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This article intends to study the asynchronous control problem for 2-D Markov jump systems (MJSs) with nonideal transition probabilities (TPs) under the Roesser model. Two practical considerations motivate the current work. First, considering that the system mode cannot always be observed accurately, a hidden Markov model (HMM) is adopted to describe the relationship between the mismatched modes. Second, considering that the TPs information related to the Markov process and the observation process is difficult to obtain, the nonideal TPs (unknown or uncertain) are simultaneously considered on the two processes. Under the considerations, several new sufficient conditions are developed for concerned closed-loop 2-D MJSs with nonideal TPs, by which the asymptotic mean square stability is ensured with an H ∞ performance index. A nonconservative separation strategy is utilized to decouple the system mode TPs and the observation TPs to facilitate the analysis of nonideal TPs. An unified LMI-based condition is finally developed for the concerned closed-loop 2-D MJSs with/without nonideal TPs, showing more satisfactory conservatism than that in the literature. In the end, we present two examples to validate the superiority of the proposed design method.

The primary focus of this article centers around the application of sliding mode control (SMC) to semi-Markov jumping systems, incorporating a dynamic event-triggered protocol (ETP) and singular perturbation. The underlying semi-Markov singularly perturbed systems (SMSPSs) exhibit mode switching behavior governed by a semi-Markov process, wherein the variation of this process is regulated by a deterministic switching signal. To simultaneously reduce the triggering rate and uphold the system performance, a novel parameter-based dynamic ETP is established. This protocol incorporates weight estimation of a radial basis function neural network (RBFNN) and introduces two internal dynamic variables. Following the Lyapunov's theory, sufficient criteria are established for ensuring the mean-square exponential stability of the resulting system. Additionally, an SMC scheme based on the convergence factor is designed to fulfill reachability conditions. Finally, two examples are carried out to validate the solvability and applicability of the attained control methodology.

This article proposes the two-layer asynchronous control scheme for a class of networked nonlinear jump systems. For the constructed system in a network environment, the data transmission may suffer from many restrictions, such as incomplete acceptable mode information and transition information, nonlinearity of system and inadequate bandwidth resources, etc. Then, the two-layer asynchronous controller is developed to stabilize the plant constructed by Takagi-Sugeno (T-S) fuzzy method and semi-Markov theory (SMT). Herein, the hidden semi-Markov process with time-varying emission probability is introduced to establish the relation between the system modes and the controller modes, in which the interval segmentation method is presented to deal with this time-varying probability. Compared with some published results, this method can make full use of the transition rate information, which may lead to the reduction of conservatism in the proposed asynchronous control design. At the same time, the limited bandwidth problem in the communication channel is addressed by introducing the bilateral quantization strategy, and the new sufficient conditions are derived on the stochastic stability of the nonlinear jump system with/without incomplete transition and sojourn-time information. Finally, the numerical simulation examples about DC motor illustrate the effectiveness and the feasibility of the proposed approach.

The event-based H ∞ control problem is investigated for a class of nonhomogeneous Markov jump systems (MJSs) with partially unknown transition probabilities (TPs). The MJS is characterized by a piecewise nonhomogeneous Markovian chain, where the switching of the system TP matrix is governed by a higher-level chain. A hidden Markov model (HMM) is employed to observe the system mode, which cannot always be correctly detected in practice. Under this framework, the partially unknown TPs existing in both higher-level TPs (HTPs) and conditional TPs (CTPs) are taken into account for practical consideration. Additionally, an observed-mode-dependent event-triggered mechanism (ETM) is employed to design an asynchronous controller, which is expected to alleviate the burden of the communication network. Evidently, the considered scenario is fairly general and covers some special cases. With the above consideration, sufficient conditions are established to guarantee stochastic stability of the resulting closed-loop system with a prescribed H ∞ performance. Finally, two examples are presented to demonstrate the effectiveness and applicability of the proposed method.

