本文将实对称矩阵特征值的交错定理推广到实对称区间矩阵,给出了实对称区间矩阵特征值确界的交错定理,并应用该定理构造了估计实对称三对角区间矩阵特征值界的算法.文中数值例子表明,本文所给算法与一些现有算法相比在使用范围、计算精度和计算量等方面都具有一定的优越性.

NONNEGATIVE matrix factorization (NMF) is an effective technique for dimensionality reduction of high-dimensional data for tasks such as machine learning and data visualization. However, for practical clustering tasks, traditional NMF ignores the manifold information of both the data space and feature space, as well as the discriminative information of the data. In this paper, we propose a semisupervised NMF called dual-graph-regularization-constrained nonnegative matrix factorization with label discrimination (DCNMFLD). DCNMFLD combines dual graph regularization and prior label information as additional constraints, making full use of the intrinsic geometric and discriminative structures of the data, and can efficiently enhance the discriminative and exclusionary nature of clustering and improve the clustering performance. The evaluation of the clustering experimental results on four benchmark datasets demonstrates the effectiveness of our new algorithm.

Several new uniqueness conditions of the stationary probability matrix of transition probability tensors arising from higher-order multivariate Markov chains are given by using contract mapping principle, the technique of inequality scaling and parameter method. It is proved that the new results are better than the one provided by Li et al. [Comput. Math. Appl., 2019, 78(3): 1008–1025]. As applications, a new convergence condition and an error bound for the power method to calculate the stationary probability matrix are given. Meanwhile, a perturbation bound for stationary probability matrix is obtained.

Some new sufficient conditions are given, which ensure that the k-subdirect sum of Nekrasov matrices and strictly diagonally dominant matrices is in the class of Nekrasov matrices. In addition, several examples are also given to illustrate the conditions presented.

One of the most common diseases among women of reproductive age is bacterial vaginosis (BV). However, the etiology of BV remains unknown. In this study, we modeled the temporal sample of the vaginal microbiome as a network and investigated the relationship between the network edges and BV. Furthermore, we used feature selection algorithms including decision tree (DT) and ReliefF (RF) to select the network feature edges associated with BV and subsequently validated these feature edges through logistic regression (LR) and support vector machine (SVM). The results show that: machine learning can distinguish vaginal community states (BV, ABV, SBV, and HEA) based on a few feature edges; selecting the top five feature edges of importance can achieve the best accuracy for the feature selection and classification model; the feature edges selected by DT outperform those selected by RF in terms of classification algorithm LR and SVM, and LR with DT feature edges is more suitable for diagnosing BV; two feature selection algorithms exhibit differences in the importance of ranking of edges; the feature edges selected by DT and RF cannot construct sub-network associated with BV. In short, the feature edges selected by our method can serve as indicators for personalized diagnosis of BV and aid in the clarification of a more mechanistic interpretation of its etiology.

Tensor recovery with tensor singular value decomposition has recently become increasingly popular in the computer vision field. One of the most important subproblem is the low-rank tensor completion with the partial and/or corrupted observations. In this paper, we propose a new low-rank tensor completion model with the robust form by minimizing the reconstruction error of approximate SVD and the γ nuclear norm of the lower triangular tensor, and then give their equivalent forms with the tensor slices in the Fourier domain. The efficient iterative algorithm is developed to solve the minimization problem, and the convergence of the algorithm is discussed. Experimental results on real-world visual data and the internet traffic data show that the proposed approaches outperform the state of the art algorithms in both (robust) recovery accuracy and computing time.

Based on the alternating least squares (ALS) technique and the singular value decomposition (SVD) technique, the algorithms for finding the structure preserving best rank-one approximations of even order paired symmetric tensors and k-mode symmetric tensors are presented. Then the convergence of the algorithms is discussed. Some numerical examples and applications are given to illustrate the feasibility and effectiveness of the proposed algorithms.

The image processing usually depends on exploring the structure and the geometric information of the tensor objects generated by image data. In the process, the decomposition of the tensor objects is very significant for the dimension reduction and the low-rank representation of image data. In this paper, based on the triple decomposition of third-order tensors and the correlation between different nonnegative tensor objects, a nonnegative triple decomposition model with manifold regularization terms is constructed. Then, an algorithm for the manifold regularization nonnegative triple decomposition is proposed, and the convergence of the algorithm is discussed. Furthermore, experiments on some real-world image data sets are given to illustrate the feasibility and effectiveness of the proposed algorithms.

