A Kullback-Leibler Divergence for Bayesian Model Diagnostics

This paper considers a Kullback-Leibler distance (KLD) which is asymptotically equivalent to the KLD by Goutis and Robert [1] when the reference model (in comparison to a competing fitted model) is correctly specified and that certain regularity conditions hold true (ref. Akaike [2]). We derive the asymptotic property of this Goutis-Robert-Akaike KLD under certain regularity conditions. We also examine the impact of this asymptotic property when the regularity conditions are partially satisfied. Furthermore, the connection between the Goutis-Robert-Akaike KLD and a weighted posterior predictive p-value (WPPP) is established. Finally, both the Goutis-Robert-Akaike KLD and WPPP are applied to compare models using various simulated examples as well as two cohort studies of diabetes.

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.

Battle damage assessment based on an improved Kullback-Leibler divergence sparse autoencoder

The nodes number of the hidden layer in a deep learning network is quite difficult to determine with traditional methods. To solve this problem, an improved Kullback-Leibler divergence sparse autoencoder （KL-SAE） is proposed in this paper, which can be applied to battle damage assessment （BDA）. This method can select automatically the hidden layer feature which contributes most to data reconstruction, and abandon the hidden layer feature which contributes least. Therefore, the structure of the network can be modified. In addition, the method can select automatically hidden layer feature without loss of the network prediction accuracy and increase the computation speed. Experiments on University ofCalifomia-Irvine （UCI） data sets and BDA for battle damage data demonstrate that the method outperforms other reference data-driven methods. The following results can be found from this paper. First, the improved KL-SAE regression network can guarantee the prediction accuracy and increase the speed of training networks and prediction. Second, the proposed network can select automatically hidden layer effective feature and modify the structure of the network by optimizing the nodes number of the hidden layer.

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 C1,αestimates across the discontinuity surfaces and provide an example to illustrate the issue regarding the regularity at the corners.

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.

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.

Phylogenetic diversity of eastern Asia-eastern North America disjunct plants is mainly associated with divergence time

The underlying causes of biodiversity disparities among geographic regions have long been a fundamental theme in ecology and evolution.However,the patterns of phylogenetic diversity(PD) and phylogenetic beta diversity(PBD) of congeners that are disjunctly distributed between eastern Asia-eastern North America(EA-ENA disjuncts) and their associated factors remain unknown.Here we investigated the standardized effect size of PD(SES-PD),PBD,and potentially associated factors in 11natural mixed forest sites(five in EA and six in ENA) where abundant EA-ENA disjuncts occur.We found that the disjuncts in ENA possessed higher SES-PD than those in EA at the continental scale(1.96vs-1.12),even though the number of disjunct species in ENA is much lower than in EA(128 vs 263).SESPD of the EA-ENA disjuncts tended to decrease with increasing latitude in 11 sites.The latitudinal diversity gradient of SES-PD was stronger in EA sites than in ENA sites.Based on the unweighted unique fraction metric(UniFrac) distance and the phylogenetic community dissimilarity,PBD showed that the two northern sites in EA were more similar to the six-site ENA group than to the remaining southern EA sites.Based on the standardized effect size of mean pairwise distances(SES-MPD),nine of eleven studied sites showed a neutral community structure(-1.96 ≤SES-MPD ≤1.96).Both Pearson’s r and structural equation modeling suggested that SES-PD of the EA-ENA disjuncts was mostly associated with mean divergence time.Moreover,SES-PD of the EA-ENA disjuncts was positively correlated with temperaturerelated climatic factors,although negatively correlated with mean diversification rate and community structure.By applying approaches from phylogenetics and community ecology,our work sheds light on historical patterns of the EA-ENA disjunction and paves the way for further research.

