Ancient Chinese algorithm: The Ying Buzu Shu (method of surplus and deficiency) vs Newton iteration method

Air exploratory discussion of an ancient Chinese algorithm, the Ying Buzu Shu, in about 2nd century BC, known as the rule of double false position in the West is given. In addition to pointing out that the rule of double false position is actually a translation version of the ancient Chinese algorithm, a comparison with well-known Newton iteration method is also made. If derivative is introduced, the ancient Chinese algorithm reduces to the Newton method. A modification of the ancient Chinese algorithm is also proposed, and some of applications to nonlinear oscillators are illustrated.

Origin of Chinese ancient glasses;study on the earliest Chinese ancient glasses

The earliest Chinese ancient glasses before the West Han Dynasty (200 BC) from different regions are studied. The glass samples were unearthed from Hunan, Hubei, Yunnan, Sichuan, Guizhou, Guangdong and Xinjiang of China. The chemical composition of these glasses samples is analyzed by proton induced X-ray emission (PIXE) technique, energy dispersive X-ray fluorescence (EDXRF) method and inductively coupled plasma atomic emission spectrometry (ICP-AES). It is shown that the glass chemical compositions belong to barium-lead silicate BaO-PbO-SiO2, potash soda lime silicate K2O (Na2O)-CaO-SiO2 (K2O/Na2O > 1), soda potash lime silicate Na2O (K2O)-CaO-SiO2 (K2O/Na2O < 1) and potash silicate K2O-SiO2 glass systems, respectively. The origins of the earliest Chinese ancient glasses are discussed from the archaeological and historical points of view. These four types of Chinese ancient glasses were all made in Chinese territory using local raw materials. The glass preparation technology was related to the Chinese ancient bronze metallurgy and proto-porcelain glaze technology. The glass technology relationship between the East and the West is analyzed at the same time.

Pitfalls in the analysis of ancient human mtDNA

The retrieval of DNA from ancient human specimens is not always successful owing to DNA deterioration and contamination although it is vital to provide new insights into the genetic structure of ancient people and to reconstruct the past history. Normally, only short DNA fragments can be retrieved from the ancient specimens. How to identify the authenticity of DNA obtained and to uncover the information it contained are difficult. We employed the ancient mtDNAs reported from Central Asia (including Xinjiang, China) as an example to discern potentially extraneous DNA contamination based on the updated mtDNA phylogeny derived from mtDNA control region, coding region, as well as complete sequence information. Our results demonstrated that many mtDNAs reported are more or less problematic. Starting from a reliable mtDNA phylogeney and combining the available modern data into analysis, one can ascertain the authenticity of the ancient DNA, distinguish the potential errors in a data set, and efficiently decipher the meager information it harbored. The reappraisal of the mtDNAs with the age of more than 2000 years from Central Asia gave support to the suggestion of extensively (pre)historical gene admixture in this region.

A mitogenomic perspective on the ancient, rapid radiation in the Galliformes with an emphasis on the Phasianidae

Background: The Galliformes is a well-known and widely distributed Order in Aves. The phylogenetic relationships of galliform birds, especially the turkeys, grouse, chickens, quails, and pheasants, have been studied intensively, likely because of their close association with humans. Despite extensive studies, convergent morphological evolution and rapid radiation have resulted in conflicting hypotheses of phylogenetic relationships. Many internal nodes have remained ambiguous. Results: We analyzed the complete mitochondrial (mt) genomes from 34 galliform species, including 14 new mt genomes and 20 published mt genomes, and obtained a single, robust tree. Most of the internal branches were relatively short and the terminal branches long suggesting an ancient, rapid radiation. The Megapodiidae formed the sister group to all other galliforms, followed in sequence by the Cracidae, Odontophoridae and Numididae. The remaining clade included the Phasianidae, Tetraonidae and Meleagrididae. The genus Arborophila was the sister group of the remaining taxa followed by Polyplectron. This was followed by two major clades: ((((Gallus, Bambusicola) Francolinus) (Coturnix, Alectoris)) Pavo) and (((((((Chrysolophus, Phasianus) Lophura) Syrmaticus) Perdix) Pucrasia) (Meleagris, Bonasa)) ((Lophophorus, Tetraophasis) Tragopan))). Conclusions: The traditional hypothesis of monophyletic lineages of pheasants, partridges, peafowls and tragopans was not supported in this study. Mitogenomic analyses recovered robust phylogenetic relationships and suggested that the Galliformes formed a model group for the study of morphological and behavioral evolution.

Reconstructing the evolutionary history of China: A caveat about inferences drawn from ancient DNA

The decipherment of the meager information provided by short fragments of ancient mitochondrial DNA (mtDNA) is notoriously difficult but is regarded as a most promising way toward reconstructing the past from the genetic perspective. By haplogroup-specific hypervariable segment (HVS) motif search and matching or near-matching with available modem data sets, most of the ancient mtDNAs can be tentatively assigned to haplogroups, which are often subcontinent specific. Further typing for mtDNA haplogroup-diagnostic coding region polymorphisms, however, is indispensable for establishing the geographic/genetic affinities of ancient samples with less ambiguity. In the present study, we sequenced a fragment (similar to 982 bp) of the mtDNA control region in 76 Han individuals from Taian, Shandong, China, and we combined these data with previously reported samples from Zibo and Qingdao, Shandong. The reanalysis of two previously published ancient mtDNA population data sets from Linzi (same province) then indicates that the ancient populations had features in common with the modem populations from south China rather than any specific affinity to the European mtDNA pool. Our results highlight that ancient mtDNA data obtained under different sampling schemes and subject to potential contamination can easily create the impression of drastic spatiotemporal changes in the genetic structure of a regional population during the past few thousand years if inappropriate methods of data analysis are employed.

Independent adaptation to riverine habitats allowed survival of ancient cetacean lineages

The four species of "river dolphins" are associated with six separate great river systems on three subcontinents and have been grouped for more than a century into a single taxon based on their similar appearance. However, several morphologists recently questioned the monophyly of that group. By using phylogenetic analyses of nucleotide sequences from three mitochondrial and two nuclear genes, we demonstrate with statistical significance that extant river dolphins are not monophyletic and suggest that they are relict species whose adaptation to riverine habitats incidentally insured their survival against major environmental changes in the marine ecosystem or the emergence of Delphinidae.

On equations for regular languages, finite automata, and sequential networks

We consider systems of equations of the form where A is the underlying alphabet, the Xi are variables, the Pi,a are boolean functions in the variables Xi, and each δi is either the empty word or the empty set. The symbols υ and denote concatenation and union of languages over A. We show that any such system has a unique solution which, moreover, is regular. These equations correspond to a type of automation, called boolean automation, which is a generalization of a nondeterministic automation. The equations are then used to determine the language accepted by a sequential network; they are obtainable directly from the network.

practical type checking of functions defined on context-free languages

A type checking method for the functional language LFC is presented. A distinct feature of LFC is that it uses Context-Free (CF) languages as data types to represent compound data structures. This makes LFC a dynamically typed language. To improve efficiency, a practical type checking method is presented, which consists of both static and dynamic type checking. Although the inclusion relation of CF.languages is not decidable,a special subset of the relation is decidable, i.e., the sentential form relation, which can be statically checked.Moreover, most of the expressions in actual LFC programs appear to satisfy this relation according to the statistic data of experiments. So, despite that the static type checking is not complete, it undertakes most of the type checking task. Consequently the run-time efficiency is effectively improved. Another feature of the type checking is that it converts the expressions with implicit structures to structured representation. Structure reconstruction technique is presented.