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The feedback control of Hopf bifurcation of nonlinear aeroelastic systems with asymmetric aerodynamic lift force and nonlinear elastic forces of the airfoil is discussed. For the Hopf bifurcation analysis, the eigenvalue problems of the state matrix and its adjoint matrix are defined. The Puiseux expansion is used to discuss the variations of the non-semi-simple eigenvalues, as the control parameter passes through the critical value to avoid the difficulty for computing the derivatives of the non-semi-simple eigenvalues with respect to the control parameter. The method of multiple scales and center-manifold reduction are used to deal with the feedback control design of a nonlinear system with non-semi-simple eigenvalues at the critical point of the Hopf bifurcation. The first order approximate solutions are developed, which include gain vector and input. The presented methods are based on the Jordan form which is the simplest one. Finally, an example of an airfoil model is given to show the feasibility and for verification of the present method.

Background and objectives The objective of this study is to compare the efficacy and the safety of ultrasound-guided microwave ablation (MWA) and laser ablation (LA) for the treatment of papillary thyroid microcarcinoma (PTMC). Study design/materials and methods A total of 67 patients with unifocal PTMC were studied retrospectively, including 33 cases who underwent MWA (MWA group) and 34 cases who received LA (LA group). The follow-up consisted of thyroid function tests, ultrasonography, contrast-enhanced ultrasonography (CEUS), and chest X-ray or computed tomography scan. The treatment response and complications were compared between the two groups. Results The follow-up time for the MWA and LA group was 23.3 ± 4.4 and 22.8 ± 4.1 months, respectively. All the ablations were successfully performed as planned without complementary ablations, and it was confirmed by CEUS after treatment in both groups. It was observed that, at the last follow-up, the mean largest diameter decreased from 5.0 ± 1.4 mm to 0.1 ± 0.4 mm (MWA group) and from 4.5 ± 1.6 mm to 0.6 ± 1.2 mm(LA group) (P 0.05). No local recurrence or distant metastasis occurred in either group. Conclusions During the short-term follow-up period, ultrasound-guided MWA and LA were both safe and effective methods in treating patients with unifocal PTMC. Lasers Surg. Med. © 2020 Wiley Periodicals, Inc.

Nitrogen (N) fertilizer placement in bands is a widely accepted agricultural practice to increase N use efficiency. An excessive ammonium concentration in a fertilizer band can increase osmotic stress on ammonia oxidizers and potentially affect nitrification and resultant nitrous oxide (N2O) emissions, which is of great significance for soil function and climate change. The objectivity of this study was to identify the effects of excessive ammonium concentration on N2O emissions and ammonia oxidizers in two agricultural soils. In this study, we established a 56-day soil microcosm receiving a series of high concentrations of urea at 600, 900, and 1200 mg N kg−1 (termed as N600, N900, and N1200, respectively), which simulated high ammonium levels in the center or proximity of a fertilizer band in two types of agricultural soils (fluvo-aquic soil and anthrosol). The mineral N concentrations, net nitrification rate, and N2O emissions were measured during the incubation. In addition, the abundances of bacterial and archaeal amoA were determined by using real-time quantitative PCR. Urea fertilization simultaneously increased the net nitrification rate and N2O emission at the early stage of incubation in both soils, suggesting N2O production was mainly from ammonia oxidation. Ammonia oxidizing bacteria (AOB) but not archaea (AOA) abundance was stimulated following urea fertilization and was positively correlated with N2O emission, indicating the dominant role of AOB in ammonia oxidation and N2O production in fertilized soils. The cumulative N2O emission was significantly higher in N1200 and N900 than N600 in both soils, but no further increase was observed in N1200 in the anthrosol. This implies restricted N2O production of ammonia oxidizers at excessive ammonium concentrations in the anthrosol. In the two soils treated with no N addition, the abundances of AOA amoA increased along the incubation time. The present study collectively suggested that excessive urea-N addition was more effective in inhibiting N2O emission in the anthrosol than in the fluvo-aquci soil. AOB rather than AOA dominated the soil nitrification and N2O emissions under high N addition in both soils. The band fertilization regime may reduce the loss of N fertilizer from nitrification without necessarily increasing N2O emissions.

