Counting and effective rigidity in algebra and geometry

The purpose of this article is to produce effective versions of some rigidity results in algebra and geometry. On the geometric side, we focus on the spectrum of primitive geodesic lengths (resp., complex lengths) for arithmetic hyperbolic 2-manifolds (resp., 3-manifolds). By work of Reid, this spectrum determines the commensurability class of the 2-manifold (resp., 3-manifold). We establish effective versions of these rigidity results by ensuring that, for two incommensurable arithmetic manifolds of bounded volume, the length sets (resp., the complex length sets) must disagree for a length that can be explicitly bounded as a function of volume. We also prove an effective version of a similar rigidity result established by the second author with Reid on a surface analog of the length spectrum for hyperbolic 3-manifolds. These effective results have corresponding algebraic analogs involving maximal subfields and quaternion subalgebras of quaternion algebras. To prove these effective rigidity results, we establish results on the asymptotic behavior of certain algebraic and geometric counting functions which are of independent interest.Comment: v.2, 39 pages. To appear in Invent. Mat

La comunicazione interculturale e l’approccio comunicativo: dall’idea allo strumento

il saggio si inserisce in un filone di ricerca aperto nel 199 e proseguito con saggi e volumi: in questo caso di descrive e discute la progettazione di un passo fondamentale, dall'elaborazione teorica del modello di riferimento alla traduzione di tale modello in strumento operativo per la consultazione e la didattica

Mixed model association scans of multi-environmental trial data reveal major loci controlling yield and yield related traits in Hordeum vulgare in Mediterranean environments

An association panel consisting of 185 accessions representative of the barley germplasm cultivated in the Mediterranean basin was used to localise quantitative trait loci (QTL) controlling grain yield and yield related traits. The germplasm set was genotyped with 1,536 SNP markers and tested for associations with phenotypic data gathered over 2 years for a total of 24 year × location combinations under a broad range of environmental conditions. Analysis of multi-environmental trial (MET) data by fitting a mixed model with kinship estimates detected from two to seven QTL for the major components of yield including 1000 kernel weight, grains per spike and spikes per m2, as well as heading date, harvest index and plant height. Several of the associations involved SNPs tightly linked to known major genes determining spike morphology in barley (vrs1 and int-c). Similarly, the largest QTL for heading date co-locates with SNPs linked with eam6, a major locus for heading date in barley for autumn sown conditions. Co-localization of several QTL related to yield components traits suggest that major developmental loci may be linked to most of the associations. This study highlights the potential of association genetics to identify genetic variants controlling complex traits

Quantitative and Qualitative Stem Rust Resistance Factors in Barley Are Associated with Transcriptional Suppression of Defense Regulons

Stem rust (Puccinia graminis f. sp. tritici; Pgt) is a devastating fungal disease of wheat and barley. Pgt race TTKSK (isolate Ug99) is a serious threat to these Triticeae grain crops because resistance is rare. In barley, the complex Rpg-TTKSK locus on chromosome 5H is presently the only known source of qualitative resistance to this aggressive Pgt race. Segregation for resistance observed on seedlings of the Q21861 × SM89010 (QSM) doubled-haploid (DH) population was found to be predominantly qualitative, with little of the remaining variance explained by loci other than Rpg-TTKSK. In contrast, analysis of adult QSM DH plants infected by field inoculum of Pgt race TTKSK in Njoro, Kenya, revealed several additional quantitative trait loci that contribute to resistance. To molecularly characterize these loci, Barley1 GeneChips were used to measure the expression of 22,792 genes in the QSM population after inoculation with Pgt race TTKSK or mock-inoculation. Comparison of expression Quantitative Trait Loci (eQTL) between treatments revealed an inoculation-dependent expression polymorphism implicating Actin depolymerizing factor3 (within the Rpg-TTKSK locus) as a candidate susceptibility gene. In parallel, we identified a chromosome 2H trans-eQTL hotspot that co-segregates with an enhancer of Rpg-TTKSK-mediated, adult plant resistance discovered through the Njoro field trials. Our genome-wide eQTL studies demonstrate that transcript accumulation of 25% of barley genes is altered following challenge by Pgt race TTKSK, but that few of these genes are regulated by the qualitative Rpg-TTKSK on chromosome 5H. It is instead the chromosome 2H trans-eQTL hotspot that orchestrates the largest inoculation-specific responses, where enhanced resistance is associated with transcriptional suppression of hundreds of genes scattered throughout the genome. Hence, the present study associates the early suppression of genes expressed in this host–pathogen interaction with enhancement of R-gene mediated resistance

Combining genetical genomics and bulked segregant analysis-based differential expression: an approach to gene localization

Positional gene isolation in unsequenced species generally requires either a reference genome sequence or an inference of gene content based on conservation of synteny with a genomic model. In the large unsequenced genomes of the Triticeae cereals the latter, i.e. conservation of synteny with the rice and Brachypodium genomes, provides a powerful proxy for establishing local gene content and order. However, efficient exploitation of conservation of synteny requires ‘homology bridges’ between the model genome and the target region that contains a gene of interest. As effective homology bridges are generally the sequences of genetically mapped genes, increasing the density of these genes around a target locus is an important step in the process. We used bulked segregant analysis (BSA) of transcript abundance data to identify genes located in a specific region of the barley genome. The approach is valuable because only a relatively small proportion of barley genes are currently placed on a genetic map. We analyzed eQTL datasets from the reference Steptoe × Morex doubled haploid population and showed a strong association between differential gene expression and cis-regulation, with 83% of differentially expressed genes co-locating with their eQTL. We then performed BSA by assembling allele-specific pools based on the genotypes of individuals at the partial resistance QTL Rphq11. BSA identified a total of 411 genes as differentially expressed, including HvPHGPx, a gene previously identified as a promising candidate for Rphq11. The genetic location of 276 of these genes could be determined from both eQTL datasets and conservation of synteny, and 254 (92%) of these were located on the target chromosome. We conclude that the identification of differential expression by BSA constitutes a novel method to identify genes located in specific regions of interest. The datasets obtained from such studies provide a robust set of candidate genes for the analysis and serve as valuable resources for targeted marker development and comparative mapping with other grass species

