scholarly journals Convergence behavior of single-step GBLUP and SNPBLUP for different termination criteria

2021 ◽  
Vol 53 (1) ◽  
Author(s):  
Jeremie Vandenplas ◽  
Mario P. L. Calus ◽  
Herwin Eding ◽  
Mathijs van Pelt ◽  
Rob Bergsma ◽  
...  
Keyword(s):  
Dairy Cattle ◽  
Relative Error ◽  
Single Step ◽  
Animal Breeding ◽  
Preconditioned Conjugate Gradient ◽  
System Of Equations ◽  
Convergence Behavior ◽  
Termination Criteria ◽  
Termination Criterion ◽  
Pcg Method

Abstract Background The preconditioned conjugate gradient (PCG) method is the current method of choice for iterative solving of genetic evaluations. The relative difference between two successive iterates and the relative residual of the system of equations are usually chosen as a termination criterion for the PCG method in animal breeding. However, our initial analyses showed that these two commonly used termination criteria may report that a PCG method applied to a single-step single nucleotide polymorphism best linear unbiased prediction (ssSNPBLUP) is not converged yet, whereas the solutions are accurate enough for practical use. Therefore, the aim of this study was to propose two termination criteria that have been (partly) developed in other fields, but are new in animal breeding, and to compare their behavior to that of the two termination criteria widely used in animal breeding for the PCG method applied to ssSNPBLUP. The convergence patterns of ssSNPBLUP were also compared to the convergence patterns of single-step genomic BLUP (ssGBLUP). Results Building upon previous work, we propose two termination criteria that take the properties of the system of equations into account. These two termination criteria are directly related to the relative error of the iterates with respect to the true solutions. Based on pig and dairy cattle datasets, we show that the preconditioned coefficient matrices of ssSNPBLUP and ssGBLUP have similar properties when using a second-level preconditioner for ssSNPBLUP. Therefore, the PCG method applied to ssSNPBLUP and ssGBLUP converged similarly based on the relative error of the iterates with respect to the true solutions. This similar convergence behavior between ssSNPBLUP and ssGBLUP was observed for both proposed termination criteria. This was, however, not the case for the termination criterion defined as the relative residual when applied to the dairy cattle evaluations. Conclusion Our results showed that the PCG method can converge similarly when applied to ssSNPBLUP and to ssGBLUP. The two proposed termination criteria always depicted these similar convergence behaviors, and we recommend them for comparing convergence properties of different models and for routine evaluations.

scholarly journals On single-step HSS iterative method with circulant preconditioner for fractional diffusion equations

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Mu-Zheng Zhu ◽  
Guo-Feng Zhang ◽  
Ya-E Qi
Keyword(s):  
Iterative Method ◽  
Coefficient Matrix ◽  
Fractional Diffusion ◽  
Single Step ◽  
Diffusion Equations ◽  
Preconditioned Conjugate Gradient ◽  
Fractional Diffusion Equations ◽  
Finite Difference Discretization ◽  
Circulant Preconditioners ◽  
Pcg Method

Abstract By exploiting Toeplitz-like structure and non-Hermitian dense property of the discrete coefficient matrix, a new double-layer iterative method called SHSS-PCG method is employed to solve the linear systems originating from the implicit finite difference discretization of fractional diffusion equations (FDEs). The method is a combination of the single-step Hermitian and skew-Hermitian splitting (SHSS) method with the preconditioned conjugate gradient (PCG) method. Further, the new circulant preconditioners are proposed to improve the efficiency of SHSS-PCG method, and the computation cost is further reduced via using the fast Fourier transform (FFT). Theoretical analysis shows that the SHSS-PCG iterative method with circulant preconditioners is convergent. Numerical experiments are given to show that our SHSS-PCG method with circulant preconditioners preforms very well, and the proposed circulant preconditioners are very efficient in accelerating the convergence rate.

scholarly journals Genotype-by-environment interaction in Holstein heifer fertility traits using single-step genomic reaction norm models

BMC Genomics ◽  
2021 ◽  
Vol 22 (1) ◽  
Author(s):  
Rui Shi ◽  
Luiz Fernando Brito ◽  
Aoxing Liu ◽  
Hanpeng Luo ◽  
Ziwei Chen ◽  
...  
Keyword(s):  
Heat Stress ◽  
Dairy Cattle ◽  
Candidate Genes ◽  
Heat Tolerance ◽  
Reaction Norm ◽  
Single Step ◽  
Conception Rate ◽  
Critical Periods ◽  
Genotype By Environment ◽  
Fertility Traits

