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Quantum state tomography, which aims to estimate quantum states that are described by density matrices, plays an important role in quantum science and quantum technology. This paper examines the eigenspace estimation and the reconstruction of large low-rank density matrix based on Pauli measurements. Both ordinary principal component analysis (PCA) and iterative thresholding sparse PCA (ITSPCA) estimators of the eigenspace are studied, and their respective convergence rates are established. In particular, we show that the ITSPCA estimator is rate-optimal. We present the reconstruction of the large low-rank density matrix and obtain its optimal convergence rate by using the ITSPCA estimator. A numerical study is carried out to investigate the finite sample performance of the proposed estimators.

We develop a mathematical model of the wild mosquito dispersal with impulsive releases of the sterile mosquitoes and obtain a threshold condition that determines the eradication and uniform persistence of the wild mosquitoes using Floquet theory and impulsive comparison theorem. The effect of the dispersal rate on dynamics is investigated by means of numerical simulation. Additionally, we investigate a three-dimensional dispersal model of mosquitoes with impulsive state feedback control to effectively control the abundance of the wild mosquitoes below the acceptable level when the density of the wild mosquitoes reaches a certain threshold. Dynamics of such state-dependent control is also presented by applying numerical simulations since it is difficult to implement theoretical analysis. Finally, a brief discussion is given.

In this paper, to study the large-scale time control and limited-time control of mosquito population in a field, a two-sex mosquito population model with stage structure and impulsive releases of sterile males is proposed. For the large-scale time control, a wild mosquito-free periodic solution is given and conditions under which it is globally stable are obtained by the use of the monotone system theory. Besides, based on the stability analysis, threshold conditions under which the wild mosquito population is eliminated or not are obtained. Then we study three different optimal release strategies for the limited-time control, which takes into account both of the population control level of wild mosquitoes and the economic input. To solve technical problems in optimal impulsive control, a time rescaling technique is applied and the gradients of cost function with respect to all control parameters are obtained. In addition, by the aid of numerical simulation, we get the optimal release amounts and release timings for each release strategy. Our study indicates that the optimal release timing control is superior to the optimal release amount control. However, simultaneous optimal selection of release amount and release timing leads to the best control performance.

The issue of bifurcation control for a novel fractional-order two-prey and one-predator system with time delay is dealt with in this paper. Firstly, the characteristic equation is investigated by picking time delay as the bifurcation parameter, and some conditions for the appearance of Hopf bifurcation are obtained. It is shown that time delay can give rise to periodic oscillations and each order has an important impact on the occurrence of Hopf bifurcation for the controlled system. Then, it is illustrated that the control result is obviously influenced by the feedback gain. It is also noted that the inception of the bifurcation can be postponed if the feedback gain decreases. Finally, two simulation examples are carried out to verify the chief theoretical results.

To reduce or eradicate mosquito-borne diseases, one of effective methods is to control the wild mosquito populations by using the sterile insect technique. Dynamical models with different releasing strategies of sterile mosquitoes have been proposed and investigated in the recent work by Cai et al. [SIAM. J. Appl. Math. 75(2014)], where some basic analysis on the dynamics are given and some complicated dynamical behaviors are found by numerical simulations. While their findings seem exciting and promising, yet the models could exhibit much more complex dynamics than it has been observed. In this paper, to further study the impact of the sterile insect technique on controlling the wild mosquito populations, we systematically study bifurcations and dynamics of the model with a proportional release rate of sterile mosquitoes by bifurcation method. We show that the model undergoes saddle-node bifurcation, subcritical and supercritical Hopf bifurcations, and Bogdanov-Takens bifurcation as the values of parameters vary. Some numerical simulations, including the bifurcation diagram and phase portraits, are also presented to illustrate the theoretical conclusions. These rich and complicated bifurcation phenomena can be regarded as a complement to the work by Cai et al. [SIAM. J. Appl. Math. 75(2014)].

