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This paper addresses the problem of finding the optimal routing policies with only trajectory information in a stochastic time-dependent network where all link travel times are temporally and spatially correlated. Two equivalent definitions are given for trajectory-adaptive routing policy. The first definition follows the mapping definition in a series of previous studies, where the trajectory information is included in the state variable. With that definition, any subpolicy of an optimal routing policy must also be optimal, and the algorithm developed in previous studies could serve as an exact solution, but the nature of the definition that trajectory information is included in the state variable determines that the number of states is prohibitively huge. Therefore, a second definition is given as a recursive definition, where the trajectory information is not included in the state variable. It is shown that, with the second definition, a subpolicy of an optimal/nondominated routing policy is not necessarily optimal/nondominated, but any subpolicy of a pure routing policy must also be pure which is a new property defined based on nondominance. An exact algorithm is designed to find optimal trajectory-adaptive routing policies based on the aforementioned property of pure routing policy. A comparison is made between the optimal trajectory-adaptive routing policies and the optimal paths in the same test networks to investigate the benefit of being adaptive. The results show that the benefit of being adaptive to trajectory information is more significant with a higher risk aversion, a higher correlation, and/or a larger network. [ABSTRACT FROM AUTHOR]

An unequal contribution of male and female lineages from parental populations to admixed ones is not uncommon in the American continents, as a consequence of directional gene flow from European men into African and Hispanic Americans in the past several centuries. However, little is known about sex-biased admixture in East Asia, where substantial migrations are recorded. Tibeto-Burman (TB) populations were historically derived from ancient tribes of northwestern China and subsequently moved to the south, where they admixed with the southern natives during the past 2,600 years. They are currently extensively distributed in China and Southeast Asia. In this study, we analyze the variations of 965 Y chromosomes and 754 mtDNAs in >20 TB populations from China. By examining the haplotype group distributions of Y-chromosome and mtDNA markers and their principal components, we show that the genetic structure of the extant southern Tibeto-Burman (STB) populations were primarily formed by two parental groups: northern immigrants and native southerners. Furthermore, the admixture has a bias between male and female lineages, with a stronger influence of northern immigrants on the male lineages (∼62%) and with the southern natives contributing more extensively to the female lineages (∼56%) in the extant STBs. This is the first genetic evidence revealing sex-biased admixture in STB populations, which has genetic, historical, and anthropological implications. [ABSTRACT FROM AUTHOR]