Background: Inflammatory bowel disease (IBD), including Crohn's disease and ulcerative colitis, is significantly influenced by intestinal flora. Understanding the genetic and microbiotic interplay is crucial for IBD prediction and treatment., Methods: We used Mendelian randomization (MR), transcriptomic analysis, and machine learning techniques, integrating data from the MiBioGen Consortium and various GWAS datasets. SNPs associated with intestinal flora were mapped to genes, with LASSO regression refining gene selection. Differentially expressed genes (DEGs) and immune infiltration patterns were identified through transcriptomic analysis. Six machine learning models were used for predictive modeling., Findings: MR analysis identified 25 gut microbiota classifications causally related to IBD. SNP mapping and gene expression analysis highlighted 24 significant genes. Drug target MR and colocalization validated these genes' causal relationships with IBD. Key pathways identified included the PI3K-Akt signaling pathway and epithelial-mesenchymal transition. Immune infiltration analysis revealed distinct patterns between high and low LASSO score groups. Machine learning models demonstrated high predictive value, with soft voting enhancing reliability., Interpretation: By integrating MR, transcriptomic analysis, and sophisticated machine learning approaches, this study elucidates the causal relationships between intestinal flora and IBD. The application of machine learning not only enhanced predictive modeling but also offered new insights into IBD pathogenesis, highlighted potential therapeutic targets, and established a robust framework for predicting IBD onset., Competing Interests: The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (© 2024 The Authors. Published by Elsevier Ltd.)

The robust LQ optimal regulator problem for discrete-time uncertain singular Markov jump systems (SMJSs) is solved by introducing a new quadratic cost function established by the penalty function method, which combines the penalty function and the weighting matrices. First, the indefinite robust optimal regulator problem for uncertain SMJSs is transformed into the robust optimal regulator problem with positive definite weighting matrices for uncertain Markov jump systems (MJSs). The transformed robust LQ problem is settled by the robust least-squares method, and the condition of the existence and analytic form of the robust optimal regulator are proposed. On the infinite horizon, the optimal state feedback is obtained, which can guarantee the regularity, causality, and stochastic stability of the corresponding optimal closed-loop system and eliminate the uncertain parameters of the closed-loop system. A numerical example and a practical example of DC motor are used to verify the validity of the conclusions.

Congenital defects and genetic diseases in the fetus are the focus of prenatal screening and prenatal diagnosis. Obstetrics and gynecology, pediatrics, medical imaging (ultrasound and magnetic resonance imaging), clinical laboratory, pathology, and other disciplines are mostly involved in this multidisciplinary work on maternal and infant health care, which aims to prevent birth defects in strict accordance with laws, regulations, and pertinent industry standards, such as the Notice of the National Health Commission on Issuing the Basic Standards for Prenatal Screening Technical Medical Institutions and the Basic Standards for Prenatal Diagnosis Technical Medical Institutions (Guowei Maternal and Child Letter [2019] No. 297). To further support the implementation of prenatal screening and diagnosis work and streamline workflow, this study has compiled the timing, inspection, and testing procedures of various projects in each link from the standpoint of the disease clinical laboratory diagnostic pathway. This approach improves communication amongst various disciplines in prenatal screening and diagnosis work and offers clinical service quality, and it also helps improve the standard of the birth population and prevent and controll severe birth defects.

In this article, we consider the cooperative tracking problem for a class of nonlinear multiagent systems (MASs) with unknown dynamics under denial-of-service (DoS) attacks. To solve such a problem, a hierarchical cooperative resilient learning method, which involves a distributed resilient observer and a decentralized learning controller, is introduced in this article. Due to the existence of communication layers in the hierarchical control architecture, it may lead to communication delays and DoS attacks. Motivated by this consideration, a resilient model-free adaptive control (MFAC) method is developed to withstand the influence of communication delays and DoS attacks. First, a virtual reference signal is designed for each agent to estimate the time-varying reference signal under DoS attacks. To facilitate the tracking of each agent, the virtual reference signal is discretized. Then, a decentralized MFAC algorithm is designed for each agent such that each agent can track the reference signal by only using the obtained local information. Finally, a simulation example is proposed to verify the effectiveness of the developed method.

Asymptotic observability of distributed Boolean networks (DBNs) is studied in this article. Via a parallel extension method, asymptotic observability of the original system is converted to reachability at a fixed point of the extended system. Based on the structure matrix of the extended system, a necessary and sufficient condition is presented for asymptotic observability. Further, for unobservable systems, mode-dependent pinning control is first introduced and applied to achieve asymptotic observability, including the selections of pinning nodes, the design of output feedback controls, and the adding approaches. Then, a set of matrices is defined for the construction of the desired structure matrix. Based on it, a necessary condition is given to guarantee the solvability of the corresponding output feedback controls and the adding approaches. Finally, a numerical example is presented to show the effectiveness of the obtained results.