This paper surveys recent theoretical advances in convex optimization approaches for community detection. We introduce some important theoretical techniques and results for establishing the consistency of convex community detection under various statistical models. In particular, we discuss the basic techniques based on the primal and dual analysis. We also present results that demonstrate several distinctive advantages of convex community detection, including robustness against outlier nodes, consistency under weak assortativity, and adaptivity to heterogeneous degrees. This survey is not intended to be a complete overview of the vast literature on this fast-growing topic. Instead, we aim to provide a big picture of the remarkable recent development in this area and to make the survey accessible to a broad audience. We hope that this expository article can serve as an introductory guide for readers who are interested in using, designing, and analyzing convex relaxation methods in network analysis., Comment: 22 pages

Generating intense ultrashort pulses with high-quality spatial modes is crucial for ultrafast and strong-field science and can be achieved by nonlinear supercontinuum generation (SCG) and pulse compression. In this work, we propose that the generation of quasi-stationary solitons in periodic layered Kerr media can greatly enhance the nonlinear light-matter interaction and fundamentally improve the performance of SCG and pulse compression in condensed media. With both experimental and theoretical studies, we successfully identify these solitary modes and reveal their unified condition for stability. Space-time coupling is shown to strongly influence the stability of solitons, leading to variations in the spectral, spatial and temporal profiles of femtosecond pulses. Taking advantage of the unique characteristics of these solitary modes, we first demonstrate single-stage SCG and the compression of femtosecond pulses from 170 to 22 fs with an efficiency >85%. The high spatiotemporal quality of the compressed pulses is further confirmed by high-harmonic generation. We also provide evidence of efficient mode self-cleaning, which suggests rich spatiotemporal self-organization of the laser beams in a nonlinear resonator. This work offers a route towards highly efficient, simple, stable and highly flexible SCG and pulse compression solutions for state-of-the-art ytterbium laser technology.

Biofertilizer can improve soil quality, especially the microbiome composition, which potentially affect soil nitrogen (N) cycling. However, little is known about the responses of nitrous oxide (N2O) emission and ammonia (NH3) volatilization from biochar-amended paddy soil to the biofertilizer application. Therefore, we conducted a soil column experiment using four 240 kg N ha−1 (equivalent to 1.7 g N pot−1) treatments consisting of biofertilizer (3 t ha−1, equivalent to 21.2 g pot−1), biochar (7.5 t ha−1, equivalent to 63.6 g pot−1), and a mixture of biofertilizer and biochar at the same rate and a control (CK). The results showed that the N2O emissions and NH3 volatilizations were equivalent to 0.15–0.28% and 18.0–31.5% of rice seasonal N applied to the four treatments, respectively. Two treatments with biofertilizer and biochar individual amendment significantly increased (P

Random features is one of the most popular techniques to speed up kernel methods in large-scale problems. Related works have been recognized by the NeurIPS Test-of-Time award in 2017 and the ICML Best Paper Finalist in 2019. The body of work on random features has grown rapidly, and hence it is desirable to have a comprehensive overview on this topic explaining the connections among various algorithms and theoretical results. In this survey, we systematically review the work on random features from the past ten years. First, the motivations, characteristics and contributions of representative random features based algorithms are summarized according to their sampling schemes, learning procedures, variance reduction properties and how they exploit training data. Second, we review theoretical results that center around the following key question: how many random features are needed to ensure a high approximation quality or no loss in the empirical/expected risks of the learned estimator. Third, we provide a comprehensive evaluation of popular random features based algorithms on several large-scale benchmark datasets and discuss their approximation quality and prediction performance for classification. Last, we discuss the relationship between random features and modern over-parameterized deep neural networks (DNNs), including the use of high dimensional random features in the analysis of DNNs as well as the gaps between current theoretical and empirical results. This survey may serve as a gentle introduction to this topic, and as a users' guide for practitioners interested in applying the representative algorithms and understanding theoretical results under various technical assumptions. We hope that this survey will facilitate discussion on the open problems in this topic, and more importantly, shed light on future research directions., Short version will be published on IEEE TPAMI

