Genetically-and environmentally-dependent processes drive interspecific and intraspecific divergence in the Chinese relict endemic genus Dipteronia

China is a hotspot of relict plant species that were once widespread throughout the Northern Hemisphere.Recent research has demonstrated that the occurrence of long-term stable refugia in the mountainous regions of central and south-western China allowed their persistence through the late Neogene climate fluctuations.One of these relict lineages is Dipteronia,an oligotypic tree genus with a fossil record extending to the Paleocene.Here,we investigated the genetic variability,demographic dynamics and diversification patterns of the two currently recognized Dipteronia species(Dipteronia sinensis and D.dyeriana).Molecular data were obtained from 45 populations of Dipteronia by genotyping three cpDNA regions,two single copy nuclear genes and 15 simple sequence repeat loci.The genetic study was combined with niche comparison analyses on the environmental space,ecological niche modeling,and landscape connectivity analysis.We found that the two Dipteronia species have highly diverged both in genetic and ecological terms.Despite the incipient speciation processes that can be observed in D.sinensis,the occurrence of long-term stable refugia and,particularly,a dispersal corridor along Daba Shan-west Qinling,likely ensured its genetic and ecological integrity to date.Our study will not only help us to understand how populations of Dipteronia species responded to the tectonic and climatic changes of the Cenozoic,but also provide insight into how Arcto-Tertiary relict plants in East Asia survived,evolved,and diversified.

ELLIPTIC EQUATIONS IN DIVERGENCE FORM WITH DISCONTINUOUS COEFFICIENTS IN DOMAINS WITH CORNERS

We study equations in divergence form with piecewise Cαcoefficients.The domains contain corners and the discontinuity surfaces are attached to the edges of the corners.We obtain piecewise C^(1,α) estimates across the discontinuity surfaces and provide an example to illustrate the issue regarding the regularity at the corners.

Kullback-Leibler Divergence Based ISAC Constellation and Beamforming Design in the Presence of Clutter

Integrated sensing and communication(ISAC)is regarded as a pivotal technology for 6G communication.In this paper,we employ Kullback-Leibler divergence(KLD)as the unified performance metric for ISAC systems and investigate constellation and beamforming design in the presence of clutters.In particular,the constellation design problem is solved via the successive convex approximation(SCA)technique,and the optimal beamforming in terms of sensing KLD is proven to be equivalent to maximizing the signal-to-interference-plus-noise ratio(SINR)of echo signals.Numerical results demonstrate the tradeoff between sensing and communication performance under different parameter setups.Additionally,the beampattern generated by the proposed algorithm achieves significant clutter suppression and higher SINR of echo signals compared with the conventional scheme.

基于随机游走模型和KL-divergence的聚类算法

聚类分析在数据挖掘领域有着广泛的应用,该文提出一个聚类新思路,它不需要任何参数的假设,只基于数据两两之间的相似性。该方法假设数据点之间存在随机游走关系,根据数据相似性构造随机游走过程的转移矩阵,当随机游走过程进入收敛期后,t阶转移矩阵揭示了数据点的分布。用迭代方法寻找最小的KL-divergence来对这些分布聚类。该方法具有严谨的概率理论基础,避免了传统算法需要参数假设、限于局部最优等不足。实验表明,该算法具有较优的聚类效果。

THE DIVERGENCE OF LAGRANGE INTERPOLATION IN EQUIDISTANT NODES

It is a classical result of Bernstein that the sequence of Lagrange interpolation polynomials to \x\ at e-qually spaced nodes in [-1.1] diverges everywhere. except at zero and the end-points. In this paper we show that the sequence of Lagrange interpolation polynomials corresponding to the functions which possess better smoothness on equidistant nodes in [-1.1] still diverges every -where in the interval except at zero and the end-points.