Bitterness, as one of the most important physiological sensations in animals, is primarily recognized through the mediation of bitter taste receptors. In recent years, it has been found that these receptors are not only expressed in taste bud cells on the tongue but also in the respiratory, cardiovascular, digestive, reproductive, and nervous systems. They are involved in regulating various fundamental physiological processes and are now considered important targets for the treatment of various diseases. This paper reviewed the structure, classification, distribution, and signaling pathways of bitter taste receptors, their relationship with different diseases, and the role of bitter taste receptors agonists, aiming to provide a basis for scientific research on bitter taste receptors.

In this article, a synchronization control method is studied for coupled neural networks (CNNs) with constant time delay using sampled-data information. A distributed control protocol relying on the sampled-data information of neighboring nodes is proposed. Lyapunov functional is constructed to analyze the synchronization of CNNs with constant time delay. Using Park's integral inequality and improved free-weight matrix integral inequality, sufficient conditions are provided for CNNs to achieve synchronization with less conservatism. In addition, the maximum sampling interval is determined by transforming the sufficient conditions into an optimization problem, and an aperiodic sampling control technique is implemented to reduce the communication energy load. Finally, numerical simulations are provided to demonstrate that the proposed method is capable of achieving synchronization.

Plant JASMONATE ZIM-DOMAIN (JAZ) genes play crucial roles in regulating the biosynthesis of specialized metabolites and stressful responses. However, understanding of JAZs controlling these biological processes lags due to numerous JAZ copies. Here, we found that two leaf-specific CwJAZ4/9 genes from Curcuma wenyujin are strongly induced by methyl-jasmonate (MeJA) and negatively correlated with terpenoid biosynthesis. Yeast two-hybrid, luciferase complementation imaging and in vitro pull-down assays confirmed that CwJAZ4/9 proteins interact with CwMYC2 to form the CwJAZ4/9-CwMYC2 regulatory cascade. Furthermore, transgenic hairy roots showed that CwJAZ4/9 acts as repressors of MeJA-induced terpenoid biosynthesis by inhibiting the terpenoid pathway and jasmonate response, thus reducing terpenoid accumulation. In addition, we revealed that CwJAZ4/9 decreases salt sensitivity and sustains the growth of hairy roots under salt stress by suppressing the salt-mediated jasmonate responses. Transcriptome analysis for MeJA-mediated transgenic hairy root lines further confirmed that CwJAZ4/9 negatively regulates the terpenoid pathway genes and massively alters the expression of genes related to salt stress signaling and responses, and crosstalks of multiple phytohormones. Altogether, our results establish a genetic framework to understand how CwJAZ4/9 inhibits terpenoid biosynthesis and confers salt tolerance, which provides a potential strategy for producing high-value pharmaceutical terpenoids and improving resistant C. wenyujin varieties by a genetic approach., (© 2024 John Wiley & Sons Ltd.)

Approximation models play a crucial role in model-based methods, as they enhance both accuracy and computational efficiency. This article studies distributed and asynchronous discretized models to approach continuous-time nonlinear systems. The considered continuous-time system consists of some distributed but physically coupled nonlinear subsystems that exchange information. We propose two Lebesgue approximation models (LAMs): 1) the unconditionally triggered LAM (CT-LAM) and 2) the CT-LAM. In both approaches, a specific LAM approximates an individual subsystem. The iteration of each LAM is triggered by either itself or its neighbors. The collection of different LAMs executing asynchronously together form the approximation of the overall distributed continuous-time system. The aperiodic nature of LAMs allows for a reduction in the number of iterations in the approximation process, particularly when the system has slow dynamics. The difference between the unconditionally and CT-LAMs is that the latter checks an "importance" condition, further reducing the computational effort in individual LAMs. Furthermore, the proposed LAMs are analyzed by constructing a distributed event-triggered system which is proved to have the same state trajectories as the LAMs with linear interpolation. Through this specific event-triggered system, we derive conditions on the quantization sizes in LAMs to ensure asymptotic stability of the LAMs, boundedness of the state errors, and prevention of Zeno behavior. Finally, simulations are carried out on a quarter-car suspension system to show the advantage and efficiency of the proposed approaches.

