Recursive Algorithm Research Articles

Association between triglyceride glucose index and depression in hypertensive population.

Growing evidence suggests that hypertensive individuals have a greater risk of developing depression, and depression can also increase the incidence of hypertension. In the hypertensive population, the association between triglyceride glucose (TyG) index and depression remains unclear. This study aimed to assess the association between TyG index and depression in hypertensive people through the cross-sectional study of the National Health and Nutrition Examination Survey (2007-2018). To assess the relationship between TyG index and depression in hypertensive population, we conducted weighted multiple logistic regression models and used a generalized additive model to probe for nonlinear correlations. In addition, we employed a recursive algorithm to determine the inflection point and established a two-piece linear regression model. This study enrolled 5897 individuals. In the model adjusted for all covariates, the ORs (95% CI) for the relationship between TyG index and depression in hypertensive population were 1.32 (1.12-1.54). A nonlinear association was found between TyG index and depression, with an inflection point at 8.7. After the inflection point, the ORs (95% CI) were 1.44 (1.15-1.79). Only the interaction with the obese population was statistically significant. Our study highlighted a nonlinear association between TyG index and depression in American hypertensive adults.

Lesion size affects the risk of technical difficulty in gastric endoscopic submucosal dissection

Current evidence shows an inter-country inconsistency in the effect of lesion size on the technical difficulty of gastric endoscopic submucosal dissection (ESD). We aimed to evaluate the specific correlation and quantify the ensuing risks. This retrospective study consisted of 405 ESD cases with gastric single lesion from April 2015 to April 2023. The correlation and risk prediction of lesion size with technical difficulty was explored to provide further clinical evidence. An additive generalized model and recursive algorithm were used to describe the non-linear association, and a linear two-piece regression was constructed to analyze the inflection point. Subgroup analysis and interaction were used to explore intergroup characteristics. Overall, difficult cases had larger lesion sizes, and the more significant the increase, the higher the risk of technical difficulty. In the full model, after adjusting for all covariates, each 1 mm, 3 mm, 5 mm, 7 mm, and one standard increase in lesion size increased the risk of technical difficulty by 8%, 26%, 42%, 72%, and 125%, respectively. There is a nonlinear positive correlation between lesion size and risk of technical difficulty, and the premeditated inflection point was 40 (mm) via two-piecewise linear regression and recursive algorithm. Subgroup analysis showed a stronger correlation between lesion size and difficult ESD in the upper site and submucosal fibrosis groups. Available evidence suggests that lesion size as a risk signal nonlinearly increases the technical difficulty of gastric ESD procedure, especially in cases of upper site and submucosal fibrosis, which deserves further investigation.

Accurate state of temperature estimation for Lithium-Ion batteries based on square root cubature Kalman filter

Accurate state of temperature estimation for lithium-ion batteries is essential to ensure its safe and efficient operations. In this study, a state of temperature estimation framework for cylindrical lithium-ion batteries is proposed based on square root cubature Kalman filter algorithm, wherein the internal and surface temperatures of power battery are accurately estimated. Firstly, the electro-thermal coupling characteristics of lithium-ion battery is characterized based on an equivalent circuit model, Bernardi battery heat generation model and two-state lumped thermal model. On this basis, the discrete time-domain characteristics of internal and external temperature of the battery are addressed. Then, the genetic algorithm and forgetting factor recursive least squares algorithm are respectively employed to identify the circuit parameters and thermal physical parameters, and the internal and surface temperatures prediction is achieved based on square root cubature Kalman filter algorithm. The feasibility of the proposed temperature estimation method is verified at different charge and discharge process under wide range ambient temperature of -20 °C to 60 °C. The experimental results manifest that the proposed method can accurately online estimate the internal temperature and surface temperature with the mean absolute error of less than 1.16 °C.

The non-linear link between non-high-density lipoprotein to high-density lipoprotein ratio and the risk of stroke in middle-aged and older adults in Chinese: a prospective cohort study from the China health and retirement longitudinal study.

