Degenerations and representations of twisted Shibukawa-Ueno R-operators

We study degenerations of the Belavin R-matrices via the infinite dimensional operators defined by Shibukawa-Ueno. We define a two-parameter family of generalizations of the Shibukawa-Ueno R-operators. These operators have finite dimensional representations which include Belavin's R-matrices in the elliptic case, a two-parameter family of twisted affinized Cremmer-Gervais R-matrices in the trigonometric case, and a two-parameter family of twisted (affinized) generalized Jordanian R-matrices in the rational case. We find finite dimensional representations which are compatible with the elliptic to trigonometric and rational degeneration. We further show that certain members of the elliptic family of operators have no finite dimensional representations. These R-operators unify and generalize earlier constructions of Felder and Pasquier, Ding and Hodges, and the authors, and illuminate the extent to which the Cremmer-Gervais R-matrices (and their rational forms) are degenerations of Belavin's R-matrix

Compost Carryover: Nitrogen Phosphorous and FT-IR Analysis of Soil Organic Matter

Compost plays a central role in organic soil fertility plans but is bulky and costly to apply. Determining compost carryover is therefore important for cost-effective soil fertility planning. This study investigated two aspects of nutritive carryover [nitrogen and phosphorus (P)], and an indicator of non-nutritive carryover [soil organic matter (SOM)] to determine the residual effect of a one-time compost application applied at four rates in a corn-squash rotation. Crop yield was measured as an integrated carryover indicator of nutritive and non-nutritive effects. Functional groups of compost and SOM were investigated using FT-IR spectroscopy and soil organic carbon (SOC). While year to year variability was great, compost had a persistent positive effect on crop yields, evident 3 years after application with no reduction in magnitude over time. Soil nitrate was low, and additions of compost at any rate generally did not increase levels beyond the year of application, with the exception of year four. Olsen P was also low, yet was higher in amended soils than in non-amended soils 3 years after application. Pronounced polysaccharide peaks, evident in compost spectra and absent in control soil, were apparent in compost-amended soils 3 years after compost treatment and SOC was greater 2 years afterwards. Compost carryover was most pronounced in year four following the incorporation of a nitrogen-fixing cover crop. These results show that compost can influence nutritive and non-nutritive soil properties many years after incorporation, thereby reinforcing the importance of including compost in organic fertility plans despite the unpredictability of year-to-year response

The non-dynamical r-matrices of the degenerate Calogero-Moser models

A complete description of the non-dynamical r-matrices of the degenerate Calogero-Moser models based on $gl_n$ is presented. First the most general momentum independent r-matrices are given for the standard Lax representation of these systems and those r-matrices whose coordinate dependence can be gauged away are selected. Then the constant r-matrices resulting from gauge transformation are determined and are related to well-known r-matrices. In the hyperbolic/trigonometric case a non-dynamical r-matrix equivalent to a real/imaginary multiple of the Cremmer-Gervais classical r-matrix is found. In the rational case the constant r-matrix corresponds to the antisymmetric solution of the classical Yang-Baxter equation associated with the Frobenius subalgebra of $gl_n$ consisting of the matrices with vanishing last row. These claims are consistent with previous results of Hasegawa and others, which imply that Belavin's elliptic r-matrix and its degenerations appear in the Calogero-Moser models. The advantages of our analysis are that it is elementary and also clarifies the extent to which the constant r-matrix is unique in the degenerate cases.Comment: 25 pages, LaTeX; expanded by an appendix detailing the proof of Theorem 1 and a concluding section in version

Designing libraries of chimeric proteins using SCHEMA recombination and RASPP

SCHEMA is a method for designing libraries of novel proteins by recombination of homologous sequences. The goal is to maximize the number of folded proteins while simultaneously generating significant sequence diversity. Here, we use the RASPP algorithm to identify optimal SCHEMA designs for shuffling contiguous elements of sequence. To exemplify the method, SCHEMA is used to recombine five fungal cellobiohydrolases (CBH1s) to produce a library of more than 390,000 novel CBH1 sequences

Expected Genotype Quality and Diploidized Marker Data from Genotyping-by-Sequencing of Urocholoa spp. Tetraploids.

Although genotyping-by-sequencing (GBS) is a well-established marker technology in diploids, the development of best practices for tetraploid species is a topic of current research. We determined the theoretical relationship between read depth and the phred-scaled probability of genotype misclassification conditioned on the true genotype, which we call expected genotype quality (EGQ). If the GBS method has 0.5% allelic error, then 17 reads are needed to classify simplex tetraploids as heterozygous with 95% accuracy (EGQ = 13) vs. 61 reads to determine allele dosage. We developed an R script to convert tetraploid GBS data in variant call format (VCF) into diploidized genotype calls and applied it to 267 interspecific hybrids of the tetraploid forage grass Urochloa. When reads were aligned to a mock reference genome created from GBS data of the Urochloa brizantha (Hochst. ex A. Rich.) R. D. Webster cultivar Marandu, 25,678 biallelic single nucleotide polymorphism (SNPs) were discovered, compared with ~3000 SNPs when aligning to the closest true reference genomes, Setaria viridis (L.) P. Beauv. and S. italica (L.) P. Beauv. Crossvalidation revealed that missing genotypes were imputed by the random forest method with a median accuracy of 0.85 regardless of heterozygote frequency. Using the Urochloa spp. hybrids, we illustrated how filtering samples based only on genotype quality (GQ) creates genotype bias; a depth threshold based on EGQ is also needed regardless of whether genotypes are called using a diploidized or allele dosage model

Genomic selection in commercial perennial crops: applicability and improvement in oil palm (Elaeis guineensis Jacq.)

