An approach version of fuzzy metric spaces including an ad hoc fixed point theorem

In this paper, inspired by two very different, successful metric theories such us the real view-point of Lowen's approach spaces and the probabilistic field of Kramosil and Michalek's fuzzymetric spaces, we present a family of spaces, called fuzzy approach spaces, that are appropriate to handle, at the same time, both measure conceptions. To do that, we study the underlying metric interrelationships between the above mentioned theories, obtaining six postulates that allow us to consider such kind of spaces in a unique category. As a result, the natural way in which metric spaces can be embedded in both classes leads to a commutative categorical scheme. Each postulate is interpreted in the context of the study of the evolution of fuzzy systems. First properties of fuzzy approach spaces are introduced, including a topology. Finally, we describe a fixed point theorem in the setting of fuzzy approach spaces that can be particularized to the previous existing measure spaces.

Efficient sampling of atomic configurational spaces.

We describe a method to explore the configurational phase space of chemical systems. It is based on the nested sampling algorithm recently proposed by Skilling (AIP Conf. Proc. 2004, 395; J. Bayesian Anal. 2006, 1, 833) and allows us to explore the entire potential energy surface (PES) efficiently in an unbiased way. The algorithm has two parameters which directly control the trade-off between the resolution with which the space is explored and the computational cost. We demonstrate the use of nested sampling on Lennard-Jones (LJ) clusters. Nested sampling provides a straightforward approximation for the partition function; thus, evaluating expectation values of arbitrary smooth operators at arbitrary temperatures becomes a simple postprocessing step. Access to absolute free energies allows us to determine the temperature-density phase diagram for LJ cluster stability. Even for relatively small clusters, the efficiency gain over parallel tempering in calculating the heat capacity is an order of magnitude or more. Furthermore, by analyzing the topology of the resulting samples, we are able to visualize the PES in a new and illuminating way. We identify a discretely valued order parameter with basins and suprabasins of the PES, allowing a straightforward and unambiguous definition of macroscopic states of an atomistic system and the evaluation of the associated free energies.

Projective Limit Random Probabilities on Polish Spaces

A pivotal problem in Bayesian nonparametrics is the construction of prior distributions on the space M(V) of probability measures on a given domain V. In principle, such distributions on the infinite-dimensional space M(V) can be constructed from their finite-dimensional marginals---the most prominent example being the construction of the Dirichlet process from finite-dimensional Dirichlet distributions. This approach is both intuitive and applicable to the construction of arbitrary distributions on M(V), but also hamstrung by a number of technical difficulties. We show how these difficulties can be resolved if the domain V is a Polish topological space, and give a representation theorem directly applicable to the construction of any probability distribution on M(V) whose first moment measure is well-defined. The proof draws on a projective limit theorem of Bochner, and on properties of set functions on Polish spaces to establish countable additivity of the resulting random probabilities.

Towards a complete dense geometric and photometric reconstruction under varying pose and illumination

This paper proposes a novel framework to construct a geometric and photometric model of a viewed object that can be used for visualisation in arbitrary pose and illumination. The method is solely based on images and does not require any specialised equipment. We assume that the object has a piece-wise smooth surface and that its reflectance can be modelled using a parametric bidirectional reflectance distribution function. Without assuming any prior knowledge on the object, geometry and reflectance have to be estimated simultaneously and occlusion and shadows have to be treated consistently. We exploit the geometric and photometric consistency using the fact that surface orientation and reflectance are local invariants. In a first implementation, we demonstrate the method using a Lambertian object placed on a turn-table and illuminated by a number of unknown point light-sources. A discrete voxel model is initialised to the visual hull and voxels identified as inconsistent with the invariants are removed iteratively. The resulting model is used to render images in novel pose and illumination. © 2004 Elsevier B.V. All rights reserved.