As a famous linear manifold learning method, orthogonal neighborhood preserving projections (ONPP) is able to provide a set of orthogonal projections for dimensionality reduction. However, a problem of ONPP is that it takes the L2-norm as the basic measurement and therefore tends to be sensitive to the outliers or the variations of the data. Aiming at strengthening the robustness of the conventional method ONPP, in this paper, a robust and sparse dimensionality reduction method based on linear reconstruction, called Robust Jointly Sparse Embedding (RJSE), is proposed by introducing L2, 1-norm as the basic measurement and regularization term. We design a simple iterative algorithm to obtain the optimal solution of the proposed robust and sparse dimensionality reduction model. Experiments on four benchmark data sets demonstrate the competitive performance of the proposed method compared with the state-of-the-art methods.

Low-rank modeling plays a pivotal role in signal processing and machine learning, with applications ranging from collaborative filtering, video surveillance, and medical imaging to dimensionality reduction and adaptive filtering. Many modern high-dimensional data and interactions thereof can be modeled as lying approximately in a low-dimensional subspace or manifold, possibly with additional structures, and its proper exploitations lead to significant cost reduction in sensing, computation, and storage. In recent years, there has been a plethora of progress in understanding how to exploit low-rank structures using computationally efficient procedures in a provable manner, including both convex and nonconvex approaches. On one side, convex relaxations such as nuclear norm minimization often lead to statistically optimal procedures for estimating low-rank matrices, where first-order methods are developed to address the computational challenges; on the other side, there is emerging evidence that properly designed nonconvex procedures, such as projected gradient descent, often provide globally optimal solutions with a much lower computational cost in many problems. This survey article provides a unified overview of these recent advances in low-rank matrix estimation from incomplete measurements. Attention is paid to rigorous characterization of the performance of these algorithms and to problems where the lowrank matrix has additional structural properties that require new algorithmic designs and theoretical analysis.

We consider the mixed regression problem with two components, under adversarial and stochastic noise. We give a convex optimization formulation that provably recovers the true solution, as well as a nonconvex formulation that works under more general settings and remains tractable. Upper bounds are provided on the recovery errors for both arbitrary noise and stochastic noise models. We also give matching minimax lower bounds (up to log factors), showing that our algorithm is information-theoretical optimal in a precise sense. Our results represent the first tractable algorithm guaranteeing successful recovery with tight bounds on recovery errors and sample complexity. Moreover, we pinpoint the statistical cost of mixtures: our minimax-optimal results indicate that the mixture poses a fundamentally more difficult problem in the low-SNR regime, where the learning rate changes.

We study two 2-dimensional Teichmüller spaces of surfaces with boundary and\ud marked points, namely, the pentagon and the punctured triangle. We show that their geometry\ud is quite different from Teichmüller spaces of closed surfaces. Indeed, both spaces are\ud exhausted by regular convex geodesic polygons with a fixed number of sides, and their\ud geodesics diverge at most linearly.

Recently, a series of deep supervised hashing methods were proposed for binary code learning. However, due to the high computation cost and the limited hardware's memory, these methods will first select a subset from the training set, and then form a mini-batch data to update the network in each iteration. Therefore, the remaining labeled data cannot be fully utilized and the model cannot directly obtain the binary codes of the entire training set for retrieval. To address these problems, this paper proposes an interesting regularized deep model to seamlessly integrate the advantages of deep hashing and efficient binary code learning by using the anchor graph. As such, the deep features and label matrix can be jointly used to optimize the binary codes, and the network can obtain more discriminative feedback from the linear combinations of the learned bits. Moreover, we also reveal the algorithm mechanism and its computation essence. Experiments on three large-scale datasets indicate that the proposed method achieves better retrieval performance with less training time compared to previous deep hashing methods.