Background: Enteric glia are essential components of the enteric nervous system. Previously believed to have a passive structural function, mounting evidence now suggests that these cells are indispensable for maintaining gastrointestinal homeostasis and exert pivotal influences on both wellbeing and pathological conditions. This study aimed to investigate the global status, research hotspots, and future directions of enteric glia., Methods: The literature on enteric glia research was acquired from the Web of Science Core Collection. VOSviewer software (v1.6.19) was employed to visually represent co-operation networks among countries, institutions, and authors. The co-occurrence analysis of keywords and co-citation analysis of references were conducted using CiteSpace (v6.1.R6). Simultaneously, cluster analysis and burst detection of keywords and references were performed., Results: A total of 514 publications from 36 countries were reviewed. The United States was identified as the most influential country. The top-ranked institutions were University of Nantes and Michigan State University. Michel Neunlist was the most cited author. "Purinergic signaling" was the largest co-cited reference cluster, while "enteric glial cells (EGCs)" was the cluster with the highest number of co-occurring keywords. As the keyword with the highest burst strength, Crohns disease was a hot topic in the early research on enteric glia. The burst detection of keywords revealed that inflammation, intestinal motility, and gut microbiota may be the research frontiers., Conclusion: This study provides a comprehensive bibliometric analysis of enteric glia research. EGCs have emerged as a crucial link between neurons and immune cells, attracting significant research attention in neurogastroenterology. Their fundamental and translational studies on inflammation, intestinal motility, and gut microbiota may promote the treatment of some gastrointestinal and parenteral disorders., Competing Interests: The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest., (Copyright © 2024 Li, Yan, Li, Ye, Wu, Hou and Chen.)

Enabled by the advances in communication networks, computational units, and control systems, cyber-physical power systems (CPPSs) are anticipated to be complex and smart systems in which a large amount of data are generated, exchanged, and processed for various purposes. Due to these strong interactions, CPPSs will introduce new security vulnerabilities. To ensure secure operation and control of CPPSs, it is essential to detect the locations of the attacked measurements and remove the state bias caused by malicious cyber-attacks such as false data inject attack, jamming attack, denial of service attack, or hybrid attack. Accordingly, this article makes the first contribution concerning the representation-learning-based convolutional neural network (RL-CNN) for intelligent attack localization and system recovery of CPPSs. In the proposed method, the cyber-attacks' locational detection problem is formulated as a multilabel classification problem for CPPSs. An RL-CNN is originally adopted as the multilabel classifier to explore and exploit the implicit information of measurements. By comparing with previous multilabel classifiers, the RL-CNN improves the performance of attack localization for complex CPPSs. Then, to automatically filter out the cyber-attacks for system recovery, a mean-squared estimator is used to handle the difficulty in state estimation with the removal of contaminated measurements. In this scheme, prior knowledge of the system state is obtained based on the outputs of the stochastic power flow or historical measurements. The extensive simulation results in three IEEE bus systems show that the proposed method is able to provide high accuracy for attack localization and perform automatic attack filtering for system recovery under various cyber-attacks.

This article addresses the resilient consensus problem of multiagent systems subject to cyber attacks on communication links, where the attacks on different links may collude to maintain undetectable. For the case with noncollusive attacks on links, a distributed fixed-time observer is designed so that the attack on each link can be detected by the two associated agents. A necessary and sufficient condition is derived to ensure the isolation of attacked links and no mistaken isolation of normal ones. For the case with collusive attacks on links, a novel attack isolation algorithm is proposed by constructing extra observers on the basis of the previous designed distributed fixed-time observer via sequentially removing the information associated with one of the links. Based on the isolation of the attacked links, a control algorithm is designed, and a necessary and sufficient condition is provided to achieve resilient consensus. Numerical examples corroborate the effectiveness of the proposed strategies.

This article investigates a nonlinear disturbance observer (NDO)-based fault-tolerant sliding-mode control (SMC) for 2-D plane vehicular platoon systems subjected to actuator faults with unknown time-varying fault direction (UTVFD), asymmetric nonlinear actuator saturation (ANAS), nonlinear unmodeled dynamics, and unknown external disturbance. The Nussbaum-type function approach is adopted to solve the problem of actuator faults with UTVFD. The designed NDO not only can estimate the lumped disturbance accurately but also can reduce the control peaking and chattering phenomena caused by the Nussbaum-type function. Then, an adaptive saturation compensator is designed to compensate for the influence of actuator saturation on the system. In addition, by combining SMC technology with the prescribed tracking performance (PTP) approach, a distributed fault-tolerant control scheme is developed to not only ensure collision avoidance and communication connectivity but also realize a variety of driving scenarios, such as multilane vehicle merging and vehicular platoon lane changing. Finally, simulation results are presented to show the proposed scheme's effectiveness and advantages.