This study aims to assess the association between the non-HDL-c/HDL-c ratio and stroke risk among middle-aged and older adults participating in the China Health and Retirement Longitudinal Study (CHARLS). This study conducted a prospective cohort analysis, enrolling a total of 10,183 participants who met the designated criteria from CHARLS between 2011 and 2012. We then used the Cox proportional-hazards regression model to explore the relationship between baseline non-HDL-c/HDL-c ratio and stroke risk. Using a Cox proportional hazards regression with cubic spline function, we were able to identify the non-linear relationship between the non-HDL-c/HDL-c ratio and stroke occurrence. A series of sensitivity analyses were also carried out. The average age of the participants included in this study was 59.16 ± 9.35 years, and 4,735 individuals (46.68%) were male. Over a median follow-up period of 7.0 years, a total of 1,191 people (11.70%) experienced a stroke. Using a Cox proportional hazards regression model that was fully adjusted, we found no statistically significant correlation between the non-HDL-c/HDL-c ratio and the risk of stroke (HR=1.022; 95% CI 0.964, 1.083). Nevertheless, we did observe a non-linear relationship and saturation effect between the non-HDL-c/HDL-c ratio and stroke. Employing a two-piece Cox proportional hazards regression model and a recursive algorithm, we determined an inflection point of 2.685 for the non-HDL-c/HDL-c ratio. In instances where the non-HDL-c/HDL-c ratio fell below 2.685, for every 1-unit decrease in the non-HDL-c/HDL-c ratio, the likelihood of stroke decreased by 21.4% (HR=1.214, 95% CI: 1.039-1.418). In contrast, when the non-HDL-c/HDL-c ratio exceeded 2.685, there was no statistically significant change in the risk of stroke for each unit decrease in the non-HDL-c/HDL-c ratio (HR: 0.967, 95% CI: 0.897-1.042). The consistency of these findings across multiple sensitivity analyses suggests their robustness. This study unveils a non-linear relationship between the non-HDL-c/HDL-c ratio and stroke risk in middle-aged and older adults in China. Specifically, when the non-HDL-c/HDL-c ratio was below 2.685, a significant and clearly positive association with stroke risk was observed. Additionally, maintaining the non-HDL-c/HDL-c ratio below 2.685 could potentially lead to a substantial reduction in the risk of stroke.

Sodium, potassium intake, and all-cause mortality: confusion and new findings

BackgroundThe World Health Organization (WHO) has established recommended daily intakes for sodium and potassium. However, there is currently some controversy regarding the association between sodium intake, potassium intake, the sodium-to-potassium ratio, and overall mortality. To assess the correlations between sodium intake, potassium intake, the sodium-to-potassium ratio, and overall mortality, as well as the potential differences in sodium and potassium intake thresholds among different population groups, we analyzed data from NHANES 2003–2018.MethodsNHANES is an observational cohort study that estimates sodium and potassium intake through one or two 24-h dietary recalls. Hazard ratios (HR) for overall mortality were calculated using multivariable adjusted Cox models accounting for sampling design. A total of 13855 out of 26288 participants were included in the final analysis. Restricted cubic spline analyses were used to examine the relationship between sodium intake, potassium intake, and overall mortality. If non-linearity was detected, we employed a recursive algorithm to calculate inflection points.ResultsBased on one or two 24-h dietary recalls, the sample consisted of 13,855 participants, representing a non-institutionalized population aged 40–80 years, totaling 11,348,771 person-months of mean follow-up 99.395 months. Daily sodium intake and daily potassium intake were inversely associated with all-cause mortality. Restrictive cubic spline analysis showed non-linear relationships between daily sodium intake, potassium intake, sodium–potassium ratio, and total mortality. The inflection point for daily sodium intake was 3133 mg/d, and the inflection point for daily potassium intake was 3501 mg/d, and the inflection point for daily sodium–potassium ratio intake was 1.203 mg/mg/d. In subgroup analyses, a significant interaction was found between age and high sodium intake, which was further confirmed by the smooth curves that showed a U-shaped relationship between sodium intake and all-cause mortality in the elderly population, with a inflection point of 3634 mg/d.ConclusionNonlinear associations of daily sodium intake, daily potassium intake and daily sodium–potassium ratio intake with all-cause mortality were observed in American individuals. The inflection point for daily sodium intake was 3133 mg/d. And the inflection point for daily sodium intake was 3634 mg/d in elderly population. The inflection point for daily potassium intake was 3501 mg/d. The inflection point for daily sodium–potassium ratio intake was 1.203 mg/mg/d, respectively, A healthy diet should be based on reasonable sodium intake and include an appropriate sodium-to-potassium ratio.