Inverted repeats (IRs) serve as potential biomarkers for genomic instability, DNA replication and other genetic processes. However, little information can be found in databases to help researchers recognize potential IR nucleotides, explore junction sites and annotate related functional genes. Plant Chloroplast Inverted Repeats (PCIR) is an interactive, web-based platform containing various sequenced chloroplast genomes that enables detection, searching and visualization of large-scale detailed information on IRs. PCIR contains many datasets, including 21 433 IRs, 113 plants chloroplast genomes, 16 948 functional genes and 21 659 visual maps. This database offers an online prediction tool for detecting IRs based on DNA sequences. PCIR can also analyze phylogenetic relationships using IR information among different species and provide users with high-quality marker maps. This database will be a valuable resource for IR distribution patterns, related genes and architectural features.

Xyloglucan endotransglycosylase/hydrolase (XTH) is a cell-wall-modifying enzyme participating in diverse cell morphogenetic processes and adaptation to stress. In this study, 48 XTH genes were identified from two pineapple (Ananas comosus) cultivars (&lsquo, F153&rsquo, and &lsquo, MD2&rsquo, ) and designated Ac(F153)XTH1 to -24 and Ac(MD2)XTH1 to -24 based on their orthology with Arabidopsis thaliana genes. Endoglucanase family 16 members were identified in addition to XTHs of glycoside hydrolase family 16. Phylogenetic analysis clustered the XTHs into three major groups (Group I/II, III and Ancestral Group) and Group III was subdivided into Group IIIA and Group IIIB. Similar gene structure and motif number were observed within a group. Two highly conserved domains, glycosyl hydrolase family 16 (GH16-XET) and xyloglucan endotransglycosylase C-terminus (C-XET), were detected by multiple sequences alignment of all XTHs. Segmental replication were detected in the two cultivars, with only the paralogous pair Ac(F153)XTH7-Ac(F153)XTH18 presented in &lsquo, prior to genomic expansion. Transcriptomic analysis indicated that XTHs were involved in the regulation of fruit ripening and crassulacean acid metabolism with tissue specificity and quantitative real-time PCR analysis suggested that Ac(MD2)XTH18 was involved in root growth. The results enhance our understanding of XTHs in the plant kingdom and provide a basis for further studies of functional diversity in A. comosus.

The task of recovering a low-rank matrix from its noisy linear measurements plays a central role in computational science. Smooth formulations of the problem often exhibit an undesirable phenomenon: the condition number, classically defined, scales poorly with the dimension of the ambient space. In contrast, we here show that in a variety of concrete circumstances, nonsmooth penalty formulations do not suffer from the same type of ill-conditioning. Consequently, standard algorithms for nonsmooth optimization, such as subgradient and prox-linear methods, converge at a rapid dimension-independent rate when initialized within constant relative error of the solution. Moreover, nonsmooth formulations are naturally robust against outliers. Our framework subsumes such important computational tasks as phase retrieval, blind deconvolution, quadratic sensing, matrix completion, and robust PCA. Numerical experiments on these problems illustrate the benefits of the proposed approach., Comment: 80 pages

Most of manifold learning based feature extraction methods are two-step methods, which first construct a weighted neighborhood graph and then use the pre-constructed graph to perform subspace learning. As a result, these methods fail to use the underlying correlation structure of data to learn an adaptive graph to preciously characterize the similarity relationship between samples. To address this problem, we propose a novel unsupervised feature extraction method called low-rank adaptive graph embedding (LRAGE), which can perform subspace learning and adaptive probabilistic neighborhood graph embedding simultaneously based on reconstruction error minimization. The proposed LRAGE is imposed with low-rank constraint for the sake of exploring the underlying correlation structure of data and learning more informative projection. Moreover, the L 2 , 1 -norm penalty is imposed on the regularization to further enhance the robustness of LRAGE. Since the resulting objective function has no closed-form solutions, an iterative optimization algorithm is elaborately designed. The convergence of the proposed algorithm is proved and the corresponding computational complexity analysis is also presented. In addition, we explore the potential properties of the proposed LRAGE by comparing it with several similar models on both synthetic and real-world data sets. Extensive experiments on five well-known face data sets and three non-face data sets demonstrate the superiority of the proposed LRAGE.

