A Relation between Resolvents of Subdifferentials and Metric Projections to Level Sets

An equation concerning with the subdifferential of convex functionals defined in real Banach spaces and the metric projections to level sets is shown. The equation is compared with the resolvents of general monotone operators, and makes the geometric properties of differential equations expressed by subdifferentials clear. Hence, it can be expected to be useful in obtaining the steepest descents defined by the convex functionals in Banach spaces. Also, it gives a similar result to the Lagrange multiplier method under certain conditions.

ON THE THEORY OF RESOLVENTS AND ITS APPLICATIONS

We extend the concept of the resolvent of a prime ideal to the concept of theresolvent of a general ideal with respect to a set of parameters and propose an algorithmto construct the generalized resolvents based on Wu-Rits’s zero decomposition algorithm.Our generalized algorithm has the following applications. (1) For a reducible variety V,we can find a direction on which V is projected birationally to an irreducible hypersurface.(2) We give a new algorithm to find a primitive element for a finite algebraic extensionof a field of characteristic zero. (3) We present a complete method of finding parametricequations for algebraic curves. (4) We give a method of solving a system of polynomialequations to any given precision.

Haplotype-resolved and chromosome-scale genomes provide insights into co-adaptation between the Amur tiger and Amur leopard

DEAR EDITOR,Big cats,such as Amur tigers(Panthera tigris altaica)and Amur leopards(P.pardus orientalis),are apex predator and have evolved specialized traits for hunting and carnivory(Moya et al.,2022),thus playing a crucial role in maintaining biodiversity and ecosystem integrity by regulating prey-predator dynamics.However,human-induced pressures,habitat fragmentation,and environmental alterations have restricted these species in small and isolated populations.Currently,all extant big cats are categorized as endangered or threatened according to their conservation status.Amur tigers and Amur leopards share overlapping geographic ranges,habitats,and certain prey species in the forests of Northeast Asia(Jiang et al.,2015).To reduce interspecies conflict,these carnivores exhibit differentiated dietary and temporal niches.Amur tigers predominantly prey on large ungulates,while Amur leopards hunt small to medium-sized animals(Sugimoto et al.,2016).Additionally,they occupy different temporal niches,with tigers being active at night and leopards more active during the day.Despite spatial and temporal niche partitioning,interspecific competition between these two species is inevitable.Tigers,benefiting from their greater size,have a competitive advantage over leopards,which can manifest in occasional leopard predation by tigers and declines in leopard populations with increasing tiger density(Jiang et al.,2015).Tigers also displace leopards from marginal habitats in nature reserves where they coexist.

Time-resolved ultra-small-angle X-ray scattering beamline(BL10U1)at SSRF

The construction of a new beamline,BL10U1,was completed at the Shanghai synchrotron radiation facility in 2020.This multipurpose beamline was designed to provide X-ray scattering techniques such as ultra-small-angle X-ray scattering(USAXS),small-angle X-ray scattering(SAXS),wide-angle X-ray scattering,and microfocus SAXS(μSAXS)for a broad user community.To realize fast time-resolved USAXS experiments,the beamline adopted an in-vacuum undulator with a total length of 1.6 m as the photon source.An in-house cryogenic-cooled double multilayer monochromator was installed to deliver a photon flux of approximately 10^(13) photons/s at a photon energy of 10 keV.The three-year successful operation of this beamline demonstrated that the monochromator operated smoothly,as expected.BL10U1 has three end stations in succession:USAXS end station,μSAXS end station,and end station for industrial applications.The minimum scattering vector q~0.0042 nm^(-1) at 10 keV can be achieved at the USAXS end station equipped with a 28 m-long and 1.8 m-diameter vacuum flight tube.At theμSAXS end station,a beam spot of less than 10×8μm was achieved for micro-SAXS experiments.In contrast,in situ experimental instruments up to 5 m high and 8 m wide can be mounted at the industrial application end station,which offers industrial scientists the opportunity to use their large industrial equipment.BL10U1 opens up a new capability to investigate phenomena such as non-equilibrium and dynamic processes of materials with a wide length scale from angstroms to micrometers with millisecond time resolution.In this paper,we also report beamline design considerations and commissioning results.

