Restricted inverse optimal value problem on linear programming under weighted l1l_1 norm

We study the restricted inverse optimal value problem on linear programming under weighted $l_1$ norm (RIOVLP $_1$). Given a linear programming problem $LP_c: \min \{cx|Ax=b,x\geq 0\}$ with a feasible solution $x^0$ and a value $K$, we aim to adjust the vector $c$ to $\bar{c}$ such that $x^0$ becomes an optimal solution of the problem LP$_{\bar c}$ whose objective value $\bar{c}x^0$ equals $K$. The objective is to minimize the distance $\|\bar c - c\|_1=\sum_{j=1}^nd_j|\bar c_j-c_j|$ under weighted $l_1$ norm.Firstly, we formulate the problem (RIOVLP$_1$) as a linear programming problem by dual theories. Secondly, we construct a sub-problem $(D^z)$, which has the same form as $LP_c$, of the dual (RIOVLP$_1$) problem corresponding to a given value $z$. Thirdly, when the coefficient matrix $A$ is unimodular, we design a binary search algorithm to calculate the critical value $z^*$ corresponding to an optimal solution of the problem (RIOVLP$_1$). Finally, we solve the (RIOV) problems on Hitchcock and shortest path problem, respectively, in $O(T_{MCF}\log\max\{d_{max},x^0_{max},n\})$ time, where we solve a sub-problem $(D^z)$ by minimum cost flow in $T_{MCF}$ time in each iteration. The values $d_{max},x^0_{max}$ are the maximum values of $d$ and $x^0$, respectively

One-step of tryptophan attenuator inactivation and promoter swapping to improve the production of L-tryptophan in Escherichia coli

<p>Abstract</p> <p>Background</p> <p>L-tryptophan is an aromatic amino acid widely used in the food, chemical and pharmaceutical industries. In <it>Escherichia coli</it>, L-tryptophan is synthesized from phosphoenolpyruvate and erythrose 4-phosphate by enzymes in the shikimate pathway and L-tryptophan branch pathway, while L-serine and phosphoribosylpyrophosphate are also involved in L-tryptophan synthesis. In order to construct a microbial strain for efficient L-tryptophan production from glucose, we developed a one step tryptophan attenuator inactivation and promoter swapping strategy for metabolic flux optimization after a base strain was obtained by overexpressing the <it>tktA</it>, mutated <it>trpE </it>and <it>aroG </it>genes and inactivating a series of competitive steps.</p> <p>Results</p> <p>The engineered <it>E. coli </it>GPT1002 with tryptophan attenuator inactivation and tryptophan operon promoter substitution exhibited 1.67 ~ 9.29 times higher transcription of tryptophan operon genes than the control GPT1001. In addition, this strain accumulated 1.70 g l^-1L-tryptophan after 36 h batch cultivation in 300-mL shake flask. Bioreactor fermentation experiments showed that GPT1002 could produce 10.15 g l^-1L-tryptophan in 48 h.</p> <p>Conclusions</p> <p>The one step inactivating and promoter swapping is an efficient method for metabolic engineering. This method can also be applied in other bacteria.</p

Detecting Cosmic 21 cm Global Signal Using an Improved Polynomial Fitting Algorithm

Detecting the cosmic 21 cm signal from Epoch of Reionization (EoR) has always been a difficult task. Although the Galactic foreground can be regarded as a smooth power-law spectrum, due to the chromaticity of the antenna, additional structure will be introduced into the global spectrum, making the polynomial fitting algorithm perform poorly. In this paper, we introduce an improved polynomial fitting algorithm - the Vari-Zeroth-Order Polynomial (VZOP) fitting and use it to fit the simulation data. This algorithm is developed for the upcoming Low-frequency Anechoic Chamber Experiment (LACE), yet it is a general method suitable for application in any single antenna-based global 21 cm signal experiment. VZOP defines a 24-hour averaged beam model that brings information about the antenna beam into the polynomial model. Assuming that the beam can be measured, VZOP can successfully recover the 21 cm absorption feature, even if the beam is extremely frequency-dependent. In real observations, due to various systematics, the corrected measured beam contains residual errors that are not completely random. Assuming the errors are frequency-dependent, VZOP is capable of recovering the 21 cm absorption feature even when the error reaches 10%. Even in the most extreme scenario where the errors are completely random, VZOP can at least give a fitting result that is not worse than the common polynomial fitting. In conclusion, the fitting effect of VZOP depends on the structure of the error and the accuracy of the beam measurement.Comment: 14 pages, 15 figures, Accepted for publication in MNRA