SnTe is a notable member of the IV–VI semiconductors with SnSe and PbTe as two representative thermoelectric materials, which is considered to be a potentially attractive thermoelectric material due to its similar rock-salt crystal structure to PbTe. However, the current researches on SnTe are limited because of the difficult synthesis in aspect of controlling morphology and size, and its thermoelectric figure of merit is also low due to the high thermal conductivity. In this study, a simple and ultra-fast microwave hydrothermal method was designed to synthesize the SnTe particles with controlled sizes from micro-scale to nano-scale. The thermoelectric properties of the corresponding SnTe bulk materials prepared by spark plasma sintering were investigated in a wide temperature range with a focus on the size effect. Due to the enhanced phonon scattering caused by the nanometer size effect, a low thermal conductivity, 0.60 W m−1 K−1 at 803 K, was obtained in the bulk specimen using 165-nm-sized nanoparticles. The corresponding maximum ZT value at 803 K is enhanced to 0.49, which is about 2.3 times that of the SnTe bulk samples using mechanically alloyed powders.

Mercury contamination in agro-ecosystems is one of the most important environmental issues. Farmland soil mercury accumulation and transference to crops in Changshu City, eastern China, were investigated to identify mercury migration capacity from soil to crops. The mean content of mercury for soil samples slightly increased year after year. The mercury accumulation capacity of rice grown (bioaccumulation factor (BAF) 0.028) in submerged soils under reductive conditions was stronger than that of wheat (BAF 0.0073) in dried soils under oxidative conditions. There were clear relationships between soil mercury with organic matter (OM), cation exchange capacity (CEC), and CaCO3 of soil samples, while apparent negative relationships between Hg in rice grain with OM, CEC, and CaCO3 of soil existed. No clear association for Hg between crops and soil was found, indicating that mercury in crop grains is mostly affected by other factors besides soil mercury. Also, soil properties and farming patterns affect...

This paper reports on an experiment designed to test electromagnetic (EM) atten- uation by radio-frequency (RF) plasma for cavity structures. A plasma reactor, in the shape of a hollow cylinder, fllled with argon gas at low pressure, driven by a RF power source, was produced by wave-transmitting material. The detailed attenuations of EM waves were investigated under difierent conditions: the incident frequency is 1-4 GHz, the RF power supply is 13.56 MHz and 1.6-3 kW, and the argon pressure is 75-200 Pa. The experimental results indicate that 5-15 dB return loss can be obtained. From a flrst estimation, the electron density in the experiment is approximately (1.5-2.2)£10 16 m i3 and the collision frequency is about 11-30 GHz. The return loss of EM waves was calculated using a flnite-difierence time-domain (FDTD) method and it was found that it has a similar development with measurement. It can be conflrmed that RF plasma is useful in the stealth of cavity structures such as jet-engine inlet.

This paper considers the problem of matrix completion when some number of the columns are completely and arbitrarily corrupted, potentially by a malicious adversary. It is well-known that standard algorithms for matrix completion can return arbitrarily poor results, if even a single column is corrupted. One direct application comes from robust collaborative filtering. Here, some number of users are so-called manipulators who try to skew the predictions of the algorithm by calibrating their inputs to the system. In this paper, we develop an efficient algorithm for this problem based on a combination of a trimming procedure and a convex program that minimizes the nuclear norm and the $\ell_{1,2}$ norm. Our theoretical results show that given a vanishing fraction of observed entries, it is nevertheless possible to complete the underlying matrix even when the number of corrupted columns grows. Significantly, our results hold without any assumptions on the locations or values of the observed entries of the manipulated columns. Moreover, we show by an information-theoretic argument that our guarantees are nearly optimal in terms of the fraction of sampled entries on the authentic columns, the fraction of corrupted columns, and the rank of the underlying matrix. Our results therefore sharply characterize the tradeoffs between sample, robustness and rank in matrix completion., Comment: This is the journal version of the paper with additional results

Hashing methods are becoming increasingly popular because they can achieve fast retrieval of large-scale data by representing the images with binary codes. However, the traditional hashing methods tend to obtain the binary codes by relaxing the discrete problems which greatly increase the information loss. In this paper, we propose a novel hash learning method, called Supervised Locality Preserving Hashing (SLPH) for image retrieval. Different from the traditional two-steps methods which learn low-dimensional features and binary codes of the data separately, we directly obtain the binary codes and thus reduce the information loss. Besides, we add graph-regularized learning on the designed model to avoid over-fitting and improve the performance. Experiments on two benchmark databases show that the proposed SLPH performs better than some state-of-the-art methods.

