svt: Singular Value Thresholding in MATLAB

Many statistical learning methods such as matrix completion, matrix regression, and multiple response regression estimate a matrix of parameters. The nuclear norm regularization is frequently employed to achieve shrinkage and low rank solutions. To minimize a nuclear norm regularized loss function, a vital and most time-consuming step is singular value thresholding, which seeks the singular values of a large matrix exceeding a threshold and their associated singular vectors. Currently MATLAB lacks a function for singular value thresholding. Its built-in svds function computes the top r singular values/vectors by Lanczos iterative method but is only efficient for sparse matrix input, while aforementioned statistical learning algorithms perform singular value thresholding on dense but structured matrices. To address this issue, we provide a MATLAB wrapper function svt that implements singular value thresholding. It encompasses both top singular value decomposition and thresholding, handles both large sparse matrices and structured matrices, and reduces the computation cost in matrix learning algorithms

An Investigation of the Effect of Chitosan on Isothermal Crystallization, Thermal Decomposition, and Melt Index of Biodegradable Poly(L-lactic acid)

Biodegradable chitosan (CS) was introduced into another biodegradable poly(L-lactic acid) (PLLA) to prepare the PLLA/CS composites, and the effect of CS on thermal behavior and melt index of PLLA was investigated using modern testing technologies including optical depolarizer, thermogravimetric analysis instrument, and melt index instrument. The relevant testing results showed that both crystallization temperature and CS concentration affected the isothermal crystallization behavior of PLLA. Compared to neat PLLA, the t1/2 of PLLA/5% CS decreased from 2991.54 s to the minimum value 208.76 s at 105°C. However, the t1/2 of PLLA/CS composites in high crystallization temperature zone was different from that in low crystallization temperature zone. The increase of CS concentration and heating rate made the thermal decomposition temperature of PLLA/CS composites shift to higher temperature. The melt index results indicated that 3% CS made the fluidity of PLLA become better

Morphology of the immature stages of Panorpa qinlingensis (Mecoptera: Panorpidae) with notes on its biology

The scorpionfly Panorpa qinlingensis Chou & Ran is described and illustrated in detail for its immature stages, including egg, larva, and pupa. The egg is oval with chorion decorated with irregular polygonal network. The larva is eruciform and peripneustic, bearing eight pairs of abdominal prolegs. A pair of prominent compound eyes are present on head. The first instar larva differs from later instars in possessing a prominent egg burster on frons and with clavate setae. The pupa is exarate and decticous, taking the shape of the adults. The scorpionfly is bivoltine, overwintering as prepupal stage in the soil. The durations of the egg, larval, and pupal stages are 5–9 d, 19–27 d, and 8–18 d respectively for the first generation. Adults emerge from mid May to early June and from late July to mid August in the Micang Mountain, central China

The Bc→ψ(2S)πB_c\rightarrow \psi(2S)\pi, ηc(2S)π\eta_c(2S)\pi decays in the perturbative QCD approach

Nonleptonic two body $B_c$ decays including radially excited $\psi(2S)$ or $\eta_c(2S)$ mesons in the final state are studied using the perturbative QCD approach based on $k_T$ factorization. The charmonium distribution amplitudes are extracted from the $n = 2, l = 0$ Schr$\ddot{o}$dinger states for the harmonic oscillator potential. Utilizing these distribution amplitudes, we calculate the numerical results of the $B_c\rightarrow \psi(2S),\eta_c(2S)$ transition form factors and branching fractions of $B_c\rightarrow \psi(2S)\pi, \eta_c(2S)\pi$ decays. The ratio between two decay modes $B_c\rightarrow \psi(2S)\pi$ and $B_c\rightarrow J/\psi\pi$ is compatible with the experimental data within uncertainties, which indicate that the harmonic oscillator wave functions for $\psi(2S)$ and $\eta_c(2S)$ work well. It is found that the branching fraction of $B_c\rightarrow \eta_c(2S)\pi$, which is dominated by the twist-3 charmonium distribution amplitude, can reach the order of $10^{-3}$. We hope it can be measured soon in the LHCb experiment.Comment: 9 pages, 3 figures,3 Table

Tetravalent edge-transitive Cayley graphs with odd number of vertices

AbstractA characterisation is given of edge-transitive Cayley graphs of valency 4 on odd number of vertices. The characterisation is then applied to solve several problems in the area of edge-transitive graphs: answering a question proposed by Xu [Automorphism groups and isomorphisms of Cayley graphs, Discrete Math. 182 (1998) 309–319] regarding normal Cayley graphs; providing a method for constructing edge-transitive graphs of valency 4 with arbitrarily large vertex-stabiliser; constructing and characterising a new family of half-transitive graphs. Also this study leads to a construction of the first family of arc-transitive graphs of valency 4 which are non-Cayley graphs and have a ‘nice’ isomorphic 2-factorisation