AC-KBO Revisited

Equational theories that contain axioms expressing associativity and commutativity (AC) of certain operators are ubiquitous. Theorem proving methods in such theories rely on well-founded orders that are compatible with the AC axioms. In this paper we consider various definitions of AC-compatible Knuth-Bendix orders. The orders of Steinbach and of Korovin and Voronkov are revisited. The former is enhanced to a more powerful version, and we modify the latter to amend its lack of monotonicity on non-ground terms. We further present new complexity results. An extension reflecting the recent proposal of subterm coefficients in standard Knuth-Bendix orders is also given. The various orders are compared on problems in termination and completion.Comment: 31 pages, To appear in Theory and Practice of Logic Programming (TPLP) special issue for the 12th International Symposium on Functional and Logic Programming (FLOPS 2014

The dependency pair framework: Combining techniques for automated termination proofs

Abstract. The dependency pair approach is one of the most powerful techniques for automated termination proofs of term rewrite systems. Up to now, it was regarded as one of several possible methods to prove termination. In this paper, we show that dependency pairs can instead be used as a general concept to integrate arbitrary techniques for termination analysis. In this way, the benefits of different techniques can be combined and their modularity and power are increased significantly. We refer to this new concept as the “dependency pair framework ” to distinguish it from the old “dependency pair approach”. Moreover, this framework facilitates the development of new methods for termination analysis. To demonstrate this, we present several new techniques within the dependency pair framework which simplify termination problems considerably. We implemented the dependency pair framework in our termination prover AProVE and evaluated it on large collections of examples.

A static higher-order dependency pair framework

We revisit the static dependency pair method for proving termination of higher-order term rewriting and extend it in a number of ways: (1) We introduce a new rewrite formalism designed for general applicability in termination proving of higher-order rewriting, Algebraic Functional Systems with Meta-variables. (2) We provide a syntactically checkable soundness criterion to make the method applicable to a large class of rewrite systems. (3) We propose a modular dependency pair framework for this higher-order setting. (4) We introduce a fine-grained notion of formative and computable chains to render the framework more powerful. (5) We formulate several existing and new termination proving techniques in the form of processors within our framework. The framework has been implemented in the (fully automatic) higher-order termination tool WANDA

Computer simulation of diffusion processes in tilt spatio-periodic potentials

Нещодавно було показано, що в істотно нерівноважних системах коефіцієнт дифузії може вести себе немонотонно з температурою. Одним із прикладів таких систем з аномальною температурної залежністю є рух броунівських часток в просторово-періодичних структурах. Метою статті було дослідження зміни температурної залежності дифузії в недодемпфованих системах з низьким коефіцієнтом тертя. В роботі методами комп'ютерного моделювання вивчено зміна коефіцієнта дифузії частинок в широкому діапазоні температур в нахилених просторово-періодичних потенціалах для різних значень коефіцієнта тертя. Показано, що дифузія досягає максимуму при певній величині зовнішньої сили. Її значення залежить від величини коефіцієнта тертя. Показано, що на відміну від звичайної залежності Аррениуса, в разі нахиленого періодичного потенціалу, максимальний коефіцієнт дифузії зростає, а не зменшується з пониженням температури експоненціальним чином. Встановлено, що така залежність характерна для всіх недодемпфованих систем. Показано, що для просторово-періодичних структур існує обмежена ділянка сил, в якому спостерігається зростання коефіцієнта дифузії зі зменшенням температури. Це область так званої температурно-аномальної дифузії (ТАД). Визначено ширина і положення області ТАД в залежності від коефіцієнта тертя γ і параметрів системи. Показано, що зі зменшенням γ, ширина області ТАД зменшується пропорційно γ. При цьому коефіцієнт дифузії в області ТАД, навпаки зростає ~γ. Отримані дані про температурно-аномальної дифузії мають важливе значення для різних областей фізики і техніки та відкривають перспективи створення новітніх технологій управління процесами дифузії.It was recently shown that in essentially nonequilibrium systems, the diffusion coefficient can behave nonmonotonically with temperature. One example of such systems with anomalous temperature dependence is the motion of Brownian particles in spatially periodic structures. The aim of the article was to study the change in the temperature dependence of diffusion in underdamped systems with a low coefficient of friction. In this paper, computer simulation methods are used to study the change in the diffusion coefficient of particles in a wide range of temperatures in oblique spatially periodic potentials for different values of the friction coefficient. It is shown that diffusion reaches a maximum at a certain external force. Its value depends on the coefficient of friction. It is shown that, in contrast to the usual Arrhenius dependence, in the case of an inclined periodic potential, the maximum diffusion coefficient increases while temperature is decreasing exponentially. It is established that such a dependence is common to all underdamped systems. It is shown that for spatially periodic structures there is a limited portion of forces in which an increase in the diffusion coefficient while decreasing temperature is observed. This is the area of the so-called temperature-anomalous diffusion (TAD). The width and position of the TAD region are determined depending on the friction coefficient γ and the system parameters. It has been shown that a decrease in γ, width TAD region decreases proportionally γ. In this case, the diffusion coefficient in the TAD region, on the contrary, increases ~γ. The data obtained on the temperature and the anomalous diffusion are important for various fields of physics and engineering, and opens new prospects for a diffusion process control technology