Explaining the evolution of cooperation represents one of the greatest challenges in both evolutionary biology and social science. However, asymmetrical interaction, as one typical characteristic of cooperative system, has not been sufficiently considered in the existing literature for the evolution of cooperation. Incorporating the asymmetry in the strategy sets, we here construct an asymmetric game model with the so-called carrot-stick strategy, which is a mixed strategy of reward and punishment. Based on mathematical analyses, it is unveiled that this asymmetric interaction can lower the dilemma of cooperation: the dominant players and recipient players might coexist through cycle frequency. Further analysis shows that the multi-equilibria are possible, which depend on the payoff parameters and the initial conditions. That is to say, by setting up different values of the cost-to-benefit, the punishment-to-benefit, and the reward-to-benefit, we can recover three basic evolutionary dynamics of systems: dominance; bistability and coexistence. These theoretical observations are consistent with existing empirical outcomes that asymmetric sanction or reward of host species might solve the conflicts between the actors in the fig-fig wasp mutualism or in the cleaner fish-client mutualism. It is thus suggested that this asymmetric strategy setup may shed new light into the solution of social dilemmas. (C) 2021 Elsevier Inc. All rights reserved.

Several new uniqueness conditions for the stationary probability matrix of transition probability tensors arising from the higher-order multivariate Markov chains are given. Numerical examples are given to demonstrate that the new results are simpler and easier to be verified than the one provided by Li et al. (Comput Math Appl 78:1008–1025, 2019). As an application, a new convergence theorem for the power method to calculate the stationary probability matrix is given. Meanwhile, several perturbation bounds of the stationary probability matrix are obtained.

The class of $$\{P_1,P_2\}$$ -Nekrasov matrices, defined in terms of permutation matrices $$P_1$$ and $$P_2$$ , is a generalization of the well-known class of Nekrasov matrices. In this paper, some computable error bounds for linear complementarity problems (LCPs) of $$\{P_1,P_2\}$$ -Nekrasov matrices are given, which depend only on the entries of the involved matrices and can be used to obtain the perturbation bounds of $$\{P_1,P_2\}$$ -Nekrasov matrices LCPs. Besides, some sufficient conditions ensuring that the subdirect sum of $$\{P_1,P_2\}$$ -Nekrasov matrices lies in the same class are also provided.

Given gut microbiota's important role in human health, a clear understanding of the microbial ecosystem dynamics is vital. Mathematical models for analyzing time-series data of gut microbiotas would, therefore, be highly beneficial. Although a generalized Lotka-Volterra (gLV) model for identifying the interactions between gut microbiota members and quantifying the effects of external factors already exists, it is limited in its practical applications. Therefore, we established a stochastic gLV model for analyzing temporal data about the gut microbiota from a local community perspective and provided a reliable parameter estimation method for our model. Our model has abilities similar to those of the existing gLV model but can also capture emigration/immigration effects and avoid the existing model's inadequacies. To test our model's applicability, we fitted our model on a previously published data set. We found the interactions between the gut microbiota of different individuals and between different periods for the same individual were different in the data sets. Analysis of the random dynamic characteristics of the gut microbiota revealed that the number of microorganisms in the local community tended to decrease as a result of random factors, but the numbers were restored by the immigration of external microbes .

应用求解算子方程的Ulm方法构造了求解一类矩阵特征值反问题(IEP)的新算法.所给算法避免了文献[Aishima K.,A quadratically convergent algorithm based on matrix equations for inverse eigenvalue problems,Linear Algebra and its Applications,2018,542:310-333]中算法在每次迭代中要求解一个线性方程组的不足,证明了在给定谱数据互不相同的条件下所给算法具有根收敛意义下的二次收敛性.数值实验表明本文所给算法在矩阵阶数较大时计算效果优于上文所给算法.