Abstract Background The effect of heat stress on livestock production is a worldwide issue. Animal performance is influenced by exposure to harsh environmental conditions potentially causing genotype-by-environment interactions (G × E), especially in highproducing animals. In this context, the main objectives of this study were to (1) detect the time periods in which heifer fertility traits are more sensitive to the exposure to high environmental temperature and/or humidity, (2) investigate G × E due to heat stress in heifer fertility traits, and, (3) identify genomic regions associated with heifer fertility and heat tolerance in Holstein cattle. Results Phenotypic records for three heifer fertility traits (i.e., age at first calving, interval from first to last service, and conception rate at the first service) were collected, from 2005 to 2018, for 56,998 Holstein heifers raised in 15 herds in the Beijing area (China). By integrating environmental data, including hourly air temperature and relative humidity, the critical periods in which the heifers are more sensitive to heat stress were located in more than 30 days before the first service for age at first calving and interval from first to last service, or 10 days before and less than 60 days after the first service for conception rate. Using reaction norm models, significant G × E was detected for all three traits regarding both environmental gradients, proportion of days exceeding heat threshold, and minimum temperature-humidity index. Through single-step genome-wide association studies, PLAG1, AMHR2, SP1, KRT8, KRT18, MLH1, and EOMES were suggested as candidate genes for heifer fertility. The genes HCRTR1, AGRP, PC, and GUCY1B1 are strong candidates for association with heat tolerance. Conclusions The critical periods in which the reproductive performance of heifers is more sensitive to heat stress are trait-dependent. Thus, detailed analysis should be conducted to determine this particular period for other fertility traits. The considerable magnitude of G × E and sire re-ranking indicates the necessity to consider G × E in dairy cattle breeding schemes. This will enable selection of more heat-tolerant animals with high reproductive efficiency under harsh climatic conditions. Lastly, the candidate genes identified to be linked with response to heat stress provide a better understanding of the underlying biological mechanisms of heat tolerance in dairy cattle.

scholarly journals A Termination Criterion for Probabilistic Point Clouds Registration

Signals ◽  
2021 ◽  
Vol 2 (2) ◽  
pp. 159-173
Author(s):  
Simone Fontana ◽  
Domenico Giorgio Sorrenti
Keyword(s):  
State Of The Art ◽  
Point Clouds ◽  
Computational Time ◽  
Termination Criteria ◽  
Practical Usefulness ◽  
Local Point ◽  
Termination Criterion ◽  
Probabilistic Point ◽  
Excessive Number ◽  
Number Of Iterations

Probabilistic Point Clouds Registration (PPCR) is an algorithm that, in its multi-iteration version, outperformed state-of-the-art algorithms for local point clouds registration. However, its performances have been tested using a fixed high number of iterations. To be of practical usefulness, we think that the algorithm should decide by itself when to stop, on one hand to avoid an excessive number of iterations and waste computational time, on the other to avoid getting a sub-optimal registration. With this work, we compare different termination criteria on several datasets, and prove that the chosen one produces very good results that are comparable to those obtained using a very large number of iterations, while saving computational time.

scholarly journals Optimisation Method for Determination of Crack Tip Position Based on Gauss-Newton Iterative Technique

2021 ◽  
Vol 34 (1) ◽  
Author(s):  
Bing Yang ◽  
Zhanjiang Wei ◽  
Zhen Liao ◽  
Shuwei Zhou ◽  
Shoune Xiao ◽  
...  
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Plastic Zone ◽  
Relative Error ◽  
Crack Tip ◽  
Image Correlation ◽  
Preconditioned Conjugate Gradient ◽  
Loading Process ◽  
Tip Position

AbstractIn the digital image correlation research of fatigue crack growth rate, the accuracy of the crack tip position determines the accuracy of the calculation of the stress intensity factor, thereby affecting the life prediction. This paper proposes a Gauss-Newton iteration method for solving the crack tip position. The conventional linear fitting method provides an iterative initial solution for this method, and the preconditioned conjugate gradient method is used to solve the ill-conditioned matrix. A noise-added artificial displacement field is used to verify the feasibility of the method, which shows that all parameters can be solved with satisfactory results. The actual stress intensity factor solution case shows that the stress intensity factor value obtained by the method in this paper is very close to the finite element result, and the relative error between the two is only − 0.621%; The Williams coefficient obtained by this method can also better define the contour of the plastic zone at the crack tip, and the maximum relative error with the test plastic zone area is − 11.29%. The relative error between the contour of the plastic zone defined by the conventional method and the area of the experimental plastic zone reached a maximum of 26.05%. The crack tip coordinates, stress intensity factors, and plastic zone contour changes in the loading and unloading phases are explored. The results show that the crack tip change during the loading process is faster than the change during the unloading process; the stress intensity factor during the unloading process under the same load condition is larger than that during the loading process; under the same load, the theoretical plastic zone during the unloading process is higher than that during the loading process.