Tunable 3D Nanofiber Architecture of Polycaprolactone by Divergence Electrospinning for Potential Tissue Engineering Applications

The creation of biomimetic cell environments with micro and nanoscale topographical features resembling native tissues is critical for tissue engineering. To address this challenge, this study focuses on an innovative electrospinning strategy that adopts a symmetrically divergent electric field to induce rapid self-assembly of aligned polycaprolactone(PCL) nanofibers into a centimeter-scale architecture between separately grounded bevels. The 3D microstructures of the nanofiber scaffolds were characterized through a series of sectioning in both vertical and horizontal directions. PCL/collagen(type I)nanofiber scaffolds with different density gradients were incorporated in sodium alginate hydrogels and subjected to elemental analysis. Human fibroblasts were seeded onto the scaffolds and cultured for 7 days. Our studies showed that the inclination angle of the collector had significant effects on nanofiber attributes, including the mean diameter, density gradient, and alignment gradient. The fiber density and alignment at the peripheral area of the 45°-collector decreased by 21% and 55%, respectively, along the z-axis,while those of the 60°-collector decreased by 71% and 60%, respectively. By altering the geometry of the conductive areas on the collecting bevels, polyhedral and cylindrical scaffolds composed of aligned fibers were directly fabricated. By using a four-bevel collector, the nanofibers formed a matrix of microgrids with a density of 11%. The gradient of nitrogen-to-carbon ratio in the scaffold-incorporated hydrogel was consistent with the nanofiber density gradient. The scaffolds provided biophysical stimuli to facilitate cell adhesion, proliferation, and morphogenesis in 3D.

Genetic variability and divergence studies in pod and seed traits of Pongamia pinnata(L.) Pierre., accessions in Bay Islands

In this study, we assessed the variability in pod, seed traits and oil content of 24 accessions of Pongamia pinnata collected from different parts of the Andaman and Nicobar Islands, India. The experiment was conducted at the Central Agricultural Research Institute, Port Blair during 2010 to 2011. The variability studies for pod and seed traits revealed that, the accession CPT-6 collected from New Wandoor in South Andaman recorded the maximum values for eight traits viz. pod length （75.51 mm）, pod width （34.62 mm）, pod thickness （17.55 mm）, 100 pod weight （770.33 g）, seed width （21.23 mm）, 100 seed weight （377.00 g）, oil percentage （43.92%） and germination percentage （94.7%）. However, the maximum seed length （26.46 mm） was recorded from CPT 2 and the maximum pod-seed ratio was obtained from CPT 13 and CPT 4 （2.50 and 2.44 respectively）. The phenotypic and genotypic coefficients of variations were also close to each other for all traits, but the 100 pod and seed weight exhibited higher phenotypic and genotypic coefficient of variation than the other traits. Estimates of broad sense heritability ranged from 0.30 （for seed length） to 0.95 （pod length） and genetic ad- vance as percent of the mean ranged between 11.66% and 57.40% with seed length giving the lowest value and 100 pod weight giving the high- est value. Both the phenotypic and genotypic correlation between pod length, pod width, pod thickness, 100 pod weight, seed width and 100 seed weight and between pod thickness, 100 pod weight, seed width, 100 seed weight and germination percentage were found to be strong. On the basis of non hierarchical Euclidian cluster analysis, 24 accessions were grouped into six clusters. The maximum numbers of seven accessions were included in cluster VI. The maximum intra cluster distance （10.238）shown by cluster VI and the maximum inter cluster distance （17.021） between V and HI followed by III and II （15.942）. Among the six clus- ters formed the cluster III recorded maximum oil percentage, 100 pod weight, 100 seed ,weight, pod length, pod thickness, pod width, seed width and. germination percentage, while cluster V recorded maximum pod seed ratio and germination percentage. The present findings suggest that the crossing between accessions of cluster V and cluster III will result in a wide spectrum of variability in subsequent generations.

THE DIVERGENCE OF LAGRANGE INTERPOLATION FOR |x|~α(2<α<4) AT EQUIDISTANT NODES

It is a classical result of Bernstein that the sequence of Lagrange interpolation polumomials to ｜x｜ at equally spaced nodes in [-1, 1] diverges everywhere, except at zero and the end-points. In the present paper, toe prove that the sequence of Lagrange interpolation polynomials corresponding to ｜x｜^α （2 〈 α 〈 4） on equidistant nodes in [-1, 1] diverges everywhere, except at zero and the end-points.