Parallelization strategies for resolved simulations of fluid-structure-particle interactions

Fluid-structure-particle interactions in three spatial dimensions happen in many environmental and engineering flows.This paper presents the parallel algorithms for the hybrid diffuse and sharp interface immersed boundary(IB)method developed in our previous work.For the moving structure modeled using the sharp interface IB method,a recursive box method is developed for efficiently classifying the background grid nodes.For the particles modeled using the diffuse interface IB method,a‘master-slave’approach is adopted.For the particle-particle interaction(PPI)and particle-structure interaction(PSI),a fast algorithm for classifying the active and inactive Lagrangian points,which discretize the particle surface,is developed for the‘dry’contact approach.The results show that the proposed recursive box method can reduce the classifying time from 52seconds to 0.3 seconds.Acceptable parallel efficiency is obtained for cases with different particle concentrations.Furthermore,the lubrication model is utilized when a particle approaches a wall,enabling an accurate simulation of the rebounding phenomena in the benchmark particle-wall collision problem.At last,the capability of the proposed computational framework is demonstrated by simulating particle-laden turbulent channel flows with rough walls.

Risk of hepatic decompensation from hepatitis B virus reactivation in hematological malignancy treatments

In this editorial,we discussed the apparent discrepancy between the findings described by Colapietro et al,in their case report and data found in the literature.Colapietro et al reported a case of hepatitis B virus(HBV)-related hepatic decompensation in a patient with chronic myeloid leukemia and a previously resolved HBV infection who was receiving Bruton’s tyrosine kinase(BTK)inhibitor therapy.First of all,we recapitulated the main aspects of the immune system involved in the response to HBV infection in order to underline the role of the innate and adaptive response,focusing our attention on the protective role of anti-HBs.We then carefully analyzed literature data on the risk of HBV reactivation(HBVr)in patients with previous HBV infection who were treated with either tyrosine kinase inhibitors or BTK inhibitors for their hematologic malignancies.Based on literature data,we suggested that several factors may contribute to the different risks of HBVr:The type of hematologic malignancy;the type of therapy(BTK inhibitors,especially second-generation,seem to be at a higher risk of HBVr than those with tyrosine kinase inhibitors);previous exposure to an anti-CD20 as first-line therapy;and ethnicity and HBV genotype.Therefore,the warning regarding HBVr in the specific setting of patients with hematologic malignancies requires further investigation.

Efficacy of activating blood and resolving stasis therapy for IgA nephropathy:a systematic review and meta-analysis

Background:To systematically evaluate the efficacy and safety of activating blood and resolving stasis in patients with IgA nephropathy.Methods:From inception to May 2022,databases including PubMed,Embase,the Cochrane Library,Web of Science,WanFang database,Chinese Biomedical Database,VIP,and China National Knowledge Infrastructure were searched for randomized controlled trials about enhancing blood circulation and removing stasis for IgA nephropathy.For the articles that satisfied the requirements,quality assessment and meta-analysis were done.Results:Seventeen randomized controlled trials with a total of 1653 patients were included.Meta-analysis showed that activating blood and resolving stasis could increase therapeutic effectiveness(risk ratio(RR)=-0.47,95%confidence interval(CI)(-0.37,-0.2),P=0.0006)and decrease levels of serum creatinine(RR=-0.47,95%CI(-0.37,-0.2),P=0.0006),urea nitrogen(RR=0.85,95%CI(1.44,0.26),P=0.005),24-hour urinary protein quantification(RR=1.6,95%CI(2.44,0.95).P=0.00001),and urine red blood cell count(RR=1.7,95%CI(2.57,0.82),P=0.0001).There was no significant difference between the two groups in terms of security(RR=0.6,95%CI(0.36,1.01),P=0.05).Conclusion:Western medicine combined activating blood and resolving stasis is more efficient than Western medicine therapy alone in treating IgA nephropathy,but it still needs to be supported by additional large-scale,multi-center randomized controlled clinical trials due to the poor quality of the included trials.

Exactly Solvable Two-Parameter Models of Relativistic δ′s -Sphere Interactions in Quantum Mechanics

We make a systematic study of two-parameter models of δ ′ s -sphere interaction and δ ′ s -sphere plus a Coulomb interaction. Where δ ′ s interaction denotes the δ ′ -sphere interaction of the second kind. We provide the mathematical definitions of Hamiltonians and obtain new results for both models, in particular the resolvents equations, spectral properties and some scattering quantities.

Viscosity Approximations by Generalized Contractions for Resolvents of Accretive Operators in Banach Spaces

In this paper, we prove a strong convergence theorem for resolvents of accretive operators in a Banach space by the viscosity approximation method with a generalized contraction mapping. The proximal point algorithm in a Banach space is also considered. The results extend some very recent theorems of W. Takahashi.

