In this investigation, maize heterotic groups and patterns were analyzed based on theplanting areas from 1992 to 2001 using 84 parent lines of 71 widely extended hybrids andclassification results by SSR markers, in wh...In this investigation, maize heterotic groups and patterns were analyzed based on theplanting areas from 1992 to 2001 using 84 parent lines of 71 widely extended hybrids andclassification results by SSR markers, in which these lines were assigned into sevenheterotic groups based on Ni-LIs genetic distances. The results indicated that acertain extent change for major heterotic groups of maize took place during past decadein China. The major heterotic groups were Lancaster, Reid, Tang SPT, Zi330 and E28 in theearly 1990s, while they became Reid, Tem-tropicⅠ, Zi330, Tang SPT and Lancaster in theearly 21st century. Tem-tropicⅠwas a new heterotic group, which contained tropic maizegermplasm. The changes for heterotic patterns also occurred. Some new heterotic patternscombining with Tem-tropicⅠappeared, such as ReidTem-tropicⅠ, Zi330Tem-tropicⅠ,Tang SPTTem-tropicⅠ, etc.. Another change was the order of heterotic patterns. In theearly and middle 1990s, the top five heterotic patterns were ReidTang SPT, Zi330Lancaster, LancasterTang SPT, LancasterE28 and ReidZi330, while they became ReidTem-tropicⅠ, ReidZi330, ReidTang SPT, Zi330Tem-tropicⅠand LancasterTang SPT inthe early 21 century. ReidTem-tropicⅠand Zi330Tem-tropicⅠwere laid on the firstand forth Chinese heterotic patterns respectively in 2001. These results providedsignificant information to understand the maize heterotic groups and patterns in Chinaat molecular level.展开更多
Understanding the heterosis in multiple environments between different heterotic groups is of fundamental importance in successful maize breeding. A total of 737 hybrids derived from 41 maize inbreds were evaluated ov...Understanding the heterosis in multiple environments between different heterotic groups is of fundamental importance in successful maize breeding. A total of 737 hybrids derived from 41 maize inbreds were evaluated over two years, with the aim of assessing the genetic diversity and their performance between heterotic groups under drought-stressed(DS) and well-watered(WW) treatments. A total of 38 737 SNPs were employed to assess the genetic diversity. The genetic distance(GD) between the parents ranged from 0.05 to 0.74, and the 41 inbreds were classified into five heterotic groups. According to the hybrid performance(high yield and early maturity between heterotic groups), the heterosis and heterotic patterns of Iowa Stiff Stalk Synthetic(BSSS)×Non-Stiff Stalk(NSS), NSS×Sipingtou(SPT) and BSSS×SPT were identified to be useful options in China’s maize breeding. The relative importance of general and specific combining abilities(GCA and SCA) suggests the importance of the additive genetic effects for grain yield traits under the WW treatment, but the non-additive effects under the DS treatment. At least one of the parental lines with drought tolerance and a high GCA effect would be required to achieve the ideal hybrid performance under drought conditions. GD showed a positive correlation with yield and yield heterosis in within-group hybrids over a certain range of GD. The present investigation suggests that the heterosis is due to the combined accumulation of superior genes/alleles in parents and the optimal genetic distance between parents, and that yield heterosis under DS treatment was mainly determined by the non-additive effects.展开更多
We utilize the topological-geometrical structure imposed by the Heterotic superstring theory on spacetime in conjunction with the K3 Kähler manifold to explain the mysterious nature of dark matter and its cou...We utilize the topological-geometrical structure imposed by the Heterotic superstring theory on spacetime in conjunction with the K3 Kähler manifold to explain the mysterious nature of dark matter and its coupling to the pure dark energy density of the cosmos. The analogous situations in the case of a Kerr black hole as well as the redundant components of the Riemannian tensor are pointed out and the final result was found to be in complete agreement with all previous theoretical ones as well as all recent accurate measurements and cosmic observations. We conclude by commenting briefly on the Cantorian model of Zitterbewegung and the connection between Olbers’s paradox and dark energy.展开更多
Heterotic group theory （HGT） has played a major role in supporting hybrid maize breeding for about 100 years. The basic content and studies of HGT, and its application in rice and maize were summarized in this paper...Heterotic group theory （HGT） has played a major role in supporting hybrid maize breeding for about 100 years. The basic content and studies of HGT, and its application in rice and maize were summarized in this paper. Additionally, difficulties and challenges for hybrid rice breeding in China were analyzed, and necessity and urgency in hybrid rice breeding by using HGT were proposed.展开更多
Utilization of heterosis to develop hybrid cultivars can significantly increase yield of most crops including foxtail millet. However, previous foxtail millet hybrid cultivars have been largely developed from crosses ...Utilization of heterosis to develop hybrid cultivars can significantly increase yield of most crops including foxtail millet. However, previous foxtail millet hybrid cultivars have been largely developed from crosses between sterile lines and conventional varieties or between sterile lines and varieties that are geographically distent from the sterile lines. The research on classification of heterotic classes and determinetaion of heterotic patterns has not been reported, which results in uncertainty in selection of parents for crosses and delays progress in utilization of high yielding hybrids in large-scale commercial production. In this study, a core collection of 128 accessions from China was grouped into six classes using combined analyses of population structure, pedigree, and clustering. The classification was conducted based mainly on molecular clustering of genotypic data, also considered the population structure and mathematical clustering using phenotypic data, and was finally validated through pedigree analysis. According to the transgressive and superstandard heterosis for grain yield, plant height, panicle length, panicle diameter, single panicle weight, grain weight per panicle, and 1000-grain weight collected from an incomplete-diallel-cross experiment, we identified six superior heterosis patterns (C2/C1, C2/C4, C2/C5, C2/C6, C1/C5 and C4/C5) and four inferior heterosis patterns (C1/C3, C1/C4, C1/C6 and C4/C6), and explored their potential applications in millet hybrid breeding. This study laid a foundation for effective use of foxtail millet heterosis in improving millet hybrid yield.展开更多
The Tangshan Sipingtou (TSSPT) germplasm in inbreds of the Tangshan Sipingtou heterotic group of maize in China was mainly derived from Huangzao4, and the source of TSSPT germplasm was severely restricted by the inbre...The Tangshan Sipingtou (TSSPT) germplasm in inbreds of the Tangshan Sipingtou heterotic group of maize in China was mainly derived from Huangzao4, and the source of TSSPT germplasm was severely restricted by the inbred Tangsipingtou. Except Tangsipingtou, the contents of TSSPT germplasm were only 50% or less in inbreds of this group, with the existence of more than 20 non-TSSPT gennplasms which resulted in abundant genetic diversity in this group. 95.22% inbreds of this group contained both TSSPT and UNS(unknown source) gennplasms in the ratio of 1 :1, with 12. 5 - 50% of each germplasm. The recombination of TSSPT and UNS germplasms had produced Huangzao4, the most important maize germplasm of compact plant form. About 90. 24% of the inbreds in this group were the inbred Huangzao4 and its derivatives. 11.11% of the derivatives contained 25 - 50% of Luda Honggu(LDHG) germplasm, and 16.67% of the derivatives contained 12. 5 - 25% Creole and 6. 25 -28.13% LSC germplasms. In addition, 97. 56% of the inbreds of this group contained one or more non-TSSPT germplasms. This indicates that the germplasm base of inbreds of the TSSPT heterotic group had changed and evolved away from actual TSSPT germplasm.展开更多
