Finding a minimum stretch of a function

Given a piecewise monotone function f : R ! R and a real value Tmin, we develop an algorithm that finds an interval of length at least Tmin for which the average value of f is minimized. The run-time of the algorithm is linear in the number of monotone pieces of f if certain operations are available in constant time for f. We use this algorithm to solve a basic problem arising in the analysis of trajectories: Finding the most similar subtrajectories of two given trajectories, provided that the duration is at least Tmin. Since the precise solution requires complex operations, we also give a simple (1+")approximation algorithm in which these operations are not needed

Finding long and similar parts of trajectories

A natural time-dependent similarity measure for two trajectories is their average distance at corresponding times. We give algorithms for computing the most similar subtrajectories under this measure, assuming the two trajectories are given as two polygonal, possibly self-intersecting lines. When a minimum duration is specified for the subtrajectories, and they must start at exactly corresponding times in the input trajectories, we give a linear-time algorithm for computing the starting time and duration of the most similar subtrajectories. The algorithm is based on a result of independent interest: We present a linear-time algorithm to find, for a piece-wise monotone function, an interval of at least a given length that has minimum average value. When the two subtrajectories can start at different times in the two input trajectories, it appears difficult to give an exact algorithm for the most similar subtrajectories problem, even if the duration of the desired two subtrajectories is fixed to some length. We show that the problem can be solved approximately, and with a performance guarantee. More precisely, we present (1 + e)-approximation algorithms for computing the most similar subtrajectories of two input trajectories for the case where the duration is specified, and also for the case where only a minimum on the duration is specified

Simultaneous saccharification and fermentation of steam exploded duckweed: Improvement of the ethanol yield by increasing yeast titre

This study investigated the conversion of Lemna minor biomass to bioethanol. The biomass was pre-treated by steam explosion (SE, 210 °C, 10 min) and then subjected to simultaneous saccharification and fermentation (SSF) using CellicÒ CTec 2 (20 U or 0.87 FPU gﰂ1 substrate) cellulase plus b-glucosidase (2 U gﰂ1 substrate) and a yeast inoculum of 10% (v/v or 8.0 ﰀ 107 cells mLﰂ1). At a substrate concentration of 1% (w/v) an ethanol yield of 80% (w/w, theoretical) was achieved. However at a substrate concentration of 20% (w/v), the ethanol yield was lowered to 18.8% (w/w, theoretical). Yields were considerably improved by increasing the yeast titre in the inoculum or preconditioning the yeast on steam exploded liquor. These approaches enhanced the ethanol yield up to 70% (w/w, theoretical) at a substrate concen- tration of 20% (w/v) by metabolising fermentation inhibitors

Effect of Chinese herbal medicines on rumen fermentation, methanogenesis and microbial flora in vitro

This study was carried out to evaluate the effects of three Chinese herbal medicines (CHMs) on rumen fermentation, methane emission and population of ruminal microbes using an in vitro gas production technique. Three healthy wethers of Dazu Black goats with similar bodyweights and permanent rumen fistulae were utilized as donors of ruminal fluid. The three botanical medicines were cablin patchouli herb (CPH), atractylodes rhizome (AR) and Amur cork tree (AC). Each CHM was added at a level of 25 g/kg to the substrate dry matter. In vitro gas production was recorded, and methane concentration was determined at 12 and 24 hours of incubation. After 24 hours, the incubation was stopped, and the inoculants were measured for pH, ammonia nitrogen and volatile fatty acids (VFAs) concentrations. Total deoxyribonucleic acid of ruminal microbes was extracted from the inocula, and populations were determined by a real-time quantitative polymerase chain reaction. Populations of total rumen methanogens, protozoa, total fungi, Ruminococcus albus, Fibrobacter succinogenes and Ruminococcus flavefaciens were expressed as a proportion of total rumen bacterial 16S ribosomal deoxyribonucleic acid. Compared to the control, CPH decreased gas production and methane production at 12 and 24 hours of incubation, and inhibited methanogens and total fungi growth. AR decreased acetate to propionate ratio, and methanogens and total fungi populations, but increased propionate molar proportion. AC decreased total VFA concentration, acetate to propionate ratio, gas production at 12 and 24 hours of incubation, methane production at 12 and 24 hours of incubation, and methanogens and total fungi growth, but increased the propionate molar proportion. In conclusion, CPH and AC both suppressed methanogenesis significantly, and the suppression was mediated primarily via the direct action against the rumen microbes involved in methane formation. AC also indirectly abates methane release by occupying the hydrogen (H2) normally utilized for methanogenesis.Keywords: In vitro gas production, methane, rumen fermentation parameter, rumen microbe