A gap-free and haplotype-resolved lemon genome provides insights into flavor synthesis and huanglongbing (HLB) tolerance

The lemon(Citrus limon;family Rutaceae)is one of the most important and popular fruits worldwide.Lemon also tolerates huan-glongbing(HLB)disease,which is a devastating citrus disease.Here we produced a gap-free and haplotype-resolved chromosome-scale genome assembly of the lemon by combining Pacific Biosciences circular consensus sequencing,Oxford Nanopore 50-kb ultra-long,and high-throughput chromatin conformation capture technologies.The assembly contained nine-pair chromosomes with a contig N50 of 35.6 Mb and zero gaps,while a total of 633.0 Mb genomic sequences were generated.The origination analysis identified 338.5Mb genomic sequences originating from citron(53.5%),147.4Mb frommandarin(23.3%),and 147.1Mb frompummelo(23.2%).The genome included 30528 protein-coding genes,and most of the assembled sequences were found to be repetitive sequences.Several significantly expanded gene families were associated with plant-pathogen interactions,plant hormone signal transduction,and the biosynthesis of major active components,such as terpenoids and f lavor compounds.Most HLB-tolerant genes were expanded in the lemon genome,such as 2-oxoglutarate(2OG)/Fe(II)-dependent oxygenase and constitutive disease resistance 1,cell wall-related genes,and lignin synthesis genes.Comparative transcriptomic analysis showed that phloem regeneration and lower levels of phloem plugging are the elements that contribute to HLB tolerance in lemon.Our results provide insight into lemon genome evolution,active component biosynthesis,and genes associated with HLB tolerance.

High-quality haplotype-resolved genome assembly of cultivated octoploid strawberry

Cultivated strawberry(Fragaria×ananassa),a perennial herb belonging to the family Rosaceae,is a complex octoploid with high heterozygosity at most loci.However,there is no research on the haplotype of the octoploid strawberry genome.Here we aimed to obtain a high-quality genome of the cultivated strawberry cultivar,“Yanli”,using single molecule real-time sequencing and high-throughput chromosome conformation capture technology.The“Yanli”genome was 823 Mb in size,with a long terminal repeat assembly index of 14.99.The genome was phased into two haplotypes,Hap1(825 Mb with contig N50 of 26.70 Mb)and Hap2(808 Mb with contig N50 of 27.51 Mb).Using the combination of Hap1 and Hap2,we obtained for the first time a haplotype-resolved genome with 56 chromosomes for the cultivated octoploid strawberry.We identified a∼10 Mb inversion and translocation on chromosome 2-1.104957 and 102356 protein-coding genes were annotated in Hap1 and Hap2,respectively.Analysis of the genes related to the anthocyanin biosynthesis pathway revealed the structural diversity and complexity in the expression of the alleles in the octoploid F.×ananassa genome.In summary,we obtained a high-quality haplotype-resolved genome assembly of F.×ananassa,which will provide the foundation for investigating gene function and evolution of the genome of cultivated octoploid strawberry.

Computing Connected Resolvability of Graphs Using Binary Enhanced Harris Hawks Optimization

In this paper,we consider the NP-hard problem offinding the minimum connected resolving set of graphs.A vertex set B of a connected graph G resolves G if every vertex of G is uniquely identified by its vector of distances to the ver-tices in B.A resolving set B of G is connected if the subgraph B induced by B is a nontrivial connected subgraph of G.The cardinality of the minimal resolving set is the metric dimension of G and the cardinality of minimum connected resolving set is the connected metric dimension of G.The problem is solved heuristically by a binary version of an enhanced Harris Hawk Optimization(BEHHO)algorithm.This is thefirst attempt to determine the connected resolving set heuristically.BEHHO combines classical HHO with opposition-based learning,chaotic local search and is equipped with an S-shaped transfer function to convert the contin-uous variable into a binary one.The hawks of BEHHO are binary encoded and are used to represent which one of the vertices of a graph belongs to the connected resolving set.The feasibility is enforced by repairing hawks such that an addi-tional node selected from V\B is added to B up to obtain the connected resolving set.The proposed BEHHO algorithm is compared to binary Harris Hawk Optimi-zation(BHHO),binary opposition-based learning Harris Hawk Optimization(BOHHO),binary chaotic local search Harris Hawk Optimization(BCHHO)algorithms.Computational results confirm the superiority of the BEHHO for determining connected metric dimension.