Lancaster Surecrop (LSC) germplasm in inbreds of the Lancaster heterotic group in China was mainly provided by the two inbreds Mol7 and Oh43. Furthermore, the source of LSC germplasm was severely restricted in two inb...Lancaster Surecrop (LSC) germplasm in inbreds of the Lancaster heterotic group in China was mainly provided by the two inbreds Mol7 and Oh43. Furthermore, the source of LSC germplasm was severely restricted in two inbreds, C103 and Oh40B. The contents of LSC germplasm are 50% or less in inbreds of the group, with the existence of more than 20 non-LSC germplasms that results in the abundant genetic diversity in the group. Most inbreds of Mol7 subgroup contain 25% - 50% LSC, 12.5% - 25% Reid Yellow Dent (RYD) and 12.5%- 25% Iowa Goldmine germplasms in the ratio of 2:1:1, and most inbreds of Zi330 subgroup contain 12.5% - 25% LSC, 6.25% - 12.5% RYD, 6.25% - 12.5% Minnesota # 13 and 25% - 50% Creole germplasms in the ratio of 2:1:1 4. AH the facts indicated that the germplasm base of the Lancaster heterotic group has stupendously changed and evolved away from actual LSC germplasm.展开更多
Heterosis is an important biological phenomenon, and it has been used to increase grain yield, quality and resistance to abiotic and biotic stresses in many crops. However, the genetic mechanism of heterosis remains u...Heterosis is an important biological phenomenon, and it has been used to increase grain yield, quality and resistance to abiotic and biotic stresses in many crops. However, the genetic mechanism of heterosis remains unclear up to now. In this study, a set of 184 chromosome segment substitution lines （CSSLs） population, which derived from two inbred lines Ix9801 （the recurrent parent） and Chang 72 （the donor parent）, were used as basal material to construct two test populations with the inbred lines Zheng 58 and Xun 9058. The two test populations were evaluated in two locations over two years, and the heterotic loci for plant height and ear height were identified by comparing the performance of each test hybrid with the corresponding CK at P〈0.05 significant level using one-way ANOVA analysis and Duncan＇s multiple comparisons. There were 24 and 29 different heterotic loci （HL） identified for plant height and ear height in the two populations at two locations over two years. Three HL （hlPH4a, hlPH7c, hlPHlb） for plant height and three （hlEHld, hlEH6b, hlEHlb） for ear height were identified in the CSSLs×Zheng 58 and CSSLs×Xun 9058 populations as contributing highly to heterosis performance of plant height and ear height across four environments. Among the 29 HL identified for ear height, 12 HL （41.4%） shared the same chromosomal region associated with the HL （50.0%） identified for plant height in the same test population and environment.展开更多
Heterosis contributes greatly to crop production, but the genetic basis of heterosis is not fully understood.To identify heterotic loci(HLs) for grain yield, 12 yield traits were evaluated in four rice(Oryza sativa L....Heterosis contributes greatly to crop production, but the genetic basis of heterosis is not fully understood.To identify heterotic loci(HLs) for grain yield, 12 yield traits were evaluated in four rice(Oryza sativa L.)mapping populations: one parental population of chromosome segment substitution lines derived from a cross between the japonica cultivar Nipponbare and indica cultivar 9311 and three connected test populations in either a homozygous 9311 genetic background or a heterozygous background. A total of 390 HLs were detected for the measured traits in two environments. The genetic bases of heterosis differed between the backcross and testcross populations. At least 10 HLs were confirmed in F1 hybrids between9311 and near-isogenic lines, each of which carried a heterotic locus of interest in the same 9311 background. All 10 showed overdominant or dominant effects on grain yield and yield components. Among them, three were verified as being associated with yield heterosis and colocalized in the same regions as those containing previously reported heterosis-associated genes. Five HLs were identified to be promising candidate loci that could be used to achieve more than 15% yield heterosis in several commercial rice hybrids. These findings suggest the potential of indica or japonica introgression for increasing yield in hybrid rice breeding programs.展开更多
Chinese semi-winter rapeseed,genetically differing from winter and spring rapeseed,has been considered to possess strong potential as parent in winter and spring rapeseed hybrid breeding programs. However,no detailed ...Chinese semi-winter rapeseed,genetically differing from winter and spring rapeseed,has been considered to possess strong potential as parent in winter and spring rapeseed hybrid breeding programs. However,no detailed researches have been documented whether winter and spring rapeseed lines have potential for Chinese semiwinter rapeseed hybrid breeding. The objectives of this study are to estimate the potential of winter and spring rapeseed for semi-winter rapeseed hybrid breeding,and to investigate the association of general combining ability(GCA) with adaptation of parental lines by combining with the data in our previous studies. Four winter and four spring male sterile lines were crossed with 14 Chinese semi-winter rapeseed lines to develop 112 hybrids,which were evaluated together with their parents for seed yield under three environments in China. The exotic parental lines were not adapted to local environment as demonstrated by late flowering,low seed weight and poor seed yield per se. However,the hybrids,especially derived from winter rapeseed exhibited strong heterosis for seed yield,indicating that winter rapeseed germplasm has a great potential for rapeseed hybrid breeding in China. Our data suggested a strong association of GCA with their adaptation ability of parental lines,since high to middle correlations were found for local parental lines and low correlations for exotic parental lines under spring,winter and semi-winter eco-growth environments. The hybrid breeding program using exotic germplasm in rapeseed was discussed.展开更多
We investigate the heterotic super-Liouville model on the base of the basic Lie super-algebra Osp(1|2).Using the super extension of Leznov-Saveliev analysis and Drinfeld Sokolov linear system, we construct the explici...We investigate the heterotic super-Liouville model on the base of the basic Lie super-algebra Osp(1|2).Using the super extension of Leznov-Saveliev analysis and Drinfeld Sokolov linear system, we construct the explicit solution of the heterotic super-Liouville system in component form. We also show that the solutions are local and periodic by calculating the exchange relation of the solution. Finally starting from the action of heterotic super-Liou ville model, we obtain the conserved current and conserved charge which possessed the BR ST properties.展开更多
We studied the characteristics of dry matterproduction and matter partitioning in hybridrice and the relationships of them with heterot-ic effect in 1993. Two popular indica hybrids, Shanyou 63(Zhenshan 97A/Minhui 63 ...We studied the characteristics of dry matterproduction and matter partitioning in hybridrice and the relationships of them with heterot-ic effect in 1993. Two popular indica hybrids, Shanyou 63(Zhenshan 97A/Minhui 63 ) and Teyou 63(Longtepu A/Minhui 63), as well as theircommon restorer line, Minhui 63 (elite cultivar展开更多