Experimental Study on the Effects of Magnetic Field Configuration near the Channel Exit on the Plume Divergence of Hall Thrusters

Experimental investigations into the effects of the magnetic field configuration near the channel exit on the plume of Hall thrusters were conducted. The magnetic field configuration near the channel exit is characterized by the inclination angle between the magnetic field lines and the thruster radial direction. Different inclination angles were obtained by varying the current ratio in the coils. The plume divergence angles were measured by a dual-directed probe. The results showed that the plume divergence angle increased obviously with the increase in the magnitude of the inclination angle near the channel exit. Therefore, in order to optimize the magnetic field for reducing plume divergence, the magnitude of the inclination angle should be reduced as much as possible. It suggests that the magnetic field configuration near the channel exit is another important factor that affects plume divergence.

New Evidence for Improving Omega Estimation by Explicitly Considering Horizontal Divergence

It is well known that the quasi-geostrophic （QG） omega equation with only two contributors respectively associated with vorticity advection （VA） and temperature advection is derived for midlatitude synoptic-scale systems only.Based on reliable reanalysis data,new evidence revealed by cyclonic and anticyclonic cases indicates that forecasters might sometimes experience problems by paying too much attention to the 500-hPa VA when estimating vertical motions not only in subtropical systems but also in systems meeting all the assumptions of the QG omega equation.Our investigations also showed that explicitly considering the vertical profiles of horizontal divergence could allow for better interpretation of vertical motions and weather in these real cases,suggesting that this equation might not be sufficient due to the presence of only two horizontaldivergence-related （HDR） mechanisms and the absence of other HDR mechanisms,e.g.,frictional force,mountain barriers,diabatic/adiabatic processes,and acceleration/deceleration of air flows.

病理心电信号的Jensen-Shannon divergence分析

目的研究快速区分不同病理心电信号的算法是当前临床医学诊断的研究热点之一。方法本文采用基于Jensen-Shannon divergence的复杂度分析方法,从MIT-BIH标准数据库中提取正常窦性心率、房性早搏、窦性心动过缓信号,分别计算它们的复杂度。结果正常心率信号复杂度最高,窦性心动过缓信号次之,房性早搏最低。方差检验结果表明,此方法得出的3种信号的复杂度具有显著性差异。结论病理心电信号的Jensen-Shannon divergence分析对临床医学检测和诊断房性早搏、窦性心动过缓信号有很好的借鉴意义。

THE DIVERGENCE OF LAGRANGE INTERPOLATION FOR |x|~a

This paper shows that the sequence of Lagrange interpolation polynomials corresponding to the rune tion f（z） =｜x｜^α（1〈α〈2） on [-1,1] can diverge everywhere in the interval except at zero and the end-points.

Sexual Dimorphism of Head Size in Phrynocephalus przewalskii: Testing the Food Niche Divergence Hypothesis

Sexual size dimorphism （SSD） is a general phenomenon in lizards, and can evolve through sexual selection or natural selection. But natural selection, which was thought to operate mainly through reducing the competition be- tween the two sexes （niche divergence hypothesis）, gave rise to a lot of controversy. We tested the niche divergence hypothesis in the toad-headed lizard Phrynocephalus przewalskii by comparing diet composition and prey sizes between males and females. The species was found to be sexual dimorphic, with males having relatively larger snout-vent length, head width, head length, and tail length, while females have relatively larger abdomen length. Based on analysis of 93 studied stomachs, a total of 1359 prey items were identified. The most common prey items were formicid, lygaeid and tenebrionid. The two sexes did not differ in the relative proportions of prey size categories they consumed and the dietary overlap based on prey species was high （O = 0.989）. In addition, the meal size, the volume or any maximal dimension of the largest prey item in the stomach was not explained by the sexes. According to our results, food niche divergence might not play an important role in the SSD evolution ofP. przewalskii.