A high catalytic system using Cu layered double hydrotalcite (Cu(II)-Mg(II)-Fe(III)LDHs) and hydrogen peroxide (H2O2) was developed for the degradation of ethylbenzene. It was identified that the degradation efficiency of ethylbenzene (0.08 mmol L−1) and TOC removal were 96.1% and 39.7% respectively in the presence of 0.1 g L−1 Cu(II)-Mg(II)-Fe(III)LDHs with (Cu2+ + Mg2+)/Fe3+ molar ratio of 5.0 and 0.16 mmol L−1 H2O2 in 6.0 h. Based on ESR and XPS data, hydroxyl radicals (•OH) were the predominant free radical specials generated from the catalytic decomposition of H2O2 for the degradation of ethylbenzene. The redox of Cu(II)/Cu(III) on the layered Cu(II)-Mg(II)-Fe(III)LDHs surface active sites accounted for the formation of •OH radicals and the cycle of Cu(II) in the Cu(II)-Mg(II)-Fe(III)LDHs/H2O2 system were proposed.

Least square regression (LSR) and principal component analysis (PCA) are two representative dimensionality reduction algorithms in the fields of machine learning. In this paper, we propose a novel method to jointly learn projections from the subspaces derived from the modified LSR and PCA. To implement simultaneous feature learning, we design a novel joint regression learning model by imposing two orthogonal constraints. Therefore, the learned projections can preserve the minimum reconstruction error and the discriminative information in the low-dimensional subspaces. Besides, since the traditional LSR and PCA are sensitive to the outliers, we utilize the robust L2,1-norm as the metric of loss function to improve the model’s robustness. A simple iterative algorithm is proposed to solve the proposed framework. Experiments on face databases show the promising performance of our method.

In this paper, we consider the mixture of sparse linear regressions model. Let ${\beta}^{(1)},\ldots,{\beta}^{(L)}\in\mathbb{C}^n$ be $ L $ unknown sparse parameter vectors with a total of $ K $ non-zero coefficients. Noisy linear measurements are obtained in the form $y_i={x}_i^H {\beta}^{(\ell_i)} + w_i$, each of which is generated randomly from one of the sparse vectors with the label $ \ell_i $ unknown. The goal is to estimate the parameter vectors efficiently with low sample and computational costs. This problem presents significant challenges as one needs to simultaneously solve the demixing problem of recovering the labels $ \ell_i $ as well as the estimation problem of recovering the sparse vectors $ {\beta}^{(\ell)} $. Our solution to the problem leverages the connection between modern coding theory and statistical inference. We introduce a new algorithm, Mixed-Coloring, which samples the mixture strategically using query vectors $ {x}_i $ constructed based on ideas from sparse graph codes. Our novel code design allows for both efficient demixing and parameter estimation. In the noiseless setting, for a constant number of sparse parameter vectors, our algorithm achieves the order-optimal sample and time complexities of $\Theta(K)$. In the presence of Gaussian noise, for the problem with two parameter vectors (i.e., $L=2$), we show that the Robust Mixed-Coloring algorithm achieves near-optimal $\Theta(K polylog(n))$ sample and time complexities. When $K=O(n^{\alpha})$ for some constant $\alpha\in(0,1)$ (i.e., $K$ is sublinear in $n$), we can achieve sample and time complexities both sublinear in the ambient dimension. In one of our experiments, to recover a mixture of two regressions with dimension $n=500$ and sparsity $K=50$, our algorithm is more than $300$ times faster than EM algorithm, with about one third of its sample cost., Comment: To appear in IEEE Transactions on Information Theory