Diverse heterotic groups have been developed in China over several decades,but their genomic divergences have not been systematically studied after improvement.In this study,we performed Maize6H-60K array of 5,822 mai...Diverse heterotic groups have been developed in China over several decades,but their genomic divergences have not been systematically studied after improvement.In this study,we performed Maize6H-60K array of 5,822 maize accessions and whole-genome re-sequencing of 150 inbred lines collected in China.Using multiple population structure analysis methods,we established a genetic boundary used to categorize heterotic groups and germplasm resources.We identified three chloroplast–cytoplasmic types that evolved during adaptation to diverse climatic environments in maize through phylogenetic and haplotype analyses.Comparative analyses revealed obvious genetic differences between heterotic groups and germplasm resources at both the chloroplast and nuclear genome levels,especially in the unique heterotic groups HG1 and HG2,which exhibited distinct regionality and genetic uniqueness.The divergent differentiation of heterotic groups from germplasm resources was driven by differential selection in specific genomic regions.Genome-wide selective sweep analysis identified core selected regions and candidate selected genes associated with traits between heterotic groups,highlighting that stress response-and plant defense-related genes were selected for environmental adaptation across a broad latitudinal range in China.Meanwhile,a genome-wide association study analysis provided evidence that core selected genes served as an important candidate gene pool with a potential role in genetic improvement.Gene exchanges among heterotic groups,which avoided the predominant heterotic patterns as much as possible,occurred to achieve population improvement during modern maize breeding.This study provides insights into the population differentiation and genetic characteristics of heterotic groups,which will facilitate the utilization of germplasm resources,the creation of novel maize germplasm,and the optimization of heterotic patterns during future maize breeding in China.展开更多
Understanding the role of heterotic genes in contributing to heterosis is essential for advancing hybrid breeding.We analyzed plant height(PH),ear height(EH),and transcriptomic data from a maize hybrid pop-ulation.Gen...Understanding the role of heterotic genes in contributing to heterosis is essential for advancing hybrid breeding.We analyzed plant height(PH),ear height(EH),and transcriptomic data from a maize hybrid pop-ulation.Genome-wide association studies(GWASs)revealed that dominance effects of quantitative trait loci(QTLs)play a significant role in hybrid traits and mid-parent heterosis.By integrating GWAS,expression GWAS(eGWAS),and module eGWAS analysis,we prioritized six candidate heterotic genes underlying six QTLs,including one QTL that spans the bZIP29 gene.In the hybrid population,bZIP29 exhibits additive expression and dominance effects for both hybrid traits and mid-parent heterosis,with its favorable allele correlating positively with PH and EH.bZIP29 demonstrates dominance or over-dominance patterns in hy-brids derived from crosses between transgenic and wild-type lines,contingent upon its expression.A tsCUT&Tag assay revealed that bZIP29 protein binds directly to a gene regulated by its associated expres-sion QTL(eQTL)and six genes within expression modules governed by its associated module-eQTLs(meQTLs).Regulatory networks involving bZIP29 are more extensive in hybrid subpopulations than in the parental population.This study offers insights into key heterotic genes and networks that underpin the robust growth of hybrid maize.展开更多
The intensification of global warming has led to the continuous outbreak of southern rust(Puccinia polysora Underw.)in major maize-producing regions worldwide.The severe outbreak in the Huang-Huai-Hai summer maize reg...The intensification of global warming has led to the continuous outbreak of southern rust(Puccinia polysora Underw.)in major maize-producing regions worldwide.The severe outbreak in the Huang-Huai-Hai summer maize region of China in 2021 caused yield losses exceeding 50%in some plots,and this disease has been included in the List of Key Crop Pests and Diseases.This paper systematically reviews the molecular resistance mechanisms of maize to southern rust,focusing on the immune mechanisms mediated by NLR family genes and the characteristics of the Bin 10.01 resistance gene cluster;it summarizes the advances in research of molecular breeding technologies such as gene marker development,map-based cloning,and gene editing;combined with the disease characteristics of the spring-sown maize region in Southwest China and the summer-sown maize region in Huang-Huai-Hai,it elaborates on regionally adapted prevention and control strategies;integrating breeding practices of Dunhuang Seed Industry Group(e.g.,Dunyu 810 and Dunyan 616),it proposes a full-chain solution of"precision gene pyramiding-heterotic group utilization-regional promotion".It is expected to provide theoretical and technical references for molecular breeding of maize resistance to southern rust.展开更多
In the present study, a set of chromosome segment introgression lines （CSILs） using Gossypium hirsutum L. TM-1 as the recipient parent and G. barbadense Hai7124 as the donor parent were used to explore the genetic b...In the present study, a set of chromosome segment introgression lines （CSILs） using Gossypium hirsutum L. TM-1 as the recipient parent and G. barbadense Hai7124 as the donor parent were used to explore the genetic basis of heterosis for interspecific hybrids. Two sets of F1 populations individually derived from CSILs crossing with both parents were configured to investigate heterotic loci （HL） and substitution effect loci （SL）. A total of 58 HL and 39 SL were identified in 3 years. One stable HL, hLP-A4-3, could be detected in all 3 years. Three HLs, hBS-A8-1, hLP-D6-1, and hSI-D7-11, could be detected in 2 years. Four SLs, sBSoD7- 1, sLP-A8-1, sLP-D7-1, and sLP-D12-1, could be detected in 2 years. HL and SL tended to be distributed in some HL-rich chromosome segments with close positions. Compared with QTL detected in a former study, HL showed little overlap with QTL, indicating that trait phenotype and heterosis might be controlled by different sets of loci. All three forms of genetic effects （partial-, full-, over-dominant） were identified, while the over-dominant effect made the main contribution to heterosis. These results may help lay the foundation for clarifying the heredity mechanism of heterosis in cotton.展开更多
