Unconditional and Conditional QTL Mapping for Tiller Numbers at Various Stages with Single Segment Substitution Lines in Rice(Oryza sativa L.)

Tiller is one of the most important agronomic traits which influences quantity and quality of effective panicles and finally influences yield in rice. It is important to understand ＂static＂ and ＂dynamic＂ information of the QTLs for tillers in rice. This work was the first time to simultaneously map unconditional and conditional QTLs for tiller numbers at various stages by using single segment substitution lines in rice. Fourteen QTLs for tiller number, distributing on the corresponding substitution segments of chromosomes 1, 2, 3, 4, 6, 7 and 8 were detected. Both the number and the effect of the QTLs for tiller number were various at different stages, from 6 to 9 in the number and from 1.49 to 3.49 in the effect, respectively. Tiller number QTLs expressed in a time order, mainly detected at three stages of 0-7 d, 14-21 d and 35-42 d after transplanting with 6 positive, 9 random and 6 negative expressing QTLs, respectively. Each of the QTLs expressed one time at least during the whole duration of rice. The tiller number at a specific stage was determined by sum of QTL effects estimated by the unconditional method, while the increasing or decreasing number in a given time interval was controlled by the total of QTL effects estimated by the conditional method. These results demonstrated that it is highly effective and accurate for mapping of the QTLs by using single segment substitution lines and the conditional analysis methodology.

A universal algorithm to generate pseudo-random numbers based on uniform mapping as homeomorphism

A specific uniform map is constructed as a homeomorphism mapping chaotic time series into [0,1] to obtain sequences of standard uniform distribution. With the uniform map, a chaotic orbit and a sequence orbit obtained are topologically equivalent to each other so the map can preserve the most dynamic properties of chaotic systems such as permutation entropy. Based on the uniform map, a universal algorithm to generate pseudo random numbers is proposed and the pseudo random series is tested to follow the standard 0-1 random distribution both theoretically and experimentally. The algorithm is not complex, which does not impose high requirement on computer hard ware and thus computation speed is fast. The method not only extends the parameter spaces but also avoids the drawback of small function space caused by constraints on chaotic maps used to generate pseudo random numbers. The algorithm can be applied to any chaotic system and can produce pseudo random sequence of high quality, thus can be a good universal pseudo random number generator.

Identification of QTL for kernel number-related traits in a rice chromosome segment substitution line and fine mapping of qSP1

A chromosome segment substitution line (CSSL) is a powerful tool for combining quantitative trait locus (QTL) mapping with the pyramiding of desirable alleles. The rice CSSL Z1364 with increased kernel number was identified in a BC3F8 population derived from a cross of Nipponbare as the recipient with Xihui 18 as the donor parent. Z1364 carried three substitution segments distributed on chromosomes 1, 6, and 8. The mean substitution length was 1.19 Mb. Of 17 QTL identified on the substitution segments, qSP1 for spikelets per panicle, qSSD1 for seed-set density, and qNSB1 for number of secondary branches explained respectively 57.34%, 87.7%, and 49.44% of the corresponding phenotypic variance and were all linked to RM6777. Chi-square analysis showed that the increased kernel number in Z1364 was inherited recessively by a single gene. By fine mapping, qSP1 was delimited to a 50-kb region on the short arm of chromosome 1. Based on DNA sequence, a previously uncharacterized rice homolog of Arabidopsis thaliana AT4G32551 was identified as a candidate gene for qSP1 in which mutation increases the number of spikelets and kernels in Z1364. qSP1 was expressed in all tissues, but particularly in 1-cm panicles. The expression levels of OsMADS22, GN1A, and DST were upregulated and those of LAX2, GNP1, and GHD7 were downregulated in Nipponbare. These results provide a foundation for functional research on qSP1.