Dairy cattle breeding.

2021 ◽  
pp. 234-291
Author(s):  
Geoff Simm ◽  
Geoff Pollott ◽  
Raphael Mrode ◽  
Ross Houston ◽  
Karen Marshall
Keyword(s):  
Genetic Analysis ◽  
Dairy Cattle ◽  
Selection Response ◽  
Animal Breeding ◽  
Technology Selection ◽  
Cattle Breeding ◽  
Breeding Values ◽  
Breeding Technology ◽  
Dairy Cattle Breeding

Abstract This chapter discussed the effects of applying the different principles in animal breeding such genetic analysis, predicting breeding values, use of tools and breeding technology, selection response within breeds, and strategies for genetic improvements in dairy cattle.

scholarly journals Accounting for Population Structure and Phenotypes From Relatives in Association Mapping for Farm Animals: A Simulation Study

2021 ◽  
Vol 12 ◽  
Author(s):  
Enrico Mancin ◽  
Daniela Lourenco ◽  
Matias Bermann ◽  
Roberto Mantovani ◽  
Ignacy Misztal
Keyword(s):  
Population Structure ◽  
Beef Cattle ◽  
Dairy Cattle ◽  
Genetic Relatedness ◽  
Association Studies ◽  
Single Step ◽  
Structured Populations ◽  
Farm Animals ◽  
Snp Analysis ◽  
Genome Wide Association Studies

Population structure or genetic relatedness should be considered in genome association studies to avoid spurious association. The most used methods for genome-wide association studies (GWAS) account for population structure but are limited to genotyped individuals with phenotypes. Single-step GWAS (ssGWAS) can use phenotypes from non-genotyped relatives; however, its ability to account for population structure has not been explored. Here we investigate the equivalence among ssGWAS, efficient mixed-model association expedited (EMMAX), and genomic best linear unbiased prediction GWAS (GBLUP-GWAS), and how they differ from the single-SNP analysis without correction for population structure (SSA-NoCor). We used simulated, structured populations that mimicked fish, beef cattle, and dairy cattle populations with 1040, 5525, and 1,400 genotyped individuals, respectively. Larger populations were also simulated that had up to 10-fold more genotyped animals. The genomes were composed by 29 chromosomes, each harboring one QTN, and the number of simulated SNPs was 35,000 for the fish and 65,000 for the beef and dairy cattle populations. Males and females were genotyped in the fish and beef cattle populations, whereas only males had genotypes in the dairy population. Phenotypes for a trait with heritability varying from 0.25 to 0.35 were available in both sexes for the fish population, but only for females in the beef and dairy cattle populations. In the latter, phenotypes of daughters were projected into genotyped sires (i.e., deregressed proofs) before applying EMMAX and SSA-NoCor. Although SSA-NoCor had the largest number of true positive SNPs among the four methods, the number of false negatives was two–fivefold that of true positives. GBLUP-GWAS and EMMAX had a similar number of true positives, which was slightly smaller than in ssGWAS, although the difference was not significant. Additionally, no significant differences were observed when deregressed proofs were used as pseudo-phenotypes in EMMAX compared to daughter phenotypes in ssGWAS for the dairy cattle population. Single-step GWAS accounts for population structure and is a straightforward method for association analysis when only a fraction of the population is genotyped and/or when phenotypes are available on non-genotyped relatives.

scholarly journals Numerical Algorithms for Computing an Arbitrary Singular Value of a Tensor Sum

Axioms ◽  
2021 ◽  
Vol 10 (3) ◽  
pp. 211
Author(s):  
Asuka Ohashi ◽  
Tomohiro Sogabe
Keyword(s):  
Eigenvalue Problem ◽  
Large Scale ◽  
Numerical Algorithms ◽  
Direct Methods ◽  
Coefficient Matrix ◽  
Lanczos Method ◽  
Singular Value ◽  
Preconditioned Conjugate Gradient ◽  
Schur Decomposition ◽  
Pcg Method