Gapless genome assembly of azalea and multi-omics investigation into divergence between two species with distinct f lower color

The genus Rhododendron(Ericaceae),with more than 1000 species highly diverse in f lower color,is providing distinct ornamental values and a model system for f lower color studies.Here,we investigated the divergence between two parental species with different f lower color widely used for azalea breeding.Gapless genome assembly was generated for the yellow-f lowered azalea,Rhododendron molle.Comparative genomics found recent proliferation of long terminal repeat retrotransposons(LTR-RTs),especially Gypsy,has resulted in a 125 Mb(19%)genome size increase in species-specific regions,and a significant amount of dispersed gene duplicates(13402)and pseudogenes(17437).Metabolomic assessment revealed that yellow f lower coloration is attributed to the dynamic changes of carotenoids/f lavonols biosynthesis and chlorophyll degradation.Time-ordered gene co-expression networks(TO-GCNs)and the comparison confirmed the metabolome and uncovered the specific gene regulatory changes underpinning the distinct f lower pigmentation.B3 and ERF TFs were found dominating the gene regulation of carotenoids/f lavonols characterized pigmentation in R.molle,while WRKY,ERF,WD40,C2H2,and NAC TFs collectively regulated the anthocyanins characterized pigmentation in the red-f lowered R simsii.This study employed a multi-omics strategy in disentangling the complex divergence between two important azaleas and provided references for further functional genetics and molecular breeding.

Variability in seed traits and genetic divergence in a clonal seed orchard of Dalbergia sissoo Roxb.

The variations in seed and pod traits, genetic superiority and genetic divergence were evaluated for a Clonal Seed Orchard （CSO） of Dalbergia sissoo Roxb. at Bithmera, India consisting of 20 clones from different agro-climatic conditions of four northern states （Uttar Pradesh, Uttarakhand, Haryana and Rajasthan）. The seeds and pods of various clones in the orchard exhibited significant variability in size, weight and other characters. Significant positive correlations were observed between seed length and seed width （p〈0.05）, seed length and sccd thickness （p〈0.01）, seed length and seed weight （p〈0.01）, seed thickness and seed weight （p〈0.01）, seed length and germination value （p〈0.05）. The ge- netic parameters for seed and pod traits also showed a wide range of variations in the orchard. Heritability values were found to be over 50 percent for most of ~e seed and pod traits. Seed weight, seed length and seed thickness showed high heritability values coupled with maximum genetic gain for these characters. Ward＇s minimum variance dendrogram of clones of D. sissoo showed three distinct clusters; cluster I was the largest with 12 better clones whereas cluster 2 and 3 consisting of seven moderate clones and one poor clone, respectively. Mean cluster values showed sufficient variation among the clusters for seed weight, germina- tion value and seed length. The possible hybridization between best clones of cluster I to the disease resistant clone of cluster 2 （resistant against deadly Gandoderma lucidum root rot disease of D. sissoo） is also suggested for further breeding programmes of the species. The deploy- ment of clone 194 （better performed and disease resistant） is also rec- ommended in future plantation programmes of D. sissoo in northern India.

Diagnosis of Moist Vorticity and Moist Divergence for a Heavy Precipitation Event in Southwestern China

A regional heavy precipitation event that occurred over Sichuan Province on 8-9 September 2015 is analyzed based on hourly observed precipitation data obtained from weather stations and NCEP FNL data. Two moist dynamic parameters, i.e., moist vorticity （mζ and moist divergence （mδ）, are used to diagnose this heavy precipitation event. Results show that the topography over southwestern China has a significant impact on the ability of these two parameters to diagnose precipitation. When the impact of topography is weak （i.e., low altitude）, rn（ cannot exactly depict the location of precipitation in the initial stage of the event. Then, as the precipitation develops, its ability to depict the location improves significantly. In particular, m（ coincides best with the location of precipitation during the peak stage of the event. Besides, the evolution of the m（ center shows high consistency with the evolution of the precipitation center. For mδ, although some false-alarm regions are apparent, it reflects the location of precipitation almost entirely during the precipitation event. However, the mδ center shows inconsistency with the precipitation center. These results suggest that both m（ and mδ have a significant ability to predict the location of precipitation. Moreover, m（ has a stronger ability than mδ in terms of predicting the variability of the precipitation center. However, when the impact of topography is strong （i.e., high altitude）, both of these two moist dynamic parameters are unable to depict the location and center of precipitation during the entire precipitation event, suggesting their weak ability to predict precipitation over complex topography.

