Adaptive varying-coefficient linear quantile model: a profiled estimating equations approach

We consider an estimating equations approach to parameter estimation in adaptive varying-coefficient linear quantile model. We propose estimating equations for the index vector of the model in which the unknown nonparametric functions are estimated by minimizing the check loss function, resulting in a profiled approach. The estimating equations have a bias-corrected form that makes undersmoothing of the nonparametric part unnecessary. The estimating equations approach makes it possible to obtain the estimates using a simple fixed-point algorithm. We establish asymptotic properties of the estimator using empirical process theory, with additional complication due to the nuisance nonparametric part. The finite sample performance of the new model is illustrated using simulation studies and a forest fire dataset.     

Solving the FCSR synthesis problem for multi-sequences by lattice basis reduction

Register synthesis for multi-sequences has significance for the security of word-oriented stream ciphers. Feedback with carry shift registers (FCSRs) are promising alternatives to linear feedback shift registers for the design of stream ciphers. In this paper, we solve the FCSR synthesis problem for multi-sequences by two rational approximation algorithms using lattice theory. One is based on the lattice reduction greedy algorithm proposed by Nguyen and Stehlé (ACM Trans Algorithms (TALG) 5(4):46, 2009). The other is based on the LLL algorithm which is a polynomial time lattice reduction algorithm. Both of these rational approximation algorithms can find the smallest common FCSR for a given multi-sequence but with different numbers of known terms. When the number of sequences within the multi-sequence is less than or equal to 3, the former is suggested because it has better time complexity and fewer terms are needed. Otherwise, the latter will have better time complexity.     

Bifurcations in a delayed differential-algebraic plankton economic system

This paper considers a phytoplankton-zooplankton bio-economic system with delay and harvesting, which is described by differential-algebraic equations. Local stability analysis of the system without delay reveals that a singularity-induced bifurcation phenomenon appears when a variation of the economic interest is taken into account, furthermore, a state feedback controller is designed to stabilize the system at the interior equilibrium. Then, we show that delay, which is considered in the toxic liberation, can induce stability switches, such that the positive equilibrium switches from stability to instability, to stability again and so on. Finally, some numerical simulations are performed to justify analytical findings.     

Hopf-zero bifurcation of a delayed predator-prey model with dormancy of predators

In this paper, We investigate Hopf-zero bifurcation with codimension 2 in a delayed predator-prey model with dormancy of predators. First we prove the specific existence condition of the coexistence equilibrium. Then we take the mortality rate and time delay as two bifurcation parameters to find the occurrence condition of Hopf-zero bifurcation in this model. Furthermore, using the Faria and Magalhases normal form method and the center manifold theory, we obtain the third order degenerate normal form with two original parameters. Finally, through theoretical analysis and numerical simulations, we give a bifurcation set and a phase diagram to show the specific relations between the normal form and the original system, and explain the coexistence phenomena of several locally stable states, such as the coexistence of multi-periodic orbits, as well as the coexistence of a locally stable equilibrium and a locally stable periodic orbit.     

具有两个同阶轨道的双轨道图的圈边连通度

一个边割被称为圈边割,如果该边割能分离图的两个不同圈.如果一个图有圈边割,称该图为圈边可分离的.一个圈边可分离图G的最小圈边割的阶数被称为圈边连通度,记作cλ（G）.定义：ζ（G）=min{w（X）｜X导出G的最短圈},其中w（X）为端点分别在X和V（G）-X中的边的数目.如果一个圈边可分离图G使得cλ（G）=ζ（G）成立,称该图是圈边最优的.Tian和Meng在文章[11]以及Yang et al在文章[15]中研究了两种不同的双轨道图的圈边最优性.本文我们将研究具有两个同阶轨道的双轨道图的圈边连通度.     