Genomic selection (GS) uses genome-wide markers to select individuals with the desired overall combination of breeding traits. A total of 1,218 individuals from a commercial population of Ulu Remis x AVROS (UR x AVROS) were genotyped using the OP200K array. The traits of interest included: shellto- fruit ratio (S/F, %), mesocarp-to-fruit ratio (M/F, %), kernel-to-fruit ratio (K/F, %), fruit per bunch (F/B, %), oil per bunch (O/B, %) and oil per palm (O/P, kg/palm/year). Genomic heritabilities of these traits were estimated to be in the range of 0.40 to 0.80. GS methods assessed were RR-BLUP, Bayes A (BA), Cπ (BC), Lasso (BL) and Ridge Regression (BRR). All methods resulted in almost equal prediction accuracy. The accuracy achieved ranged from 0.40 to 0.70, correlating with the heritability of traits. By selecting the most important markers, RR-BLUP B has the potential to outperform other methods. The marker density for certain traits can be further reduced based on the linkage disequilibrium (LD). Together with in silico breeding, GS is now being used in oil palm breeding programs to hasten parental palm selection

Computer vision and machine learning for robust phenotyping in genome-wide studies

Traditional evaluation of crop biotic and abiotic stresses are time-consuming and labor-intensive limiting the ability to dissect the genetic basis of quantitative traits. A machine learning (ML)-enabled image-phenotyping pipeline for the genetic studies of abiotic stress iron deficiency chlorosis (IDC) of soybean is reported. IDC classification and severity for an association panel of 461 diverse plant-introduction accessions was evaluated using an end-to-end phenotyping workflow. The workflow consisted of a multi-stage procedure including: (1) optimized protocols for consistent image capture across plant canopies, (2) canopy identification and registration from cluttered backgrounds, (3) extraction of domain expert informed features from the processed images to accurately represent IDC expression, and (4) supervised ML-based classifiers that linked the automatically extracted features with expert-rating equivalent IDC scores. ML-generated phenotypic data were subsequently utilized for the genome-wide association study and genomic prediction. The results illustrate the reliability and advantage of ML-enabled image-phenotyping pipeline by identifying previously reported locus and a novel locus harboring a gene homolog involved in iron acquisition. This study demonstrates a promising path for integrating the phenotyping pipeline into genomic prediction, and provides a systematic framework enabling robust and quicker phenotyping through ground-based systems

New algorithm improves fine structure of the barley consensus SNP map

<p>Abstract</p> <p>Background</p> <p>The need to integrate information from multiple linkage maps is a long-standing problem in genetics. One way to visualize the complex ordinal relationships is with a directed graph, where each vertex in the graph is a bin of markers. When there are no ordering conflicts between the linkage maps, the result is a directed acyclic graph, or DAG, which can then be linearized to produce a consensus map.</p> <p>Results</p> <p>New algorithms for the simplification and linearization of consensus graphs have been implemented as a package for the R computing environment called DAGGER. The simplified consensus graphs produced by DAGGER exactly capture the ordinal relationships present in a series of linkage maps. Using either linear or quadratic programming, DAGGER generates a consensus map with minimum error relative to the linkage maps while remaining ordinally consistent with them. Both linearization methods produce consensus maps that are compressed relative to the mean of the linkage maps. After rescaling, however, the consensus maps had higher accuracy (and higher marker density) than the individual linkage maps in genetic simulations. When applied to four barley linkage maps genotyped at nearly 3000 SNP markers, DAGGER produced a consensus map with improved fine structure compared to the existing barley consensus SNP map. The root-mean-squared error between the linkage maps and the DAGGER map was 0.82 cM per marker interval compared to 2.28 cM for the existing consensus map. Examination of the barley hardness locus at the 5HS telomere, for which there is a physical map, confirmed that the DAGGER output was more accurate for fine structure analysis.</p> <p>Conclusions</p> <p>The R package DAGGER is an effective, freely available resource for integrating the information from a set of consistent linkage maps.</p

STAR: predicting recombination sites from amino acid sequence

BACKGROUND: Designing novel proteins with site-directed recombination has enormous prospects. By locating effective recombination sites for swapping sequence parts, the probability that hybrid sequences have the desired properties is increased dramatically. The prohibitive requirements for applying current tools led us to investigate machine learning to assist in finding useful recombination sites from amino acid sequence alone. RESULTS: We present STAR, Site Targeted Amino acid Recombination predictor, which produces a score indicating the structural disruption caused by recombination, for each position in an amino acid sequence. Example predictions contrasted with those of alternative tools, illustrate STAR'S utility to assist in determining useful recombination sites. Overall, the correlation coefficient between the output of the experimentally validated protein design algorithm SCHEMA and the prediction of STAR is very high (0.89). CONCLUSION: STAR allows the user to explore useful recombination sites in amino acid sequences with unknown structure and unknown evolutionary origin. The predictor service is available from