QTL mapping for grain number per spikelet in wheat using a high-density genetic map

Grain number per spikelet (GNS) is a key determinant of grain yield in wheat.A recombinant inbred line population comprising 300 lines was developed from a cross between a high GNS variety H461 and Chinese Spring from which the reference genome assembly of bread wheat was obtained.Both parents and the recombinant inbred lines were genotyped using the wheat 55K single nucleotide polymorphism(SNP) array.A high-density genetic map containing 21,197 SNPs was obtained.These markers covered each of the 21 chromosomes with a total linkage distance of 3792.71 c M.Locations of these markers in this linkage map were highly consistent with their physical locations in the genome assembly of Chinese Spring.The two parents and the whole RIL population were assessed for GNS in two consecutive years at two different locations.Based on multi-environment phenotype data and best liner unbiased prediction values,three quantitative trait loci (QTL) for GNS were identified.One of them located on chromosomes 2B and the other two on 2D.Phenotypic variation explained by these loci varied from 3.07%to26.57%.One of these QTL,QGns.sicau-2D-2,was identified in each of all trials conducted.Based on the best linear unbiased prediction values,this locus explained 19.59%–26.57%of phenotypic variation.A KASP(Kompetitive Allele-Specific PCR) marker closely linked with this locus was generated and used to validate the effects of this locus in three different genetic backgrounds.The identified QTL and the KASP marker developed for it will be highly valuable in fine-mapping the locus and in exploiting it for markerassisted selection in wheat breeding programs.

Mining Applicable Elite Alleles of Growth Duration, Plant Height and Panicle Number per Plant by Conditional QTL Mapping in Japonica Rice

Unconditional and conditional QTL mapping were conducted for growth duration (GD), plant height (PH) and effective panicle number per plant (PN) using a recombinant inbred line (RIL) population derived from a cross between two japonica rice varieties Xiushui 79 and C Bao. The RIL population consisted of 254 lines was planted in two environments, Nanjing and Sihong, Jiangsu Province, China. Results showed that additive effects were major in all of QTLs for GD, PH and PN detected by the two methods, and the epistatic effects explained a small proportion of phenotypic variation. No interactions were detected between additive QTL and environment, and between epistatic QTL pairs and environment. After growth duration was adjusted to an identical level, RM80-160bp was detected as an applicable elite allele for PN, with an additive effect of 0.71. When effective panicle number per plant was adjusted to an identical level, RM448-240bp was detected as an applicable elite allele for GD, with an additive effect of 4.64. After plant height was adjusted to an identical level, RM80-160bp was detected as an applicable elite allele for PN, with an additive effect of 0.62, and RM448-240bp was detected as an applicable elite allele for GD, with an additive effect of 3.89. These applicable elite alleles could be used to improve target traits without influencing the other two traits.

ON THE NUMBER OF EULERIAN PLANAR MAPS

This paper presents the number of combinatorially distinct rooted Eulerian planar maps with the number of non-root-vertices and the number of non-root-faces as two parameters. The parametric expressions for determining the number in tha loopless Eulerian case are also obtained.

Genetic dissection of husk number and length across multiple environments and fine-mapping of a major-effect QTL for husk number in maize(Zea mays L.)

Husk number(HN)and husk length(HL)influence the mechanical harvesting of maize grain.We investigated the genetic basis of HN and HL using a population of 204 recombinant inbred lines phenotypically evaluated in five environments.The two husk traits showed broad phenotypic variation and high heritability.Nine stable quantitative trait loci(QTL)were identified by single-environment mapping,comprising four QTL for HN and five for HL,and three QTL explained>10%of the phenotypic variation.Joint mapping revealed 22 additive QTL and 46 epistatic QTL.Both additive and epistatic(additive×additive)effects as well as a few large-effect QTL and some minor-effect QTL appeared to contribute to the genetic architecture of HN and HL.The QTL for HN located on chromosome 7,q HN7,which accounted for^20%of phenotypic variation,was detected in all five environments.q HN7 was fine-mapped to a 721.1 kb physical region based on the maize B73 Ref Gen_v3 genome assembly.Within this interval,four genes associated with plant growth and development were selected as candidate genes.The results will be useful for improvement of maize husk traits by molecular breeding and provide a basis for the cloning of q HN7.

