HPM-Based Dynamic Sparse Grid Approach for Perona-Malik Equation

The Perona-Malik equation is a famous image edge-preserved denoising model, which is represented as a nonlinear 2-dimension partial differential equation. Based on the homotopy perturbation method (HPM) and the multiscale interpolation theory, a dynamic sparse grid method for Perona-Malik was constructed in this paper. Compared with the traditional multiscale numerical techniques, the proposed method is independent of the basis function. In this method, a dynamic choice scheme of external grid points is proposed to eliminate the artifacts introduced by the partitioning technique. In order to decrease the calculation amount introduced by the change of the external grid points, the Newton interpolation technique is employed instead of the traditional Lagrange interpolation operator, and the condition number of the discretized matrix different equations is taken into account of the choice of the external grid points. Using the new numerical scheme, the time complexity of the sparse grid method for the image denoising is decreased to O(4J+2j) from O(43J), (j≪J). The experiment results show that the dynamic choice scheme of the external gird points can eliminate the boundary effect effectively and the efficiency can also be improved greatly comparing with the classical interval wavelets numerical methods

Interval Shannon Wavelet Collocation Method for Fractional Fokker-Planck Equation

Metzler et al. introduced a fractional Fokker-Planck equation (FFPE) describing a subdiffusive behavior of a particle under the combined influence of external nonlinear force field and a Boltzmann thermal heat bath. In this paper, we present an interval Shannon wavelet numerical method for the FFPE. In this method, a new concept named “dynamic interval wavelet” is proposed to solve the problem that the numerical solution of the fractional PDE is usually sensitive to boundary conditions. Comparing with the traditional wavelet defined in the interval, the Newton interpolator is employed instead of the Lagrange interpolation operator, so, the extrapolation points in the interval wavelet can be chosen dynamically to restrict the boundary effect without increase of the calculation amount. In order to avoid unlimited increasing of the extrapolation points, both the error tolerance and the condition number are taken as indicators for the dynamic choice of the extrapolation points. Then, combining with the finite difference technology, a new numerical method for the time fractional partial differential equation is constructed. A simple Fokker-Planck equation is taken as an example to illustrate the effectiveness by comparing with the Grunwald-Letnikov central difference approximation (GL-CDA)

Melaminium sulfate

In the title compound, C3H8N6 2+·SO4 2−, the melaminium cations and sulfate anions are inter­connected by N—H⋯N and N—H⋯O hydrogen bonds, forming a layer in the (101) plane. The layers are connected through multiple hydrogen bonds and π–π stacking inter­actions (centroid–centroid distance of about 3.4 Å)

Production of the neutral top-pion πt0\pi_{t}^{0} in association with a high-pTp_{T} jet at the LHCLHC

In the framework of the topcolor-assisted technicolor $(TC2)$ model, we study production of the neutral top-pion $\pi_{t}^{0}$ in association with a high-$p_{T}$ jet at the $LHC$, which proceeds via the partonic processes $gg\longrightarrow \pi_{t}^{0}g$, $gq\longrightarrow \pi_{t}^{0}q$, $q\bar{q}\longrightarrow \pi_{t}^{0}g$, $gb(\bar{b})\longrightarrow \pi_{t}^{0}b(\bar{b})$, and $b\bar{b}\longrightarrow \pi_{t}^{0}g$. We find that it is very challenging to detect the neutral top-pion $\pi_{t}^{0}$ via the process $pp\longrightarrow \pi_{t}^{0}+jet+X\to t\bar{t}+jet+X$, while the possible signatures of $\pi_{t}^{0}$ might be detected via the process $pp\longrightarrow \pi_{t}^{0}+jet+X\to(\bar{t}c+t\bar{c})+jet+X$ at the $LHC$.Comment: 13 pages, 4 figures; typos correcte

5-Methyl-N-[2-(trifluoro­meth­yl)phen­yl]isoxazole-4-carboxamide

In the title compound, C12H9F3N2O2, the benzene ring is nearly perpendicular to the isoxazole ring, making a dihedral angle of 82.97 (2)°. In the crystal, mol­ecules are linked by N—H⋯O hydrogen bonds into a supra­molecular chain running along the c axis

The topological differences between visitation and pollen transport networks: a comparison in species rich communities of the Himalaya–Hengduan Mountains

Pollination networks are usually constructed and assessed by direct field observations which commonly assume that all flower visitors are true pollinators. However, this assumption is often invalid and the use of data based on mere visitors to flowers may lead to a misunderstanding of intrinsic pollination networks. Here, using a large dataset by both sampling floral visitors and analyzing their pollen loads, we constructed 32 networks pairs (visitation versus pollen transport) across one flowering season at four elevation sites in the Himalaya–Hengduan Mountains region. Pollen analysis was conducted to determine which flower visitors acted as potential pollinators (pollen vectors) or as cheaters (those not carrying pollen of the visited plants). We tested whether there were topological differences between visitation and pollen transport networks and whether different taxonomic groups of insect visitors differed in their ability to carry pollen of the visited plants. Our results indicated that there was a significantly higher degree of specialization at both the network and species levels in the pollen transport networks in contrast to the visitation networks. Modularity was lower but nestedness was higher in the visitation networks compared to the pollen transport networks. All the cheaters were identified as peripheral species and most of them contributed positively to the nested structure. This may explain in part the differences in modularity and nestedness between the two network types. Bees carried the highest proportion of pollen of the visited plants. This was followed by Coleoptera, other Hymenoptera and Diptera. Lepidoptera carried the lowest proportion of pollen of the visited plants. Our study shows that the construction of pollen transport networks could provide a more in-depth understanding of plant–pollinator interactions. Moreover, it suggests that detecting and removing cheater interactions when studying the topology of other mutualistic networks might be also important.This study was supported by Strategic Priority Research Program of the Chinese Academy of Sciences (XDB31020000), National Key Basic Research Program of China (2014CB954100), Joint Fund of the National Natural Science Foundation of China-Yunnan Province (U1502261), Major International Joint Research Project of NSF China (31320103919), Applied Fundamental Research Foundation of Yunnan Province (2014GA003), National Natural Science Foundation of China (31700361), Yunlin Scholarship of Yunnan Province to H. Wang (YLXL20170001) and CAS ‘Light of West China’ Program to Y.H. Zhao. A. Lázaro was supported by a Ramóny Cajal contract financed by the Spanish Ministry of Economy and Competitiveness