Terrestrial laser scanning (TLS) can be used as a millimeter-level measurement tool for forest inventories. However, the stem diameter retrieval accuracy in sample plot scanning is not yet convincing. The errors in each step of stem diameter retrieval algorithms must be evaluated. In this study, six numerical calculation methods for the numerical calculation step, i.e., cylinder fitting (CYF), circle fitting (CF), convex hull line fitting (CLF), the proposed caliper simulation method (CSM), closure B-spline curve fitting (SP) and closure Bézier curve fitting with global convexity (SPC), were applied to stem diameter retrieval, and the similarities and differences were evaluated. The ovality, completeness and roughness were used to evaluate the stem slice point cloud quality. A total of 165 stem slice point clouds at breast height collected from three Larix kaempferi plots were used. Compared with the field-measured stem diameters at breast height (DBHs), the root mean square errors (RMSEs) of the CYF, CF, CLF, CSM, SP and SPC methods were 0.30 cm, 0.30 cm, 0.51 cm, 0.51 cm, 0.56 cm and 0.54 cm, respectively. Compared with the SPC method results, the RMSE of the CSM results was 0.05 cm. The results illustrated that the CYF and CF methods performed the same, as did the CLF and CSM methods. Most DBHs retrieved by the CYF and CF methods were smaller than the field-measured DBHs, and most DBHs retrieved by the CLF, CSM, SP and SPC methods were larger than the field-measured DBHs. This study demonstrated that the CYF and CF methods perform the best and are the most robust, and the measurements by a diameter tape and a caliper are similar enough for forestry inventories. Evaluating and preprocessing stem slice point clouds is a potential way to improve stem diameter retrieval accuracy.

To investigate the release strategies of sterile mosquitoes for the wild population control, we propose mathematical models for the interaction between two-mosquito populations incorporating impulsive releases of sterile ones. The long-term control model is first studied, and the existence and stability of the wild mosquito-extinction periodic solution are exploited. Thresholds of the release amount and release period which can guarantee the elimination of the wild mosquitos are obtained. Then for the limited-time control model, three different optimal strategies in impulsive control are investigated. By applying a time rescaling technique and an optimization algorithm based on gradient, the optimal impulsive release timings and amounts of sterile mosquitoes are obtained. Our results show that the optimal selection of release timing is more important than the optimal selection of release amount, while mixed optimal control has the best comprehensive effect.

Multilabel classification is one of the most challenging tasks in natural language processing, posing greater technical difficulties than single-label classification. At the same time, multilabel classification has more natural applications. For individual labels, the whole piece of text has different focuses or component distributions, which require full use of local information of the sentence. As a widely adopted mechanism in natural language processing, attention becomes a natural choice for the issue. This paper proposes a multilayer self-attention model to deal with aspect category and word attention at different granularities. Combined with the BERT pretraining model, it achieves competitive performance in aspect category detection and electronic medical records’ classification.

This paper’s goal is to delve into the fractional modeling and bifurcation control for a predator-prey model with prey dispersal and gestation delay. First, the bifurcation criteria for the uncontrolled system are obtained by viewing gestation delay as a bifurcation parameter. It is revealed that gestation delay can induce periodic oscillations. Then, an extended feedback controller is deeply conceived to suppress Hopf bifurcation for the underlying system. The results reflect that the stability behaviors of the uncontrolled system are saliently enhanced by adjusting feedback gain and feedback delay if other coefficients are fixed. To protrude the correctness and excellent feature of our works, two simulation examples are eventually carried out.

Wide attention has been paid to named entity recognition (NER) in specific fields. Among the representative tasks are the aspect term extraction (ATE) in user online comments and the biomedical named entity recognition (BioNER) in medical documents. Existing methods only perform well in a particular field, and it is difficult to maintain an advantage in other fields. In this article, we propose a supervised learning method that can be used for much special domain NER tasks. The model consists of two parts, a multidimensional self-attention (MDSA) network and a CNN-based model. The multidimensional self-attention mechanism can calculate the importance of the context to the current word, select the relevance according to the importance, and complete the update of the word vector. This update mechanism allows the subsequent CNN model to have variable-length memory of sentence context. We conduct experiments on benchmark datasets of ATE and BioNER tasks. The results show that our model surpasses most baseline methods.