The USDA Barley Core Collection:Genetic Diversity, Population Structure, and Potential for Genome-Wide Association Studies

New sources of genetic diversity must be incorporated into plant breeding programs if they are to continue increasing grain yield and quality, and tolerance to abiotic and biotic stresses. Germplasm collections provide a source of genetic and phenotypic diversity, but characterization of these resources is required to increase their utility for breeding programs. We used a barley SNP iSelect platform with 7,842 SNPs to genotype 2,417 barley accessions sampled from the USDA National Small Grains Collection of 33,176 accessions. Most of the accessions in this core collection are categorized as landraces or cultivars/breeding lines and were obtained from more than 100 countries. Both STRUCTURE and principal component analysis identified five major subpopulations within the core collection, mainly differentiated by geographical origin and spike row number (an inflorescence architecture trait). Different patterns of linkage disequilibrium (LD) were found across the barley genome and many regions of high LD contained traits involved in domestication and breeding selection. The genotype data were used to define 'mini-core' sets of accessions capturing the majority of the allelic diversity present in the core collection. These 'mini-core' sets can be used for evaluating traits that are difficult or expensive to score. Genome-wide association studies (GWAS) of 'hull cover', 'spike row number', and 'heading date' demonstrate the utility of the core collection for locating genetic factors determining important phenotypes. The GWAS results were referenced to a new barley consensus map containing 5,665 SNPs. Our results demonstrate that GWAS and high-density SNP genotyping are effective tools for plant breeders interested in accessing genetic diversity in large germplasm collections

The global meningitis genome partnership.

Genomic surveillance of bacterial meningitis pathogens is essential for effective disease control globally, enabling identification of emerging and expanding strains and consequent public health interventions. While there has been a rise in the use of whole genome sequencing, this has been driven predominately by a subset of countries with adequate capacity and resources. Global capacity to participate in surveillance needs to be expanded, particularly in low and middle-income countries with high disease burdens. In light of this, the WHO-led collaboration, Defeating Meningitis by 2030 Global Roadmap, has called for the establishment of a Global Meningitis Genome Partnership that links resources for: N. meningitidis (Nm), S. pneumoniae (Sp), H. influenzae (Hi) and S. agalactiae (Sa) to improve worldwide co-ordination of strain identification and tracking. Existing platforms containing relevant genomes include: PubMLST: Nm (31,622), Sp (15,132), Hi (1935), Sa (9026); The Wellcome Sanger Institute: Nm (13,711), Sp (> 24,000), Sa (6200), Hi (1738); and BMGAP: Nm (8785), Hi (2030). A steering group is being established to coordinate the initiative and encourage high-quality data curation. Next steps include: developing guidelines on open-access sharing of genomic data; defining a core set of metadata; and facilitating development of user-friendly interfaces that represent publicly available data

The use of high resolution melting (HRM) to map single nucleotide polymorphism markers linked to a covered smut resistance gene in barley

Using an established genetic map, a single gene conditioning covered smut resistance, Ruh.7H, was mapped to the telomere region of chromosome 7HS in an Alexis/ Sloop doubled haploid barley population. The closest marker to Ruh.7H, abg704 was 7.5 cM away. Thirteen loci on the distal end of 7HS with potential to contain single nucleotide polymorphisms (SNPs) were identiWed by applying a comparative genomics approach using rice sequence data. Of these, one locus produced polymorphic co-dominant bands of diVerent size while two further loci contained SNPs that were identiWed using the recently developed high resolution melting (HRM) technique. Two of these markers Xanked Ruh.7H with the proximal marker located 3.8 cM and the distal marker 2.7 cM away. This is the Wrst report on the application of the HRM technique to SNP detection and to rapid scoring of known cleaved ampliWed polymorphic sequence (CAPS) markers in plants. This simple, precise post-PCR technique should Wnd widespread use in the Wne-mapping of genetic regions of interest in complex cereal and other plant genomes

Real Estate Investment Funds: Performance and Portfolio Considerations

This paper presents the results of a study dealing with a number of issues regarding real estate investment. Utilizing a data set consisting of returns from two of the oldest, continuously operating commingled real estate funds (CREFs), questions relative to investment performance, inflation hedging attributes and diversification benefits are addressed. The methodology used in exploring these issues are variants of the traditional capital asset pricing model (CAPM), extended to consider uncertain inflation (CAPMUI) and an arbitrage pricing model in which real estate performance is judged relative to a more inclusive market index representing larger numbers of substitute investments. Finally, issues relative to portfolio performance are considered by constructing portfolios containing all possible combinations of real estate, stocks and bonds to assess the potential for diversification benefits and portfolio performance. Copyright American Real Estate and Urban Economics Association.