Article
Mathematics, Applied
David Hartman, Milan Hladik, David Riha
Summary: The study introduces an algorithm for computing the spectral decomposition of interval matrices and applies it to computing powers of interval matrices. By tight outer estimations of eigenvalues and eigenvectors, the algorithm achieves a total time complexity of O(n(4), discussing general interval matrices and symmetric interval matrices.
APPLIED MATHEMATICS AND COMPUTATION
(2021)
Article
Physics, Fluids & Plasmas
Wojciech Tarnowski
Summary: This paper investigates the properties of eigenvalues when randomness is introduced at the level of real matrix elements. It is found that in the limit of large matrix size, the density of real eigenvalues is proportional to the square root of the asymptotic density of complex eigenvalues continuated to the real line.
Article
Computer Science, Information Systems
Jana Jankova, Sara van de Geer
Summary: Sparse principal component analysis has become widely used for dimensionality reduction, and this paper proposes a methodology for uncertainty quantification with construction of confidence intervals and tests for the principal eigenvector. The novel estimator achieves minimax optimal rates, has a Gaussian limiting distribution, and can be used for hypothesis testing and support recovery of the first eigenvector. The empirical performance of the new estimator is demonstrated on synthetic data and shown to compare favorably with classical PCA in moderately high-dimensional regimes.
IEEE TRANSACTIONS ON INFORMATION THEORY
(2021)
Article
Ecology
Floriane Plard, Julia A. Barthold Jones, Jean-Michel Gaillard, Tim Coulson, Shripad Tuljapurkar
Summary: Phenotypic traits play a role in determining survival and reproduction, with their transmission from parent to offspring influencing phenotypic parent-offspring correlation (C). This study investigates the impact of fertility and viability selections, trait ontogeny, and inheritance on C, highlighting how demographic processes can significantly affect the correlation between parental and offspring phenotypic traits, potentially more so than ontogeny and inheritance.
ECOLOGICAL MONOGRAPHS
(2021)
Article
Statistics & Probability
Yangchang Xu, Ningning Xia
Summary: This paper investigates the limiting behavior of eigenvectors of the sample spatial sign covariance matrix (SSCM) by introducing the eigenvector empirical spectral distribution (VESD) with weights depending on the eigenvectors. The results show that the VESD of a large-dimensional sample SSCM converges to a generalized Marcenko-Pastur distribution when both the dimension p of observations and the sample size n tend to infinity proportionally. In addition, the central limit theorem of linear spectral statistics of VESD is established, implying that the eigenmatrix of sample SSCM and the classical sample covariance matrix are asymptotically the same.
JOURNAL OF MULTIVARIATE ANALYSIS
(2023)
Article
Economics
Ilya Archakov, Peter Reinhard Hansen
Summary: This study presents a novel parametrization method for correlation matrices, allowing modeling of correlations and covariance matrices using an unrestricted vector and has various potential applications. An algorithm is provided for reconstructing a unique n x n correlation matrix from any vector in Rn(n-1)/2, with its numerical complexity derived.
Article
Physics, Multidisciplinary
S. Hema Surya, T. Nirmala, K. Ganesan
Summary: Finding the simplest form of a set of quantities is crucial in Mathematics, and diagonalizing matrices is a common technique to achieve this. This article introduces a novel methodology called the pairing technique to diagonalize interval matrices, making it easier to classify and investigate them. The benefits of diagonalization are demonstrated through real-world applications on planar systems and linear discrete dynamical systems.
Article
Multidisciplinary Sciences
Mehdi Rahimi, Mateo Hernandez
Summary: Phenotypic-genotypic covariance and correlation are important in crop and animal breeding. Estimating these covariances based on statistical designs can be difficult and time-consuming when there are multiple traits. This study develops a SAS program to calculate these covariance matrices based on expected values, making the estimation process easier.
