Quasi-Newton Method for Absolute Value Equation Based on Upper Uniform Smoothing Approximation

In this paper, an upper uniform smooth approximation function of absolute value function is proposed, and some properties of uniform smooth approximation function are studied. Then, absolute value equation (AVE), Ax - |x| = b, where A is a square matrix whose singular values exceed one, is transformed into smooth optimization problem by using the upper uniform smooth approximation function, and solved by quasi-Newton method. Numerical results in solving given AVE problems demonstrated that our algorithm is valid and superior to lower uniform smooth approximation function

Iteration Methods for Linear Systems with Positive Definite Matrix

Two classical first order iteration methods, Richardson iteration and HSS iteration for linear systems with positive definite matrix, are demonstrated. Theoretical analyses and computational results show that the HSS iteration has the advantages of fast convergence speed, high computation efficiency, and without requirement of symmetry

Improved Harmony Search Algorithm with Chaos for Absolute Value Equation

 In this paper, an improved harmony search with chaos (HSCH) is presented for solving NP-hard absolute value equation (AVE) Ax - |x| = b, where A is an arbitrary square matrix whose singular values exceed one. The simulation results in solving some given AVE problems demonstrate that the HSCH algorithm is valid and outperforms the classical HS algorithm (HS) and HS algorithm with differential mutation operator (HSDE)

An Improved Harmony Search Based on Teaching-Learning Strategy for Unconstrained Optimization Problems

Harmony search (HS) algorithm is an emerging population-based metaheuristic algorithm, which is inspired by the music improvisation process. The HS method has been developed rapidly and applied widely during the past decade. In this paper, an improved global harmony search algorithm, named harmony search based on teaching-learning (HSTL), is presented for high dimension complex optimization problems. In HSTL algorithm, four strategies (harmony memory consideration, teaching-learning strategy, local pitch adjusting, and random mutation) are employed to maintain the proper balance between convergence and population diversity, and dynamic strategy is adopted to change the parameters. The proposed HSTL algorithm is investigated and compared with three other state-of-the-art HS optimization algorithms. Furthermore, to demonstrate the robustness and convergence, the success rate and convergence analysis is also studied. The experimental results of 31 complex benchmark functions demonstrate that the HSTL method has strong convergence and robustness and has better balance capacity of space exploration and local exploitation on high dimension complex optimization problems

Cellulose-Pectin Spatial Contacts Are Inherent to Never-Dried Arabidopsis Primary Cell Walls: Evidence from Solid-State Nuclear Magnetic Resonance

The structural role of pectins in plant primary cell walls is not yet well understood because of the complex and disordered nature of the cell wall polymers. We recently introduced multidimensional solid-state nuclear magnetic resonance spectroscopy to characterize the spatial proximities of wall polysaccharides. The data showed extensive cross peaks between pectins and cellulose in the primary wall of Arabidopsis (Arabidopsis thaliana), indicating subnanometer contacts between the two polysaccharides. This result was unexpected because stable pectin-cellulose interactions are not predicted by in vitro binding assays and prevailing cell wall models. To investigate whether the spatial contacts that give rise to the cross peaks are artifacts of sample preparation, we now compare never-dried Arabidopsis primary walls with dehydrated and rehydrated samples. One-dimensional 13C spectra, two-dimensional 13C-13C correlation spectra, water-polysaccharide correlation spectra, and dynamics data all indicate that the structure, mobility, and intermolecular contacts of the polysaccharides are indistinguishable between never-dried and rehydrated walls. Moreover, a partially depectinated cell wall in which 40% of homogalacturonan is extracted retains cellulose-pectin cross peaks, indicating that the cellulose-pectin contacts are not due to molecular crowding. The cross peaks are observed both at −20°C and at ambient temperature, thus ruling out freezing as a cause of spatial contacts. These results indicate that rhamnogalacturonan I and a portion of homogalacturonan have significant interactions with cellulose microfibrils in the native primary wall. This pectin-cellulose association may be formed during wall biosynthesis and may involve pectin entrapment in or between cellulose microfibrils, which cannot be mimicked by in vitro binding assays.United States. Department of Energy. Office of Basic Energy Sciences (grant no. DE–SC0001090)National Institutes of Health (U.S.) (grant no. EB002026

Two new species of Craterellus (Cantharellales, Hydnaceae) with veined hymenophore from north-eastern China

In this contribution to the genus Craterellus in northern China, two new species are introduced: Craterellus connatus and C. striatus. These species and C. atrobrunneolus, initially described in south-western China, are highly similar and closely related. The species delimitation is molecularly supported by multigene phylogenetic analysis of the nr LSU and tef-1α region. Craterellus connatus is characterised by its medium-sized basidiomata, greyish-brown and smooth pileus with an off-white margin, the hymenophore with a strongly anastomosing vein, turning khaki upon drying, connate stipe, broad ellipsoid to ellipsoid basidiospores (6.1–7.8 × 4.8–5.9 μm), slender basidia with (2)4–6 sterigmata and the absence of clamp connection. Craterellus striatus is characterised by its small-sized basidiomata, fibrillose, greyish-brown to yellowish-brown, fully perforated pileus with a brown fringe, the hymenophore with a forking vein, the stipe inflated at the base, broad ellipsoid to ellipsoid basidiospores (6.8–8.0 × 5.1–6.0 μm), 2–6 spored basidia, encrusted hyphae and the absence of clamp connection. Detailed macroscopic and microscopic descriptions, accompanied by illustrations and a taxonomic discussion, are presented. A key to the Chinese Craterellus species is also provided