A high-resolution map of soil organic carbon in cropland of Southern China

An accurate and fine map of soil organic carbon (SOC) plays a vital role in understanding the global carbon cycle and achieving soil carbon sequestration potential. Although global and national maps of SOC are already available with various spatial resolutions, limited sample size, and relative coarse resolution hinder its accuracy and application in local regions. Here, we collected 13,424 soil samples and information of 45 environmental covariates from cropland in Jiangxi Province, Southern China during 2012 and 2013. Then, the optimal covariates were selected by a recursive feature elimination algorithm for mapping SOC. After that, we deployed the random forest (RF) to produce a fine map (30 m) of SOC in the cropland of Jiangxi Province and 100 times bootstrapping was performed to calculate the prediction uncertainty. Finally, we determined the impacts of various covariates on SOC variability using RF and partial least squares structural equation modeling. Our results showed that compared with the predictive model without soil management information, introducing soil management information improved the predictability of SOC with an increase in R2 by 7.35 % (0.73 vs 0.68) and decrease in RMSE by 7.03 % (2.91 vs 3.13 g kg−1). Our results well estimated the uncertainty of the predicted result with a PICP of 0.91 for a 90 % prediction interval. Soil properties and soil management activities make the largest contribution for modelling SOC. Specifically, the total nitrogen content, straw return amount, total potassium content, and multi-resolution valley bottom flatness were found as the most important factors for mapping SOC in the cropland of our study area. Overall, this study deepened our knowledge of the variation of SOC and also emphasizes that incorporating soil management information could help us to achieve more accurate predictions of SOC.

Second-Order Approximate Reflection Coefficient of Thin Interbeds with Vertical Fractures

The horizontal fractures in the strata will close in the compaction effect of overlying strata, while the vertical cracks are widely developed, which can be equivalent to HTI (transverse isotropy with a horizontal axis of symmetry) medium. When an S-wave propagates into HTI media, the shear wave will divide into two types of waves: a fast S-wave and slow S-wave. When the strata of HTI are thin and overlapping, called the thin interbeds model, the wave field exhibits complex primary reflections, converted waves, and multiples. We introduce a new second-order approximation of the total reflection coefficient, with the incidence angle lower than the critical angle in thin-interbed HTI media using a recursive algorithm. We verify the effectiveness of the second-order approximation by analyzing the energy of multiples. Comparing the second-order approximate solution that degenerates the HTI medium into isotropic and Kennett’s exact solution, we find that our solution has an accuracy of over 99.9% in any azimuth, with the incidence angle lower than the critical angle under P-wave incidence. However, our solution of the SP wave field is suitable for incidence azimuth angles between 0–75° and 120–180°, with the lowest accuracy occurring at an incidence angle of 25° and a relative error of 6.4%. The approximate solution in the SS wave field has the same applicable range as the SP wave, with the maximum error of 6.3% occurring at the incident angle of 1°. This new second-order approximate formula for the total reflection coefficient of thin interbeds composed of HTI helps us to understand the reflection characteristics of complex thin interbeds. It also lays a theoretical foundation for the development of AVO (Amplitude Versus Offset) analysis and inversion techniques for lithological and stratigraphic oil and gas reservoirs.

WHRIME: A weight-based recursive hierarchical RIME optimizer for breast cancer histopathology image segmentation

In medical image processing, multi-threshold image segmentation has been challenging, as selecting appropriate thresholds is crucial for distinguishing different structures within an image, especially when dealing with breast cancer images. Breast cancer images are complex with multiple tissue types, which pose challenges to precise diagnosis. A weight-based recursive hierarchical bootstrapping rime algorithm (WHRIME) is proposed to tackle this case effectively. The proposed WHRIME segregates the population into elite and non-elite individuals. The hierarchical bootstrapping strategy ensures comprehensive exploration of the solution space, with elite individuals guiding the position updates of non-elite individuals. A weighted method is introduced based on solution quality differences to maintain population diversity and enhance convergence accuracy. We apply WHRIME in multi-threshold image segmentation on breast cancer histopathology images. Experimental results on both the IEEE CEC 2017 benchmark suit and breast cancer histopathology images from the Databiox dataset validate the superiority of WHRIME over competing algorithms, affirming WHRIME’s capability in addressing complex breast cancer histopathology image segmentation problems.