Density-dependent diffusion plays an important role in the process of viral infection. In this paper, we construct mathematical models to investigate the dynamics of the viruses and their control. Single strain and multi-strain viral infections are both considered in this work. Using the method proposed by Pao and Ruan (2013), we prove the well-posedness of the models. By constructing appropriate Lyapunov functions, we proved the global asymptotical stabilities of the models. For the multi-strain model, we show that when the basic reproduction number for each strain is greater than one, all viral strains coexist. Since the effect of different treatments may result in competitive exclusion, it is essential to employ the treatment with combined therapy. We find with surprise that the density-dependent diffusion of the virus does not influence the global stabilities of the model with homogeneous Neumann boundary conditions.

This paper deals with the complementarity system over the second-order cone (denoted by CSSOC) which contains a wide class of problems. We extend a class of regularized Chen–Harker–Kanzow–Smale smoothing functions studied by Huang and Sun (Appl Math Optim 52:237–262, 2005) for the linear complementarity problem to the CSSOC. Based on this class of functions, we propose a smoothing algorithm for solving the CSSOC. Under weak assumptions, we prove that the proposed algorithm has global and local quadratic convergence. The proposed algorithm is different from existing smoothing algorithms for solving the CSSOC because it adopts a new nonmonotone line search rule. In addition, our algorithm solves a new equation reformulation of the CSSOC. Numerical experiments indicate that the proposed algorithm is quite effective.

In this paper, we consider semi-continuous dynamical systems with linear impulsive conditions, which have a convex order one periodic solution of unilateral asymptotic type. By constructing a sequence of switched systems and using the square approximation of the order one periodic solution, some stability criteria of the order one periodic solution are obtained. Compared with the continuous dynamical system, these criteria are very similar and also easily to be applied in the research of practical problems.

This paper considers the linear weighted complementarity problem (denoted by LWCP). We introduce a parametric smoothing function which is a broad class of smoothing functions for the LWCP and enjoy...

Considering how to exploit the lake resource reasonably, we propose a phytoplankton–fish model with the impulsive feedback control and investigate the sufficient conditions for the existence of the order-1 periodic solution by means of successor function. The stability of the order-1 periodic solution is discussed by a novel stability criterion on the basis of the stability theory of limit cycle. Furthermore, harvesting profit is maximized by using Pontryagin’s maximum principle subject to the impulsive feedback control. Finally, our results are justified by some numerical simulations.

Cloth simulation usually refers to using computer programs to simulate the true representation of flexible tensile materials in nature. This article is based on the traditional Mass-Spring model. The main improvement method is: giving a reasonable range of Hook variable to the original model, constraining the abnormal deformation of the spring under the action of powerful external force, which is called "Hyperelastic phenomenon"; In the case of the same types of traditional force, imitating the natural performance of the wind field to cloth, increase the pressure difference caused by the Bernoulli effect, resulting in a more realistic cloth simulation in wind field; Using the Symplectic Euler method to solve the differential equation of particle motion, since this method belongs to the implicit Euler method, it has a more stable performance than the explicit Euler method; Using mature geometric calculation formulas, collision detection is realized with less space and time complexity. Through this experiment, it is verified that the cloth simulation optimization based on this method has a better real-time and On-site reduction effect.

In this paper, a pest management predator–prey model with weak Allee effect on predator and state feedback impulsive control on prey is introduced and analysed, where the yield of predator released and intensity of pesticide sprayed are assumed to be linearly dependent on the selected pest control level. For the proposed model, the existence and stability of the order-1 periodic orbit of the control system are discussed. Meanwhile, with the aim of minimizing the input cost in practice, an optimization model is constructed to determine the optimal quantity of the predator released and the intensity of pesticide sprayed. The theoretical results and numerical simulations indicated that the number of pests can be limited to below an economic threshold and displays periodic variation under the proposed control strategy. In addition, it indicated in numerical simulations that an order-2 periodic orbit exists for some certain parameters.