ANAIS DA ACADEMIA BRASILEIRA DE CIENCIAS
(2022)
Article
Computer Science, Information Systems
Rodrigo Girdo Serrao, M. Rosario Oliveira, Lina Oliveira
Summary: In this study, a novel interval Principal Component Analysis method is proposed which only deals with symbolic data. A theoretical framework is developed to define symbolic principal components, allowing for the transformation of the original data coherent with the framework. Real-world data from the telecommunications sector is explored to detect Internet redirection attacks in real-time and improve an existing anomaly detection method.
INFORMATION SCIENCES
(2023)
Article
Ecology
Nima Khalilisamani, Peter Campbell Thomson, Herman Willem Raadsma, Mehar Singh Khatkar
Summary: Estimating heritability based on individual phenotypic and genotypic measurements can be expensive and labour-intensive in commercial aquaculture breeding. This study investigated the feasibility of estimating heritability using within-family means of phenotypes and allelic frequencies. The results showed that at least 200 families of 60 progeny per family divided equally in two pools per family were required to effectively estimate the heritability of family means. Increasing the size of pools resulted in increasing the heritability of family means towards one.
Article
Plant Sciences
Ana Uhlarik, Marina Ceran, Dalibor Zivanov, Radu Grumeza, Leif Skot, Ellen Sizer-Coverdale, David Lloyd
Summary: Phenotypic and genotypic characterization of pea genotypes used for increasing pea production area were assessed. The study found that thousand seed weight had the highest heritability, while seed yield showed the highest coefficient of variation. Positive correlation was observed between number of seeds per plant and number of pods per plant, while negative correlation was found between seed yield and protein content. Hierarchical clustering and principal component analysis categorized pea germplasm based on use and type. The results suggest that pea breeding should focus on traits with consistent heritability and positive effect on seed yield.
Article
Mathematics, Applied
Cui-E Yu, Xin Liu, Yang Zhang
Summary: This paper introduces the concept of the quaternionic adjoint matrix of an elliptic biquaternion matrix, which allows for discussion of fundamental problems and solutions to related equations. The least-squares solutions to specific matrix equations are derived and a Sylvester-type equation is also considered.
ADVANCES IN APPLIED CLIFFORD ALGEBRAS
(2021)
Article
Mathematics, Applied
Joao Meidanis, Leonid Chindelevitch
Summary: Biological genomes can be represented by matrices, and the rank distance between genomes is related to the minimum number of rearrangement mutations explaining their differences. The median problem in genome matrices is computationally complex, but fast algorithms exist for orthogonal matrices. These algorithms use rank-1 steps towards the median and can be found in polynomial time.
LINEAR ALGEBRA AND ITS APPLICATIONS
(2021)
Article
Plant Sciences
Haitham E. M. Zaki, Khlode S. A. Radwan
Summary: The study aims to develop new high-yielding cowpea varieties through hybridization and selection. The results show that traits related to seed yield have high heritability in cowpea breeding. The selection of hybrids and parents enhances the performance of cowpea varieties and demonstrates genetic diversity and the potential for selection.
FRONTIERS IN PLANT SCIENCE
(2022)
Article
Agriculture, Dairy & Animal Science
Henner Simianer, Johannes Heise, Stefan Rensing, Torsten Pook, Johannes Geibel, Christian Reimer
Summary: This paper focuses on the relationships between economic weights, genetic progress, and phenotypic progress in genomic breeding programs. A methodological framework for calculating expected genetic and phenotypic progress for complex breeding objectives is provided. The study also proposes a novel approach for deriving the covariance structure of estimated breeding values and explores the implications of modified breeding goals.
GENETICS SELECTION EVOLUTION
(2023)
Review
Agronomy
J. Jesus Ceron-Rojas, Jose Crossa
Summary: A linear selection index (LSI) is used to predict unobservable individual traits' breeding values and plays an important role in breeding programs. LSIs can be based on different parameters and can be either single-stage or multi-stage, constrained or unconstrained. Additionally, the LSI theory can be explained in a simple form.