Development of a tool for predicting HNF1B mutations in children and young adults with congenital anomalies of the kidneys and urinary tract

BackgroundWe aimed to develop a tool for predicting HNF1B mutations in children with congenital abnormalities of the kidneys and urinary tract (CAKUT).MethodsThe clinical and laboratory data from 234 children and young adults with known HNF1B mutation status were collected and analyzed retrospectively. All subjects were randomly divided into a training (70%) and a validation set (30%). A random forest model was constructed to predict HNF1B mutations. The recursive feature elimination algorithm was used for feature selection for the model, and receiver operating characteristic curve statistics was used to verify its predictive effect.ResultsA total of 213 patients were analyzed, including HNF1B-positive (mut + , n = 109) and HNF1B-negative (mut − , n = 104) subjects. The majority of patients had mild chronic kidney disease. Kidney phenotype was similar between groups, but bilateral kidney anomalies were more frequent in the mut + group. Hypomagnesemia and hypermagnesuria were the most common abnormalities in mut + patients and were highly selective of HNF1B. Hypomagnesemia based on age-appropriate norms had a better discriminatory value than the age-independent cutoff of 0.7 mmol/l. Pancreatic anomalies were almost exclusively found in mut + patients. No subjects had hypokalemia; the mean serum potassium level was lower in the HNF1B cohort. The abovementioned, discriminative parameters were selected for the model, which showed a good performance (area under the curve: 0.85; sensitivity of 93.67%, specificity of 73.57%). A corresponding calculator was developed for use and validation.ConclusionsThis study developed a simple tool for predicting HNF1B mutations in children and young adults with CAKUT.Graphical abstract A higher resolution version of the Graphical abstract is available as Supplementary information

Subdivision algorithms with modular arithmetic

We study the de Casteljau subdivision algorithm for Bezier curves and the Lane-Riesenfeld algorithm for uniform B-spline curves over the integers mod m, where m>2 is an odd integer. We place the integers mod m evenly spaced around a unit circle so that the integer k mod m is located at the position on the unit circle ate2πki/m=cos(2kπ/m)+isin(2kπ/m)↔(cos(2kπ/m),sin(2kπ/m)).Given a sequence of integers (s0,…,sm)mod m, we connect consecutive values sjsj+1 on the unit circle with straight line segments to form a control polygon. We show that if we start these subdivision procedures with the sequence (0,1,…,m)mod m, then the sequences generated by these recursive subdivision algorithms spawn control polygons consisting of the regular m-sided polygon and regular m-pointed stars that repeat with a period equal to the minimal integer k such that 2k=±1modm. Moreover, these control polygons represent the eigenvectors of the associated subdivision matrices corresponding to the eigenvalue 2−1modm. We go on to study the effects of these subdivision procedures on more general initial control polygons, and we show in particular that certain control polygons, including the orbits of regular m-sided polygons and the complete graphs of m-sided polygons, are fixed points of these subdivision procedures.

Role of Phonon Scattering on the Transport and Performance of an N-Channel Monolayer Black Phosphorus Transistor

We investigate the influence of phonon scattering on the transport properties and performance metrics of a monolayer n-channel black phosphorus transistor within a four-band tight binding Hamiltonian, employing a recursive Green's function algorithm and Buttiker probe scattering model. Our analysis reveals that electron-phonon scattering significantly degrades the on-state current, while its effects in the subthreshold region are found to be negligible. Further examination identifies optical phonons as the primary contributors to the degradation of on-state current, with acoustic phonons playing a less prominent role. The ballisticity of the device declines from 42% to 24% when transitioning from solely acoustic phonon scattering to the combined influence of acoustic and optical phonons. Expanding the placement of Buttiker probes from beneath the gate region to cover the entire path from source to drain results in a further 48% reduction in on-state current. The on-state current exhibits a parabolic relationship with the inverse Kelvin temperature. To quantify the effects of phonon scattering on device performance, we assess the key parameters, transconductance and unity current gain frequency. Phonon scattering is observed to severely impact both the parameters. The on-state transconductance declines from its ballistic value of 24.9 mS/µm to 3.99 mS/µm when both acoustic and optical phonons are concurrently active. Similarly, the unity current gain frequency decreases from 1.18 to 0.2 THz due to phonon scattering. Additionally, our analysis reveals that approximately 7–9% of the total power dissipated within the device is attributed to phonon scattering effects, while the remainder is released through thermalization in the device's contacts. Phonon scattering is shown to induce both lattice cooling and heating, depending on the presence or absence of potential barriers. When a potential barrier exists in the channel, electrons injected from the source experience lattice cooling before the barrier region and lattice heating after crossing the barrier. Including the source and drain contact resistances in our model unveils that achieving a contact resistance value of approximately 100 Ω-µm is crucial for the effective functioning of black phosphorus devices.

