A rescaled method for RBF approximation

A new method to compute stable kernel-based interpolants has been presented by the second and third authors. This rescaled interpolation method combines the standard kernel interpolation with a properly defined rescaling operation, which smooths the oscillations of the interpolant. Although promising, this procedure lacks a systematic theoretical investigation. Through our analysis, this novel method can be understood as standard kernel interpolation by means of a properly rescaled kernel. This point of view allow us to consider its error and stability properties. First, we prove that the method is an instance of the Shepard\u2019s method, when certain weight functions are used. In particular, the method can reproduce constant functions. Second, it is possible to define a modified set of cardinal functions strictly related to the ones of the not-rescaled kernel. Through these functions, we define a Lebesgue function for the rescaled interpolation process, and study its maximum - the Lebesgue constant - in different settings. Also, a preliminary theoretical result on the estimation of the interpolation error is presented. As an application, we couple our method with a partition of unity algorithm. This setting seems to be the most promising, and we illustrate its behavior with some experiments

A rescaled method for RBF approximation

In the recent paper [8], a new method to compute stable kernel-based interpolants has been presented. This \textit{rescaled interpolation} method combines the standard kernel interpolation with a properly defined rescaling operation, which smooths the oscillations of the interpolant. Although promising, this procedure lacks a systematic theoretical investigation. Through our analysis, this novel method can be understood as standard kernel interpolation by means of a properly rescaled kernel. This point of view allow us to consider its error and stability properties

Variational formulas of higher order mean curvatures

In this paper, we establish the first variational formula and its Euler-Lagrange equation for the total $2p$-th mean curvature functional $\mathcal {M}_{2p}$ of a submanifold $M^n$ in a general Riemannian manifold $N^{n+m}$ for $p=0,1,...,[\frac{n}{2}]$. As an example, we prove that closed complex submanifolds in complex projective spaces are critical points of the functional $\mathcal {M}_{2p}$, called relatively $2p$-minimal submanifolds, for all $p$. At last, we discuss the relations between relatively $2p$-minimal submanifolds and austere submanifolds in real space forms, as well as a special variational problem.Comment: 13 pages, to appear in SCIENCE CHINA Mathematics 201

Y(so(5)) symmtry of the nonlinear Schro¨\ddot{o}dinger model with four-cmponents

The quantum nonlinear Schr$\ddot{o}$dinger(NLS) model with four-component fermions exhibits a $Y(so(5))$ symmetry when considered on an infintite interval. The constructed generators of Yangian are proved to satisfy the Drinfel'd formula and furthermore, the $RTT$ relation with the general form of rational R-matrix given by Yang-Baxterization associated with $so(5)$ algebraic structure.Comment: 10 pages, no figure

Cryo-EM structure of the mature dengue virus at 3.5-Å resolution.

Regulated by pH, membrane-anchored proteins E and M function during dengue virus maturation and membrane fusion. Our atomic model of the whole virion from cryo-electron microscopy at 3.5-Å resolution reveals that in the mature virus at neutral extracellular pH, the N-terminal 20-amino-acid segment of M (involving three pH-sensing histidines) latches and thereby prevents spring-loaded E fusion protein from prematurely exposing its fusion peptide. This M latch is fastened at an earlier stage, during maturation at acidic pH in the trans-Golgi network. At a later stage, to initiate infection in response to acidic pH in the late endosome, M releases the latch and exposes the fusion peptide. Thus, M serves as a multistep chaperone of E to control the conformational changes accompanying maturation and infection. These pH-sensitive interactions could serve as targets for drug discovery

Cellulase production by Trichoderma sp. on apple pomace under solid state fermentation

The feasibility of using apple pomace for cellulase production by Trichoderma sp. under solid state fermentation was evaluated in this study. Our results indicated that initial moisture level of the medium, incubation temperature and inoculum size influenced the cellulase production greatly. The optimuminitial moisture level, incubation temperature and inoculum size were 70%, 32 and 2×108 spores/flask, respectively. The supplement of lactose and corn-steep solid to the apple pomace favored the enzyme formation markedly