Duplication and transcriptional divergence of three Kunitz protease inhibitor genes that modulate insect and pathogen defenses in tea plant(Camellia sinensis)

Kunitz protease inhibitors(KPIs)are ubiquitous in plants and act as crucial compounds in defense responses against insect attack and pathogen infection.However,the influence of gene duplication on the postdivergence of the CsKPI genes involved in biotic stresses in tea plant is not well known.Here,we identified three CsKPI genes from tea plant(Camellia sinensis)and characterized their expression and evolutionary patterns among plant species.We found that CsKPI1,CsKPI2,and CsKPI3 diverged from their common ancestor 72.94 million years ago(MYA),and the tandem duplication of CsKPI2 and CsKPI3 occurred 26.78 MYA.An in vitro protein assay showed that the three CsKPI proteins were functional and inhibited the production of p-nitroanilide(PNA)from an artificial substrate.The three CsKPI-GFP fusion proteins localized to the cytoplasm.We showed that salicylic acid(SA)and transcripts of CsKPI2 and CsKPI3 significantly accumulated after infection with Glomerella cingulata.The application of exogenous SA stimulated the high expression of both CsKPI2 and CsKPI3 by activating cis-elements within their promoters.Under Ectropis oblique attack,CsKPI1 expression and jasmonic acid(JA)levels were more abundant in both insect-damaged leaf tissues and undamaged neighboring leaves.The application of jasmonic acid methyl ester elicited high expression levels of CsKPI1,suggesting that CsKPI1 accumulation requires JA production in tea plant.The overall findings suggest that the transcriptional divergence of KPI genes after duplication led to the specialized role of CsKPI1 in the physiological response to insect stress;the functional conservation between CsKPI2 and CsKPI3 confers resistance to pathogen infection in tea plant.

Mechanisms of species divergence through visual adaptation and sexual selection:Perspectives from a cichlid model system

The theory of ecological speciation suggests that assortative mating evolves most easily when mating preferences aredirectly linked to ecological traits that are subject to divergent selection. Sensory adaptation can play a major role in this process,because selective mating is often mediated by sexual signals: bright colours, complex song, pheromone blends and so on. Whendivergent sensory adaptation affects the perception of such signals, mating patterns may change as an immediate consequence.Alternatively, mating preferences can diverge as a result of indirect effects: assortative mating may be promoted by selectionagainst intermediate phenotypes that are maladapted to their (sensory) environment. For Lake Victoria cichlids, the visual environmentconstitutes an important selective force that is heterogeneous across geographical and water depth gradients. We investigatethe direct and indirect effects of this heterogeneity on the evolution of female preferences for alternative male nuptial colours(red and blue) in the genus Pundamilia. Here, we review the current evidence for divergent sensory drive in this system, extractgeneral principles, and discuss future perspectives [Current Zoology 56 (3): 285-299, 2010].

Image reconstruction for cone-beam computed tomography using total p-variation plus Kullback-Leibler data divergence

Accurate reconstruction from a reduced data set is highly essential for computed tomography in fast and/or low dose imaging applications. Conventional total variation（TV）-based algorithms apply the L1 norm-based penalties, which are not as efficient as Lp（0〈p〈1） quasi-norm-based penalties. TV with a p-th power-based norm can serve as a feasible alternative of the conventional TV, which is referred to as total p-variation（TpV）. This paper proposes a TpV-based reconstruction model and develops an efficient algorithm. The total p-variation and Kullback-Leibler（KL） data divergence, which has better noise suppression capability compared with the often-used quadratic term, are combined to build the reconstruction model. The proposed algorithm is derived by the alternating direction method（ADM） which offers a stable, efficient, and easily coded implementation. We apply the proposed method in the reconstructions from very few views of projections（7 views evenly acquired within 180°）. The images reconstructed by the new method show clearer edges and higher numerical accuracy than the conventional TV method. Both the simulations and real CT data experiments indicate that the proposed method may be promising for practical applications.