Article
Plant Sciences
Osval Antonio Montesinos-Lopez, Abelardo Montesinos-Lopez, Ricardo Acosta, Rajeev K. Varshney, Alison Bentley, Jose Crossa
Summary: Genomic selection is a predictive method used in plant breeding that trains machine learning models with a reference population to predict new lines. This study proposes using incomplete block designs for allocating lines to locations, which outperforms random allocation in terms of predictive performance.
Article
Agronomy
Sikiru Adeniyi Atanda, Velu Govindan, Ravi Singh, Kelly R. Robbins, Jose Crossa, Alison R. Bentley
Summary: Sparse testing using genomic prediction can increase the number of testing environments in the early yield testing stage without increasing the budget. The overlap between lines and genetic relationships between environments are the main drivers of prediction accuracy in multi-environment yield trials. Genomic best linear unbiased prediction is the best predictor of true breeding value.
THEORETICAL AND APPLIED GENETICS
(2022)
Article
Plant Sciences
Osval Antonio Montesinos-Lopez, Henry Nicole Gonzalez, Abelardo Montesinos-Lopez, Maria Daza-Torres, Morten Lillemo, Jose Cricelio Montesinos-Lopez, Jose Crossa
Summary: Genomic selection is a predictive methodology that is changing plant breeding. In this study, the performance of two algorithms (TGBLUP and GBM) was compared on wheat datasets, and GBM outperformed TGBLUP in terms of prediction accuracy. Further research is encouraged to explore the virtues of GBM in genomic selection.
Article
Agronomy
Aldo Rosales, Jose Crossa, Jaime Cuevas, Luisa Cabrera-Soto, Thanda Dhliwayo, Thokozile Ndhlela, Natalia Palacios-Rojas
Summary: This study used Bayesian and modified partial least square regression models to predict the content of provitamin A carotenoids in maize genotypes using near-infrared spectroscopy data. Both regression methods showed similar accuracies in predicting carotenoid content, offering opportunities for cost-effective and high-throughput phenotyping in maize breeding.
Article
Agriculture, Multidisciplinary
Rodomiro Ortiz, Fredrik Reslow, Jaime Cuevas, Jose Crossa
Summary: This research estimated the genetic gains of potato breeding in western Europe over the past 200 years under high yield potential and stress-prone environments. The results showed that the genetic gains of foreign cultivars were small or negative in the Nordic testing sites. Additionally, breeding contributed just over half of the productivity gains in potato grown in Sweden, and the genetic gains for flesh composition and disease resistance were also small.
JOURNAL OF AGRICULTURAL SCIENCE
(2022)
Article
Plant Sciences
Raysa Gevartosky, Humberto Fanelli Carvalho, Germano Costa-Neto, Osval A. Montesinos-Lopez, Jose Crossa, Roberto Fritsche-Neto
Summary: This study aimed to design optimized training sets for genomic prediction considering multi-trait multi-environment trials and how those methods may increase accuracy reducing phenotyping costs. The combined use of genomic and enviromic data efficiently designs optimized training sets for genomic prediction, improving the response to selection per dollar invested.
Article
Agronomy
J. Jesus Ceron-Rojas, Manje Gowda, Fernando Toledo, Yoseph Beyene, Alison R. Bentley, Leo Crespo-Herrera, Keith Gardner, Jose Crossa
Summary: The profit function is used to predict net genetic merit (H) in plant breeding by deriving trait economic weights using the linear phenotypic selection index (LPSI). Economic weight reflects the increase in profit achieved by improving a specific trait by one unit and should consider market situation rather than arbitrary values. To overcome the challenges in assigning economic weights in maize and wheat breeding programs, a profit function was constructed using the market price of grain yield and its conditional expectation, and validated using simulated and real datasets.