Responses of chemical composition, amino acid and fatty acid profiles of breast muscle to dietary crude fibre levels in China Micro-Ducks

The effects of dietary crude fibre (CF) levels on the chemical composition, amino acid (AA) and fatty acid (FA) profiles of breast muscle in male China Micro-ducks (21 - 56 d) were investigated in this study. The birds were randomly allocated to four treatments, of which dietary CF levels were 16.7, 42.6, 77.9 and 101.6 g/kg of dry matter (DM), respectively. No influences on the proportions of crude ash, crude protein, lysine, methionine, threonine, phenylalanine, histidine, arginine, aspartic acid, glutamic acid, glycine, alanine, serine, cysteine, tyrosine, proline, C12:0, C18:0, C18:1n9, C20:0 and C22:1n9 in muscle were observed across the treatments. Consequently, the concentrations of semi-essential AA, non-essential AA, total AA, aromatic AA and delicious AA in muscle, along with the Δ-9-desaturase (18) index, were not affected by the treatments. Significant lower concentrations of valine, leucine, isoleucine, essential AA, branched-chain AA, C16:1n7 and monounsaturated FA in muscle, along with a lower ratio of branched-chain to aromatic AA, were noted in a dietary treatment with a CF level of 16.7 g/kg DM compared to other dietary treatments. The rise of the dietary CF level significantly increased the proportions of DM, ether extract, gross energy, C18:2n6, C18:3n3, C20:4n6, unsaturated FA, total FA, polyunsaturated FA, n-3 polyunsaturated FA, n-6 polyunsaturated FA, essential FA, and the Δ-9-desaturase (16) index. Furthermore, the rise of the dietary CF level increased the ratios of unsaturated to saturated FA, polyunsaturated to saturated FA, and n-6 to n-3 polyunsaturated FA in muscle. However, it decreased the atherogenic index and the proportions of C14:0, C16:0, and saturated FA significantly. In conclusion, depending largely on dietary levels, CF profoundly and positively influenced the nutritional quality of breast muscle, especially the FA profile.Keywords: China Micro-duck, dietary fibre, fatty acid, nutritional quality of meat, fatty aci

Two-Body Cabibbo-Suppressed Charmed Meson Decays

Singly-Cabibbo-suppressed decays of charmed particles governed by the quark subprocesses $c \to s u \bar s$ and $c \to d u \bar d$ are analyzed using a flavor-topology approach, based on a previous analysis of the Cabibbo-favored decays governed by $c \to s u \bar d$. Decays to $PP$ and $PV$, where $P$ is a pseudoscalar meson and $V$ is a vector meson, are considered. We include processes in which $\eta$ and $\eta '$ are produced.Comment: 18 pages, latex, 2 figures, to be submitted to Phys. Rev.

Z(3) Flavor Symmetry and Possible Implications

We show in this paper that the Z(3) flavor symmetry, which can successfully produce the tri-bimaximal mixing and flavor pattern of neutrino sector, has a possible explanation in the framework of gauge symmetry by constructing a wavefunction of flavor state particles with the help of the Wilson loop. In this implementation of Z(3) flavor symmetry, we suggest that the flavor charge in weak interaction can be interpreted as a topological charge. Its possible implications and generalizations to the quark sector are also discussed.Comment: 9 pages, no figures, final version for Phys. Lett.

Charmless Two-body Baryonic B Decays

We study charmless two-body baryonic B decays in a diagramatic approach. Relations on decay amplitudes are obtained. In general there are more than one tree and more than one penguin amplitudes. The number of independent amplitudes can be reduced in the large m_B limit. It leads to more predictive results. Some prominent modes for experimental searches are pointed out.Comment: 15 pages, 2 figures. To appear in Phys. Rev.