Since the outbreak of the COVID-19 pandemic in 2019, medical imaging has emerged as a primary modality for diagnosing COVID-19 pneumonia. In clinical settings, the segmentation of lung infections from computed tomography images enables rapid and accurate quantification and diagnosis of COVID-19. Segmentation of COVID-19 infections in the lungs poses a formidable challenge, primarily due to the indistinct boundaries and limited contrast presented by ground glass opacity manifestations. Moreover, the confounding similarity among infiltrates, lung tissues, and lung walls further complicates this segmentation task. To address these challenges, this paper introduces a novel deep network architecture, called CAD-Unet, for segmenting COVID-19 lung infections. In this architecture, capsule networks are incorporated into the existing Unet framework. Capsule networks represent a novel type of network architecture that differs from traditional convolutional neural networks. They utilize vectors for information transfer among capsules, facilitating the extraction of intricate lesion spatial information. Additionally, we design a capsule encoder path and establish a coupling path between the unet encoder and the capsule encoder. This design maximizes the complementary advantages of both network structures while achieving efficient information fusion. Finally, extensive experiments are conducted on four publicly available datasets, encompassing binary segmentation tasks and multi-class segmentation tasks. The experimental results demonstrate the superior segmentation performance of the proposed model. The code has been released at: https://github.com/AmanoTooko-jie/CAD-Unet.

The problem of low-rank tensor recovery has garnered significant attention, particularly in applications involving visual data, within the tensor singular value decomposition (t-SVD) framework. However, most existing approaches are limited to third-order tensors, restricting their applicability to higher-order data such as fourth-order color videos or fifth-order light field images. In this work, we address the challenge of high-order tensor recovery by leveraging the recently proposed high-order transformed t-SVD framework. Specifically, we utilize the high-order transformed tensor nuclear norm to model the global low-rank structure of these visual tensor datasets, while incorporating high-order total variation (TV) regularization to preserve local piecewise smoothness. To solve the resulting models for both tensor completion and robust principal component analysis (RPCA), we design efficient algorithms based on the alternating direction method of multipliers (ADMM) framework. We also rigorously establish the global convergence of these algorithms. Extensive experiments on a variety of visual datasets demonstrate the superiority of our proposed methods when compared to numerous state-of-the-art techniques.

This article presents an adaptive control algorithm for stochastic nonholonomic systems subject to state constraints and input saturation simultaneously. We give a state‐input scaling transformation and a novel auxiliary variable to transform the stochastic nonholonomic system into a new one to make it easier to design the controller, and adopt a switching strategy to eliminate the phenomenon of uncontrollability. By introducing a barrier Lyapunov function and defining a suitable adaptive parameter, we construct a novel adaptive neural network controller with only one adaptive law, which can alleviate computation burden. The presented controller not only overcomes the effects of both full‐state constraints and full‐input saturation on system performance, but also ensures that all states of the closed‐loop are semi‐globally uniformly ultimately bounded in probability. Additionally, all state variables are restricted to the predefined compact sets. Finally, an example is used to validate the efficacy of the established controller.

This paper formulates two novel theoretical designs of input -to -state stabilizing control for a class of recurrent neural networks with multiple proportional delays. The analysis tool developed in this paper is based on Lyapunov function and inverse optimality method, which does not require solving Hamilton-Jacobi-Bellman equations. Two inverse optimal feedback laws are constructed via the dimensions of state and input, which ensure the input -state stability for the considered system. When the dimensions of state and input are different, we establish a scalar function and give one of the control laws by Sontag's formula. Furthermore, the designs of inverse optimal control reach both global inverse optimality and global asymptotic stability of the system for some meaningful cost functional. Four numerical examples are provided to show the effectiveness of the inverse optimal control.