Calculation of the properties of the rotational bands of 155,157^{155,157}Gd

We reexamine the long-standing problem of the microscopic derivation of a particle-core coupling model. We base our research on the Klein-Kerman approach, as amended by D\"onau and Frauendorf. We describe the formalism to calculate energy spectra and transition strengths in some detail. We apply our formalism to the rotational nuclei $^{155,157}$Gd, where recent experimental data requires an explanation. We find no clear evidence of a need for Coriolis attenuation.Comment: 27 pages, 13 uuencoded postscript figures. Uses epsf.st

E0 Transitions and the Depopulation of SD Bands

We present the results of calculations showing that E0 transitions may successfully compete with other types of electromagnetic transitions in the decay out of SD bands

Transcriptome analysis of Bupleurum chinense focusing on genes involved in the biosynthesis of saikosaponins

<p>Abstract</p> <p>Background</p> <p><it>Bupleurum chinense </it>DC. is a widely used traditional Chinese medicinal plant. Saikosaponins are the major bioactive constituents of <it>B. chinense</it>, but relatively little is known about saikosaponin biosynthesis. The 454 pyrosequencing technology provides a promising opportunity for finding novel genes that participate in plant metabolism. Consequently, this technology may help to identify the candidate genes involved in the saikosaponin biosynthetic pathway.</p> <p>Results</p> <p>One-quarter of the 454 pyrosequencing runs produced a total of 195, 088 high-quality reads, with an average read length of 356 bases (NCBI SRA accession SRA039388). A <it>de novo </it>assembly generated 24, 037 unique sequences (22, 748 contigs and 1, 289 singletons), 12, 649 (52.6%) of which were annotated against three public protein databases using a basic local alignment search tool (E-value ≤1e-10). All unique sequences were compared with NCBI expressed sequence tags (ESTs) (237) and encoding sequences (44) from the <it>Bupleurum </it>genus, and with a Sanger-sequenced EST dataset (3, 111). The 23, 173 (96.4%) unique sequences obtained in the present study represent novel <it>Bupleurum </it>genes. The ESTs of genes related to saikosaponin biosynthesis were found to encode known enzymes that catalyze the formation of the saikosaponin backbone; 246 cytochrome P450 (<it>P450</it>s) and 102 glycosyltransferases (<it>GT</it>s) unique sequences were also found in the 454 dataset. Full length cDNAs of 7 <it>P450</it>s and 7 uridine diphosphate <it>GT</it>s (<it>UGT</it>s) were verified by reverse transcriptase polymerase chain reaction or by cloning using 5' and/or 3' rapid amplification of cDNA ends. Two <it>P450</it>s and three <it>UGT</it>s were identified as the most likely candidates involved in saikosaponin biosynthesis. This finding was based on the coordinate up-regulation of their expression with <it>β-AS </it>in methyl jasmonate-treated adventitious roots and on their similar expression patterns with <it>β-AS </it>in various <it>B. chinense </it>tissues.</p> <p>Conclusions</p> <p>A collection of high-quality ESTs for <it>B. chinense </it>obtained by 454 pyrosequencing is provided here for the first time. These data should aid further research on the functional genomics of <it>B. chinense </it>and other <it>Bupleurum </it>species. The candidate genes for enzymes involved in saikosaponin biosynthesis, especially the <it>P450</it>s and <it>UGT</it>s, that were revealed provide a substantial foundation for follow-up research on the metabolism and regulation of the saikosaponins.</p