Winter cabbage is an important crop cultivated through winter in the region near the Yangtze River, enabling the supply of fresh cabbage there at that time of year. However, a problem has emerged regarding the newly d...Winter cabbage is an important crop cultivated through winter in the region near the Yangtze River, enabling the supply of fresh cabbage there at that time of year. However, a problem has emerged regarding the newly developed parents of winter cabbage, which is completely different from spring and autumn cabbage, namely, how to combine these parents to breed an elite hybrid. To classify the heterotic groups and improve the efficiency of parent selection in winter cabbage breeding, 20 polymorphic SSR markers were selected to screen 63 winter cabbage inbred lines. Seventeen pairs among the 20 SSR markers amplified polymorphic bands. These primers amplified two to six bands,with an average of 2.8 bands per primer, and a total of 47 polymorphic bands were generated in the 63 inbred lines. These lines included flatheaded morphotype and round-headed morphotype, thus they were separately classified into heterotic groups based on the SSR markers. The flat-headed morphotype contained 21 inbred lines and was classified into three heterotic groups, named Hanchun 4, Jiali, and Dongsheng, in accordance with the representative germplasm contained in each group. The round-headed morphotype contained 42 inbred lines and was classified into five heterotic groups, named Parte, Bejo1039, YK-143, SCA002, and Golden B90. Meanwhile, parent analysis of 20 developed elite combinations showed that their parents were all distributed in different heterotic groups, indicating that the group classification was reasonable,which can provide a basis for further parent selection in winter cabbage breeding. Furthermore, polymorphic SSR primers were successfully used to identify the hybrid purity of three elite varieties.展开更多
Genetic similarities of 13 inbred lines of maize (Zea mays L.) were analyzed by restriction fragment length polymorphisms (RFLPs). The objectives of the study were to detect genetic similarities among 13 inbreds and t...Genetic similarities of 13 inbred lines of maize (Zea mays L.) were analyzed by restriction fragment length polymorphisms (RFLPs). The objectives of the study were to detect genetic similarities among 13 inbreds and to assign them to heterotic groups. By means of 24 probe_enzyme combinations (PECs) selected for locus specificity, clear patterns and reproducibility, 85 alleles were found with an average of 3.3 alleles per locus. The allelic frequency data were used to estimate genetic similarities among lines, and as a result the diversity index of 0.499 was obtained. Genetic similarities between the pairs of 13 lines ranged from 0.523 up to 0.802 with an average of 0.649. The UPGMA clustering algorithm analysis classified the 13 lines into five groups, which generally corresponded to known maize heterotic groups based on pedigree information. The authors concluded that RFLP_based markers could be used for investigating genetic relationships between maize inbred lines and assigning them to heterotic groups, but it seemed that a large number of PECs were needed to obtain reliable estimates of genetic similarity.展开更多
The classification of heterotic groups is essential to maize breeding because knowledge of heterotic groups could be interest to both the combination of outstanding hybrids and the improvement of elite inbred lines. R...The classification of heterotic groups is essential to maize breeding because knowledge of heterotic groups could be interest to both the combination of outstanding hybrids and the improvement of elite inbred lines. RFLP has provided a powerful tool to assign maize inbred lines into heterotic groups. In this investigation, 45 inbred lines, used widely in south and southwest China, were chosen for RFLP analysis, among which 4 lines came from American, representing different heterotic groups in U.S. corn belt. 54 RFLP core markers covering 10 chromosomes of maize were used. A total DNA of each sample was digested with EcoR I, BamH I and Hind 1. The procedure of RFLP was employed as described by a manual from maize RFLP lab at University of Missouri, Columbia. A total of 860 bands were detected among 45 inbred lines based on RFLP analysis, which were involved in 212 loci. Alleles at each locus ranged from 2 to 9 with an average of 4.06. In total, The 45 inbred lines were classified into 6 heterotic groups according to RFLP data with Ward's method. 3 heterotic groups, including Mol7, B73 and Oh43 respectively, seemed to be the same to U. S. heterotic groups. 21 inbred lines, most of which derived from Chinese local germplasm, were classified together into two heterotic groups, indicating domistic germplasm was different from U. S. germplasm at the molecular level and played an important role in maize hybrid production in China. Two inbred lines from tropic germplasm were assigned in the same group. These results provided useful information for our understanding maize heterotic groups and heterotic patterns in China.展开更多
The present paper is basically a synthesis resulting from incorporating Kerr spinning black hole geometry into E-infinity topology, then letting the result bares on the vacuum zero point Casimir effect as well as the ...The present paper is basically a synthesis resulting from incorporating Kerr spinning black hole geometry into E-infinity topology, then letting the result bares on the vacuum zero point Casimir effect as well as the cosmic dark energy and dark matter density. In E-infinity theory a quantum particle is represented by a Hausdorff dimension Φ where Φ =2/(√5+1) . The quantum wave on the other hand is represented by Φ2 . To be wave and a particle simultaneously intersection theory leads us to?(Φ) (Φ)2= Φ3 which will be shown here to be twice the value of the famous Casimir force of the vacuum for a massless scalar field. Thus in the present work a basically topological interpretation of the Casimir effect is given as a natural intrinsic property of the geometrical topological structure of the quantum-Cantorian micro spacetime. This new interpretation compliments the earlier conventional interpretation as vacuum fluctuation or as a Schwinger source and links the Casimir energy to the so called missing dark energy density of the cosmos. From the view point of the present work Casimir pressure is a local effect acting on the Casimir plates constituting the local boundary condition while dark energy is nothing but the global combined effect of infinitely many quantum waves acting on the Möbius-like boundary of the holographic boundary of the entire universe. Since this higher dimensional Möbius-like boundary is one sided, there is no outside to balance the internal collective Casimir pressure which then manifests itself as the force behind cosmic expansion, that is to say, dark energy. Thus analogous to the exact irrational value of ordinary energy density of spacetime E(O)=(Φ5/2) mc2 we now have P (Casimir) = (Φ3/2)(ch/d2) where c is the speed of light, m is the mass, h is the Planck constant and d is the plate separation. In addition the new emerging geometry combined with the topology of E-infinity theory leads directly to identifying dark matter with the quasi matter of the ergosphere. As a direct consequence of this new insight E=mc2 which can be written as E = E (O) + E (D)?where the exact rational approximation is E (O)=mc2/22 is?the ordinary energy density of the cosmos and the exact rational approximation E (D)=mc2/(21/22) is the corresponding dark energy which could be subdivided once more albeit truly approximately into E(D)=mc2/(5/22)?+mc2/(16/22)??where 5 is the Kaluza Klein spacetime dimension, 16 are the bosonic extra dimensions of Heterotic superstrings and 5/22 □?22% is approximately the density of the dark matter-like energy of the ergosphere of the Kerr geometry. As for the actual design of our nano reactor, this is closely related to branching clusters of polymer, frequently called lattice animals. In other words we will have Casimir spheres instead of Casimir plates and these spheres will be basically nano particles modelling lattice animals. Here D=?4 will be regarded as spacetime dimensionality while D=6 of percolations are the compactified super string dimensions and D=8 is the dimension of a corresponding super space.展开更多
基金This work was supported by the National Basic Research Project(2001CB108801)Modern Agricultural Project in National 863 Pragram,China.