基于Kullback-Leibler散度的多指标群体评价算法研究

针对目前高校、科研机构中科研业绩考核使用量化打分存在重数量、轻质量等问题,通过引入同行评议机制,建立基于Kullback-Leibler(KL)散度的多指标群体评价模型。首先利用熵权法求解出指标的客观权重;然后基于Kullback-Leibler散度确定群体评价的集成权重,给出了多指标群体决策问题的求解算法。与传统算法相比较,KL散度方法能逼近先验分布概率,无需反复迭代和人为调整参数,在计算时间上有较为明显的优势;算例分析验证了模型和算法的有效性。

Pangenome of water caltrop reveals structural variations and asymmetric subgenome divergence after allopolyploidization

Water caltrop(Trapa spp.,Lythraceae)is a traditional but currently underutilized non-cereal crop.Here,we generated chromosome-level genome assemblies for the two diploid progenitors of allotetraploid Trapa.natans(4x,AABB),i.e.,diploid T.natans(2x,AA)and Trapa incisa(2x,BB).In conjunction with four published(sub)genomes of Trapa,we used gene-based and graph-based pangenomic approaches and a pangenomic transposable element(TE)library to develop Trapa genomic resources.The pangenome displayed substantial gene-content variationwith dispensable and private gene clusters occupying a large proportion(51.95%)of the total cluster sets in the six(sub)genomes.Genotyping of presence-absence variation(PAVs)identified 40453 PAVs associated with 2570 genes specific to A-or B-lineages,of which 1428were differentially expressed,andwere enriched in organ development process,organic substancemetabolic process and response to stimulus.Comparative genome analyses showed that the allotetraploid T.natans underwent asymmetric subgenome divergence,with the B-subgenome being more dominant than the A-subgenome.Multiple factors,including PAVs,asymmetrical amplification of TEs,homeologous exchanges(HEs),and homeolog expression divergence,together affected genome evolution after polyploidization.Overall,this study sheds lights on the genome architecture and evolution of Trapa,and facilitates its functional genomic studies and breeding program.

Evaluation of Genetic Divergence in Various Potato Genotypes Grown in Bangladesh through Different Traits Assessment

The goal of the study was to quantify the genetic diversity of different potato varieties. Five groups were named to classify the 25 genres of potatoes as: Cluster I (Lalpakri, Diamond), Cluster II (Hagrai, Green Mountain, G.M.O., Elvera), Cluster III (Atlantic, Shepody, Raja, Fundy, Multa, Granulla, Shibilati, Japanese Red), Cluster IV (Atlas, Brondy, Yucon Gold, Monona, Petrones, Cheroki), and Cluster V (Calwhite, Prelude, Allblue, Russet, Burbank, TPS-67). The highest and lowest genotypes are found in Clusters III and I, respectively. The two groups’ maximum inter-cluster distance (the cluster’s distance between them) demonstrates the enormous diversity between Clusters II & III. Cluster III had the greatest intra-cluster distance (distance within a set), whereas Cluster V had the smallest. In most cases, the distance between gaps was more significant than the distance within the holes, showing greater genetic diversity between different groups’ genotypes. The highest, second highest, and third highest eigenvalues, accompanying the positive canonical values for Vectors I and II of three characteristics: average tuber weight in each plant, the tubers number in each plant, and the eyes number in each tuber, showed the most outstanding contribution to the complete difference between genotypes. Of the nine features, the smaller leaves number in each plant, the shorter plant height, the more minor genotypes, the fewer eyes per tube generated from Cluster I, the maximum height of the plants, the high-quality tubers in each plant, the tubers number in each plant, the fresh weight in each plant, and the leaf number in each plant from Cluster II could be chosen in the role of parents in this program for hybridization. Given the size of the genetic distance, the various characteristics that contribute to the overall difference, and the average population size, Hagrai, Green Mountain, O.M.G., Elvera Cluster II and Cluster I, Lalpakri, and Diamond genotypes can be regarded as parents of hybridization programs in the future. Thus, producers can get guidance to enhance genetic diversity by selecting materials from different relatives and reducing their vulnerability to diseases and climate change.