Transcranial magneto-acoustical stimulation (TMAS) uses ultrasonic waves and a static magnetic field to generate electric current in nerve tissues for the purpose of modulating neuronal activities. It has the advantage of high spatial resolution and penetration depth. Neuronal firing rhythms carry and transmit nerve information in neural systems. In this study, we investigated the phase-locking characteristics of neuronal firing rhythms with TMAS based on the Hodgkin-Huxley neuron model. The simulation results indicate that the modulation frequency of ultrasound can affect the phase-locking behaviors. The results of this study may help us to explain the potential firing mechanism of TMAS.

We investigate magnetoplasmon resonances and their coupling effects in gyroelectric cylinders. In individual cylinders, the dipole plasmon can be excited by plane wave illumination, and the dipole plasmon splits into lower energy and higher energy rotational magnetoplasmons in the presence of an external magnetic field. With respect to the external magnetic field, the two magnetoplasmons carry either right-handed chirality or left-handed chirality. In addition, originally dark plasmons can also be excited as the magnetic field increases. They are lower-order bulk plasmons (such as the radial breathing mode). In cylindrical dimers, the optically bright modes are combinations of magnetoplasmons with the same chirality. If the magnetic fields are antiparallel, the absorption spectra will be different for light incident from two opposite directions. This asymmetry can be well understood by carrying out eigenstate analysis, where the eigenstate does not possess mirror symmetry respecting the dimer axis. The dark modes engineering and asymmetrical optical behavior could have potential for terahertz device applications.

Feature extraction is an important way to improve the performance of image recognition. Compared to most of feature extraction methods, the 2-D principal component analysis (2-DPCA) better preserves the structural information of images since it is unnecessary to transform the small size image matrices into high dimensional vectors during the calculation process. In order to improve the robustness of 2-DPCA, nuclear norm-based 2-DPCA (N-2-DPCA) was proposed using nuclear norm as matrix distance measurement. However, 2-DPCA and N-2-DPCA lack the function of sparse feature extraction and selection. Thus, in this paper, we extend N-2-DPCA to sparse case, which is called SN-2-DPCA, for sparse subspace learning. To efficiently solve the model, an alternatively iterative algorithm will also be presented. The proposed SN-2-DPCA would be compared with some advanced 1-D and 2-D feature extraction methods using four well-known data sets. Experimental results indicate the competitive advantage of SN-2-DPCA.

Two-Dimensional Principal Component Analysis (2D-PCA) is one of the most simple and effective feature extraction methods in the field of pattern recognition. However, the traditional 2D-PCA lacks robustness and the function of sparse feature extraction. In this paper, we propose a new feature extraction approach based on the traditional 2D-PCA, which is called Nuclear Norm Based Two-Dimensional Sparse Principal Component Analysis (N-2D-SPCA). To improve the robustness of 2D-PCA, we utilize nuclear norm to measure the reconstruction error of loss function. At the same time, we obtain sparse feature extraction by adding [Formula: see text]-norm and [Formula: see text]-norm regularization terms to the model. By designing an alternatively iterative algorithm, we can solve the optimization problem and learn a projection matrix for use with feature extraction. Besides, we present a bilateral projections model (BN-2D-SPCA) to further compress the dimensions of the feature matrix. We verify the effectiveness of our method on four benchmark face databases including AR, ORL, FERET and Yale databases. Experimental results show that the proposed method is more robust than some state-of-the-art methods and the traditional 2D-PCA.

Locality preserving projections (LPP) has been widely studied and extended in recent years, because of its promising performance in feature extraction. In this paper, we propose a modified version of the LPP by constructing a novel regression model. To improve the performance of the model, we impose a low-rank constraint on the regression matrix to discover the latent relations between different neighbors. By using the $L_{2,1}$ -norm as a metric for the loss function, we can further minimize the reconstruction error and derive a robust model. Furthermore, the $L_{2,1}$ -norm regularization term is added to obtain a jointly sparse regression matrix for feature selection. An iterative algorithm with guaranteed convergence is designed to solve the optimization problem. To validate the recognition efficiency, we apply the algorithm to a series of benchmark datasets containing face and character images for feature extraction. The experimental results show that the proposed method is better than some existing methods. The code of this paper can be downloaded from http://www.scholat.com/laizhihui .