文摘In this investigation, maize heterotic groups and patterns were analyzed based on theplanting areas from 1992 to 2001 using 84 parent lines of 71 widely extended hybrids andclassification results by SSR markers, in which these lines were assigned into sevenheterotic groups based on Ni-LIs genetic distances. The results indicated that acertain extent change for major heterotic groups of maize took place during past decadein China. The major heterotic groups were Lancaster, Reid, Tang SPT, Zi330 and E28 in theearly 1990s, while they became Reid, Tem-tropicⅠ, Zi330, Tang SPT and Lancaster in theearly 21st century. Tem-tropicⅠwas a new heterotic group, which contained tropic maizegermplasm. The changes for heterotic patterns also occurred. Some new heterotic patternscombining with Tem-tropicⅠappeared, such as ReidTem-tropicⅠ, Zi330Tem-tropicⅠ,Tang SPTTem-tropicⅠ, etc.. Another change was the order of heterotic patterns. In theearly and middle 1990s, the top five heterotic patterns were ReidTang SPT, Zi330Lancaster, LancasterTang SPT, LancasterE28 and ReidZi330, while they became ReidTem-tropicⅠ, ReidZi330, ReidTang SPT, Zi330Tem-tropicⅠand LancasterTang SPT inthe early 21 century. ReidTem-tropicⅠand Zi330Tem-tropicⅠwere laid on the firstand forth Chinese heterotic patterns respectively in 2001. These results providedsignificant information to understand the maize heterotic groups and patterns in Chinaat molecular level.
基金supported by the National Natural Science Foundation of China(31760424)the Scientific and Technological Project of Xinjiang Production and Construction Corps of China(2019AB021)。
文摘Understanding the heterosis in multiple environments between different heterotic groups is of fundamental importance in successful maize breeding. A total of 737 hybrids derived from 41 maize inbreds were evaluated over two years, with the aim of assessing the genetic diversity and their performance between heterotic groups under drought-stressed(DS) and well-watered(WW) treatments. A total of 38 737 SNPs were employed to assess the genetic diversity. The genetic distance(GD) between the parents ranged from 0.05 to 0.74, and the 41 inbreds were classified into five heterotic groups. According to the hybrid performance(high yield and early maturity between heterotic groups), the heterosis and heterotic patterns of Iowa Stiff Stalk Synthetic(BSSS)×Non-Stiff Stalk(NSS), NSS×Sipingtou(SPT) and BSSS×SPT were identified to be useful options in China’s maize breeding. The relative importance of general and specific combining abilities(GCA and SCA) suggests the importance of the additive genetic effects for grain yield traits under the WW treatment, but the non-additive effects under the DS treatment. At least one of the parental lines with drought tolerance and a high GCA effect would be required to achieve the ideal hybrid performance under drought conditions. GD showed a positive correlation with yield and yield heterosis in within-group hybrids over a certain range of GD. The present investigation suggests that the heterosis is due to the combined accumulation of superior genes/alleles in parents and the optimal genetic distance between parents, and that yield heterosis under DS treatment was mainly determined by the non-additive effects.
文摘We utilize the topological-geometrical structure imposed by the Heterotic superstring theory on spacetime in conjunction with the K3 Kähler manifold to explain the mysterious nature of dark matter and its coupling to the pure dark energy density of the cosmos. The analogous situations in the case of a Kerr black hole as well as the redundant components of the Riemannian tensor are pointed out and the final result was found to be in complete agreement with all previous theoretical ones as well as all recent accurate measurements and cosmic observations. We conclude by commenting briefly on the Cantorian model of Zitterbewegung and the connection between Olbers’s paradox and dark energy.
基金supported by the grant from the program of Introducing Talents of Discipline to University of China(Grant No.B08025)
文摘Heterotic group theory （HGT） has played a major role in supporting hybrid maize breeding for about 100 years. The basic content and studies of HGT, and its application in rice and maize were summarized in this paper. Additionally, difficulties and challenges for hybrid rice breeding in China were analyzed, and necessity and urgency in hybrid rice breeding by using HGT were proposed.
文摘Utilization of heterosis to develop hybrid cultivars can significantly increase yield of most crops including foxtail millet. However, previous foxtail millet hybrid cultivars have been largely developed from crosses between sterile lines and conventional varieties or between sterile lines and varieties that are geographically distent from the sterile lines. The research on classification of heterotic classes and determinetaion of heterotic patterns has not been reported, which results in uncertainty in selection of parents for crosses and delays progress in utilization of high yielding hybrids in large-scale commercial production. In this study, a core collection of 128 accessions from China was grouped into six classes using combined analyses of population structure, pedigree, and clustering. The classification was conducted based mainly on molecular clustering of genotypic data, also considered the population structure and mathematical clustering using phenotypic data, and was finally validated through pedigree analysis. According to the transgressive and superstandard heterosis for grain yield, plant height, panicle length, panicle diameter, single panicle weight, grain weight per panicle, and 1000-grain weight collected from an incomplete-diallel-cross experiment, we identified six superior heterosis patterns (C2/C1, C2/C4, C2/C5, C2/C6, C1/C5 and C4/C5) and four inferior heterosis patterns (C1/C3, C1/C4, C1/C6 and C4/C6), and explored their potential applications in millet hybrid breeding. This study laid a foundation for effective use of foxtail millet heterosis in improving millet hybrid yield.
