Decay estimates for one Aharonov-Bohm solenoid in a uniform magnetic field I: Schr\"odinger equation

This is the first of a series of papers in which we investigate the decay estimates for dispersive equations with Aharonov-Bohm solenoids in a uniform magnetic field. In this first starting paper, we prove the local-in-time dispersive estimates and Strichartz estimates for Schr\"odinger equation with one Aharonov-Bohm solenoid in a uniform magnetic field. The key ingredient is the construction of Schr\"odinger propagator, we provide two methods to construct the propagator. The first one is combined the strategies of \cite{FFFP1} and \cite{GYZZ22, FZZ22}, and the second one is based on the Schulman-Sunada formula in sprit of \cite{stov, stov1} in which the heat kernel has been studied. In future papers, we will continue investigating this quantum model for wave with one or multiple Aharonov-Bohm solenoids in a uniform magnetic field.Comment: 22 page

Decay estimates for one Aharonov-Bohm solenoid in a uniform magnetic field II: wave equation

This is the second of a series of papers in which we investigate the decay estimates for dispersive equations with Aharonov-Bohm solenoids in a uniform magnetic field. In our first starting paper \cite{WZZ}, we have studied the Strichartz estimates for Schr\"odinger equation with one Aharonov-Bohm solenoid in a uniform magnetic field. The wave equation in this setting becomes more delicate since a difficulty is raised from the square root of the eigenvalue of the Schr\"odinger operator $H_{\alpha, B_0}$ so that we cannot directly construct the half-wave propagator. An independent interesting result concerning the Gaussian upper bounds of the heat kernel is proved by using two different methods. The first one is based on establishing Davies-Gaffney inequality in this setting and the second one is straightforward to construct the heat kernel (which efficiently captures the magnetic effects) based on the Schulman-Sunada formula. As byproducts, we prove optimal bounds for the heat kernel and show the Bernstein inequality and the square function inequality for Schr\"odinger operator with one Aharonov-Bohm solenoid in a uniform magnetic field.Comment: 35 pages, comments are welcome

PPCR: Learning Pyramid Pixel Context Recalibration Module for Medical Image Classification

Spatial attention mechanism has been widely incorporated into deep convolutional neural networks (CNNs) via long-range dependency capturing, significantly lifting the performance in computer vision, but it may perform poorly in medical imaging. Unfortunately, existing efforts are often unaware that long-range dependency capturing has limitations in highlighting subtle lesion regions, neglecting to exploit the potential of multi-scale pixel context information to improve the representational capability of CNNs. In this paper, we propose a practical yet lightweight architectural unit, Pyramid Pixel Context Recalibration (PPCR) module, which exploits multi-scale pixel context information to recalibrate pixel position in a pixel-independent manner adaptively. PPCR first designs a cross-channel pyramid pooling to aggregate multi-scale pixel context information, then eliminates the inconsistency among them by the well-designed pixel normalization, and finally estimates per pixel attention weight via a pixel context integration. PPCR can be flexibly plugged into modern CNNs with negligible overhead. Extensive experiments on five medical image datasets and CIFAR benchmarks empirically demonstrate the superiority and generalization of PPCR over state-of-the-art attention methods. The in-depth analyses explain the inherent behavior of PPCR in the decision-making process, improving the interpretability of CNNs.Comment: 10 page

Determination of Camellia oleifera Abel. Germplasm Resources of Genetic Diversity in China using ISSR Markers

Camellia oleifera is one of the four woody oil plants in the world, which is widely cultivated in South China. To examine the genetic diversity of C. oleifera in China, the diversity and genetic relationships among and within major populations of 109 varieties of C. oleifera were analyzed using ISSR markers. Twenty-three ISSR primers out of 49 primers yielded approximately 487 legible bands. A total of 335 of these bands were polymorphic markers, and the ratio of polymorphism was 68.86%. From the results, Zhejiang province showed the highest populations genetic diversity (H value 0.18), while Guangxi population showed the lowest genetic diversity (H 0.0851). Base on the bands, the genetic similarity coefficient ranged from 0.61 to 0.93 using NTSYS2.10e software. When coefficient was 0.75, 109 cultivars were divided into 11 categories and categories I contain 79 varieties by UPGMA cluster analysis. The test varieties divided into 7 sub-groups when categories were 0.75, which show a close genetic relationship. Results advised that Hunan is the main producing area of C. oleifera, with enriched C. oleifera variety and complex topography, and therefore has a high genetic diversity. Meanwhile, the main varieties of C. oleifera in Hubei are imported from Hunan, which results in fewer varieties and reduces the genetic diversity of C. oleifera. The ISSR profiles can improve C. oleifera germplasm management and provide potential determine correlations between different varieties and its distribution in different province

