In this paper, combining the idea of difference method and finite element method, we construct a difference scheme for a self-adjoint problem in conservation form. Its solution uniformly converges to that of the origi...In this paper, combining the idea of difference method and finite element method, we construct a difference scheme for a self-adjoint problem in conservation form. Its solution uniformly converges to that of the original differential equation problem with order h3.展开更多
In the present paper, a new numerical method for solving initial-boundary value problems of evolutionary equations is proposed and studied, combining difference method with high accuracy with boundary integral equatio...In the present paper, a new numerical method for solving initial-boundary value problems of evolutionary equations is proposed and studied, combining difference method with high accuracy with boundary integral equation method. The numerical approximate schemes for both problems on a bounded or unbounded domain in R3 are proposed and their prior error estimates are obtained.展开更多
The paternally inherited Y chromosome has been widely used in forensics for personal identification, in anthropology and population genetics to understand origin and migration of human populations, and also in medical...The paternally inherited Y chromosome has been widely used in forensics for personal identification, in anthropology and population genetics to understand origin and migration of human populations, and also in medical and clinical studies （Wang and Li, 2013; Wang et al., 2014）. There are two kinds of extremely useful markers in Y chromosome, single nucle- otide polymorphism （SNP） and short tandem repeats （STRs）. With a very low mutation rate on the order of 3.0 x 10-8 mutations/nucleotide/generation （Xue et al., 2009）, SNP markers have been used in constructing a robust phylogeny tree linking all the Y chromosome lineages from world pop- ulations （Karafet et al., 2008）. Those lineages determined by the pattern of SNPs are called haplogroups. That is to say, we have to genotype an appropriate number of SNPs in order to assign a given Y chromosome to a haplogroup. Compared with SNPs, the mutation rates of STR markers are about four to five orders of magnitude higher （Gusmgo et al., 2005; Ballantyne et al., 2010）. Typing STR has advantages of saving time and cost compared with typing SNPs in phylogenetic assignment of a Y chromosome （Wang et al., 2010）. A set of STR values for an individual is called a haplotype. Because of the disparity in mutation rates between SNP and STR, one SNP haplogroup could actually comprise many STR haplotypes （Wang et al., 2010）. It is most interesting that STR variability is clustered more by haplogroups than by populations （Bosch et al., 1999; Behar et al., 2004）, which indicates that STR haplotypes could be used to infer the haplogroup information of a given Y chromosome. There has been increasing interest in this cost- effective strategy for predicting the haplogroup from a given STR haplotype when SNP data are unavailable. For instance, Vadim Urasin＇s YPredictor （http：//predictor.ydna.ru/）, Whit Atheys＇ haplogroup predictor （http：//www.hprg.com/hapest5/） （Athey, 2005, 2006）, and haplogroup classifier of Arizona University （Schlecht et al., 2008） have been widely employed in previous studies for haplogroup prediction （Larmuseau et al., 2010; Bembea et al., 2011; Larmuseau et al., 2012; Tarlykov et al., 2013）.展开更多
文摘In this paper, combining the idea of difference method and finite element method, we construct a difference scheme for a self-adjoint problem in conservation form. Its solution uniformly converges to that of the original differential equation problem with order h3.
基金This research was supported by the National Natural Science Foundation of China
文摘In the present paper, a new numerical method for solving initial-boundary value problems of evolutionary equations is proposed and studied, combining difference method with high accuracy with boundary integral equation method. The numerical approximate schemes for both problems on a bounded or unbounded domain in R3 are proposed and their prior error estimates are obtained.
基金supported by the National Excellent Youth Science Foundation of China(No.31222030)the National Natural Science Foundation of China(No.91131002)+3 种基金the Shanghai Rising-Star Program(No.12QA1400300)the China Ministry of Education Scientific Research Major Project(Nos. 311016 and 113022A)the MOE University Doctoral Research Supervisor's Funds(No.20120071110021)the Shanghai Professional Development Funding(No.2010001)
文摘The paternally inherited Y chromosome has been widely used in forensics for personal identification, in anthropology and population genetics to understand origin and migration of human populations, and also in medical and clinical studies （Wang and Li, 2013; Wang et al., 2014）. There are two kinds of extremely useful markers in Y chromosome, single nucle- otide polymorphism （SNP） and short tandem repeats （STRs）. With a very low mutation rate on the order of 3.0 x 10-8 mutations/nucleotide/generation （Xue et al., 2009）, SNP markers have been used in constructing a robust phylogeny tree linking all the Y chromosome lineages from world pop- ulations （Karafet et al., 2008）. Those lineages determined by the pattern of SNPs are called haplogroups. That is to say, we have to genotype an appropriate number of SNPs in order to assign a given Y chromosome to a haplogroup. Compared with SNPs, the mutation rates of STR markers are about four to five orders of magnitude higher （Gusmgo et al., 2005; Ballantyne et al., 2010）. Typing STR has advantages of saving time and cost compared with typing SNPs in phylogenetic assignment of a Y chromosome （Wang et al., 2010）. A set of STR values for an individual is called a haplotype. Because of the disparity in mutation rates between SNP and STR, one SNP haplogroup could actually comprise many STR haplotypes （Wang et al., 2010）. It is most interesting that STR variability is clustered more by haplogroups than by populations （Bosch et al., 1999; Behar et al., 2004）, which indicates that STR haplotypes could be used to infer the haplogroup information of a given Y chromosome. There has been increasing interest in this cost- effective strategy for predicting the haplogroup from a given STR haplotype when SNP data are unavailable. For instance, Vadim Urasin＇s YPredictor （http：//predictor.ydna.ru/）, Whit Atheys＇ haplogroup predictor （http：//www.hprg.com/hapest5/） （Athey, 2005, 2006）, and haplogroup classifier of Arizona University （Schlecht et al., 2008） have been widely employed in previous studies for haplogroup prediction （Larmuseau et al., 2010; Bembea et al., 2011; Larmuseau et al., 2012; Tarlykov et al., 2013）.