文摘The Tangshan Sipingtou (TSSPT) germplasm in inbreds of the Tangshan Sipingtou heterotic group of maize in China was mainly derived from Huangzao4, and the source of TSSPT germplasm was severely restricted by the inbred Tangsipingtou. Except Tangsipingtou, the contents of TSSPT germplasm were only 50% or less in inbreds of this group, with the existence of more than 20 non-TSSPT gennplasms which resulted in abundant genetic diversity in this group. 95.22% inbreds of this group contained both TSSPT and UNS(unknown source) gennplasms in the ratio of 1 :1, with 12. 5 - 50% of each germplasm. The recombination of TSSPT and UNS germplasms had produced Huangzao4, the most important maize germplasm of compact plant form. About 90. 24% of the inbreds in this group were the inbred Huangzao4 and its derivatives. 11.11% of the derivatives contained 25 - 50% of Luda Honggu(LDHG) germplasm, and 16.67% of the derivatives contained 12. 5 - 25% Creole and 6. 25 -28.13% LSC germplasms. In addition, 97. 56% of the inbreds of this group contained one or more non-TSSPT germplasms. This indicates that the germplasm base of inbreds of the TSSPT heterotic group had changed and evolved away from actual TSSPT germplasm.
文摘Lancaster Surecrop (LSC) germplasm in inbreds of the Lancaster heterotic group in China was mainly provided by the two inbreds Mol7 and Oh43. Furthermore, the source of LSC germplasm was severely restricted in two inbreds, C103 and Oh40B. The contents of LSC germplasm are 50% or less in inbreds of the group, with the existence of more than 20 non-LSC germplasms that results in the abundant genetic diversity in the group. Most inbreds of Mol7 subgroup contain 25% - 50% LSC, 12.5% - 25% Reid Yellow Dent (RYD) and 12.5%- 25% Iowa Goldmine germplasms in the ratio of 2:1:1, and most inbreds of Zi330 subgroup contain 12.5% - 25% LSC, 6.25% - 12.5% RYD, 6.25% - 12.5% Minnesota # 13 and 25% - 50% Creole germplasms in the ratio of 2:1:1 4. AH the facts indicated that the germplasm base of the Lancaster heterotic group has stupendously changed and evolved away from actual LSC germplasm.
基金supported by the National Basic Research Program of China (2014CB138203)the National Natural Science Foundation of China (31271732)
文摘Heterosis is an important biological phenomenon, and it has been used to increase grain yield, quality and resistance to abiotic and biotic stresses in many crops. However, the genetic mechanism of heterosis remains unclear up to now. In this study, a set of 184 chromosome segment substitution lines （CSSLs） population, which derived from two inbred lines Ix9801 （the recurrent parent） and Chang 72 （the donor parent）, were used as basal material to construct two test populations with the inbred lines Zheng 58 and Xun 9058. The two test populations were evaluated in two locations over two years, and the heterotic loci for plant height and ear height were identified by comparing the performance of each test hybrid with the corresponding CK at P〈0.05 significant level using one-way ANOVA analysis and Duncan＇s multiple comparisons. There were 24 and 29 different heterotic loci （HL） identified for plant height and ear height in the two populations at two locations over two years. Three HL （hlPH4a, hlPH7c, hlPHlb） for plant height and three （hlEHld, hlEH6b, hlEHlb） for ear height were identified in the CSSLs×Zheng 58 and CSSLs×Xun 9058 populations as contributing highly to heterosis performance of plant height and ear height across four environments. Among the 29 HL identified for ear height, 12 HL （41.4%） shared the same chromosomal region associated with the HL （50.0%） identified for plant height in the same test population and environment.
基金supported by the Fundamental Research Funds for the Central Universities(2662018YJ025)National Natural Science Foundation of China(31971864)+1 种基金National High Technology Research and Development Program of China(2014AA10A604)the Major Project of Science and Technology of Hubei(2019ABA104,2020ABA016)。
文摘Heterosis contributes greatly to crop production, but the genetic basis of heterosis is not fully understood.To identify heterotic loci(HLs) for grain yield, 12 yield traits were evaluated in four rice(Oryza sativa L.)mapping populations: one parental population of chromosome segment substitution lines derived from a cross between the japonica cultivar Nipponbare and indica cultivar 9311 and three connected test populations in either a homozygous 9311 genetic background or a heterozygous background. A total of 390 HLs were detected for the measured traits in two environments. The genetic bases of heterosis differed between the backcross and testcross populations. At least 10 HLs were confirmed in F1 hybrids between9311 and near-isogenic lines, each of which carried a heterotic locus of interest in the same 9311 background. All 10 showed overdominant or dominant effects on grain yield and yield components. Among them, three were verified as being associated with yield heterosis and colocalized in the same regions as those containing previously reported heterosis-associated genes. Five HLs were identified to be promising candidate loci that could be used to achieve more than 15% yield heterosis in several commercial rice hybrids. These findings suggest the potential of indica or japonica introgression for increasing yield in hybrid rice breeding programs.
基金Forschungs-und Entwicklungsfonds RapsGrants from the Fundamental Research Funds for the Central Universities to Qian wei+1 种基金National Natural Science Foundation of China(No.31171585)Chongqing Science&Technology Commission(No.201180001)
文摘Chinese semi-winter rapeseed,genetically differing from winter and spring rapeseed,has been considered to possess strong potential as parent in winter and spring rapeseed hybrid breeding programs. However,no detailed researches have been documented whether winter and spring rapeseed lines have potential for Chinese semiwinter rapeseed hybrid breeding. The objectives of this study are to estimate the potential of winter and spring rapeseed for semi-winter rapeseed hybrid breeding,and to investigate the association of general combining ability(GCA) with adaptation of parental lines by combining with the data in our previous studies. Four winter and four spring male sterile lines were crossed with 14 Chinese semi-winter rapeseed lines to develop 112 hybrids,which were evaluated together with their parents for seed yield under three environments in China. The exotic parental lines were not adapted to local environment as demonstrated by late flowering,low seed weight and poor seed yield per se. However,the hybrids,especially derived from winter rapeseed exhibited strong heterosis for seed yield,indicating that winter rapeseed germplasm has a great potential for rapeseed hybrid breeding in China. Our data suggested a strong association of GCA with their adaptation ability of parental lines,since high to middle correlations were found for local parental lines and low correlations for exotic parental lines under spring,winter and semi-winter eco-growth environments. The hybrid breeding program using exotic germplasm in rapeseed was discussed.
文摘We investigate the heterotic super-Liouville model on the base of the basic Lie super-algebra Osp(1|2).Using the super extension of Leznov-Saveliev analysis and Drinfeld Sokolov linear system, we construct the explicit solution of the heterotic super-Liouville system in component form. We also show that the solutions are local and periodic by calculating the exchange relation of the solution. Finally starting from the action of heterotic super-Liou ville model, we obtain the conserved current and conserved charge which possessed the BR ST properties.
