forecasts. Key open questions are whether assimilation of lower-level data products such as radar freeboard (RFB) can further improve model performance and what performance gains can be achieved through joint assimilation of these data products in combination with a snow depth product. The Arctic Mission Benefit Analysis system was developed to address this type of question. Using the quantitative network design (QND) approach, the system can evaluate, in a mathematically rigorous fashion, the observational constraints imposed by individual and groups of data products. We demonstrate the approach by presenting assessments of the observation impact (added value) of different Earth observation (EO) products in terms of the uncertainty reduction in a 4-week forecast of sea ice volume (SIV) and snow volume (SNV) for three regions along the Northern Sea Route in May 2015 using a coupled model of the sea ice–ocean system, specifically the Max Planck Institute Ocean Model. We assess seven satellite products: three real products and four hypothetical products. The real products are monthly SIT, sea ice freeboard (SIFB), and RFB, all derived from CryoSat-2 by the Alfred Wegener Institute. These are complemented by two hypothetical monthly laser freeboard (LFB) products with low and high accuracy, as well as two hypothetical monthly snow depth products with low and high accuracy.On the basis of the per-pixel uncertainty ranges provided with the CryoSat-2 SIT, SIFB, and RFB products, the SIT and RFB achieve a much better performance for SIV than the SIFB product. For SNV, the performance of SIT is only low, the performance of SIFB is higher and the performance of RFB is yet higher. A hypothetical LFB product with low accuracy (20&thinsp;cm uncertainty) falls between SIFB and RFB in performance for both SIV and SNV. A reduction in the uncertainty of the LFB product to 2&thinsp;cm yields a significant increase in performance.Combining either of the SIT or freeboard products with a hypothetical snow depth product achieves a significant performance increase. The uncertainty in the snow product matters: a higher-accuracy product achieves an extra performance gain. Providing spatial and temporal uncertainty correlations with the EO products would be beneficial not only for QND assessments, but also for assimilation of the products.</p

On Vanishing Theorems For Vector Bundle Valued p-Forms And Their Applications

Let $F: [0, \infty) \to [0, \infty)$ be a strictly increasing $C^2$ function with $F(0)=0$. We unify the concepts of $F$-harmonic maps, minimal hypersurfaces, maximal spacelike hypersurfaces, and Yang-Mills Fields, and introduce $F$-Yang-Mills fields, $F$-degree, $F$-lower degree, and generalized Yang-Mills-Born-Infeld fields (with the plus sign or with the minus sign) on manifolds. When $F(t)=t, \frac 1p(2t)^{\frac p2}, \sqrt{1+2t} -1,$ and $1-\sqrt{1-2t},$ the $F$-Yang-Mills field becomes an ordinary Yang-Mills field, $p$-Yang-Mills field, a generalized Yang-Mills-Born-Infeld field with the plus sign, and a generalized Yang-Mills-Born-Infeld field with the minus sign on a manifold respectively. We also introduce the $E_{F,g}-$energy functional (resp. $F$-Yang-Mills functional) and derive the first variational formula of the $E_{F,g}-$energy functional (resp. $F$-Yang-Mills functional) with applications. In a more general frame, we use a unified method to study the stress-energy tensors that arise from calculating the rate of change of various functionals when the metric of the domain or base manifold is changed. These stress-energy tensors, linked to $F$-conservation laws yield monotonicity formulae. A "macroscopic" version of these monotonicity inequalities enables us to derive some Liouville type results and vanishing theorems for $p-$forms with values in vector bundles, and to investigate constant Dirichlet boundary value problems for 1-forms. In particular, we obtain Liouville theorems for $F-$harmonic maps (e.g. $p$-harmonic maps), and $F-$Yang-Mills fields (e.g. generalized Yang-Mills-Born-Infeld fields on manifolds). We also obtain generalized Chern type results for constant mean curvature type equations for $p-$forms on $\Bbb{R}^m$ and on manifolds $M$ with the global doubling property by a different approach. The case $p=0$ and $M=\mathbb{R}^m$ is due to Chern.Comment: 1. This is a revised version with several new sections and an appendix that will appear in Communications in Mathematical Physics. 2. A "microscopic" approach to some of these monotonicity formulae leads to celebrated blow-up techniques and regularity theory in geometric measure theory. 3. Our unique solution of the Dirichlet problems generalizes the work of Karcher and Wood on harmonic map

Challenges of Loss to Follow-up in Tuberculosis Research.

In studies evaluating methods for diagnosing tuberculosis (TB), follow-up to verify the presence or absence of active TB is crucial and high dropout rates may significantly affect the validity of the results. In a study assessing the diagnostic performance of the QuantiFERON®-TB Gold In-Tube test in TB suspect children in Tanzania, factors influencing patient adherence to attend follow-up examinations and reasons for not attending were examined. In 160 children who attended and 102 children who did not attend scheduled 2-month follow-up baseline health characteristics, demographic data and risk factors for not attending follow-up were determined. Qualitative interviews were used to understand patient and caretakers reasons for not returning for scheduled follow-up. Being treated for active tb in the dots program (OR: 4.14; 95% CI:1.99-8.62;p-value<0.001) and receiving money for the bus fare (OR:129; 95% CI 16->100;P-value<0.001) were positive predictors for attending follow-up at 2 months, and 21/85(25%) of children not attending scheduled follow-up had died. Interviews revealed that limited financial resources, i.e. lack of money for transportation and poor communication, were related to non-adherence. Patients lost to follow-up is a potential problem for TB research. Receiving money for transportation to the hospital and communication is crucial for adherence to follow-up conducted at a study facility. Strategies to ensure follow-up should be part of any study protocol

Bourgeois behavior and freeloading in the colonial orb web spider Parawixia bistriata (Araneae, Araneidae).

Spiders of the tropical American colonial orb weaver Parawixia bistriata form a communal bivouac in daytime. At sunset, they leave the bivouac and construct individual, defended webs within a large, communally built scaffolding of permanent, thick silk lines between trees and bushes. Once spiders started building a web, they repelled other spiders walking on nearby scaffolding with a bounce behavior. In nearly all cases (93%), this resulted in the intruder leaving without a fight, akin to the bourgeois strategy, in which residents win and intruders retreat without escalated contests. However, a few spiders (6.5%) did not build a web due to lack of available space.Webless spiders were less likely to leave when bounced (only 42% left) and instead attempted to freeload, awaiting the capture of prey items in nearby webs. Our simple model shows that webless spiders should change their strategy from bourgeois to freeloading satellite as potential web sites become increasingly occupied