Extensive amounts of multi-omics data and multiple cancer subtyping methods have been developed rapidly, and generate discrepant clustering results, which poses challenges for cancer molecular subtype research. Thus, the development of methods for the identification of cancer consensus molecular subtypes is essential. The lack of intuitive and easy-to-use analytical tools has posed a barrier. Here, we report on the development of the COnsensus Molecular SUbtype of Cancer (COMSUC) web server. With COMSUC, users can explore consensus molecular subtypes of more than 30 cancers based on eight clustering methods, five types of omics data from public reference datasets or users’ private data, and three consensus clustering methods. The web server provides interactive and modifiable visualization, and publishable output of analysis results. Researchers can also exchange consensus subtype results with collaborators via project IDs. COMSUC is now publicly and freely available with no login requirement at http://comsuc.bioinforai.tech/ (IP address: http://59.110.25.27/). For a video summary of this web server, see S1 Video and S1 File., Author summary A number of methods have been developed for omics data-based subtyping, which has been widely accepted as a relevant source of cancer classification. However, discrepant results hamper the translational and clinical utility of these methods. In this study, we have developed the COnsensus Molecular SUbtype of Cancer (COMSUC) web server to provide a user-friendly tool for integrating discrepant clustering results based on multiple platform, multiple omics data and multiple methods. COMSUC provides powerful support to users to decipher the cancer Consensus Molecular Subtypes (CMSs), a consensus classification system integrating different clustering results.

Human immunodeficiency virus (HIV) can infect various types of cell populations such as CD4+ T cells and macrophages. The heterogeneity of these target cells implies different birth, death, infection rates, and so on. To investigate the within-host dynamics of HIV which can infect n different types of target cells, a theoretical model with infection-age structure for each type of target cells and a general nonlinear incidence rate is proposed in this manuscript. The model, in the form of a hyperbolic system of partial differential equations (PDE) for infected target cells coupled with several ordinary differential equations, is shown to be biologically reasonable with the establishment of existence, positivity, and boundedness of solutions. Although the PDE form poses novel challenges to theoretical investigation, rigorous analysis is performed to show the uniform persistence of the virus when the basic reproduction number is greater than one. Furthermore, by constructing suitable Lyapunov functionals, we show that the infection-free steady state is globally asymptotically stable when the basic reproduction number is less than unity, while the positive steady state is globally asymptotically stable when the basic reproduction number is greater than one.

Nonlinear error-in-variable models can advance the development of the systems of additive biomass equations and lead to much higher prediction accuracy of tree biomass than nonlinear seemingly unrelated regression. In this study, the approach of nonlinear error-in-variable models (NEIVM) was compared with nonlinear seemingly unrelated regressions (NSUR) for developing a system of nonlinear additive biomass equations using the data collected in Southern China for Pinus massoniana Lamb. Various tree variables were assessed to explore their contributions to improvement of biomass prediction using the systems of equations. It was found that diameter at breast height (D), total tree height (H) and crown width (CW) significantly contributed to the increase of prediction accuracy. The combinations of D, H, and CW led to three sets of independent variables: (1) D alone; (2) both D and H; and (3) D, H and CW together, which were used for the development of one-predictor, two-predictor and three-predictor systems of biomass equations, respectively. The results showed that both NEIVM and NSUR had high prediction accuracy of biomass for all the systems of biomass equations. For the one-predictor systems of biomass equations, both NEIVM and NSUR led to very similar predictions. However, for the two-predictor and three-predictor systems of biomass equations, the prediction accuracy of NEIVM was much higher than that of NSUR. When the two-predictor system of equations was used, in particular, NEIVM with one-step procedure, that is, by directly partitioning total tree biomass into four basic components, showed a higher accuracy of biomass prediction than NSUR for all the one-predictor, two-predictor and three-predictor systems of equations. This study implies that the NEIVM approach could provide a greater potential to develop a system of biomass equations that are dependent on the predictors with significant measurement errors.

There is a widely known intriguing phenomenon that discrete-time GARCH and stochastic volatility (SV) models share the same continuous-time diffusion model as their weak convergence limit, but statistically, the GARCH model is not asymptotically equivalent to the SV or diffusion model. This paper investigates GARCH-type quasi-likelihood ratios for the SV and diffusion models whose own likelihoods are analytically intractable. We show that the two quasi-likelihood ratios for the SV and diffusion models asymptotically have the same closed-form expression that is different from the limiting likelihood ratio of the GARCH model.

In this paper, three competitive systems with different kinds of state-dependent control are presented and investigated. The existence of the order-1 homoclinic orbit and order-1 periodic solution of the two systems that incorporate just one kind of state-dependent control is obtained by applying differential equation geometry theory, and the stability of the order-1 periodic solution of each system is also given. Besides, sufficient conditions for the existence and stability of the order-2 periodic solution of the system that incorporate two kinds of state-dependent control are gained by successor function method and analogue of Poincaré criterion, respectively. Finally, numerical simulations are carried out to verify the theoretical results.