The class of {P_1,P_2} -Nekrasov matrices, defined in terms of permutation matrices P_1 and P_2 , is a generalization of the well-known class of Nekrasov matrices. In this paper, some computable error bounds for linear complementarity problems (LCPs) of {P_1,P_2} -Nekrasov matrices are given, which depend only on the entries of the involved matrices and can be used to obtain the perturbation bounds of {P_1,P_2} -Nekrasov matrices LCPs. Besides, some sufficient conditions ensuring that the subdirect sum of {P_1,P_2} -Nekrasov matrices lies in the same class are also provided.

Currently, the tensor completion problem has been paid high attention in the machine learning, especially in the field of computer vision and image processing. The low-rank tensor completion methods based on the tensor singular value decomposition and the tensor nuclear norm minimization has been proposed. However, they have limitations in computing speed, since they are SVD-based methods and need high computational cost for high dimensional tensor. In this paper, based on the tensor QR decomposition and the tensor nuclear norm, a fast low-rank tensor completion method is proposed. By reducing the dimensions of the tensor in the nuclear norm regularization term, the performance of the completion is substantially improved. Numerical experiments for color images, MRI and videos demonstrate that the effectiveness of the proposed method.

Wang et al. gave four Z-eigenvalue inclusion intervals for tensors in [Discrete and Continuous Dynamical Systems Series B, 1 (2017), 187-198]. However, these intervals always include zero, and hence could not be used to identify the positive definiteness of a homogeneous polynomial form. In this note, we present a new Z-eigenvalue inclusion interval with parameters for evenorder tensors, which not only overcomes the above shortcomings under certain conditions, but also provides a checkable sufficient condition for the positive definiteness of homogeneous polynomial forms, as well as the asymptotically stability of time-invariant polynomial systems.

The condition for strong ellipticity of the equilibrium equations plays a significant role in the theory of elasticity. For isotropic elastic materials and anisotropic linearly elastic materials, identification of the strong ellipticity conditions for the corresponding equilibrium equations has been discussed in many references and obtained some equivalent checkable criteria. But for general nonlinearly elastic materials, it is hardly possible to give checkable equivalent criteria for the strong ellipticity condition of the associated equilibrium equations. In 2009, Qi et al. pointed that the strong ellipticity condition of the equilibrium equations can be equivalently transformed into the strong ellipticity condition of partially symmetric tensors. In this paper, using the M-eigenvalues of partially symmetric tensors, we give some easily computable and verifiable sufficient conditions for the strong ellipticity of partially symmetric tensors. Based on these criteria, some direct algorithms for identifying the strong ellipticity condition of partially symmetric tensors are derived. Numerical examples show that the proposed criteria are efficient in identifying the strong ellipticity condition of the equilibrium equations, especially for general nonlinearly elastic materials.

The class of {P-1,P-2}-Nekrasov matrices, defined in terms of permutation matrices P-1 and P-2, is a generalization of the well-known class of Nekrasov matrices. In this paper, some computable error bounds for linear complementarity problems (LCPs) of {P-1,P-2}-Nekrasov matrices are given, which depend only on the entries of the involved matrices and can be used to obtain the perturbation bounds of {P-1,P-2}-Nekrasov matrices LCPs. Besides, some sufficient conditions ensuring that the subdirect sum of {P-1,P-2}-Nekrasov matrices lies in the same class are also provided.

应用修正矩阵理论和α-型及Brauer-型矩阵特征值包含区域,获得随机矩阵非1特征值新的α-型和Brauer-型特征值包含区域及其非奇异的充分条件.最后用数值例子验证所得的包含区域比一些已有的包含区域更精确,且能用其更好地估计随机矩阵的谱隙.

为降低三维打印（three-dimensional printing）耗材费用并进一步提高打印效率,给出一种面向熔融沉积制造的三维打印路径规划算法。该算法综合考虑打印耗材、打印效率以及打印表面质量等因素,通过网格模型及其支撑的相邻层片轮廓关系求得可稀疏打印区域;基于多边形扫描线算法以及多边形单调链关系,得到能够连续打印的路径区域;最终通过区域路径稀疏化得到改进的打印路径。通过复杂网格模型的三维打印路径规划实例,验证了算法的有效性。该算法能够降低打印耗材数量,并进一步提高打印效率。