On the exact and population bi-dimensional reproduction numbers in a stochastic SVIR model with imperfect vaccine

We aim to quantify the spread of a direct contact infectious disease that confers permanent immunity after recovery, within a non-isolated finite and homogeneous population. Prior to the onset of the infection and to prevent the spread of this disease, a proportion of individuals was vaccinated. But the administered vaccine is imperfect and can fail, which implies that some vaccinated individuals get the infection when being in contact with infectious individuals. We study the evolution of the epidemic process over time in terms of a continuous-time Markov chain, which represents a general SIR model with an additional compartment for vaccinated individuals. In our stochastic framework, we study two bi-dimensional variables recording infection events, produced by a single infectious individual or by the whole infected group, taking into account if the newly infected individual was previously vaccinated or not. Theoretical schemes and recursive algorithms are derived in order to compute joint probability mass functions and factorial moments for these random variables. We illustrate the applicability of our techniques by means of a set of numerical experiments.

Fast-tracking method of inertial constant based on system identification

Aiming at the problem of quantitative inertia evaluation of a new energy electric power system, the system inertia constant tracking method based on system identification is studied. The method is divided into two categories: non-recursive algorithm and recursive algorithm. The non-recursive algorithm uses a batch of data for batch processing to obtain the estimated value of the identification model parameters. The recursive algorithm is based on the estimated value of the model parameter at the previous moment and corrects the estimated value based on the new data currently obtained. From the perspective of the identification principle, the difference and internal relationship between the two in terms of calculation storage and identification speed are analyzed. The IEEE typical system is used to compare and verify the experimental examples. Theoretical analysis and experimental results show that the recursive algorithm has high identification accuracy, stable identification results and fast identification speed. It is suitable for the identification of objects with large numbers of nodes and complex structures, which is conducive to real-time monitoring and fast perception of the inertia constant of the new energy power system.

Recursive identification with regularization and on-line hyperparameters estimation

This paper presents a regularized recursive identification algorithm with simultaneous on-line estimation of both the model parameters and the algorithms hyperparameters. A new kernel is proposed to facilitate the algorithm development. The performance of this novel scheme is compared with that of the recursive least squares algorithm in simulation.

Comparison and Efficiency of Different Algorithms to Count and Determine the Composition of All Possible Riffle Shuffles Used in Magic

As part of a Technical and Scientific Project offered to L2 students of ISEP over a period of four months at the rate of one hour per week supervised, a study of the composition and the total number of all riffle shuffles used in magic was requested. The riffle shuffle consists of taking a deck of cards, cutting it into any two parts, then inserting randomly the cards of the first packet into the second. In first approximation there are 52! possible riffle shuffles. This number is an upper limit since the cards in a subdeck cannot change their relative position to their neighbours. A card A below a card B in the same subdeck will not be able to find itself above in the final shuffle. The first goal of the project is to compare one single algorithm implemented either recursively or iteratively in terms of execution time depending on the number of cards. The second goal is to compare the implementation of the same algorithm (either iterative or recursive) in several different programming languages (Python, Language C, Matlab, etc.) and to compare execution times according to the used language. Thus, a recursive algorithm was proposed to the students. All the students tried to code this algo and make it iterative … except one! He imagined another algorithm. The algorithm of the student and the teacher were compared in terms of execution time: do the student exceed the master? The aim of this article is to share my experience. I leave it to you to imagine educational sequences around this project in adequacy with your desires and the level of your students.

Non-linear relationship between red blood cell distribution width and gastrointestinal bleeding risk in stroke patients: results from multi-center ICUs.

