CONTACT GEOMETRY OF THIRD-ORDER PARTIAL DIFFERENTIAL EQUATIONS WITH TWO INDEPENDENT VARIABLES

We develop rigorously a geometric theory of third-order partial differential equations for a scalar function. Under our framework, we can define a notion of nilpotent graded Lie algebras as an invariant useful to study geometry of third-order equations. In terms of these graded Lie algebras, we provide a classification for some classes of third-order equations under a contact equivalence. By this classification, together with model equations, we also clarify several aspects for each subcategory of equations

BAO Extractor: bias and redshift space effects

We study a new procedure to measure the sound horizon scale via Baryonic Acoustic Oscillations (BAO). Instead of fitting the measured power spectrum (PS) to a theoretical model containing the cosmological informations and all the nonlinear effects, we define a procedure to project out (or to "extract") the oscillating component from a given nonlinear PS. We show that the BAO scale extracted in this way is extremely robust and, moreover, can be reproduced by simple theoretical models at any redshift. By using N-body simulations, we discuss the effect of the nonlinear evolution of the matter field, of redshift space distortions and of scale-dependent halo bias, showing that all these effects can be reproduced with sub-percent accuracy. We give a one-parameter theoretical model based on a simple (IR) modification of 1-loop perturbation theory, which reproduces the BAO scale from measurements of halo clustering in redshift space at better than $0.1\%$ level and does not need any external UV input, such as coefficients measured from N-body simulations.Comment: Published version. 32 pages, 15 figure

Left–Right Reversal Recurrently Evolved Regardless of Diaphanous-Related Formin Gene Duplication or Loss in Snails

Bilateria exhibit whole-body handedness in internal structure. This left–right polarity is evolutionarily conserved with virtually no reversed extant lineage, except in molluscan Gastropoda. Phylogenetically independent snail groups contain both clockwise-coiled (dextral) and counterclockwise-coiled (sinistral) taxa that are reversed from each other in bilateral handedness as well as in coiling direction. Within freshwater Hygrophila, Lymnaea with derived dextrality have diaphanous related formin (diaph) gene duplicates, while basal sinistral groups possess one diaph gene. In terrestrial Stylommatophora, dextral Bradybaena also have diaph duplicates. Defective maternal expression of one of those duplicates gives rise to sinistral hatchlings in Lymnaea and handedness-mixed broods in Bradybaena, through polarity change in spiral cleavage of embryos. These findings led to the hypothesis that diaph duplication was crucial for the evolution of dextrality by reversal. The present study discovered that diaph duplication independently occurred four times and its duplicate became lost twice in gastropods. The dextrality of Bradybaena represents the ancestral handedness conserved across gastropods, unlike the derived dextrality of Lymnaea. Sinistral lineages recurrently evolved by reversal regardless of whether diaph had been duplicated. Amongst the seven formin gene subfamilies, diaph has most thoroughly been conserved across eukaryotes of the 14 metazoan phyla and choanoflagellate. Severe embryonic mortalities resulting from insufficient expression of the duplicate in both of Bradybaena and Lymnaea also support that diaph duplicates bare general roles for cytoskeletal dynamics other than controlling spiralian handedness. Our study rules out the possibility that diaph duplication or loss played a primary role for reversal evolution.journal articl

Quantum-number projection in the path-integral renormalization group method

We present a quantum-number projection technique which enables us to exactly treat spin, momentum and other symmetries embedded in the Hubbard model. By combining this projection technique, we extend the path-integral renormalization group method to improve the efficiency of numerical computations. By taking numerical calculations for the standard Hubbard model and the Hubbard model with next nearest neighbor transfer, we show that the present extended method can extremely enhance numerical accuracy and that it can handle excited states, in addition to the ground state.Comment: 11 pages, 7 figures, submitted to Phys. Rev.

Effects of specific cultivar usage and preparation methods in Japanese potato starches.

Potato starch is one of the important agricultural products in Hokkaido, the northernmost and second largest island of Japan. The aim of this study was to evaluate the effects of cultivars and starch preparation methods on the quality parameters of Japanese potato starch. Potato starches from four cultivars, Hokkaikogane, Eniwa, Benimaru and Norin No. 1, grown over a period of several years in Hokkaido were used. The starches produced with tap water in a local starch factory and with distilled water in a laboratory were investigated for phosphorus content, median granule size and peak viscosity and breakdown as determined with a Rapid Visco Analyzer (RVA). Among the starch samples used in this study, significant differences were observed across starch quality parameters. We investigated the differences in quality parameters as an effect of individual cultivars. The starch median granule size among potato cultivars varied in the following order: Benimaru (43.1 μm) > Hokkaikogane (39.1 μm) ≈Eniwa (38.2 μm) > Norin No. 1 (33.9 μm). We found that starches of Hokkaikogane and Eniwa, both with a measurably higher phosphorus content, displayed significantly higher peak viscosity and breakdown than those of Benimaru and Norin No. 1. We also examined the effect that the preparation method has on starch quality parameters within the same potato cultivar. We found that the starch preparation method had a little or no influence on phosphorus content. Median granule size was also completely independent on the preparation method. The RVA evaluation revealed that, even within the same cultivar, starches produced in a factory showed lower peak viscosity and breakdown than those produced in a laboratory

Chemical Characterization of Flour Fractions from Five Yam (Dioscorea alata) Cultivars in Indonesia

The purpose of this study was to investigate the influence of particle size on  the  chemical properties  of yam flour  in five  cultivars, yellow/YY, orange/OY, light purple/LPY, purple/PY, and dark purple/DPY. With a mesh sieve, three  flour fractions  were separated according to particle size:  small (128.6-139.7 µm), medium (228.7-257.9 µm), and large (475.4-596.3 µm). The content of moisture (6.81-11.26 %db) and lipids (4.48-9.85 %db) decreased with the increase of particle size, while proteins (4.48-9.85 %db) and carbohydrates (78.12-83.76 %db) were not influenced by particle size. Folin-Ciocalteu reagent and chlorogenic acid were used as standard to investigate the total phenolic compounds  in  the  yam  flour,  and  high-performance liquid chromatography (HPLC) was used to investigate the anthocyanin and carotene contents. It was found that there was no size influence on the content of phenolics (0.27-2.82%db), anthocyanin (2.25-15.27  mg/100g db) in LPY, PY, DPY  or  carotene (23.75-132.12 mg/100g db) in YY, OY. The differences in chemical composition were due to differences in particle size and heat treatment, but may also have been caused by the different composition of the milling process