An exact quantum master equation formalism is constructed for the efficient evaluation of quantum non-Markovian dissipation beyond the weak system-bath interaction regime in the presence of time-dependent external field. A novel truncation scheme is further proposed and compared with other approaches to close the resulting hierarchically coupled equations of motion. The interplay between system-bath interaction strength, non-Markovian property, and required level of hierarchy is also demonstrated with the aid of simple spin-boson systems.

Two recombinant inbred (RI) populations having 194 and 222 lines each, derived, respectively, from a highly heterotic inter-(IJ ) and intrasubspecific (II ) hybrid, were backcrossed to their respective parents. The RI and two backcross populations along with F 1 and its two parents of each hybrid were evaluated for nine important traits, including grain yield and eight other yield-related traits. A total of 76 quantitative trait loci (QTL) for the IJ hybrid and 41 QTL for the II hybrid were detected in the RI population, midparent heterosis of two backcross populations, and two independent sets of data by summation (L 1 1 L 2 ) and by subtraction (L 1 À L 2 ) of two backcross populations (L 1 and L 2 ). The variance explained by each QTL ranged from 2.6 to 58.3%. In the IJ hybrid, 42% (32) of the QTL showed an additive effect, 32% (24) a partial-tocomplete dominant effect, and 26% (20) an overdominant effect. In the II hybrid, 32% (13) of the QTL demonstrated an additive effect, 29% (12) a partial-to-complete dominant effect, and 39% (16) an overdominant effect. There were 195 digenic interactions detected in the IJ hybrid and 328 in the II hybrid. The variance explained by each digenic interaction ranged from 2.0 to 14.9%. These results suggest that the heterosis in these two hybrids is attributable to the orchestrated outcome of partial-to-complete dominance, overdominance, and epistasis. H ETEROSIS, a term to describe the superiority of heterozygous genotypes over their corresponding parental genotypes (Shull 1908), has been under investigation for $100 years, but no consensus exists about the genetic basis underlying this very important phenomenon. Two contending hypotheses, the dominance hypothesis and the overdominance hypothesis, were proposed to explain this phenomenon about one century ago. The dominance hypothesis attributes heterosis to canceling of deleterious or inferior recessive alleles contributed by one parent, by beneficial or superior dominant alleles contributed by the other parent in the heterozygous genotypes at different loci (Davenport 1908;Bruce 1910;Jones 1917). The overdominance hypothesis attributes heterosis to the superior fitness of heterozygous genotypes over homozygous genotypes at a single locus (East 1908;Shull 1908).Molecular markers and their linkage maps have greatly facilitated the identification of individual loci conditioning heterosis and the estimation of gene action of underlying loci. Quantitative trait locus (QTL) mapping studies aiming at understanding the genetic basis of heterosis have been conducted in rice and other crops (Xiao et al. 1995;Li et al. 1997Li et al. , 2001Yu et al. 1997;Luo et al. 2001;Hua et al. 2002Hua et al. , 2003Semel et al. 2006;Frascaroli et al. 2007; Melchinger et al. 2007a,b). Evidence from such studies suggests that heterosis may be attributable to dominance (Xiao et al. 1995;Cockerham and Zeng 1996), overdominance (Stuber et al. 1992;Li et al. 2001;Luo et al. 2001), pseudooverdominance due to tightly linked loci with beneficial ...

For quantum transport through mesoscopic systems, a quantum master-equation approach is developed in terms of compact expressions for the transport current and the reduced density matrix of the system. The present work is an extension of Gurvitz's approach for quantum transport and quantum measurement, namely, to finite temperature and arbitrary bias voltage. Our derivation starts from a second-order cumulant expansion of the tunneling Hamiltonian; then follows the conditional average over the electrode reservoir states. As a consequence, in the usual weak-tunneling regime, the established formalism is applicable for a wide range of transport problems. The validity of the formalism and its convenience in application are well illustrated by a number of examples.