Development of diabetic complications and influencing factors among 32653 type 2 diabetes patients:retrospective cohort study using a multi-state Markov

Background:Patients with type 2 diabetes are at high risk for developing multiple chronic complications.However,there is a lack of studies of the cumulative number of diabetic complications in China.Methods:A retrospective cohort study was performed from 2009 to 2021.Type 2 diabetes patients who were first diagnosed after the age of 35 years between January 1,2009,and December 31,2017,were included.Five states were defined according to the number of chronic complications:no(S0),one(S1),two(S2),three(S3),and four or more complications(S4).A multi-state Markov model was constructed to estimate transition probability,transition intensity,mean sojourn time,and the possible factors for each state.Results:The study included 32653 type 2 diabetes patients(mean age,59.59 years;15929(48.8%)male),and mean follow-up time of 7.75 years.In all,4375 transitions were observed.The 12-year transition probability of from state S0 to S1 was the lowest at 16.4%,while that from S2 to S3 was the highest,at 45.6%.Higher fasting blood glucose,lower high-density lipoprotein cholesterol,higher total cholesterol,and an unhealthy diet were associated with higher risk of progression from S0 to S1.Being female,less than 60 years old,weekly physical activity,and vegetarian diet decreased this risk.Being female and less than 60 years old reduced the likelihood of transition from S1 to S2,whereas lower high-density lipoprotein cholesterol increased this likelihood.Conclusions:Following the occurrence of two complications in type 2 diabetes patients,the risk for accumulating a third complication within a short time is significantly increased.It is important to take advantage of the stable window period when patients have fewer than two complications,strengthen the monitoring of blood glucose and blood lipids,and encourage patients to maintain good living habits to prevent further deterioration.

A Two-Step Algorithm to Estimate Variable Importance for Multi-State Data:An Application to COVID-19

Survival data with amulti-state structure are frequently observed in follow-up studies.An analytic approach based on a multi-state model(MSM)should be used in longitudinal health studies in which a patient experiences a sequence of clinical progression events.One main objective in the MSM framework is variable selection,where attempts are made to identify the risk factors associated with the transition hazard rates or probabilities of disease progression.The usual variable selection methods,including stepwise and penalized methods,do not provide information about the importance of variables.In this context,we present a two-step algorithm to evaluate the importance of variables formulti-state data.Three differentmachine learning approaches(randomforest,gradient boosting,and neural network)as themost widely usedmethods are considered to estimate the variable importance in order to identify the factors affecting disease progression and rank these factors according to their importance.The performance of our proposed methods is validated by simulation and applied to the COVID-19 data set.The results revealed that the proposed two-stage method has promising performance for estimating variable importance.

Capacitated stochastic coloured Petri net-based approach for computing two-terminal reliability of multi-state network

Classical network reliability problems assume both net- works and components have only binary states, fully working or fully failed states. But many actual networks are multi-state, such as communication networks and transportation networks. The nodes and arcs in the networks may be in intermediate states which are not fully working either fully failed. A simulation ap- proach for computing the two-terminal reliability of a multi-state network is described. Two-terminal reliability is defined as the probability that d units of demand can be supplied from the source to sink nodes under the time threshold T. The capacities of arcs may be in a stochastic state following any discrete or continuous distribution. The transmission time of each arc is also not a fixed number but stochastic according to its current capacity and de- mand. To solve this problem, a capacitated stochastic coloured Petri net is proposed for modelling the system behaviour. Places and transitions respectively stand for the nodes and arcs of a net- work. Capacitated transition and self-modified token colour with route information are defined to describe the multi-state network. By the simulation, the two-terminal reliability and node importance can be estimated and the optimal route whose reliability is highest can also be given. Finally, two examples of different kinds of multi- state networks are given.

Importance measure of system reliability upgrade for multi-state consecutive k-out-of-n systems

Importance measures in reliability systems are used to identify weak components in contributing to a proper function of the system. Traditional importance measures mainly concerned the changing value of the system reliability caused by the change of the reliability of the component, and seldom considered the joint effect of the probability distribution, improvement rate of the object component. This paper studies the rate of the system reliability upgrading with an improvement of the component reliability for the multi-state consecutive k-out-of-n system. To verify the multi-state consecutive k-out-of-n system reliability upgrading by improving one component based on its improvement rate, an increasing potential importance （IPI） and its physical meaning are described at first. Secondly, the relationship between the IPI and Birnbaum importance measures are discussed. And the IPI for some different improvement actions of the component is further discussed. Thirdly, the characteristics of the IPI are analyzed. Finally, an application to an oil pipeline system is given.

Reliability Modeling and Evaluation of Complex Multi-State System Based on Bayesian Networks Considering Fuzzy Dynamic of Faults

In the traditional reliability evaluation based on the Bayesian method,the failure probability of nodes is usually expressed by the average failure rate within a period of time.Aiming at the shortcomings of traditional Bayesian network reliability evaluation methods,this paper proposes a Bayesian network reliability evaluation method considering dynamics and fuzziness.The fuzzy theory and the dynamic of component failure probability are introduced to construct the dynamic fuzzy set function.Based on the solving characteristics of the dynamic fuzzy set and Bayesian network,the fuzzy dynamic probability and fuzzy dynamic importance degree of the fault state of leaf nodes are solved.Finally,through the dynamic fuzzy reliability analysis of CNC machine tool hydraulic system balance circuit,the application of this method in system reliability evaluation is verified,which provides support for fault diagnosis of CNC machine tools.

