For structural comparisons of paired prokaryotic genomes,an important topic in synthetic and evolutionary biology,the locations of shared orthologous genes(henceforth orthologs)are observed as binned data.This and oth...For structural comparisons of paired prokaryotic genomes,an important topic in synthetic and evolutionary biology,the locations of shared orthologous genes(henceforth orthologs)are observed as binned data.This and other data,e.g.,wind directions recorded at monitoring sites and intensive care unit arrival times on the 24-hour clock,are counted in binned circular arcs,thus modeling them by discrete circular distributions(DCDs)is required.We propose a novel method to construct a DCD from a base continuous circular distribution(CCD).The probability mass function is defined to take the normalized values of the probability density function at some pre-fixed equidistant points on the circle.Five families of constructed DCDs which have normalizing constants in closed form are presented.Simulation studies show that DCDs outperform the corresponding CCDs in modeling grouped(discrete)circular data,and minimum chi-square estimation outperforms maximum likelihood estimation for parameters.We apply the constructed DCDs,invariant wrapped Poisson and wrapped discrete skew Laplace to compare the structures of paired bacterial genomes.Specifically,discrete four-parameter wrapped Cauchy(nonnegative trigonometric sums)distribution models multi-modal shared orthologs in Clostridium(Sulfolobus)better than the others considered,in terms of AIC and Freedman’s goodness-of-fit test.The result that different DCDs fit the shared orthologs is consistent with the fact they belong to two kingdoms.Nevertheless,these prokaryotes have a common favored site around 70°on the unit circle;this finding is important for building synthetic prokaryotic genomes in synthetic biology.These DCDs can also be applied to other binned circular data.展开更多
A dynamic analysis approcach to investigate the state of load distribution among contact bearings of double circular are belical gears is proposed and a computer program is developed for calculating the factor of iced...A dynamic analysis approcach to investigate the state of load distribution among contact bearings of double circular are belical gears is proposed and a computer program is developed for calculating the factor of iced distribution based on the theory of W-N gears. The changing situations of load distribution among contact bearings of the gears influenced by main issues are analyzed by a series of parametric studies.展开更多
基金supported by JSPS KAKENHI Grant Number 18K13459 and Grace S.Shieh was supported in part by MOST 106-2118-M-001-017 and MOST 107-2118-M-001-009-MY2.
文摘For structural comparisons of paired prokaryotic genomes,an important topic in synthetic and evolutionary biology,the locations of shared orthologous genes(henceforth orthologs)are observed as binned data.This and other data,e.g.,wind directions recorded at monitoring sites and intensive care unit arrival times on the 24-hour clock,are counted in binned circular arcs,thus modeling them by discrete circular distributions(DCDs)is required.We propose a novel method to construct a DCD from a base continuous circular distribution(CCD).The probability mass function is defined to take the normalized values of the probability density function at some pre-fixed equidistant points on the circle.Five families of constructed DCDs which have normalizing constants in closed form are presented.Simulation studies show that DCDs outperform the corresponding CCDs in modeling grouped(discrete)circular data,and minimum chi-square estimation outperforms maximum likelihood estimation for parameters.We apply the constructed DCDs,invariant wrapped Poisson and wrapped discrete skew Laplace to compare the structures of paired bacterial genomes.Specifically,discrete four-parameter wrapped Cauchy(nonnegative trigonometric sums)distribution models multi-modal shared orthologs in Clostridium(Sulfolobus)better than the others considered,in terms of AIC and Freedman’s goodness-of-fit test.The result that different DCDs fit the shared orthologs is consistent with the fact they belong to two kingdoms.Nevertheless,these prokaryotes have a common favored site around 70°on the unit circle;this finding is important for building synthetic prokaryotic genomes in synthetic biology.These DCDs can also be applied to other binned circular data.
文摘A dynamic analysis approcach to investigate the state of load distribution among contact bearings of double circular are belical gears is proposed and a computer program is developed for calculating the factor of iced distribution based on the theory of W-N gears. The changing situations of load distribution among contact bearings of the gears influenced by main issues are analyzed by a series of parametric studies.