To study the finite-time control of plasma glucose for diabetic patients with impulsive injections of insulin, we propose an impulsive differential equation model with initial and boundary conditions. The goal of glucose control is supposed to be achieved if the system has a solution, otherwise the goal cannot be achieved. By constructing two comparison systems and using a comparison principle, several conditions under which the system has a solution are obtained. Furthermore, some numerical simulations are given. The results show that a relatively higher initial insulin level is beneficial for the glucose control. For a predefined finite time, injection dose and injection period are two important adjustable factors which can guarantee the achievement of the control goal.

Estimating individual tree diameters at breast height (DBH) from delineated crowns and tree heights on the basis of airborne light detection and ranging (LiDAR) data provides a good opportunity for large-scale forest inventory. Generally, ground-based measurements are more accurate, but LiDAR data and derived DBH values can be obtained over larger areas for a relatively smaller cost if a right procedure is developed. A nonlinear least squares (NLS) regression is not an appropriate approach to predict the aboveground biomass (AGB) of individual trees from the estimated DBH because both the response variable and the regressor are subject to measurement errors. In this study, a system of compatible individual tree DBH and AGB error-in-variable models was developed using error-in-variable regression techniques based on both airborne LiDAR and field-measured datasets of individual Picea crassifolia Kom. trees, collected in northwestern China. Two parameter estimation algorithms, i.e., the two-stage error-in-variable model (TSEM) and the nonlinear seemingly unrelated regression (NSUR), were proposed for estimating the parameters in the developed system of compatible individual tree DBH and AGB error-in-variable models. Moreover, two model structures were applied to estimate AGB for comparison purposes: NLS with AGB estimation depending on DBH (NLS&DD) and NLS with AGB estimation not depending on DBH (NLS&NDD). The results showed that both TSEM and NSUR led to almost the same parameter estimates for the developed system. Moreover, the developed system effectively accounted for the inherent correlation between DBH and AGB as well as for the effects of measurement errors in the DBH on the predictions of AGB, whereas NLS&DD and NLS&NDD did not. A leave-one-out cross-validation indicated that the prediction accuracy of the developed system of compatible individual tree DBH and AGB error-in-variable models with NSUR was the highest among those estimated by the four methods evaluated, but, statistically, the accuracy improvement was not significantly different from zero. The main reason might be that, except for the measurement errors, other source errors were ignored in the modeling. This study implies that, overall, the proposed method provides the potential to expand the estimations of both DBH and AGB from individual trees to stands by combining the error-in-variable modeling and LiDAR data and improve their estimation accuracies, but its application needs to be further validated by conducting a systematical uncertainty analysis of various source errors in a future study.

A kind of consumer-resource system is proposed to describe the bidirectional interactions of the algae and the fish in an eutrophic water body. The dynamical properties of the proposed continuous system are given. For the bistable case, an impulsive semidynamical system with state feedback control, which depends on the biomass of the algae, is formulated and investigated to consider the feasibility of state feedback control for the aim of maintaining two species coexisting. The impulsive semidynamical system has three cases corresponding to three kinds of control measures: releasing fish, spraying algaecide, integrated control combining releasing fish and spraying algaecide. The existences of order-1 periodic solutions of three models are discussed by using successor function, respectively. The conditions under which the order-1 periodic solution is stable are given by using the Poincare map and the analogue of Poincare criterion. Mathematical results show that, for every one of three control strategies, there exists a range of control parameter in which the corresponding control is feasible. Finally, those mathematical results are verified by numerical simulations and the practical meanings are given.

A kind of cylindrical dynamic system with impulsive state feedback control is formulated and investigated. Based on the qualitative properties of the corresponding continuous system, the existence of order- k ( k ∈ Z + ) periodic solutions of the cylindrical dynamic system with impulsive state feedback control is discussed on the cylinder with perimeter 2 π . If the equilibrium of the corresponding continuous system in the rectangle coordinate system is an unstable node, then the cylindrical dynamic system has two one-side stable minimum limit sets. If the equilibrium is an unstable focus, then, for different parameters, the cylindrical dynamic system has the periodic solutions with different periods and different orders. Finally, numerical simulations are given to verify the theoretical results.