Within the tensor singular value decomposition (T-SVD) framework, existing robust low-rank tensor completion approaches have made great achievements in various areas of science and engineering. Nevertheless, these methods involve the T-SVD based low-rank approximation, which suffers from high computational costs when dealing with large-scale tensor data. Moreover, most of them are only applicable to third-order tensors. Against these issues, in this article, two efficient low-rank tensor approximation approaches fusing randomized techniques are first devised under the order-d (d >= 3) T-SVD framework. On this basis, we then further investigate the robust high-order tensor completion (RHTC) problem, in which a double nonconvex model along with its corresponding fast optimization algorithms with convergence guarantees are developed. To the best of our knowledge, this is the first study to incorporate the randomized low-rank approximation into the RHTC problem. Empirical studies on large-scale synthetic and real tensor data illustrate that the proposed method outperforms other state-of-the-art approaches in terms of both computational efficiency and estimated precision.

This paper develops new practical stability criteria for impulsive stochastic functional differential systems with distributed-delay dependent impulses by using the Lyapunov–Razumikhin approach and some inequality techniques. In the given systems, the state variables on the impulses are concerned with a history time period, which is very appropriate for modelling some practical problems. Moreover, different from the existing practical stabilization results for the systems with unstable continuous stochastic dynamics and stabilizing impulsive effects, we take the systems with stable continuous stochastic dynamics and destabilizing impulsive effects into account. It shows that under the impulsive perturbations, the practical exponential stability of the stochastic functional differential systems can remain unchanged when the destabilizing distributed-delay dependent impulses satisfy some conditions on the frequency and amplitude of the impulses. In other words, it reveals that how to control the impulsive perturbations such that the corresponding stochastic functional differential systems still maintain practically exponentially stable. Finally, an example with its numerical simulation is offered to demonstrate the efficiency of the theoretical findings.

This paper develops new practical stability criteria for continuous-time stochastic nonlinear system with uncertainties and external disturbances. Two cases of the system are considered: the system with state-dependent disturbance and the system with state-independent disturbance. Based on the event-triggered mechanism and Lyapunov function, we establish the input-to-state practical exponential stability in mean square for each case of the system. The obtained results improve some previous works in the literature. Finally, several examples are given to show the effectiveness and practicability of the main results.

Summary This paper is concerned with the problem of practical exponential stability for hybrid impulsive stochastic functional differential systems with delayed impulses, which comprise three classes of systems: the systems with unstable continuous stochastic dynamics and stable discrete dynamics, the systems with stable continuous stochastic dynamics and unstable discrete dynamics, and the systems where both the continuous stochastic dynamics and the discrete dynamics are stable. By using the Lyapunov‐Razumikhin approach, several new sufficient conditions for the practical exponential stability are established for each class of systems. It shows that the stabilizing and destabilizing delayed impulses that satisfy some conditions on their frequency and amplitude can stabilize the systems with unstable continuous stochastic dynamics in the practical exponential stability sense and ensure the practical exponential stability of the systems with stable continuous stochastic dynamics, respectively. Conversely, if the continuous stochastic dynamics are practically exponentially stable and the delayed impulses are stabilizing, then the systems can be practically exponentially stable regardless of the restrictions on the delayed impulses frequency and amplitude. Finally, two numerical examples are presented to illustrate the efficiency of the results.

The latest tensor recovery methods based on tensor Singular Value Decomposition (t-SVD) mainly utilize the tensor nuclear norm (TNN) as a convex surrogate of the rank function. However, TNN minimization treats each rank component equally and tends to over-shrink the dominant ones, thereby usually leading to biased solutions. To handle this critical issue, we put forward a weighted tensor Schantten-p (0 < p ≤ 1) norm (WTSN) as high-order tensor rank’s more flexible nonconvex relaxation. Furthermore, another nonconvex ℓ q (0 < q ≤ 1) sparse regularization item on the extensively existed noises/outliers is incorporated into the WSTN minimization to enhance its robustness in the impulsive scenarios. Finally, we propose an efficient and scalable robust high-order tensor recovery method solving a double nonconvex optimization with convergence guarantees. Synthetic and real experiments demonstrate that the proposed approach outperforms the state-of-the-art ones in terms of both accuracy and computational complexity.