Mining Elite Alleles of Growth Duration and Productive Panicle Number per Plant by Association Mapping with Conditional Phenotypic Value in Japonica Rice

To provide genetic information and materials for breeding hybrid japonica rice with wide adaptability and strong competitive advantage of yield, elite alleles and their carrier varieties of growth duration （GD） and productive panicle number per plant （PN） were detected. A natural population composed of 94 japonica varieties was phenotyped for the GD, PN and plant height （PH） in two environments. The conditional phenotypic data were transferred by the linear model method in software QGAStation 1.0, and association mapping based on the unconditional and conditional phenotype values of GD and PN was analyzed by using general linear model in software TASSEL. A total of 34 simple sequence repeat （SSR） marker loci associated with GD and PN were detected in the two environments. Among them, 15 were associated with GD, and 19 were associated with PN. Four elite alleles of RM8095-120bp, RM7102-176bp, RM72-170bp and RM72-178bp were associated with GD, and their carrier varieties were Hongmangshajing, Nipponbare, Hongmangshajing and Nannongjing 62401, respectively. These elite alleles from the carrier varieties can shorten GD by 2.03-9.93 d when they were introduced into improved materials. RM72-182bp associated with PN was an elite allele, and its carrier variety was Xiaoqingzhong. It can increase PN by three when introduced into improved materials. Moreover, these elite alleles can be used to improve target traits without influencing another two traits.

The Pointwise Characterizations of Fuzzy Mappings and Fuzzy Cardinal Numbers

In this paper,the pointwise characterizations of fuzzy mappings are given. Based of this definition,we give a few of new properties of fuzzy cardinal numbers.

Identification of a candidate QTG for seed number per silique by integrating QTL mapping and RNA-seq in Brassica napus L.

Seed number per silique(SNPS)is one of seed yield components in rapeseed,but its genetic mechanism remains elusive.Here a double haploid(DH)population derived from a hybrid between female 6Q006with 35–40 SNPS and male 6W26 with 10–15 SNPS was investigated for SNPS in the year 2017,2018,2019 and 2021,and genotyped with Brassica 60K Illumina Infinium SNP array.An overlapping major QTL(qSNPS.C09)explaining 51.50%of phenotypic variance on average was narrowed to a 0.90 Mb region from 44.87 Mb to 45.77 Mb on chromosome C09 by BSA-seq.Subsequently,two DEGs in this interval were detected between extreme individuals in DH and F_2populations by transcriptome sequencing at7 and 14 days after pollination siliques.Of which,BnaC09g45400D encoded an adenine phosphoribosyltransferase 5(APT5)has a 48-bp InDel variation in the promoter of two parents.Candidate gene association analysis showed that this InDel variation was associated with SNPS in a nature population of rapeseed,where 54 accessions carrying the same haplotype as parent 6Q006 had higher SNPS than103 accessions carrying the same haplotype as parent 6W26.Collectively,the findings are helpful for rapeseed molecular breeding of SNPS,and provide new insight into the genetic and molecular mechanism of SNPS in rapeseed.

Comparison of QTL for Grain Number per Panicle in Three Populations Sharing 3 Parents and Fine Mapping of Gn1c

Complex traits, such as yield components, are inherited in a quantitative manner and typically controlled by quantitative trait loci (QTL). Grain number per panicle (GN) is an important component of yield in rice and

Cardinal Numbers of Fuzzy Sets

Up to now, the study on the cardinal number of fuzzy sets has advanced at on pace since it is very hard to give it an appropriate definition. Althrough for it in [1], it is with some harsh terms and is not reasonable as we point out in this paper. In the paper, we give a general definition of fuzzy cardinal numbers. Based on this definition, we not only obtain a large part of results with re spect to cardinal numbers, but also give a few of new properties of fuzzy cardinal numbers.

对DMAPS野外采集程序的改进

随着数字化测图的开展和深入,安徽省测绘局DMAPS成图软件野外采集程序的原有功能已不能较好的满足数字化生产需求,但其本身和其它数字化成图软件的野外采集程序相比又有较多的优点,如加以适当改进,便能更好的适应数字化测图的需要,本文论述对野外采集程序加以改进的方法。

Conditional QTL mapping of three yield components in common wheat(Triticum aestivum L.)

Spike number per m^2(SN),kernel number per spike(KNPS) and thousand-kernel weight(TKW)are the three main components determining wheat(Triticum aestivum L.) yield.To evaluate the relationships among them a doubled haploid(DH) population consisting of 168 lines grown at three locations for three years was analyzed by unconditional and conditional QTL mapping.Thirty-three unconditional QTL and fifty-nine conditional QTL were detected.Among them,two QTL(QSN-DH-2B and QSN-DH-3A-1.1) improved SN,with no effect on KNPS.QKNPS-DH-2B-2.1 improved KNPS,with no effect on SN.QKNPS-DH-1A-1.1,QKNPS-DH-2D-1.1and QKNPS-DH-6A improved KNPS,with no effect on SN or TKW.QKNPS-DH-6B was associated with increased SN and TKW.In addition,QTKW-DH-4B,QTKW-DH-5B and QTKW-DH-7B increased TKW without decreasing KNPS.These results provide useful information for marker assisted selection(MAS) and improvement in wheat yield.

