We study insertions of composite operators into Wilson loops in N = 4 supersymmetric Yang-Mills theory in four dimensions. The loops follow a circular or straight path and the composite insertions transform in the adjoint representation of the gauge group. This provides a gauge invariant way to define the correlator of non-singlet operators. Since the basic loop preserves an SL(2, R) subgroup of the conformal group, we can assign a conformal dimension to those insertions and calculate the corrections to the classical dimension in perturbation theory. The calculation turns out to be very similar to that of single-trace local operators and may also be expressed in terms of a spin-chain. In this case the spin-chain is open and at one-loop order has Neumann boundary conditions on the type of scalar insertions that we consider. This system is integrable and we write the Bethe ansatz describing it. We compare the spectrum in the limit of large angular momentum both in the dilute gas approximation and the thermodynamic limit to the relevant string solution in the BMN limit and in the full AdS 5 × S 5 metric and find agreement.

For the purpose of analyzing non-perturbative dynamics of string theory, Nishimura and Sugino have applied an improved mean field approximation (IMFA) to IIB matrix model. We have extracted the essence of the IMFA and obtained a general scheme, the improved Taylor expansion, that can be applied to a wide class of series which is not necessarily convergent. This approximation scheme with the help of the 2PI free energy enables us to perform higher order calculations. We have shown that the value of the free energy is stable at higher orders, which supports the validity of the approximation. Moreover, the ratio between the extent of "our" space-time and that of the internal space is found to increase rapidly as we take the higher orders into account. Our results suggest that the four dimensional space-time emerges spontaneously in IIB matrix model.

We investigate the dynamics of open membrane boundaries in a constant C-field background. We follow the analysis for open strings in a B-field background, and take some approximations. We find that open membrane boundaries do show noncommutativity in this case by explicit calculations. Membrane boundaries are one dimensional strings, so we face a new type of noncommutativity, that is, noncommutative strings.

We have analyzed the IIB matrix model on the basis of the improved mean field approximation (IMFA) and have obtained evidence suggesting that the four-dimensional space-time appears as its most stable vacuum. This method is a systematic way to obtain an improved perturbation series and was first applied to the IIB matrix model by Nishimura and Sugino. In a previous paper, we reformulated this method and proposed a criterion for the convergence of the improved series, that is, the appearance of a "plateau". In this paper, we carry out higher-order calculations, and find that our improved free energy tends to have a plateau, which shows that IMFA works well in the IIB matrix model. * )

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We investigated the diversity and phylogeography of mitochondrial DNA (mtDNA) in Japanese macaques (Macaca fuscata), an endemic species in Japan that has the northernmost distribution of any non-human primate species. DNA samples from 135 localities representing the entire range of this species were compared. A total of 53 unique haplotypes were observed for the 412-bp partial mtDNA control region sequence, with length variation distinguishing the two subspecies. Clustering analyses suggested two putative major haplogroups, of which one was geographically distributed in eastern Japan and the other in western Japan. The populations in the east showed lower mtDNA diversity than those in the west. Phylogeographical relationships of haplotypes depicted with minimum spanning network suggested differences in population structure. Population expansion was significant for the eastern but not the western population, suggesting establishment of the ancestral population was relatively long ago in the west and recent in the east. Based on fossil evidence and past climate and vegetation changes, we inferred that the postulated population expansion may have taken place after the last glacial period (after 15,000 years ago). Mitochondrial DNA showed contrasting results in both variability and phylogenetic status of local populations to those of previous studies using protein variations, particularly for populations in the periphery of the range, with special inference on habitat change during the glacial period in response to cold adaptation.

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We found this population to be panmictic, with a low degree of genetic variability. On the basis of an mtDNA phylogeny, we inferred that these macaques' ancestors originated from Java in Asia. Weak gametic disequilibrium was observed, suggesting decay of non-random associations between genomic genes at the time of founding. The results suggest that macaques bred in Mauritius are valuable as model animals for biomedical research because of their genetic homogeneity.