A voltage support control strategy based on three-port flexible multi-state switch in distribution networks

Voltage sags in power system may lead to serious problems such as the off-grid of distributed generation and electrical equipment failures.As a novel type of power electronic equipment,a flexible multi-state switch(FMSS)is capable to support the voltage during the grid faults.In this paper,a voltage control strategy to support the voltage in a distribution network is proposed by introducing three-port FMSS.The positive-negative-sequence compensation(PNSC)scheme is adopted to control the active and reactive current.This control scheme eliminates active power oscillations at the port of voltage sags and reduces coupling oscillations of other ports.Based on the characteristics of the voltage support under PNSC scheme,two voltage support strategies are proposed.A proportional-integral controller is introduced to provide the reactive power references,which eliminates the errors when estimating the grid voltage and impedance.A current limiting scheme is adopted to keep the port current in a safe range by adjusting the active and reactive power references.The voltage support strategies in two different voltage sags are simulated,and results show the feasibility and effectiveness of the proposed control strategies.

Integrated importance measure for multi-state coherent systems of k level

To verify the effectiveness of the integrated importance measure （IIM） for multi-state coherent systems of k level, the definition and physical meaning of IIM are demonstrated. Then, the improvement potential and Δ-importance measures are generalized to multi-state coherent systems based on the system performance level, and the relationships between IIM and traditional importance measures are discussed. The characteristics of IIM are demonstrated in both series and parallel systems. Also, an application to an oil transportation system is given. The comparison results show that： （i） IIM has some useful properties that are not possessed by traditional importance measures; （ii） IIM is effective in evaluating the component role in multi-state systems when the component reliability and the failure rate are simultaneously considered.

Importance Analysis of a Multi-state System Based on Direct Partial Logic Derivatives and Multi-valued Decision Diagrams

Importance analysis quantifies the critical degree of individual component. Compared with the traditional binary state system,importance analysis of the multi-state system is more aligned with the practice. Because the multi-valued decision diagram( MDD) can reflect the relationship between the components and the system state bilaterally, it was introduced into the reliability calculation of the multi-state system( MSS). The building method,simplified criteria,and path search and probability algorithm of MSS structure function MDD were given,and the reliability of the system was calculated. The computing methods of importance based on MDD and direct partial logic derivatives( DPLD) were presented. The diesel engine fuel supply system was taken as an example to illustrate the proposed method. The results show that not only the probability of the system in each state can be easily obtained,but also the influence degree of each component and its state on the system reliability can be obtained,which is conducive to the condition monitoring and structure optimization of the system.

The Mechanical Stabilization and Multi-States of the Stretched VWF A2 Domain

At the vascular injury sites,the ultra-large (UL) multimeric von willebrand Factor (VWF) is released in response to physiological and pathophysiological stimuli,and mediates platelet adhesion,aggregation,and cross-linking to maintain hemostasis.This UL-VWF is specifically cleaved by ADAMTS13(A Disintegrin And Metalloprotease with a ThromboSpondintype-1 motif,member 13)to prevent microvascular thrombosis.Each VWF monomer consists of five types of repeat domains in the order of D1-D2-D’-D3-A1-A2-A3-D4-C1-C2-C3-C4-C5-C6-CK,in which the A2 domain contains the ADAMTS13cleavage site(Tyr1605-Met1606),exposure of which requires mechanical or chemical stimuli.Under flows,fluid shear stress regulates VWF degradation and size distribution through opening the A2 domain and exposing its cleavage site for ADAMTS13.VWF A2 domain contains a C-terminal vicinal disulfide bond,a calcium binding sites,and a flexibleα4-less-loop.These unique structure features together make A2 more sensitive to mechanical signal than other VWF A subdomains,i.e.A1 and A3 domains.It is believed that A2 is first bound with and then cleaved by ADAMTS13,together with force-induced conformation transformation.To reveal molecular basis of this two-step model of VWF hydrolyzation by ADAMTS13,we here examined stretch-induced unfolding processes of VWF A2 domain in more detail by Steered molecular dynamics(SMD)simulations,with the use of crystal structure of VWF A2(PDB ID 3GXB),and observed that there were multiple quasi-stable conformations of stretched A2 until itsβ4-strand and a3-helix were pulled away the central hydrophobic core and the cleavage sites were fully accessible to solvent.Our MD simulation data showed that,in unfolding,at first,the cleavage site residue Tyr1605 was exposed partially and binding sites for Spacer domain of ADAMTS13 were exposed to a high level whenα6-helix was separated from A2 body;then,withβ6-strand and a5-helix been pulled away,the binding sites for Cysrich domain of ADAMTS13 was exposed completely while the exposure degree of Tyr1605 was not improved;further,separation ofβ5-strand andα4-less-loop made Tyr1605 and Met1606 and the respective binding sites for ADAMTS13 Spacer domain,Cys-rich domain,and Disintegrin-like domain be fully exposed to reach the optimal catalytic state;lastly,withβ4-strand separation,the cleavage sites and binding sites all were overstretched,leading to mismatch of ADAMTS13 and A2 conformation especially in the binding sites.This conformational mismatch may cause reduction of ADAMTS13 hydrolysis efficiency.Furthermore,the data of SMD simulations under constant forces demonstrated that,the stretched A2 conformation had different quasi-stable states,which all had the better mechanical stability within simulation time of 100 ns;and the conformational transformation from one state to another must overcome their respective potential barriers.The hydrolysis efficiency should depend on each state of the stretched A2 conformation,because of the exclusive matched-degree of A2 and ADMATS13.This computer prediction on the mechanical stability and multi-states of stretched A2 provides a novel insight into the mechano-chemical regulation on cleavage of A2 by ADAMTS13.It would be helpful for design of related drug targeting the binding sites on A2 and exosites on ADAMTS13 for the treatment of patients with acquired TTP.