Article
Biodiversity Conservation
Nick S. Fradgley, James Bacon, Alison R. Bentley, Germano Costa-Neto, Andrew Cottrell, Jose Crossa, Jaime Cuevas, Matthew Kerton, Edward Pope, Stephanie M. Swarbreck, Keith A. Gardner
Summary: Wheat, a major global crop, is highly valued for its grain quality. This study used quantitative genetics and climate model outputs to investigate genotypic adaptation for wheat quality traits in the UK. The research found that the impact of climate change on wheat quality varies geographically and current wheat germplasm in the UK has low adaptability to future climates.
GLOBAL CHANGE BIOLOGY
(2022)
Article
Genetics & Heredity
Germano Costa-Neto, Leonardo Crespo-Herrera, Nick Fradgley, Keith Gardner, Alison R. Bentley, Susanne Dreisigacker, Roberto Fritsche-Neto, Osval A. Montesinos-Lopez, Jose Crossa
Summary: This study developed a data-driven approach based on Environment-Phenotype Association (EPA) to recycle important G x E information from historical breeding data. The results showed that introducing EPA as an intermediary learning step significantly improved G x E prediction accuracy.
G3-GENES GENOMES GENETICS
(2023)
Article
Genetics & Heredity
Susanne Dreisigacker, Paulino Perez-Rodriguez, Leonardo Crespo-Herrera, Alison R. Bentley, Jose Crossa
Summary: This study demonstrates the potential of rapid-cycle recurrent genomic selection (RCRGS) to increase grain yield in wheat, achieving a consistent genetic gain of 12.3% over 3 cycles of recombination.
G3-GENES GENOMES GENETICS
(2023)
Article
Genetics & Heredity
Abelardo Montesinos-Lopez, Carolina Rivera, Francisco Pinto, Francisco Pinera, David Gonzalez, Mathew Reynolds, Paulino Perez-Rodriguez, H. Li, Osval A. Montesinos-Lopez, Jose Crossa
Summary: By comparing a novel DL method with conventional GP models, this study found that DL method has higher accuracy in predicting genomic phenotypes in plant breeding research and can account for the complexity of genotype-environment interaction. However, traditional GP models can also achieve high accuracy in certain situations.
G3-GENES GENOMES GENETICS
(2023)
Article
Plant Sciences
Osval A. Montesinos-Lopez, Brandon A. Mosqueda-Gonzalez, Josafat Salinas-Ruiz, Abelardo Montesinos-Lopez, Jose Crossa
Summary: Sparse testing is crucial for improving the efficiency of genomic selection by reducing the number of genotypes evaluated. We evaluated four methods for allocating lines to environments and found that M4 was the best method, while M1 was the worst. There were no significant differences between M3 and M4. We concluded that both M4 and M3 are efficient in the context of sparse testing for multi-trait prediction.
Article
Plant Sciences
Osval A. Montesinos-Lopez, Alison R. Bentley, Carolina Saint Pierre, Leonardo Crespo-Herrera, Leonardo Rebollar-Ruellas, Patricia Edwigis Valladares-Celis, Morten Lillemo, Abelardo Montesinos-Lopez, Jose Crossa
Summary: Genomic selection (GS), proposed by Meuwissen et al. more than 20 years ago, is revolutionizing plant and animal breeding. In our study of 14 real datasets, we found that the average gain in prediction accuracy when genomic information is considered was 26.31%. The quality of the markers and relatedness of the individuals can greatly impact the increase in prediction accuracy.
Article
Genetics & Heredity
Osval A. Montesinos Lopez, Brandon Alejandro Mosqueda Gonzalez, Abelardo Montesinos Lopez, Jose Crossa
Summary: Genomic selection (GS) is revolutionizing plant breeding, but a basic understanding of statistical machine-learning methods is necessary. We introduce the Sparse Kernel Methods (SKM) R library, which provides complete guidelines for implementing seven statistical machine-learning methods for genomic prediction, making it easier for breeders and scientists to use these methods.