The complex hexaploid oil‐Camellia genome traces back its phylogenomic history and multi‐omics analysis of Camellia oil biosynthesis

Summary: Oil‐Camellia (Camellia oleifera), belonging to the Theaceae family Camellia, is an important woody edible oil tree species. The Camellia oil in its mature seed kernels, mainly consists of more than 90% unsaturated fatty acids, tea polyphenols, flavonoids, squalene and other active substances, which is one of the best quality edible vegetable oils in the world. However, genetic research and molecular breeding on oil‐Camellia are challenging due to its complex genetic background. Here, we successfully report a chromosome‐scale genome assembly for a hexaploid oil‐Camellia cultivar Changlin40. This assembly contains 8.80 Gb genomic sequences with scaffold N50 of 180.0 Mb and 45 pseudochromosomes comprising 15 homologous groups with three members each, which contain 135 868 genes with an average length of 3936 bp. Referring to the diploid genome, intragenomic and intergenomic comparisons of synteny indicate homologous chromosomal similarity and changes. Moreover, comparative and evolutionary analyses reveal three rounds of whole‐genome duplication (WGD) events, as well as the possible diversification of hexaploid Changlin40 with diploid occurred approximately 9.06 million years ago (MYA). Furthermore, through the combination of genomics, transcriptomics and metabolomics approaches, a complex regulatory network was constructed and allows to identify potential key structural genes (SAD, FAD2 and FAD3) and transcription factors (AP2 and C2H2) that regulate the metabolism of Camellia oil, especially for unsaturated fatty acids biosynthesis. Overall, the genomic resource generated from this study has great potential to accelerate the research for the molecular biology and genetic improvement of hexaploid oil‐Camellia, as well as to understand polyploid genome evolution

Multipole plasmon resonances in self-assembled metal hollow-nanospheres

MOST of China under the 973 programs [2009CB930704]; National Natural Science Foundation of China [61106118]; Science and Technology Project of Fujian Province of China [2013H0046]; Natural Science Foundation of Fujian Province of China [2011J01362]; Fundamental Research Funds for the Central Universities [2011121026]Recently, multipole plasmonic mode resonances in metal hollow structures, such as dipole, quadrupole, and octupole modes, have been widely investigated by researchers with the aim for potential applications in bio-sensing, fluorescence, nanolasers or nonlinear nano-photonics. Here, in this work, the multipole plasmon resonances in self-assembled metal hollow-nanospheres (HNSs) are theoretically and experimentally demonstrated and the hot spots originating from the higher order mode plasmonic resonance and interparticle coupling effect are proposed to be used for Raman scattering enhancements. Dipole, quadrupole, octupole and hexadecapole mode plasmonic resonances were clearly resolved in the extinction spectra of these Ag HNS arrays showing good agreement with the theoretical simulation results. Strong regular hot spots were obtained around the surface and in the gaps of the Ag HNSs through the higher order mode plasmonic resonances and corresponding interparticle coupling effect between the HNSs. Maximum local field intensity was accomplished by optimizing the size of as well as the coupling distance between the HNSs and then it was applied to SERS sensing. Raman mapping also demonstrated these self-assembled plasmonic cavity arrays to be a stable and uniform SERS-active substrate

Self-Organization of 3D Triangular GaN Nanoislands and the Shape Variation to Hexagonal

We report on the self-organization of large-scale uniform aligned three-dimensional (3D) GaN islands with distinct triangular (0001) and smooth side facets and the shape variations of the (0001) facets from triangular to hexagonal during metalorganic vapor-phase epitaxy (MOVPE) growth of GaN films on Si-rich SiNx patterned sapphire substrates. The triangular island shaping during the recrystallization processes of GaN nucleation layers (NLs) can be attributed to the enhanced diffusion and regrowth anisotropy. The island shape transition from triangular to hexagonal in the early stages of high-temperature growth of GaN epilayers is due to the gas-phase transport dominating growth mechanism and the limited diffusion length of edge adatoms compared with the increased island size

Self-organization of 3D triangular GaN nanoislands and the shape variation to hexagonal

We report on the self-organization of large-scale uniform aligned three-dimensional (3D) GaN islands with distinct triangular (0001) and smooth side facets and the shape variations of the (0001) facets from triangular to hexagonal during metalorganic vapor-phase epitaxy (MOVPE) growth of GaN films on Si-rich SiNx patterned sapphire substrates. The triangular island shaping during the recrystallization processes of GaN nucleation layers (NLs) can be attributed to the enhanced diffusion and regrowth anisotropy. The island shape transition from triangular to hexagonal in the early stages of high-temperature growth of GaN epilayers is due to the gas-phase transport dominating growth mechanism and the limited diffusion length of edge adatoms compared with the increased island size