Rich Collection of n-Propylamine and Isopropylamine Conformers: Rotational Fingerprints and State-of-the-Art Quantum Chemical Investigation

The conformational isomerism of isopropylamine and n-propylamine has been investigated by means of an integrated strategy combining high-level quantum-chemical calculations and high-resolution rotational spectroscopy. The equilibrium structures (and thus equilibrium rotational constants) as well as relative energies of all conformers have been computed using the so-called "cheap" composite scheme, which combines the coupled-cluster methodology with second-order Møller-Plesset perturbation theory for extrapolation to the complete basis set. Methods rooted in the density functional theory have been instead employed for computing spectroscopic parameters and for accounting for vibrational effects. Guided by quantum-chemical predictions, the rotational spectra of isopropylamine and n-propylamine have been investigated between 2 and 400 GHz with Fourier transform microwave and frequency-modulation millimeter/submillimeter spectrometers. Spectral assignments confirmed the presence of several conformers with comparable stability and pointed out possible Coriolis resonance effects between some of them

How to Identify and Separate Bright Galaxy Clusters from the Low-frequency Radio Sky?

In this work we simulate the $50-200$ MHz radio sky that is constrained in the field of view ($5^{\circ}$ radius) of the 21 Centimeter Array (21CMA), by carrying out Monte-Carlo simulations to model redshifted cosmological reionization signals and strong contaminating foregrounds, including emissions from our Galaxy, galaxy clusters, and extragalactic point sources. As an improvement of previous works, we consider in detail not only random variations of morphological and spectroscopic parameters within the ranges allowed by multi-band observations, but also evolution of radio halos in galaxy clusters, assuming that relativistic electrons are re-accelerated in the ICM in merger events and lose energy via both synchrotron emission and inverse Compton scattering with CMB photons. By introducing a new approach designed on the basis of independent component analysis (ICA) and wavelet detection algorithm, we prove that, with a cumulative observation of one month with the 21CMA array, about $80\%$ of galaxy clusters with central brightness temperatures of $> 10~{\rm K}$ at 65 MHz can be safely identified and separated from the overwhelmingly bright foreground. We find that the morphological and spectroscopic distortions are extremely small as compared to the input simulated clusters, and the reduced $\chi^2$ of brightness temperature profiles and spectra are controlled to be $\lesssim 0.5$ and $\lesssim 1.3$, respectively. These results robustly indicate that in the near future a sample of dozens of bright galaxy clusters will be disentangled from the foreground in 21CMA observations, the study of which will greatly improve our knowledge about cluster merger rates, electron acceleration mechanisms in cluster radio halos, and magnetic field in the ICM.Comment: 35 pages, 10 figures, Accepted for publication in The Astrophysical Journa

Elevational Patterns of Species Richness, Range and Body Size for Spiny Frogs

Quantifying spatial patterns of species richness is a core problem in biodiversity theory. Spiny frogs of the subfamily Painae (Anura: Dicroglossidae) are widespread, but endemic to Asia. Using spiny frog distribution and body size data, and a digital elevation model data set we explored altitudinal patterns of spiny frog richness and quantified the effect of area on the richness pattern over a large altitudinal gradient from 0–5000 m a.s.l. We also tested two hypotheses: (i) the Rapoport's altitudinal effect is valid for the Painae, and (ii) Bergmann's clines are present in spiny frogs. The species richness of Painae across four different altitudinal band widths (100 m, 200 m, 300 m and 400 m) all showed hump-shaped patterns along altitudinal gradient. The altitudinal changes in species richness of the Paini and Quasipaini tribes further confirmed this finding, while the peak of Quasipaini species richness occurred at lower elevations than the maxima of Paini. The area did not explain a significant amount of variation in total, nor Paini species richness, but it did explain variation in Quasipaini. Five distinct groups across altitudinal gradient were found. Species altitudinal ranges did not expand with an increase in the midpoints of altitudinal ranges. A significant negative correlation between body size and elevation was exhibited. Our findings demonstrate that Rapoport's altitudinal rule is not a compulsory attribute of spiny frogs and also suggest that Bergmann's rule is not generally applicable to amphibians. The study highlights a need to explore the underlying mechanisms of species richness patterns, particularly for amphibians in macroecology