The stochastic block model (SBM), a popular framework for studying community detection in networks, is limited by the assumption that all nodes in the same community are statistically equivalent and have equal expected degrees. The degree-corrected stochastic block model (DCSBM) is a natural extension of SBM that allows for degree heterogeneity within communities. To find the communities under DCSBM, this paper proposes a convexified modularity maximization approach, which is based on a convex programming relaxation of the classical (generalized) modularity maximization formulation, followed by a novel doubly-weighted $\ell_{1}$-norm $k$-medoids procedure. We establish nonasymptotic theoretical guarantees for approximate and perfect clustering, both of which build on a new degree-corrected density gap condition. Our approximate clustering results are insensitive to the minimum degree, and hold even in sparse regime with bounded average degrees. In the special case of SBM, our theoretical guarantees match the best-known results of computationally feasible algorithms. Numerically, we provide an efficient implementation of our algorithm, which is applied to both synthetic and real-world networks. Experiment results show that our method enjoys competitive performance compared to the state of the art in the literature.

The capacitively coupled radio frequency (CCRF) plasma has been widely used in various fields. In some cases, it requires us to estimate the range of key plasma parameters simpler and quicker in order to understand the behavior in plasma. In this paper, a glass vacuum chamber and a pair of plate electrodes were designed and fabricated, using 13.56 MHz radio frequency (RF) discharge technology to ionize the working gas of Ar. This discharge was mathematically described with equivalent circuit model. The discharge voltage and current of the plasma were measured at different pressures and different powers. Based on the capacitively coupled homogeneous discharge model, the equivalent circuit and the analytical formula were established. The plasma density and temperature were calculated by using the equivalent impedance principle and energy balance equation. The experimental results show that when RF discharge power is 50–300 W and pressure is 25–250 Pa, the average electron temperature is about 1.7–2.1 eV and the average electron density is about 0.5 × 1017–3.6 × 1017 m−3. Agreement was found when the results were compared to those given by optical emission spectroscopy and COMSOL simulation.

Transcranial magneto-acoustical stimulation (TMAS) utilizes low-intensity focused ultrasound and a magnetostatic field to generate an electric current in nerve tissue with high spatial resolution and penetration depth. The analysis of the neuronal firing rhythm that carries different stimulation signals is of great significance for the study of neural information coding. Moreover, the change in intracellular Ca2+ concentration is a response of neurons to external stimuli. However, how the TMAS affect the neuronal firing rhythm and Ca2+ concentration are unclear. In our study, we investigate the neuronal firing rhythm and Ca2+ concentration with TMAS under three types of ultrasound based on the Chay neuron model with simulation. The simulation results show that the modulation of the neuronal firing rhythm and Ca2+ concentration by TMAS is strongly dependent on types and parameters of ultrasound. This study indicates that TMAS can modulate the neuronal firing rhythm and Ca2+ concentration.

We investigate transcranial magneto–acoustical stimulation (TMAS) for noninvasive brain neuromodulation in vivo. TMAS as a novel technique uses an ultrasound wave to induce an electric current in the brain tissue in the static magnetic field. It has the advantage of high spatial resolution and penetration depth. The mechanism of TMAS onto a neuron is analyzed by combining the TMAS principle and Hodgkin–Huxley neuron model. The anesthetized rats are stimulated by TMAS, resulting in the local field potentials which are recorded and analyzed. The simulation results show that TMAS can induce neuronal action potential. The experimental results indicate that TMAS can not only increase the amplitude of local field potentials but also enhance the effect of focused ultrasound stimulation on the neuromodulation. In summary, TMAS can accomplish brain neuromodulation, suggesting a potentially powerful noninvasive stimulation method to interfere with brain rhythms for diagnostic and therapeutic purposes.