In this paper, an epidemic dynamical model with vaccination is proposed. Vaccination of both newborn and susceptible is included in the present model. The impact of the vaccination strategy with the vaccine efficacy is explored. In particular, the model exhibits backward bifurcations under the vaccination level, and bistability occurrence can be observed. Mathematically, a bifurcation analysis is performed, and the conditions ensuring that the system exhibits backward bifurcation are provided. The global dynamics of the equilibrium in the model are also investigated. Numerical simulations are also conducted to confirm and extend the analytic results.

A korean pine forest model with impulsive thinning measure is presented by using impulsive state feedback system to investigate the periodicity of the regeneration process of the forest. Based on the qualitative properties of the corresponding continuous system, the existences of order-1 periodic solutions are discussed. If the positive equilibrium of the continuous system is globally stable, then the impulsive state feedback system has an order-1 periodic solution and no order- k ( k ? 2 ) periodic solution. The conditions for the orbitally asymptotical stability of order-1 periodic solution are given and discussed by the analogue of the Poincare criterion. For the case that the continuous system has a stable limit cycle, the existence of order-1 periodic solution of the impulsive state feedback system are also discussed, the results show that there are three kinds of order-1 periodic solutions. Finally, the mathematical results are verified by the numerical simulations. Moreover, the numerical results show that the impulsive state feedback system has order k ( k ? 1 ) periodic solutions in the interior of the limit cycle of the continuous system for some parameters.

The dynamics of SEIR epidemic model with saturated incidence rate and saturated treatment function are explored in this paper. The basic reproduction number that determines disease extinction and disease survival is given. The existing threshold conditions of all kinds of the equilibrium points are obtained. Sufficient conditions are established for the existence of backward bifurcation. The local asymptotical stability of equilibrium is verified by analyzing the eigenvalues and using the Routh-Hurwitz criterion. We also discuss the global asymptotical stability of the endemic equilibrium by autonomous convergence theorem. The study indicates that we should improve the efficiency and enlarge the capacity of the treatment to control the spread of disease. Numerical simulations are presented to support and complement the theoretical findings.

Nonlinear mixed-effects (NLME) models have become popular in various disciplines over the past several decades. However, the existing methods for parameter estimation implemented in standard statistical packages such as SAS and R/S-Plus are generally limited to single- or multi-level NLME models that only allow nested random effects and are unable to cope with crossed random effects within the framework of NLME modeling. In this study, we propose a general formulation of NLME models that can accommodate both nested and crossed random effects, and then develop a computational algorithm for parameter estimation based on normal assumptions. The maximum likelihood estimation is carried out using the first-order conditional expansion (FOCE) for NLME model linearization and sequential quadratic programming (SQP) for computational optimization while ensuring positive-definiteness of the estimated variance-covariance matrices of both random effects and error terms. The FOCE-SQP algorithm is evaluated using the height and diameter data measured on trees from Korean larch (L. olgensis var. Changpaiensis) experimental plots as well as simulation studies. We show that the FOCE-SQP method converges fast with high accuracy. Applications of the general formulation of NLME models are illustrated with an analysis of the Korean larch data.

In this paper, we consider a Lotka-Volterra model with birth pulse and impulsive catching or poisoning for the prey at different moment and stage structure on the predator. We prove that all solutions of the system are uniformly ultimately bounded. Sufficient conditions of the global attractivity of predator-extinction periodic solution and the permanence of the system are obtained. These results show that impulsive effects on the prey play an important role for the permanence of the system. In this paper, the main feature is to introduce birth pulse and impulse catching into Lotka-Volterra model and to give pest management strategies.

Two delayed virus dynamics models with multi-target cells and bilinear incidence rate or general incidence rate are studied in this paper. The delays correspond to be the time needed for a newly infected cell to start producing viruses and the time needed for a newly produced virus to become infectious, respectively. Our models include \(n\) uninfected target cells, \(n\) infected target cells and the virus particles. By constructing Lyapunov functionals, we establish the global asymptotic stabilities of the infection-free equilibria and positive equilibria of these models.