New fuzzy models for time-cost trade-off problem

The time-cost trade-off problem is a specific type of the project scheduling problem which studies how to modify project activities so as to achieve the trade-off between the completion time and the project cost. In real projects, the trade-off between the project cost and the completion time, and the uncertainty of the environment are both considerable aspects for managers. In this paper, three new fuzzy time-cost trade-off models are proposed, in which credibility theory is applied to describe the uncertainty of activity duration times. A searching method by integrating fuzzy simulation and genetic algorithm is produced to search the quasi-optimal schedules under some decision-making criteria. The purpose of the paper is to reveal how to obtain the optimal balance of the completion time and the project cost in fuzzy environments.     

Multiple bifurcation analysis in a NDDE arising from van der Pol’s equation with extended delay feedback

Van der Pol’s equation with extended delay feedback control is considered, which is equivalent to a system of neutral differential–difference equations (NDDEs). Fold bifurcation and Hopf bifurcation in this NDDE are studied by the formal adjoint theory, the center manifold theorem and the normal form method. These methods are also first employed in studying the Bogdanov–Takens singularity of NDDE. Bifurcation sets theoretically indicate the existence of a homoclinic orbit and the coexistence of three periodic solutions, which are all illustrated by the numerical methods. The coexistence of three stable periodic solutions and the existence of stable torus near the Hopf–fold and Hopf–Hopf bifurcations are also illustrated, respectively.     

Nonlinear waves in complex oscillator network with delay

We investigate the spatio-temporal patterns of Hopf bifurcating periodic solutions in a delay complex oscillator network. Firstly, we calculate the critical values of Hopf bifurcation. Secondly, the bifurcating periodic solutions can take on two cases: one is synchronization or anti-synchronization, and another is the coexistence of two phase-locked, N mirror-reflecting and N standing waves, because the system has group symmetry. Finally, the stability of these nonlinear oscillations is determined using the center manifold theorem and normal form method with the imaginary eigenvalues being simple and double.     

Pressure effects on structural,electronic, absorption,and thermodynamic properties of crystalline 2,4,6‐triamino‐3,5‐dinitropyridine‐1‐oxide: A DFT study

Density functional theory calculations have been performed to study the structural, electronic, absorption, and thermodynamic properties of crystalline 2,4,6‐triamino‐3,5‐dinitropyridine‐1‐oxide (TANPyo) in the pressure range of 0–50 GPa. The variation trends of the lattice constants, bond lengths, bond angles, intramolecular H‐bonds, and dihedral angles under compression show that there are two structural transformations at 17 and 38 GPa, respectively. The remarkable changes in the bond lengths indicate that there are two possible initiation decomposition mechanisms of TANPyo under compression. As the pressure increases, the intramolecular H‐bond strengthens. The obvious changes of the dihedral angles show that the planar structure of the TANPyo molecule is damaged under compression. Its absorption spectra show that as the pressure increases, the absorption coefficient of the N–H stretching decreases, while that of the O–H stretching increases. TANPyo has relatively high optical activity at high pressure. An analysis of thermodynamic properties indicates that both two structural transformations are endothermic and not spontaneous at room temperature. Copyright © 2013 John Wiley & Sons, Ltd.     

Light‐Driven Kinetic Resolution of α‐Functionalized Carboxylic Acids Enabled by an Engineered Fatty Acid Photodecarboxylase

Chiral α‐functionalized carboxylic acids are valuable precursors for a variety of medicines and natural products. Herein, we described an engineered fatty acid photodecarboxylase (CvFAP)‐catalyzed kinetic resolution of α‐amino acids and α‐hydroxy acids, which provides the unreacted R‐configured substrates with high yields and excellent stereoselectivity (ee up to 99 %). This efficient light‐driven process requires neither NADPH recycling nor prior preparation of esters, which were required in previous biocatalytic approaches. The structure‐guided engineering strategy is based on the scanning of large amino acids at hotspots to narrow the substrate binding tunnel. To the best of our knowledge, this is the first example of asymmetric catalysis by an engineered CvFAP.