Estructura y propiedades térmicas de oleogeles a base de cera de abejas con diferentes tipos de aceites vegetales

Beeswax-based oleogels with different types of vegetable oil, including camellia oil (CO), soybean oil (SO), sunflower oil (SFO), or flaxseed oil (FO), were prepared and their structure and thermal properties were evaluated. The critical concentration of oleogel obtained from each of CO, SO, and SFO at 25 °C was 3% (w/w), and that from FO was 4%. Thermal measurements revealed similar thermodynamic curves for oleogels in different lipid phases. X-Ray diffraction showed orthorhombic perpendicular subcell packing and characteristic peaks of the β’ form. Furthermore, a morphology analysis of the crystals showed that they were needle shaped. Fourier transform-infrared spectra revealed that beeswax-based oleogels were formed via non-covalent bonds and may be stabilized with physical entanglements. The oleogels showed oil type-dependent oxidative abilities, but they were all stable and showed no obvious changes in peroxide value during 90 days of storage at 5 °C.Se prepararon oleogeles a base de cera de abejas con diferentes tipos de aceite vegetal, incluido el aceite de camelia (CO), de soja (SO), girasol (SFO) y linaza (FO), y se evaluaron la estructura y las propiedades térmicas. La concentración crítica de oleogel obtenida de cada uno de los aceites de CO, SO y SFO a 25 °C fue del 3% (p / p), y la del FO fue del 4%. Las medidas térmicas dieron curvas termodinámicas similares para los oleogeles en diferentes fases lipídicas. La difracción de rayos X mostró un empaquetamiento subcelular perpendicular ortorrómbico y picos característicos de la forma β’. Además, el análisis de la morfología de los cristales mostró que tenían forma de aguja. Los espectros infrarrojos de transformada de Fourier revelaron que los oleogeles basados en cera de abejas se formaron a través de enlaces no covalentes y pueden estabilizarse con enlaces físicos. Los oleogeles mostraron capacidades oxidativas dependientes del tipo de aceite, pero todos eran estables y no tuvieron cambios obvios en el valor del peróxido durante 90 días de almacenamiento a 5 °C

Characterization of Zika virus endocytic pathways in human glioblastoma cells

Zika virus (ZIKV) infections can cause microcephaly and neurological disorders. However, the early infection events of ZIKV in neural cells remain to be characterized. Here, by using a combination of pharmacological and molecular approaches and the human glioblastoma cell T98G as a model, we first observed that ZIKV infection was inhibited by chloroquine and NH4Cl, indicating a requirement of low intracellular pH. We further showed that dynamin is required as the ZIKV entry was affected by the specific inhibitor dynasore, small interfering RNA (siRNA) knockdown of dynamin, or by expressing the dominant-negative K44A mutant. Moreover, the ZIKV entry was significantly inhibited by chlorpromazine, pitstop2, or siRNA knockdown of clathrin heavy chain, indicating an involvement of clathrin-mediated endocytosis. In addition, genistein treatment, siRNA knockdown of caveolin-1, or overexpression of a dominant-negative caveolin mutant impacted the ZIKV entry, with ZIKV particles being observed to colocalize with caveolin-1, implying that caveola endocytosis can also be involved. Furthermore, we found that the endocytosis of ZIKV is dependent on membrane cholesterol, microtubules, and actin cytoskeleton. Importantly, ZIKV infection was inhibited by silencing of Rab5 and Rab7, while confocal microscopy showed that ZIKV particles localized in Rab5- and Rab7-postive endosomes. These results indicated that, after internalization, ZIKV likely moves to Rab5-positive early endosome and Rab7-positive late endosomes before delivering its RNA into the cytoplasm. Taken together, our study, for the first time, described the early infection events of ZIKV in human glioblastoma cell T98G

A new tow-parameter integrable model of strongly correlated electrons with quantum superalgebra symmetry

A new two-parameter integrable model with quantum superalgebra $U_q[gl(3|1)]$ symmetry is proposed, which is an eight-state electron model with correlated single-particle and pair hoppings as well as uncorrelated triple-particle hopping. The model is solved and the Bethe ansatz equations are obtained.Comment: 6 pages, RevTe