This paper examines the dynamics of the exponential population growth system with mixed fractional Brownian motion. First, we establish some useful lemmas that provide powerful tools for studying the stochastic differential equations with mixed fractional Brownian motion. We offer some explicit expressions and numerical characteristics such as mathematical expectation and variance of the solutions of the exponential population growth system with mixed fractional Brownian motion. Second, we propose two sufficient and necessary conditions for the almost sure exponential stability and the kth moment exponential stability of the solution of the constant coefficient exponential population growth system with mixed fractional Brownian motion. Furthermore, we conduct some large deviation analysis of this mixed fractional population growth system. To the best of the authors' knowledge, this is the first paper to investigate how the Hurst index affects the exponential stability and large deviations in the biological population system. It is interesting that the phenomenon of large deviations always occurs for addressed system when1/2<H<1. Moreover, several numerical simulations are reported to show the effectiveness of the proposed approach.

对一类具有时变时滞的随机递归神经网络模型,研究了其系统的全局渐近稳定性,并给出了一个新的控制器设计方法.基于逆最优方法和Lyapunov函数,在不需要求解Hamilton-Jacobi-Bellman方程情形下,对于一个有意义的成本函数,反馈控制器的设计既能使系统达到全局最优,又能保证系统的全局渐近稳定性.

It is well known that stability is one of most important topics in economy and control. In this paper, we focus on the practical stability problem for a class of stochastic age-dependent (vintage) capital system with Lévy noise. Compared with the classical Lyapunov stability theory, practical stability can depict not only qualitative behavior but also quantitative properties, such as specific trajectory bounds and specific transient behavior. With the help of the stochastic analysis theory and Itô's formula, we establish some novel criteria for the mean square and almost sure practical exponential stability of the addressed system. The obtained results improve some previous works given in the literature. Moreover, an example is provided to illustrate the theoretical results.

研究了具有时滞的分数阶模糊细胞神经网络,应用不等式与Banach不动点定理得到了系统解的存在唯一性条件和一致稳定性结果.最后,通过例子验证了定理的有效性.

In this paper,we study the existence of solutions to the stochastic fuzzy differential equations with infinite delay (ISFDEs in short) under non-Lipschitz condition and weak linear growth condition.The solutions and their uniqueness are considered to be in a strong sense.

本文给出具有Poisson跳的随机年龄相关种群方程.在局部非Lipschitz条件下,证明了Hilbert空间中随机年龄相关种群方程解的存在唯一性.

In this paper, we introduce a class of stochastic neural networks with fractional Brownian motion (fBm) and Poisson jumps. We also concern mean-square dissipativity of numerical methods applied to a class of stochastic neural networks with fBm and jumps. The conditions under which the underlying systems are mean-square dissipative are considered. It is shown that the mean-square dissipativity is preserved by the compensated split-step backward Euler method and compensated backward Euler method without any restriction on stepsize, while the split-step backward Euler method and backward Euler method could reproduce mean-square dissipativity under a stepsize constraint. The results indicate that compensated numerical methods achieve superiority over non-compensated numerical methods in terms of mean-square dissipativity. Finally, an example is given for illustration.

In this paper, we introduce a class of stochastic age-dependent population equations driven by Levy processes. Existence and uniqueness of energy solutions for stochastic age-dependent population dynamic system are proved under Lipschitz condition in Hilbert space. The moment boundedness of the approximate solution by the Galerkin method is considered. We discuss by using the energy equality the exponential stability theorems of the energy solution to stochastic age-dependent population equations.

The main aim of this paper is to discuss the almost surely asymptotic stability of the stochastic age-dependent population equations with Markovian switching. An example will be discussed to illustrate the theory.

A numerical method proposed to approximate the solution of a class of stochastic age-dependent populations. We show that under certain conditions, weaker than Linear growth and Global Lips-chits, the Euler scheme applied to Stochastic age-dependent population, converges to the analytic solution, and provide information on the order of approximation.

The convergence of numerical approximation of stochastic age-dependent population equations with Poisson jumps and Markovian switching is studied.It is proved that the numerical approximation solutions converge to the analytic solutions of the equations under the given conditions.The order of the Euler approximation is also provided.