ZOOMit与RESOLVE高级扩散加权成像技术在肛瘘评估中的应用价值

目的对比分析ZOOMit与RESOLVE高级扩散加权成像(DWI)技术的肛管图像质量及瘘管可见性,以选择最优的肛管磁共振成像(MRI)扫描方案。方法回顾性收集2021年3月至8月临床诊断为肛瘘且行MRI检查的22例患者的临床资料,所有患者均行肛管ZOOMit与RESOLVE扫描。分析两种DWI序列的图像质量及信噪比(SNR)。结果ZOOMit DWI图像失真或伪影、整体图像质量主观评分高于RESOLVE DWI,差异具有统计学意义(P<0.001)。ZOOMit DWI瘘管可见性主观评分高于RESOLVE DWI,差异具有统计学意义(P<0.001)。ZOOMit DWI与RESOLVE DWI SNR-b50比较,差异具有统计学意义(P<0.05)。ZOOMit DWI与RESOLVE DWI SNR-b1000比较,差异具有统计学意义(P<0.05)。结论ZOOMit DWI具有较高的图像质量,且瘘管可见性和图像SNR均高于RESOLVE DWI,可以作为肛管MRI扩散成像的首选序列。

Minimal Doubly Resolving Sets of Certain Families of Toeplitz Graph

The doubly resolving sets are a natural tool to identify where diffusion occurs in a complicated network.Many realworld phenomena,such as rumour spreading on social networks,the spread of infectious diseases,and the spread of the virus on the internet,may be modelled using information diffusion in networks.It is obviously impractical to monitor every node due to cost and overhead limits because there are too many nodes in the network,some of which may be unable or unwilling to send information about their state.As a result,the source localization problem is to find the number of nodes in the network that best explains the observed diffusion.This problem can be successfully solved by using its relationship with the well-studied related minimal doubly resolving set problem,which minimizes the number of observers required for accurate detection.This paper aims to investigate the minimal doubly resolving set for certain families of Toeplitz graph Tn(1,t),for t≥2 and n≥t+2.We come to the conclusion that for Tn(1,2),the metric and double metric dimensions are equal and for Tn(1,4),the double metric dimension is exactly one more than the metric dimension.Also,the double metric dimension for Tn(1,3)is equal to the metric dimension for n=5,6,7 and one greater than the metric dimension for n≥8.

Promise of spatially resolved omics for tumor research

Tumors are spatially heterogeneous tissues that comprise numerous cell types with intricate structures.By interacting with the microenvironment,tumor cells undergo dynamic changes in gene expression and metabolism,resulting in spatiotemporal variations in their capacity for proliferation and metastasis.In recent years,the rapid development of histological techniques has enabled efficient and high-throughput biomolecule analysis.By preserving location information while obtaining a large number of gene and molecular data,spatially resolved metabolomics(SRM)and spatially resolved transcriptomics(SRT)approaches can offer new ideas and reliable tools for the in-depth study of tumors.This review provides a comprehensive introduction and summary of the fundamental principles and research methods used for SRM and SRT techniques,as well as a review of their applications in cancer-related fields.

Effects of temperature on critical resolved shear stresses of slip and twining in Mg single crystal via experimental and crystal plasticity modeling

Magnesium(Mg)single crystal specimens with three different orientations were prepared and tested from room temperature to 733 K in order to systematically evaluate effects of temperature on the critical resolved shear stress(CRSS)of slips and twinning in Mg single crystals.The duplex non-basal slip took place in the temperature range from 613 to 733 K when the single crystal samples were stretched along the<0110>direction.In contrast,the single basal slip and prismatic slip were mainly activated in the temperature range from RT to 733 K when the tensile directions were inclined at an angle of 45°with the basal and the prismatic plane,respectively.Viscoplastic self-consistent(VPSC)crystal modeling simulations with genetic algorithm code(GA-code)were carried out to obtain the best fitted CRSSs of major deformation modes,such as basal slip,prismatic slip,pyramidalⅡ,{1012}tensile twinning and{1011}compressive twinning when duplex slips accommodated deformation.Additionally,CRSSs of the basal and the prismatic slip were derived using the Schmid factor(SF)criterion when the single slip mainly accommodated deformation.From the CRSSs of major deformation modes obtained by the VPSC simulations and the SF calculations,the CRSSs for basal slip and{1012}tensile twinning were found to show a weak temperature dependence,whereas those for prismatic,slip and{1011}compressive twinning exhibited a strong temperature dependence.From the comparison of previous results,VPSC-GA modeling was proved to be an effective method to obtain the CRSSs of various deformation modes of Mg and its alloys.