We consider computing an arbitrary singular value of a tensor sum: T:=In⊗Im⊗A+In⊗B⊗Iℓ+C⊗Im⊗Iℓ∈Rℓmn×ℓmn, where A∈Rℓ×ℓ, B∈Rm×m, C∈Rn×n. We focus on the shift-and-invert Lanczos method, which solves a shift-and-invert eigenvalue problem of (TTT−σ˜2Iℓmn)−1, where σ˜ is set to a scalar value close to the desired singular value. The desired singular value is computed by the maximum eigenvalue of the eigenvalue problem. This shift-and-invert Lanczos method needs to solve large-scale linear systems with the coefficient matrix TTT−σ˜2Iℓmn. The preconditioned conjugate gradient (PCG) method is applied since the direct methods cannot be applied due to the nonzero structure of the coefficient matrix. However, it is difficult in terms of memory requirements to simply implement the shift-and-invert Lanczos and the PCG methods since the size of T grows rapidly by the sizes of A, B, and C. In this paper, we present the following two techniques: (1) efficient implementations of the shift-and-invert Lanczos method for the eigenvalue problem of TTT and the PCG method for TTT−σ˜2Iℓmn using three-dimensional arrays (third-order tensors) and the n-mode products, and (2) preconditioning matrices of the PCG method based on the eigenvalue and the Schur decomposition of T. Finally, we show the effectiveness of the proposed methods through numerical experiments.

Possibility of reducing milk recording and sampling in Holstein dairy cattle of Iran

2003 ◽  
Vol 2003 ◽  
pp. 137-137
Author(s):  
Ayatollahi-Mehrdjardy ◽  
M. Moradi-Shahrbabak ◽  
A. Nikkhah ◽  
A. Moghimy
Keyword(s):  
Dairy Cattle ◽  
Milk Fat ◽  
Animal Breeding ◽  
Recording System ◽  
Protein Yield ◽  
Milk Samples ◽  
Breeding Center ◽  
Potential Benefits

The Iranian Animal Breeding Center (IABC) is currently milk recording and sampling three time per test-day(8 hours interval) approximately once every month. Milk samples are analyzed for fat and protein contents. There are some difficulties for having precise milk samples in some farms especially for three times sampling per day, and the costs of three times recording and sampling is also a problem. Estimation of lactation yield for milk, fat and protein yield is done based on test-day records and samples and the accuracy of there estimates depend on the precision of test day records especially milk sampling. The results of milk content are not satisfactory for farmer and specialist in the current milk recording system. Some researches have been done to reduce milk recording and sampling per test day (1, 2). In addition potential benefits of reducing milk recording and sampling are that more herds can be supervised and recorded per month. The objective of this research was to consider the possibility of reducing milk recording and sampling in herds with three times milking per test-day in industrial Holstein farms.

SSOR-PCG Method for Real Time Temperature Simulation on Caohe River Aqueduct in South to North Water Transfer Project during Construction Period

2011 ◽  
Vol 243-249 ◽  
pp. 4466-4471
Author(s):  
Ping Zhang ◽  
Bin Tian ◽  
Bo Zhang
Keyword(s):  
Temperature Field ◽  
Temperature Stress ◽  
Simulation Analysis ◽  
Direct Method ◽  
Linear Equations ◽  
Water Transfer ◽  
Preconditioned Conjugate Gradient ◽  
Construction Period ◽  
North Water ◽  
Pcg Method

The temperature stress due to temperature changes is often more than the concrete tensile strength during construction period and operation period in massive concrete structures in hydraulic engineering, so the analysis of temperature stress, temperature control and measures to prevent the cracks become very important. The solution of large sparse linear equations is essential to finite element simulation in simulation analysis of temperature field. However, the traditional direct method will cost too much memory and calculation time, and the nodes is limited. The symmetric successive over relaxation (SSOR)-preconditioned conjugate gradient (PCG) method is a very efficient iterative method for solving large sparse linear equations. Construction process simulation and temperature filed calculation during construction period about Caohe river landing rectangle aqueduct of Beijing-Shijiazhuang emergency water supply engineering of middle-route of south-to-north water transfer project are carried out by FEM code using SSOR-PCG method, then the calculation result and monitoring value are compared. The comparison result shows that temperature field during construction can be accurately simulated by simulation calculation, which is helpful for guiding construction and choosing construction scheme, and worthy to popularize to other similar projects.

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