The Landscape of the Spiked Tensor Model

We consider the problem of estimating a large rank-one tensor u ^⊗k ∈ (ℝⁿ)^⊗k , k ≥ 3 , in Gaussian noise. Earlier work characterized a critical signal-to-noise ratio λ  _Bayes = O(1) above which an ideal estimator achieves strictly positive correlation with the unknown vector of interest. Remarkably, no polynomial-time algorithm is known that achieved this goal unless λ ≥ Cn^{(k − 2)/4} , and even powerful semidefinite programming relaxations appear to fail for 1 ≪ λ ≪ n^{(k − 2)/4} . In order to elucidate this behavior, we consider the maximum likelihood estimator, which requires maximizing a degree-k homogeneous polynomial over the unit sphere in n dimensions. We compute the expected number of critical points and local maxima of this objective function and show that it is exponential in the dimensions n , and give exact formulas for the exponential growth rate. We show that (for λ larger than a constant) critical points are either very close to the unknown vector u or are confined in a band of width Θ(λ^{−1/(k − 1)}) around the maximum circle that is orthogonal to u . For local maxima, this band shrinks to be of size Θ(λ^{−1/(k − 2)}) . These “uninformative” local maxima are likely to cause the failure of optimization algorithms. © 2019 Wiley Periodicals, Inc.     

Multi-stable quantum droplets in optical lattices

Nonlinear Dynamics - We address the nonlinear dynamics of binary Bose-Einstein condensates with mutually symmetric spinor components trapped in an optical lattice. The interaction between the...     

Fractional damping enhances chaos in the nonlinear Helmholtz oscillator

Nonlinear Dynamics - The main purpose of this paper is to study both the underdamped and the overdamped dynamics of the nonlinear Helmholtz oscillator with a fractional-order damping. For that...     

Controlled synthesis of ZnO nanoparticles from a Zn(II) coordination polymer: Structural characterization,optical properties and photocatalytic activity

A zinc coordination polymer derived from pyridine-2,6-dicarboxylate (PDC), {[Zn₂(PDC)₂]}_n, was successfully prepared via conventional, sonication and microwave-irradiation methods. The composition and characteristics of the obtained coordination polymers (CPs) were investigated by elemental analysis, TGA/DTA, X-ray diffraction and spectroscopic techniques. The so obtained CPs were heat-treated in the air at 600 °C for 2 h to produce ZnO of nanosized particles (NPs). It is of interest to note that the synthesis approach of the precursor greatly affects both the nanoparticle size and the structure of the resulting ZnO NPs. Moreover, the smallest particle size was associated with the sample derived from the ultrasonically prepared precursor. TEM analysis revealed that all samples have sphere-like morphologies. Structural analysis of the prepared ZnO samples was conducted and compared using Rietveld analysis of their PXRD patterns. Optical band gap calculations based on analysis of the UV–vis spectra of ZnO samples using Tauc's power law were achieved. The highest band gap of 3.63 eV was observed for ZnO sample obtained from the ultrasonically prepared precursor. Furthermore, the photocatalytic activity of ZnO NPs for the removal of Eosin Y color was monitored. The highest removal efficiency was recorded for ZnO originated from the ultrasonically synthesized precursor. Enhancement of removal efficiency that reached 98% was attained in only a period of 8 min. Its recycling test showed that it can be reused without structural changes over four cycling experiments.     

Comparative absorption kinetics of seven active ingredients of Eucommia ulmoides extracts by intestinal in situ circulatory perfusion in normal and spontaneous hypertensive rats

Eucommia ulmoides Oliv. (E. ulmoides) is a valuable and nourishing medicinal herb in China that has been used in the treatment of hypertension. Given the fact that most traditional Chinese medicine is mainly used to treat disease, investigating the pharmacokinetics of traditional Chinese medicines in the pathological state is more useful than that in the normal state. However, the differences in the absorption kinetics of active ingredients of E. ulmoides extract between pathological and physiological conditions have not been reported. Therefore, in this study, the rat intestinal in situ circulatory perfusion model was used to investigate the differences in absorption kinetics of seven active ingredients of E. ulmoides extract in normal and spontaneously hypertensive rats, namely, genipinic acid, protocatechuic acid, neochlorogenic acid, chlorogenic acid, cryptochlorogenic acid, (+)-pinoresinol di-O-β-D -glucopyranoside and (+)-pinoresinol 4′-O-β-D -glucopyranoside. Our results indicate that the pathological state of spontaneous hypertension may change the absorption of active components of E. ulmoides extracts, and these findings may provide a reference for improving the rational use of E. ulmoides in the clinic.     

Anti-neuraminidase activity of chemical constituents of Balanophora involucrata

Balanophora involucrata J. D. Hooker has been known to possess potential anti-inflammatory and antibacterial activities; however, its antiviral activity has not been evaluated so far. In order to find new neuraminidase inhibitors (NAIs), the neuraminidase (NA) inhibition activity of different B. involucrata extracts was evaluated. In this study, an in vitro NA inhibition assay was performed to identify which extract of B. involucrata exhibits (maximal) inhibitory activity against NA. Ultra high performance liquid chromatography/quadrupole time-of-flight–tandem mass spectroscopy (MS/MS) and molecular docking techniques were used to identify the specific compounds responsible for the anti-influenza activity of the extract, and to explore the potential natural NAIs. The ethyl acetate extract of B. involucrata exhibited significant inhibitory activity against NA with 50% inhibitory concentration (IC₅₀) value of 159.5 μg/mL. Twenty compounds were identified according to the MS/MS spectra; among them two compounds (quercitrin and phloridzin) showed obvious inhibitory activity against NA, with IC₅₀ of 311.76 and 347.32 μmol/L, respectively. This study suggested that B. involucrata can be a potential natural source of NAIs and may be useful in the fight against ferocious influenza viruses.     

Probing the Catalytic Activity of Reduced Graphene Oxide Decorated with Au Nanoparticles Triggered by Visible Light

Hybrid materials in which reduced graphene oxide (rGO) is decorated with Au nanoparticles (rGO–Au NPs) were obtained by the in situ reduction of GO and AuCl₄^?_(aq) by ascorbic acid. On laser excitation, rGO could be oxidized as a result of the surface plasmon resonance (SPR) excitation in the Au NPs, which generates activated O₂ through the transfer of SPR‐excited hot electrons to O₂ molecules adsorbed from air. The SPR‐mediated catalytic oxidation of p‐aminothiophenol (PATP) to p,p′‐dimercaptoazobenzene (DMAB) was then employed as a model reaction to probe the effect of rGO as a support for Au NPs on their SPR‐mediated catalytic activities. The increased conversion of PATP to DMAB relative to individual Au NPs indicated that charge‐transfer processes from rGO to Au took place and contributed to improved SPR‐mediated activity. Since the transfer of electrons from Au to adsorbed O₂ molecules is the crucial step for PATP oxidation, in addition to the SPR‐excited hot electrons of Au NPs, the transfer of electrons from rGO to Au contributed to increasing the electron density of Au above the Fermi level and thus the Au‐to‐O₂ charge‐transfer process.