This article considers the output tracking control problem of nonidentical linear multiagent systems (MASs) using a model-free reinforcement learning (RL) algorithm, where partial followers have no prior knowledge of the leader's information. To lower the communication and computing burden among agents, an event-driven adaptive distributed observer is proposed to predict the leader's system matrix and state, which consists of the estimated value of relative states governed by an edge-based predictor. Meanwhile, the integral input-based triggering condition is exploited to decide whether to transmit its private control input to its neighbors. Then, an RL-based state feedback controller for each agent is developed to solve the output tracking control problem, which is further converted into the optimal control problem by introducing a discounted performance function. Inhomogeneous algebraic Riccati equations (AREs) are derived to obtain the optimal solution of AREs. An off-policy RL algorithm is used to learn the solution of inhomogeneous AREs online without requiring any knowledge of the system dynamics. Rigorous analysis shows that under the proposed event-driven adaptive observer mechanism and RL algorithm, all followers are able to synchronize the leader's output asymptotically. Finally, a numerical simulation is demonstrated to verify the proposed approach in theory.

High-temperature lithiation is one of the crucial steps for the synthesis of Li- and Mn-rich layered metal oxide (LMLO) cathodes. A profound insight of the micromorphology and crystal structure evolution during calcination helps to realize the finely controlled preparation of final cathodes, finally achieving a desired electrochemical performance. In this work, two typical precursors (hydroxide and oxalate) were selected to prepare LMLO. It is found that the influence of the lithium source on reaction pathways is determined by the properties of precursors. In the case of hydroxide as a precursor, whatever lithium sources it is, the flake morphology of LMLO is inherited from hydroxide precursors. This is because the crystal structure of cathode products has a high similarity with its precursor in terms of the oxygen array arrangement, and the topological transformation occurs from hydroxide ( P- 3 ml ) to LMLOs ( C/2m and R 3 m ). Thus, the morphology and microstructure of LMLO cathodes could be well controlled only by tuning the properties of hydroxide precursors. Conversely, the decomposition of a lithium source has a great influence on the intermediate transformation when oxalate is used as the precursor. This is because a large amount of CO 2 is released from the oxalate precursor after the decomposition reaction, resulting in drastic structural changes. At this time, the diffusion ability of the lithium source leads to the competition between the spinel phase and layered phase. Based on this point, the formation of a spinel intermediate phase can be reduced by accelerating the decomposition of the lithium source, contributing to the generation of a highly pure layered phase, thus exhibiting higher electrochemical performance. These insights provide an exciting cue to the rational selection and design of raw materials and lithium sources for the controlled synthesis of LMLO cathodes., Competing Interests: The authors declare no competing financial interest., (© 2024 The Authors. Published by American Chemical Society.)

The oncogenic role of circRNA in cancers including esophageal cancer (EC) has been well studied. However, whether and how circRNAs are involved in cancer cell metabolic processes remains largely unknown. Here, we reported that circRNA, circHIPK3, is highly expressed in ESCC cell lines and tissues. Knockdown of circHIPK3 significantly restrained cell proliferation, colony formation, migration, and invasion in vitro and inhibited tumor growth in vivo. Mechanistically, circHIPK3 was found to act as a ceRNA by sponging miR-637 to regulate FASN expression and fatty acid metabolism in ESCC cells. Anti-sense oligonucleotide (ASO) targeting circHIPK3 substantially inhibited ESCC both in vitro and in vivo. Therefore, these results uncover a modulatory axis constituting of circHIPK3/miR-637/FASN may be a potential biomarker and therapeutic target for ESCC in the clinic., (© 2024. The Author(s).)

The neural network-based adaptive backstepping method is an effective tool to solve the cooperative tracking problem for nonlinear multiagent systems (MASs). However, this method cannot be directly extended to the case without continuous communication. It is because the discontinuous communication results in discontinuous signals in this case, the standard backstepping method is inapplicable. To solve this problem, a hierarchical design scheme that involves distributed cooperative estimators and neural network-based decentralized tracking controllers is proposed. By introducing a dynamic event-triggered mechanism, cooperative intermediate parameter estimators are first designed to estimate the unknown parameters of the leader. By using the interpolation polynomial method, these estimators are extended to smooth estimators with high-order derivatives to guarantee that the backstepping method is applicable. Based on the state of the smooth estimators, a backstepping-based decentralized neural network tracking controller is designed. It is shown that the tracking errors are asymptotically convergent and all the signals in the closed-loop systems are bounded. Compared with the existing cooperative tracking results for nonlinear MASs with event-triggered communication, a more general class of MASs is considered in this article and a better performance in terms of asymptotic tracking is achieved. Finally, a simulation example is given to show the effectiveness of our developed method.