文摘We studied the characteristics of dry matterproduction and matter partitioning in hybridrice and the relationships of them with heterot-ic effect in 1993. Two popular indica hybrids, Shanyou 63(Zhenshan 97A/Minhui 63 ) and Teyou 63(Longtepu A/Minhui 63), as well as theircommon restorer line, Minhui 63 (elite cultivar
基金funded by the Biological Breeding-National Science and Technology Major Project(2022ZD04017)the Construction and Scientific and Technological Innovation Capacity of Beijing Academy of Agriculture and Forestry Sciences(No.KJCX20230301)National Innovation Center forDigital Seed Industry。
文摘Diverse heterotic groups have been developed in China over several decades,but their genomic divergences have not been systematically studied after improvement.In this study,we performed Maize6H-60K array of 5,822 maize accessions and whole-genome re-sequencing of 150 inbred lines collected in China.Using multiple population structure analysis methods,we established a genetic boundary used to categorize heterotic groups and germplasm resources.We identified three chloroplast–cytoplasmic types that evolved during adaptation to diverse climatic environments in maize through phylogenetic and haplotype analyses.Comparative analyses revealed obvious genetic differences between heterotic groups and germplasm resources at both the chloroplast and nuclear genome levels,especially in the unique heterotic groups HG1 and HG2,which exhibited distinct regionality and genetic uniqueness.The divergent differentiation of heterotic groups from germplasm resources was driven by differential selection in specific genomic regions.Genome-wide selective sweep analysis identified core selected regions and candidate selected genes associated with traits between heterotic groups,highlighting that stress response-and plant defense-related genes were selected for environmental adaptation across a broad latitudinal range in China.Meanwhile,a genome-wide association study analysis provided evidence that core selected genes served as an important candidate gene pool with a potential role in genetic improvement.Gene exchanges among heterotic groups,which avoided the predominant heterotic patterns as much as possible,occurred to achieve population improvement during modern maize breeding.This study provides insights into the population differentiation and genetic characteristics of heterotic groups,which will facilitate the utilization of germplasm resources,the creation of novel maize germplasm,and the optimization of heterotic patterns during future maize breeding in China.
基金supported by the National Key R&D Program of China(2023YFF1000400)the Biological Breeding-National Science and Technology Major Project(2023ZD04076)+1 种基金the China Agriculture Research System of Maize(CARS-02-13)the Innovation Program of the Chinese Academy of Agricultural Sciences.
文摘Understanding the role of heterotic genes in contributing to heterosis is essential for advancing hybrid breeding.We analyzed plant height(PH),ear height(EH),and transcriptomic data from a maize hybrid pop-ulation.Genome-wide association studies(GWASs)revealed that dominance effects of quantitative trait loci(QTLs)play a significant role in hybrid traits and mid-parent heterosis.By integrating GWAS,expression GWAS(eGWAS),and module eGWAS analysis,we prioritized six candidate heterotic genes underlying six QTLs,including one QTL that spans the bZIP29 gene.In the hybrid population,bZIP29 exhibits additive expression and dominance effects for both hybrid traits and mid-parent heterosis,with its favorable allele correlating positively with PH and EH.bZIP29 demonstrates dominance or over-dominance patterns in hy-brids derived from crosses between transgenic and wild-type lines,contingent upon its expression.A tsCUT&Tag assay revealed that bZIP29 protein binds directly to a gene regulated by its associated expres-sion QTL(eQTL)and six genes within expression modules governed by its associated module-eQTLs(meQTLs).Regulatory networks involving bZIP29 are more extensive in hybrid subpopulations than in the parental population.This study offers insights into key heterotic genes and networks that underpin the robust growth of hybrid maize.
基金Supported by Central Government Funds for Guiding Local Scientific and Technological Development(24ZYQF002)Major Science and Technology Project of Gansu Province(24ZDNF001)+1 种基金National Key R&D Program"Exploration and Utilization of Disease-and Pest-Resistant and High-Yield Gene Resources in Maize"(2022YDF1201800)Key Laboratory of Mechanized Maize Variety Creation,Ministry of Agriculture and Rural Affairs.
文摘The intensification of global warming has led to the continuous outbreak of southern rust(Puccinia polysora Underw.)in major maize-producing regions worldwide.The severe outbreak in the Huang-Huai-Hai summer maize region of China in 2021 caused yield losses exceeding 50%in some plots,and this disease has been included in the List of Key Crop Pests and Diseases.This paper systematically reviews the molecular resistance mechanisms of maize to southern rust,focusing on the immune mechanisms mediated by NLR family genes and the characteristics of the Bin 10.01 resistance gene cluster;it summarizes the advances in research of molecular breeding technologies such as gene marker development,map-based cloning,and gene editing;combined with the disease characteristics of the spring-sown maize region in Southwest China and the summer-sown maize region in Huang-Huai-Hai,it elaborates on regionally adapted prevention and control strategies;integrating breeding practices of Dunhuang Seed Industry Group(e.g.,Dunyu 810 and Dunyan 616),it proposes a full-chain solution of"precision gene pyramiding-heterotic group utilization-regional promotion".It is expected to provide theoretical and technical references for molecular breeding of maize resistance to southern rust.
基金supported by grants from the Shandong Province System of Modern Agriculture Industrial Technology(Cotton industry)the Science and Technology Development Project of Shandong Province (2012GGB01026)the Shandong Agricultural Breeding Project(2010LZ005-01)
文摘In the present study, a set of chromosome segment introgression lines （CSILs） using Gossypium hirsutum L. TM-1 as the recipient parent and G. barbadense Hai7124 as the donor parent were used to explore the genetic basis of heterosis for interspecific hybrids. Two sets of F1 populations individually derived from CSILs crossing with both parents were configured to investigate heterotic loci （HL） and substitution effect loci （SL）. A total of 58 HL and 39 SL were identified in 3 years. One stable HL, hLP-A4-3, could be detected in all 3 years. Three HLs, hBS-A8-1, hLP-D6-1, and hSI-D7-11, could be detected in 2 years. Four SLs, sBSoD7- 1, sLP-A8-1, sLP-D7-1, and sLP-D12-1, could be detected in 2 years. HL and SL tended to be distributed in some HL-rich chromosome segments with close positions. Compared with QTL detected in a former study, HL showed little overlap with QTL, indicating that trait phenotype and heterosis might be controlled by different sets of loci. All three forms of genetic effects （partial-, full-, over-dominant） were identified, while the over-dominant effect made the main contribution to heterosis. These results may help lay the foundation for clarifying the heredity mechanism of heterosis in cotton.