Improving Middle Square Method RNG Using Chaotic Map

One of the classic approaches in PRNGs is the middle square method in which with a simple mathe-matical model generating pseudorandom numbers in high speed and minimum correlation between output numbers. Despite these unique characteristics, the method contains weaknesses that a broader application of this algo- rithm will face. In this paper is studied middle square method and then a logistic chaotic map is introduced with its specific features and its improved weaknesses via using these characteristics. Finally the NIST tests suite s are presented, in order to detect the specific characteristics expected from truly random sequences.

基于WeatherMap的城域网流量、用户拓扑监控系统

在三网融合的背景下,随着公司对集团用户专网业务和VOD互动点播业务的大力开展,双向业务的用户数量成指数上升,为了保障网络质量,需要实时监控网络流量和各种业务的在线用户数量,公司采用开源的Cacti配合其WeatherMap组件搭建了一套可以在网络拓扑图上以不同颜色直观显示流量和用户数的监控系统。

Some Theorems About Unitons of Harmonic Maps into U(N)

By using the simplified method of factorization given by Valli, and the correspondence between the harmonic map φ∶S 2→U(N) and U(N) uniton bundle ν(φ) with energy corresponding to the bundles’ second Chern class, which is established by Anand, the energy in a case φ∶S 2→U(N) is investigated in order to estimate the energy of a uniton using the uniton number. It is proved that Uhlenbeck’s factorization is energy decreasing. And a method of estimating the energy of a uniton by the uniton number is given.

An Equivalent Condition for （K） Integrability of Fuzzy-valued Mappings

In this paper, we first discuss the relationship between the McShane integral and Pettis integral for vector-valued functions. Then by using the embedding theorems for the fuzzy number space E^1, we give a new equivalent condition for （K） integrabihty of a fuzzy set-valued mapping F ： [a, b] → E^1.

Variant Map System to Simulate Complex Properties of DNA Interactions Using Binary Sequences

Stream cipher, DNA cryptography and DNA analysis are the most important R&D fields in both Cryptography and Bioinformatics. HC-256 is an emerged scheme as the new generation of stream ciphers for advanced network security. From a random sequencing viewpoint, both sequences of HC-256 and real DNA data may have intrinsic pseudo-random properties respectively. In a recent decade, many DNA sequencing projects are developed on cells, plants and animals over the world into huge DNA databases. Researchers notice that mammalian genomes encode thousands of large noncoding RNAs (lncRNAs), interact with chromatin regulatory complexes, and are thought to play a role in localizing these complexes to target loci across the genome. It is a challenge target using higher dimensional visualization tools to organize various complex interactive properties as visual maps. The Variant Map System (VMS) as an emerging scheme is systematically proposed in this paper to apply multiple maps that used four Meta symbols as same as DNA or RNA representations. System architecture of key components and core mechanism on the VMS are described. Key modules, equations and their I/O parameters are discussed. Applying the VM System, two sets of real DNA sequences from both sample human (noncoding DNA) and corn (coding DNA) genomes are collected in comparison with pseudo DNA sequences generated by HC-256 to show their intrinsic properties in higher levels of similar relationships among relevant DNA sequences on 2D maps. Sample 2D maps are listed and their characteristics are illustrated under controllable environment. Visual results are briefly analyzed to explore their intrinsic properties on selected genome sequences.

QUASIMEROMORPHIC MAPPINGS OF SEVERAL COMPLEX VARIABLES

The definitions of quasimeromorphic mappings from Cn to P1n, where P1 C U {∞}, P1n= P1×P1× ×P1(n-times) are introduced. From an inequality of the value distribution of quasimeromorphic functions of single variable, it follows that a normal criterion for the family of quasimeromorphic functions of several complex variables. Futhermore, a normal criterion for the family of quasimeromorphic mappings from Cn to P1n has been obtained.