Model-Free Ultra-High-Dimensional Feature Screening for Multi-Classified Response Data Based on Weighted Jensen-Shannon Divergence

In ultra-high-dimensional data, it is common for the response variable to be multi-classified. Therefore, this paper proposes a model-free screening method for variables whose response variable is multi-classified from the point of view of introducing Jensen-Shannon divergence to measure the importance of covariates. The idea of the method is to calculate the Jensen-Shannon divergence between the conditional probability distribution of the covariates on a given response variable and the unconditional probability distribution of the covariates, and then use the probabilities of the response variables as weights to calculate the weighted Jensen-Shannon divergence, where a larger weighted Jensen-Shannon divergence means that the covariates are more important. Additionally, we also investigated an adapted version of the method, which is to measure the relationship between the covariates and the response variable using the weighted Jensen-Shannon divergence adjusted by the logarithmic factor of the number of categories when the number of categories in each covariate varies. Then, through both theoretical and simulation experiments, it was demonstrated that the proposed methods have sure screening and ranking consistency properties. Finally, the results from simulation and real-dataset experiments show that in feature screening, the proposed methods investigated are robust in performance and faster in computational speed compared with an existing method.

Study of beam divergence and thrust vector eccentricity characteristics of the Hall thruster based on dual Faraday probe array planes and its applications

The accurate knowledge of the thrust vector eccentricity and beam divergence characteristics of Hall thrusters are of significant engineering value for the beneficial integration and successful application of Hall thrusters on spacecraft.For the characteristics of the plume bipolar diffusion due to the annular discharge channel of the Hall thruster,a Gaussian-fitted method for thrust vector deviation angle and beam divergence of Hall thrusters based on dual Faraday probe array planes was proposed in respect of the Hall thruster beam characteristics.The results show that the ratios of the deviation between the maximum and minimum values of the beam divergence angle and the thrust vector eccentricity angle using a Gaussian fit to the optimized Faraday probe dual plane to the mean value are 1.4%and 11.5%,respectively.The optimized thrust vector eccentricity angle obtained has been substantially improved,by approximately 20%.The beam divergence angle calculated using a Gaussian fitting to the optimized Faraday probe dual plane is approximately identical to the non-optimized one.The beam divergence and thrust vector eccentricity angles for different anode mass flow rates were obtained by averaging the beam divergence and thrust vector eccentricity angles calculated by the dual-plane,Gaussian-fitted ion current density method for different cross-sections.The study not only allows for an immediate and effective tool for determining the design of thrust vector adjustment mechanisms of spacecraft with different power Hall thrusters but also for characterizing the 3D spatial distribution of the Hall thruster plume.

A test of genetic divergence of a bird existing in the Sichuan Basin and its surrounding mountain ranges

Island ecosystems,serving as natural laboratories,facilitate geographical isolation,ecological specialization,and species divergence.The Sichuan Basin,surrounded by mountain ranges,represents a typical continental island due to its marked environmental spatial heterogeneity.This heterogeneity may contribute to geographical isolation and habitat heterogeneity,resulting in genetic divergence within populations.Therefore,we used the White-browed Laughingthrush(Garrulax sannio)as a model specimen to investigate the genetic divergence in the Sichuan Basin and its surrounding mountain ranges,given its presence in various habitats within and beyond this basin.Employing a RAD-seq dataset of 140 G.sannio individuals from 17 distinct ecological zones in the Sichuan Basin and its surrounding mountain ranges,we conducted PCA,population structure analysis,phylogenetic tree construction,and gene flow analysis to comprehensively analyze G.sannio groups.Additionally,in conjunction with geographical and ecological data,we performed isolation by distance,isolation by environment,PCA,and latent factor mixed model analysis to identify factors influencing the genetic divergence among these G.sannio groups.In summary,the 17 G.sannio groups were categorized into high-elevation,medium-elevation,and lowelevation groups.Genetic divergence in G.sannio may be attributed to both geographical distance and key ecological factors,particularly elevation and key climatic variables.Notably,the high-elevation group exhibited a greater number of SNPs and selected genes associated with the key ecological factors compared to the lowelevation group.The ADCY9 gene and several associated key pathways were identified as crucial elements driving ecological adaptation(elevation and key climatic variables)in the high-elevation group.Furthermore,climate changes during the glacial cycles may have facilitated gene flow among these groups residing in the Sichuan Basin and its surrounding mountain ranges.Our findings provide evidence of genetic divergence in G.sannio influenced by the geographical distance and key ecological factors between the Sichuan Basin and its surrounding mountain ranges.These results lay the groundwork for future research on the molecular systematics of continental islands.