In this article, a data-efficient off-policy reinforcement learning (RL) approach is proposed for distributed output tracking control of heterogeneous multiagent systems (HMASs) using approximate dynamic programming (ADP). Different from existing results that the kinematic model of the exosystem is addressable to partial or all agents, the dynamics of the exosystem are assumed to be completely unknown for all agents in this article. To solve this difficulty, an identifiable algorithm using the experience-replay method is designed for each agent to identify the system matrices of the novel reference model instead of the original exosystem. Then, an output-based distributed adaptive output observer is proposed to provide the estimations of the leader, and the proposed observer not only has a low dimension and less data transmission among agents but also is implemented in a fully distributed way. Besides, a data-efficient RL algorithm is given to design the optimal controller offline along with the system trajectories without solving output regulator equations. An ADP approach is developed to iteratively solve game algebraic Riccati equations (GAREs) using online information of state and input in an online way, which relaxes the requirement of knowing prior knowledge of agents' system matrices in an offline way. Finally, a numerical example is provided to verify the effectiveness of theoretical analysis.

D-A type axially chiral biphenyl luminescent molecules are directly constructed through ingenious functionalization of the octahydro-binaphthol skeleton without optical resolution. The circularly polarized organic light-emitting diodes based on them display remarkable circularly polarized electroluminescence emission, a high luminance of >10 000 cd m -2 , a maximum external quantum efficiency of 6.6%, and an extremely low-efficiency roll-off. This work provides a universal strategy for developing efficient and diverse axially chiral biphenyl emitters.

Recently, boron (B)/nitrogen (N)-embedded polycyclic aromatic hydrocarbons (PAHs), characterized by multiple resonances (MR), have attracted significant attention owing to their remarkable features of efficient narrowband emissions with small full width at half maxima (FWHMs). However, developing ultra-narrowband pure-green emitters that comply with the Broadcast Service Television 2020 (BT2020) standard remains challenging. Precise regulation of the MR distribution regions allows simultaneously achieving the emission maximum, FWHM value, and spectral shape that satisfy the BT2020 standard. The proof-of-concept molecule TPABO-DICz exhibited ultrapure green emission with a dominant peak at 515 nm, an extremely small FWHM of 17 nm, and Commission Internationale de l'Eclairage (CIE) coordinates of (0.17, 0.76). The corresponding bottom-emitting organic light-emitting diode (OLED) exhibited a remarkably high CIEy value (0.74) and maximum external quantum efficiency (25.8 %). Notably, the top-emitting OLED achieved nearly BT2020 green color (CIE: 0.14, 0.79) and exhibited a state-of-the-art maximum current efficiency of 226.4 cd A -1 , thus fully confirming the effectiveness of the above strategy., (© 2023 Wiley-VCH GmbH.)

Background and Aims: The older people bears a severe burden of disease due to frailty and depressive symptoms, however, the results of association between the two in the older Chinese people have been conflicting. Therefore, this study aimed to investigate the developmental trajectories and interactions of frailty and depressive symptoms in the Chinese middle-aged and older adults., Methods: The study used four waves of data from 2011, 2013, 2015 and 2018 in the China Health and Retirement Longitudinal Study (CHARLS) database, focused on middle-aged and older people ≥ 45 years of age, and analyzed using latent growth models and cross-lagged models., Results: The parallel latent growth model showed that the initial level of depressive symptoms had a significant positive predictive effect on the initial level of frailty. The rate of change in depressive symptoms significantly positively predicted the rate of change in frailty. The initial level of frailty had a significant positive predictive effect on the initial level of depressive symptoms, but a significant negative predictive effect on the rate of change in depressive symptoms. The rate of change in frailty had a significant positive predictive effect on the rate of change in depressive symptoms. The results of the cross-lagged analysis indicated a bidirectional causal association between frailty and depressive symptoms in the total sample population. Results for the total sample population grouped by age and gender were consistent with the total sample., Conclusions: This study recommends advancing the age of concern for frailty and depressive symptoms to middle-aged adults. Both men and women need early screening and intervention for frailty and depressive symptoms to promote healthy aging., (© 2024. The Author(s).)