基金supported by grants from the Major State Research Development Program (2016YFD0101702)the Science and Technology Innovation Program of Chinese Academy of Agricultural Sciences (CAAS-ASTIP-IVFCAAS)the earmarked fund for the Modern Agro-Industry Technology Research System, China (nycytx-35-gw01)
文摘Winter cabbage is an important crop cultivated through winter in the region near the Yangtze River, enabling the supply of fresh cabbage there at that time of year. However, a problem has emerged regarding the newly developed parents of winter cabbage, which is completely different from spring and autumn cabbage, namely, how to combine these parents to breed an elite hybrid. To classify the heterotic groups and improve the efficiency of parent selection in winter cabbage breeding, 20 polymorphic SSR markers were selected to screen 63 winter cabbage inbred lines. Seventeen pairs among the 20 SSR markers amplified polymorphic bands. These primers amplified two to six bands,with an average of 2.8 bands per primer, and a total of 47 polymorphic bands were generated in the 63 inbred lines. These lines included flatheaded morphotype and round-headed morphotype, thus they were separately classified into heterotic groups based on the SSR markers. The flat-headed morphotype contained 21 inbred lines and was classified into three heterotic groups, named Hanchun 4, Jiali, and Dongsheng, in accordance with the representative germplasm contained in each group. The round-headed morphotype contained 42 inbred lines and was classified into five heterotic groups, named Parte, Bejo1039, YK-143, SCA002, and Golden B90. Meanwhile, parent analysis of 20 developed elite combinations showed that their parents were all distributed in different heterotic groups, indicating that the group classification was reasonable,which can provide a basis for further parent selection in winter cabbage breeding. Furthermore, polymorphic SSR primers were successfully used to identify the hybrid purity of three elite varieties.
文摘Genetic similarities of 13 inbred lines of maize (Zea mays L.) were analyzed by restriction fragment length polymorphisms (RFLPs). The objectives of the study were to detect genetic similarities among 13 inbreds and to assign them to heterotic groups. By means of 24 probe_enzyme combinations (PECs) selected for locus specificity, clear patterns and reproducibility, 85 alleles were found with an average of 3.3 alleles per locus. The allelic frequency data were used to estimate genetic similarities among lines, and as a result the diversity index of 0.499 was obtained. Genetic similarities between the pairs of 13 lines ranged from 0.523 up to 0.802 with an average of 0.649. The UPGMA clustering algorithm analysis classified the 13 lines into five groups, which generally corresponded to known maize heterotic groups based on pedigree information. The authors concluded that RFLP_based markers could be used for investigating genetic relationships between maize inbred lines and assigning them to heterotic groups, but it seemed that a large number of PECs were needed to obtain reliable estimates of genetic similarity.
基金the National Nature Science Foundation ( No. 39893350 ).
文摘The classification of heterotic groups is essential to maize breeding because knowledge of heterotic groups could be interest to both the combination of outstanding hybrids and the improvement of elite inbred lines. RFLP has provided a powerful tool to assign maize inbred lines into heterotic groups. In this investigation, 45 inbred lines, used widely in south and southwest China, were chosen for RFLP analysis, among which 4 lines came from American, representing different heterotic groups in U.S. corn belt. 54 RFLP core markers covering 10 chromosomes of maize were used. A total DNA of each sample was digested with EcoR I, BamH I and Hind 1. The procedure of RFLP was employed as described by a manual from maize RFLP lab at University of Missouri, Columbia. A total of 860 bands were detected among 45 inbred lines based on RFLP analysis, which were involved in 212 loci. Alleles at each locus ranged from 2 to 9 with an average of 4.06. In total, The 45 inbred lines were classified into 6 heterotic groups according to RFLP data with Ward's method. 3 heterotic groups, including Mol7, B73 and Oh43 respectively, seemed to be the same to U. S. heterotic groups. 21 inbred lines, most of which derived from Chinese local germplasm, were classified together into two heterotic groups, indicating domistic germplasm was different from U. S. germplasm at the molecular level and played an important role in maize hybrid production in China. Two inbred lines from tropic germplasm were assigned in the same group. These results provided useful information for our understanding maize heterotic groups and heterotic patterns in China.
文摘The present paper is basically a synthesis resulting from incorporating Kerr spinning black hole geometry into E-infinity topology, then letting the result bares on the vacuum zero point Casimir effect as well as the cosmic dark energy and dark matter density. In E-infinity theory a quantum particle is represented by a Hausdorff dimension Φ where Φ =2/(√5+1) . The quantum wave on the other hand is represented by Φ2 . To be wave and a particle simultaneously intersection theory leads us to?(Φ) (Φ)2= Φ3 which will be shown here to be twice the value of the famous Casimir force of the vacuum for a massless scalar field. Thus in the present work a basically topological interpretation of the Casimir effect is given as a natural intrinsic property of the geometrical topological structure of the quantum-Cantorian micro spacetime. This new interpretation compliments the earlier conventional interpretation as vacuum fluctuation or as a Schwinger source and links the Casimir energy to the so called missing dark energy density of the cosmos. From the view point of the present work Casimir pressure is a local effect acting on the Casimir plates constituting the local boundary condition while dark energy is nothing but the global combined effect of infinitely many quantum waves acting on the Möbius-like boundary of the holographic boundary of the entire universe. Since this higher dimensional Möbius-like boundary is one sided, there is no outside to balance the internal collective Casimir pressure which then manifests itself as the force behind cosmic expansion, that is to say, dark energy. Thus analogous to the exact irrational value of ordinary energy density of spacetime E(O)=(Φ5/2) mc2 we now have P (Casimir) = (Φ3/2)(ch/d2) where c is the speed of light, m is the mass, h is the Planck constant and d is the plate separation. In addition the new emerging geometry combined with the topology of E-infinity theory leads directly to identifying dark matter with the quasi matter of the ergosphere. As a direct consequence of this new insight E=mc2 which can be written as E = E (O) + E (D)?where the exact rational approximation is E (O)=mc2/22 is?the ordinary energy density of the cosmos and the exact rational approximation E (D)=mc2/(21/22) is the corresponding dark energy which could be subdivided once more albeit truly approximately into E(D)=mc2/(5/22)?+mc2/(16/22)??where 5 is the Kaluza Klein spacetime dimension, 16 are the bosonic extra dimensions of Heterotic superstrings and 5/22 □?22% is approximately the density of the dark matter-like energy of the ergosphere of the Kerr geometry. As for the actual design of our nano reactor, this is closely related to branching clusters of polymer, frequently called lattice animals. In other words we will have Casimir spheres instead of Casimir plates and these spheres will be basically nano particles modelling lattice animals. Here D=?4 will be regarded as spacetime dimensionality while D=6 of percolations are the compactified super string dimensions and D=8 is the dimension of a corresponding super space.
