We consider genomic imputation for low-coverage genotyping-by-sequencing data with high levels of missing data. We compensate for this loss of information by utilizing family relationships in multiparental experimental crosses. This nearly quadruples the number of usable markers when applied to a large rice Multiparent Advanced Generation InterCross (MAGIC) study.

Inmice, the heart nearly quadruples in size from early preadolescence (postnatal day 10 [P10]) to puberty ( P35) (Naqvi et al., 2014). Because it is widely believed that mammalian cardiomyocytes (CMs) are incapable of replication after birth, it has been assumed that early postnatal heart growth is driven solely by CM hypertrophy. Our findings question this view and provide insights into how th...

In this paper the known upper bound 10 for the number of Diophantine quintuples is reduced to 6.8·10. The key ingredient for the improvement is that certain individual bounds on parameters are now combined with a more efficient counting of tuples, and estimated by sums over divisor functions. As a side effect, we also improve the known upper bound 4 ·10 for the number of D(−1)-quadruples to 5 ·...

This paper presents a new digital watermarking algorithm for color halftone images. According to the Minimal Brightness Variation Quadruples (MBVQ), this paper gets the conclusion that each pixel of color halftone image belongs to one of the five MBVQs. Based on the edge and MBVQ, this algorithm implements the watermark embedding in the halftone process. Experimental results show that the algor...

It is proven that if k ≥ 2 is an integer and d is a positive integer such that the product of any two distinct elements of the set {k − 1, k + 1, 16k − 4k, d} increased by 1 is a perfect square, then d = 4k or d = 64k−48k+8k. Together with a recent result of Fujita, this shows that all Diophantine quadruples of the form {k − 1, k + 1, c, d} are regular.

In this paper we prove that there does not exist a set of four non-zero polynomials from \(\mathbb{Z}[X]\), all constant, such the product any two its distinct elements decreased by \(3\) is square polynomial \(\mathbb{Z}[X]\).