Single-cell and spatially resolved omics:Advances and limitations

Recent advances in experimental and computational single-cell and spatially resolved omics have opened new avenues for research in biology and medicine.These technologies allow for the study of individual cells in unprecedented detail,providing insights into the heterogeneity within tissues and organs,and how different cells interact with each other.Humans and other eukaryotes are composed of billions of cells,each with vastly heterogeneous cell types and functional cell states determined by intrinsic and extrinsic factors.

The haplotype-resolved autotetraploid genome assembly provides insights into the genomic evolution and fruit divergence in wax apple(Syzygium samarangense(Blume)Merr.and Perry)

Wax apple(Syzygium samarangense)is an economically important fruit crop with great potential value to human health because of its richness in antioxidant substances.Here,we present a haplotype-resolved autotetraploid genome assembly of the wax apple with a size of 1.59 Gb.Comparative genomic analysis revealed three rounds of whole-genome duplication(WGD)events,including two independent WGDs after WGT-γ.Resequencing analysis of 35 accessions partitioned these individuals into two distinct groups,including 28 landraces and seven cultivated species,and several genes subject to selective sweeps possibly contributed to fruit growth,including the KRP1-like,IAA17-like,GME-like,and FLACCA-like genes.Transcriptome analysis of three different varieties during flower and fruit development identified key genes related to fruit size,sugar content,and male sterility.We found that AP2 also affected fruit size by regulating sepal development in wax apples.The expression of sugar transport-related genes(SWEETs and SUTs)was high in‘ZY’,likely contributing to its high sugar content.Male sterility in‘Tub’was associated with tapetal abnormalities due to the decreased expression of DYT1,TDF1,and AMS,which affected early tapetum development.The chromosome-scale genome and large-scale transcriptome data presented in this study offer new valuable resources for biological research on S.samarangense and shed new light on fruit size control,sugar metabolism,and male sterility regulatory metabolism in wax apple.

Two haplotype-resolved genomes reveal important flower traits in bigleaf hydrangea(Hydrangea macrophylla)and insights into Asterid evolution

The Hydrangea genus belongs to the Hydrangeaceae family,in the Cornales order of flowering plants,which early diverged among the Asterids,and includes several species that are commonly used ornamental plants.Of them,Hydrangea macrophylla is one of the most valuable species in the nursery trade,yet few genomic resources are available for this crop or closely related Asterid species.Two high-quality haplotype-resolved reference genomes of hydrangea cultivars‘Veitchii’and‘Endless Summer’[highest quality at 2.22 gigabase pairs(Gb),396 contigs,N5022.8 megabase pairs(Mb)]were assembled and scaffolded into the expected 18 pseudochromosomes.Utilizing the newly developed high-quality reference genomes along with high-quality genomes of other related flowering plants,nuclear data were found to support a single divergence point in the Asterids clade where both the Cornales and Ericales diverged from the euasterids.Genetic mapping with an F1 hybrid population demonstrated the power of linkage mapping combined with the new genomic resources to identify the gene for inflorescence shape,CYP78A5 located on chromosome 4,and a novel gene,BAM3 located on chromosome 17,for causing double flower.Resources developed in this study will not only help to accelerate hydrangea genetic improvement but also contribute to understanding the largest group of flowering plants,the Asterids.

Metric Basis of Four-Dimensional Klein Bottle

The Metric of a graph plays an essential role in the arrangement of different dimensional structures and finding their basis in various terms.The metric dimension of a graph is the selection of the minimum possible number of vertices so that each vertex of the graph is distinctively defined by its vector of distances to the set of selected vertices.This set of selected vertices is known as the metric basis of a graph.In applied mathematics or computer science,the topic of metric basis is considered as locating number or locating set,and it has applications in robot navigation and finding a beacon set of a computer network.Due to the vast applications of this concept in computer science,optimization problems,and also in chemistry enormous research has been conducted.To extend this research to a four-dimensional structure,we studied the metric basis of the Klein bottle and proved that the Klein bottle has a constant metric dimension for the variation of all its parameters.Although the metric basis is variying in 3 and 4 values when the values of its parameter change,it remains constant and unchanged concerning its order or number of vertices.The methodology of determining the metric basis or locating set is based on the distances of a graph.Therefore,we proved the main theorems in distance forms.