The red blood cell distribution width (RDW) is closely linked to the prognosis of multiple diseases. However, the connection between RDW and gastrointestinal bleeding (GIB) in stroke patients is not well understood. This study aimed to clarify this association. This retrospective study involved 11,107 hospitalized patients from 208 hospitals in the United States, admitted between January 1, 2014, and December 31, 2015. We examined clinical data from 7,512 stroke patients in the intensive care unit (ICU). Multivariate logistic regression assessed the link between RDW and in-hospital GIB in stroke patients. Generalized additive model (GAM) and smooth curve fitting (penalty spline method) were utilized to explore the non-linear relationship between RDW and GIB in stroke patients. The inflection point was calculated using a recursive algorithm, and interactions between different variables were assessed through subgroup analyses. Among the 11,107 screened stroke patients, 7,512 were included in the primary analysis, with 190 identified as having GIB. The participants had a mean age of (61.67 ± 12.42) years, and a median RDW of 13.9%. Multiple logistic analysis revealed RDW as a risk factor for in-hospital GIB in stroke patients (OR = 1.28, 95% CI 1.21, 1.36, p < 0.05). The relationship between RDW and in-hospital GIB in stroke patients was found to be non-linear. Additionally, the inflection point of RDW was 14.0%. When RDW was ≥14.0%, there was a positive association with the risk of GIB (OR: 1.24, 95% CI: 1.16, 1.33, p < 0.0001). Conversely, when RDW was <14.0%, this association was not significant (OR: 1.02, 95% CI: 0.97-1.07, p = 0.4040). This study showed a substantial non-linear link between RDW and the risk of GIB in stroke patients. Maintaining the patient's RDW value below 14.0% could lower the risk of in-hospital GIB.

High Precision, Low Complexity, and Fast Calculation Based on Hybrid Recursive DFT and FFT Algorithms for Electrochemical Impedance Spectroscopy System

High Precision, Low Complexity, and Fast Calculation Based on Hybrid Recursive DFT and FFT Algorithms for Electrochemical Impedance Spectroscopy System

Sparseness Controlled Proportionate RLS Algorithm for Sparse and Non-Sparse Systems

This paper proposes a novel sparse adaptive technique to handle variable sparsity. The algorithm is based on the measure of sparseness. A proportionate matrix distributes the gain factor for all filter taps during each iteration. Each filter coefficient of the adaptive filter is updated by the corresponding diagonal element of the proportionate matrix, and that depends on the degree of sparseness. The classical recursive least square algorithm (RLS) is amended by accommodating the proportionate matrix to propose the sparseness-controlled proportionate recursive least square (SC-PRLS) algorithm. The convergence control parameter is incorporated into the algorithm to achieve faster convergence and better steady-state error. The performance of Mean squared error and stead state error of the proposed algorithm are also compared with standard RLS and proportionate RLS (PRLS). The simulation results indicate that SC-PRLS is more effective than PRLS and traditional RLS. An increase in the degree of sparseness leads to an increase in steady-state error and it can be controlled by convergence control parameter, while the convergence rate remains intact in the SC-PRLS. It performs superior in sparse as well as in non-sparse environment so this algorithm can handle large variations in the sparseness. Keywords: SC-PRLS, Sparseness Controlled Proportionate Adaptive Algorithm, Sparse and Non-Sparse Systems, RLS.

Online Lithium-ion Battery Modeling and State of Charge Estimation via Concurrent State and Parameter Estimation

This paper develops a novel approach for online Lithium-ion (Li-ion) battery model identification and state of charge (SOC) estimation. To account for the SOC-dependent battery dynamics and the static nonlinearity between the open-circuit voltage (OCV) and SOC, we formulate a grey box nonlinear state-space model, in which elements depend on SOC in a polynomial way. For model identification, we propose an online concurrent state and parameter estimation by alternating the recursive least squares algorithm and particle filter; the SOC is computed via Coulomb counting during the modeling. The identified grey box model is then applied for SOC estimation using the particle filter. Simulation with real-world battery measurements demonstrates the effectiveness of the model structure and the estimation approach, which is reflected in accurate terminal voltage estimation and nonlinear OCV-SOC relation, and superior performance regarding SOC estimation compared to state-of-the-art approaches.

Finite-Horizon H∞ State Estimation for Complex Networks With Uncertain Couplings and Packet Losses: Handling Amplify-and-Forward Relays.

This article is concerned with the state estimation problem for a class of complex networks (CNs) with uncertain inner couplings and packet losses over communication networks. The inner couplings are allowed to be uncertain and varying in a specific interval. The amplify-and-forward (AaF) relay protocols are introduced to improve the communication quality and enhance the propagation distance. The Bernoulli random variables are used to characterize the randomly occurring packet losses encountered in communication channels. The focus of this article is on the design of a state estimator for each node of CNs such that a prescribed H∞ performance constraint is satisfied for the dynamical error system over a finite horizon. A sufficient condition is first provided to verify the existence of the desired H∞ state estimator, and the estimator gain is then determined by solving two coupled backward Riccati difference equations (RDEs). Subsequently, a recursive state estimation algorithm is put forward that is suitable for online computation. Finally, a numerical example is given to demonstrate the effectiveness of the proposed estimation method.