Phylogenetic study of complete cytochrome b genes in musk deer (genus Moschus) using museum samples

As an endangered animal group, musk deer (genus Moschus) are not only a great concern of wildlife conservation, but also of special interest to evolutionary studies due to long-standing arguments on the taxonomic and phylogenetic associations in this group. Using museum samples, we sequenced complete mitochondrial cytochrome b genes (1140 bp) of all suggested species of musk deer in order to reconstruct their phylogenetic history through molecular information. Our results showed that the cytochrome b gene tree is rather robust and concurred for all the algorithms employed (parsimony, maximum likelihood, and distance methods). Further, the relative rate test indicated a constant sequence substitution rate among all the species, permitting the dating of divergence events by molecular clock. According to the molecular topology, M. moschiferus branched off the earliest from a common ancestor of musk deer (about 700,000 years ago); then followed the bifurcation forming the M. berezouskii lineage and the lineage clustering M. fuscus, M. chrysogaster, and M. leucogaster (around 370,000 years before present), interestingly the most recent speciation event in musk deer happened rather recently (140,000 years ago), which might have resulted from the diversified habitats and geographic barriers in southwest China caused by gigantic movements of the Qinghai-Tibetan Plateau in history. Combining the data of current distributions, fossil records, and molecular data of this study, we suggest that the historical dispersion of musk deer might be from north to south in China. Additionally, in our further analyses involving other pecora species, musk deer was strongly supported as a monophyletic group and a valid family in Artiodactyla, closely related to Cervidae. (C) 1999 Academic Press.

Molecular Phylogeny of Slow Lorises ( Nycticebus) Revealed by D2loop Sequences and Complete Cytochrome bGene Sequences of Mitochondrial DNA

本研究测定了懒猴属( Nycticebus) D 环的部分序列和细胞色素b 基因的全序列(1 140 bp) , 分析了 该属物种之间的系统发育进化关系。在DNA 水平上, 序列分析结果一致地提供了新的分类学证据: 支持Rata2 jszczak 和Groves 的观点, 即N1intermedus 只是N1 pygmaeus 的成体(Ratajszczak , 1998 ; Groves , 1971) 。对两种 序列的数据做了联合及个别分析, 获得相似的系统树, 支持懒猴属由两个单系群组成: 第一群由N1 pygmaeus 聚成, 第二群由N1coucang 聚成。该结果也提供了新的分子遗传证据, 支持懒猴属由N1coucang 和 N1 pygmaeus 两物种组成。

Identification of native American founder mtDNAs through the analysis of complete mtDNA sequences: Some caveats

In this study, a detailed analysis of both previously published and new data was performed to determine whether complete, or almost complete, mtDNA sequences can resolve the long-debated issue of which Asian mtDNAs were founder sequences for the Native American mtDNA pool. Unfortunately, we now know that coding region data and their analysis are not without problems. To obtain and report reasonably correct sequences does not seem to be a trivial task, and to discriminate between Asian-and Native American mtDNA ancestries may be more complex than previously believed. It is essential to take into account the effects of mutational hot spots in both the control and coding regions, so that the number of apparent Native American mtDNA founder sequences is not erroneously inflated. As we report here, a careful analysis of all available data indicates that there is very little evidence that more than five founder mtDNA sequences entered Beringia before the Last Glacial Maximum and left their traces in the current Native American mtDNA pool.

Phylogeny of East Asian mitochondrial DNA lineages inferred from complete sequences

The now-emerging mitochondrial DNA ( mtDNA) population genomics provides information for reconstructing a well-resolved mtDNA phylogeny and for discerning the phylogenetic status of the subcontinentally specific haplogroups. Although several major East Asian mtDNA haplogroups have been identified in studies elsewhere, some of the most basal haplogroups, as well as numerous minor subhaplogroups, were not yet determined or fully characterized. To fill the lacunae, we selected 48 mtDNAs from >2,000 samples across China for complete sequencing that cover virtually all ( sub) haplogroups discernible to date in East Asia. This East Asian mtDNA phylogeny can henceforth serve as a solid basis for phylogeographic analyses of mtDNAs, as well as for studies of mitochondrial diseases in East and Southeast Asia.