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BackgroundWatermelon is an important vegetable crop with dual use of both fruit and seeds. Understanding the genetic basis of fruit quality and seed size-related traits is important for efficient marker-assisted breeding in watermelon. Linkage mapping in watermelon segregating populations using genotyping-by-sequencing (GBS) provides insights into genetic control of fruit- and seed-related traits and genome collinearity in commercial watermelon cultivars. ResultsIn the present study, we conducted QTL mapping of 12 horticulturally important traits on external and internal fruit quality and seed size/weight using segregating populations derived a cross between two commercial varieties. A high-density genetic map was developed with GBS which contained more than 6,000 SNP loci in 1,004 bins with a total map length of 1261.1 cM and average marker interval of 1.26 cM or 329 kb. Phenotypic data of fruit rind color (RC), rind stripe pattern (RSP), flesh color (FFC), fruit diameter (FD), fruit length (FL), fruit shape index (FSI), fruit weight (FW), Brix content central (BCC), Brix content edge (BCE), seed length (SL), width (SW), and weight (20SWT) were collected from two locations in two years. QTL analysis identified 47 QTL for the 12 traits, of which 24 had moderate- or major-effects, and 34 were novel QTL not identified in previous studies. The QTL for RSP were identified overlapped with previous reports, and mapped the QTL to a small interval on chromosome 6. From the detected novel QTL, we identify FD (qfd2.1), FL (qfl2.1) co-located with FSI (qfsi2.1) QTL on chromosome 2, and the minor QTL qfw3.2 co-located with previously reported fruit shape QTL (qfd3.1, qfl3.1, qfsi3.1), and SW (qsw10.1) co-located with 20SWT QTL (q20swt10.1) on chromosome 10, and 5 minor QTL (qbcc2.1, qbcc5.1, qbce2.1, qbce2.2, qbce5.1) were found to be likely new locus for Brix content.ConclusionWe conducted GBS consisting of 120 F2 individuals and developed a high-density linkage map with more than 6,000 SNP loci in 1004 bins in watermelon. We identified 47 QTL for 12 fruit and seed related traits including 34 novel QTL. Our work expands the molecular breeding toolbox for watermelon to improve the yield and fruit quality.

In this study, a new method is proposed for analysing the non-linear dynamics and stability in lane changes on highways by large buses. Unlike most of the literature associated with a simulated linear dynamic model for large buses, a verified 4DOF mechanical model with non-linear tire based on vehicle test is used in the lane-change simulation, including sinusoidal steering and steer returning. According to Jacobian matrix eigenvalues of the vehicle model, bifurcations of steady steering, sinusoidal steering and steer returning with disturbance on highways are investigated using a numerical method. The numerical simulation results reveal that Hopf bifurcations are identified in steady and sinusoidal steering conditions, which translates into an oscillatory behaviour leading to instability. Various equilibrium forms of stability are found, as well as saddle and Hopf bifurcations with disturbance ζ variety. The derived knowledge of the bifurcations set is hugely important to fully understand the actual dynamic motions of vehicles when lane changing on an even surface. It is a valuable reference for safety design of large buses to improve the traffic safety of driver–vehicle–road closed-loop system.

We present weighted Golub-Kahan-Lanczos algorithms. We demonstrate their applications to the eigenvalue problem of a product of two symmetric positive definite matrices and an eigenvalue problem for the linear response problem. A convergence analysis is provided and numerical test results are reported. As another application we make a connection between the proposed algorithms and the preconditioned conjugate gradient (PCG) method.