How Classical, Quantum-Mechanical, and Relativistic Wave and Field Equations Are Uniformly Generated by Velocity-Field Divergence Equations

We expand previously established results concerning the uniform representability of classical and relativistic gravitational field equations by means of velocity-field divergence equations by demonstrating that conservation equations for (probability) density functions give rise to velocity-field divergence equations the solutions of which generate—by way of superposition—the totality of solutions of various well-known classical and quantum-mechanical wave equations.

RIGHT MEAN FOR THEα-z BURES-WASSERSTEIN QUANTUM DIVERGENCE

The optimization problem to minimize the weighted sum ofα-z Bures-Wasserstein quantum divergences to given positive definite Hermitian matrices has been solved.We call the unique minimizer theα-z weighted right mean,which provides a new non-commutative version of generalized mean(H?lder mean).We investigate its fundamental properties,and give many interesting operator inequalities with the matrix power mean including the Cartan mean.Moreover,we verify the trace inequality with the Wasserstein mean and provide bounds for the Hadamard product of two right means.

Long-read genome assemblies reveal a cis-regulatory landscape associated with phenotypic divergence in two sister Siniperca fish species

Due to the difficulty in accurately identifying structural variants(SVs) across genomes,their impact on cisregulato ry diverge n ce of closely related species,especially fish,remains to be explored.Recently identified broad H3K4me3 domains are essential for the regulation of genes involved in several biological processes.However,the role of broad H3K4me3 domains in phenotypic divergence remains poorly understood.Siniperca chuatsi and S.scherzeri are closely related but divergent in several phenotypic traits,making them an ideal model to study cis-regulatory evolution in sister species.Here,we generated chromosome-level genomes of S.chuatsi and S.scherzeri,with assembled genome sizes of 716.35 and740.54 Mb,respectively.The evolutionary histories of S.chuatsi and S.scherzeri were studied by inferring dynamic changes in ancestral population sizes.To explore the genetic basis of adaptation in S.chuatsi and S.scherzeri,we performed gene family expansion and contraction analysis and identified positively selected genes(PSGs).To investigate the role of SVs in cis-regulatory divergence of closely related fish species,we identified high-quality SVs as well as divergent H3K27ac and H3K4me3 domains in the genomes of S.chuatsi and S.scherzeri.Integrated analysis revealed that cis-regulatory divergence caused by SVs played an essential role in phenotypic divergence between S.chuatsi and S.scherzeri.Additionally,divergent broad H3K4me3 domains were mostly associated with cancer-related genes in S.chuatsi and S.scherzeri and contributed to their phenotypic divergence.

The Meaning of Divergence

The concept of the divergence is fundamental in electromagnetic field theory, yet they are especially difficult mathematical concepts. Understanding this concept requires strong spatial and abstract thinking. When teaching, through the graphical and quantitative methods presented herein, the significance of the divergence is displayed by a quantitative method for the first time. Through these methods, the concepts of the divergence can be grasped more easily. These explanations will be helpful for students to strengthen the understanding of this concept and has a certain reference significance.

常见分布的最大Kullback-Leibler距离

在Kullback-Leibler距离的基础上,定义了两个概率分布之间的最大Kullback-Leibler距离,证明了这个距离具有欧式距离的对称性,三角不等式性等分析性质,依照该定义,计算了两个不同的二项分布,两个不同的正态分布等一些常见分布之间的最大Kullback-Leibler距离.还定义了多元最大Kullback-Leibler距离,并且计算两个矩阵Γ分布的Kullback-Leibler距离.另外在Kullback-Leibler距离下,还得到了一种正态分布逼近指数分布的条件.

两个一元t-分布之间的Kullback-Leibler距离

该文首次求出了两个一元 t-分布之间的 Kullback-