The mismatch distribution is a good descriptive summary statistic that describes the phenomena of population genetics. This article scanned mismatch distribution on human genome with single nucleotide polymorphism （...The mismatch distribution is a good descriptive summary statistic that describes the phenomena of population genetics. This article scanned mismatch distribution on human genome with single nucleotide polymorphism （SNP） data from the International HapMap Project. It is found that the abnormal mismatch distribution could imply some special segments on some chromosomes. One of the segments, on chromosome 8, was proved as an inversion. Other special segments may also imply some special structure on chromo- somes, such as duplication. The conjectures of other segments still need further research.展开更多
This work is concerned with the asymptotic behavior of systems of parabolic equations arising from null-recurrent switching diffusions, which are diffusion processes modulated by continuous-time Markov chains. A suffi...This work is concerned with the asymptotic behavior of systems of parabolic equations arising from null-recurrent switching diffusions, which are diffusion processes modulated by continuous-time Markov chains. A sufficient condition for null recurrence is presented. Moreover, convergence rate of the solutions of systems of homogeneous parabolic equations under suitable conditions is established. Then a case study on verifying one of the conditions proposed is provided with the use of a two-state Markov chain. To verify the condition, boundary value problems （BVPs） for parabolic systems are treated, which are not the usual two-point BVP type. An extra condition in the interior is needed resulting in jump discontinuity of the derivative of the corresponding solution.展开更多
文摘The mismatch distribution is a good descriptive summary statistic that describes the phenomena of population genetics. This article scanned mismatch distribution on human genome with single nucleotide polymorphism （SNP） data from the International HapMap Project. It is found that the abnormal mismatch distribution could imply some special segments on some chromosomes. One of the segments, on chromosome 8, was proved as an inversion. Other special segments may also imply some special structure on chromo- somes, such as duplication. The conjectures of other segments still need further research.
基金the National Science Foundation under DMS-0603287the National Security Agency,MSPF-068-029 the National Natural Science Foundation of China under No.60574069
文摘This work is concerned with the asymptotic behavior of systems of parabolic equations arising from null-recurrent switching diffusions, which are diffusion processes modulated by continuous-time Markov chains. A sufficient condition for null recurrence is presented. Moreover, convergence rate of the solutions of systems of homogeneous parabolic equations under suitable conditions is established. Then a case study on verifying one of the conditions proposed is provided with the use of a two-state Markov chain. To verify the condition, boundary value problems （BVPs） for parabolic systems are treated, which are not the usual two-point BVP type. An extra condition in the interior is needed resulting in jump discontinuity of the derivative of the corresponding solution.