Reliability Improvement of Large Multi-state Series-parallel Systems

In the paper, excess methods for improving the reliability of multi-state series-parallel systems are presented： for the hot reserve of single components, the cold reserve of single components, and the mixed （hot and cold） reserve of single components. A process is also introduced to improve the reliability of these methods by replacing their components with more reliable ones. New theorems for multi-state limit reliability functions in homogeneous and non-homogeneous series-parallel large systems composed of components with improved reliability are presented, and applied to compare the effects of these systems in different reliability improving methods.

Reliability Evaluation and Sensitivity Analysis for Multi-state System Based on Time Degradation Measures

The performance and state of multi-state system depend on its structure and different state combinations of the components. In order to evaluate the reliability of multi-state system effectively,a reliability evaluation and sensitivity analysis method based on the time degradation measures was proposed. The equivalence sets of the multi-state system under different output performances were established. The state combinations were classified according to the performance level. The degradation probability models under different states were established,and the new reliability measures,such as dynamic probability of multi-state system,holding time in each state,dynamic expectation function and integrated expectation function of the performance,were proposed and used to implement the dynamic reliability evaluation and sensitivity analysis. A certain diesel engine fuel feeding system was taken as an application example to illustrate the proposed method. The results show that not only the holding time in the desired state of the components and the system can be predicted,but also the best state component in a certain time period can be obtained.

On the use of residual dipolar couplings in multi-state structure calculation of two-domain proteins

Residual dipolar couplings(RDCs)are powerful nuclear magnetic resonance(NMR)probes for the structure calculation of biomacromolecules.Typically,an alignment tensor that defines the orientation of the entire molecule relative to the magnetic field is determined either before refinement of individual bond vectors or simultaneously with this refinement.For single-domain proteins this approach works well since all bond vectors can be described within the same coordinate frame,which is given by the alignment tensor.However,novel approaches are sought after for systems where no universal alignment tensor can be used.Here,we present an approach that can be applied to two-domain proteins that enables the calculation of multiple states within each domain as well as with respect to the relative positions of the two domains.

Optimal transmission lines assignment with maximal reliabilities in multi-source multi-sink multi-state computer network

The optimal transmission lines assignment with maximal reliabilities (OTLAMR) in the multi-source multi-sink multi-state computer network (MMMCN) was investigated. The OTLAMR problem contains two sub-problems: the MMMCN reliabilities evaluation and multi-objective transmission lines assignment optimization. First, a reliability evaluation with a transmission line assignment (RETLA) algorithm is proposed to calculate the MMMCN reliabilities under the cost constraint for a certain transmission lines configuration. Second, the non-dominated sorting genetic algorithm II (NSGA-II) is adopted to find the non-dominated set of the transmission lines assignments based on the reliabilities obtained from the RETLA algorithm. By combining the RETLA and the NSGA-II algorithms together, the RETLA-NSGA II algorithm is proposed to solve the OTLAMR problem. The experiments result show that the RETLA-NSGA II algorithm can provide efficient solutions in a reasonable time, from which the decision makers can choose the best solution based on their preferences and experiences.

A multi-state weather generator for daily precipitation for the Torne River basin, northern Sweden/western Finland

This paper describes a new weather generator e the 10-state empirical model e that combines a 10-state, first-order Markov chain with a non-parametric precipitation amounts model. Using a doubly-stochastic transition-matrix results in a weather generator for which the overall precipitation distribution(including both wet and dry days) and the temporal-correlation can be modified independently for climate change studies. This paper assesses the ability of the 10-state empirical model to simulate daily area-average precipitation in the Torne River catchment in northern Sweden/western Finland in the context of 3 other models: a 10-state model with a parametric(Gamma) amounts model; a wet/dry chain with the empirical amounts model; and a wet/dry chain with the parametric amounts model. The ability to accurately simulate the distribution of multi-day precipitation in the catchment is the primary consideration.Results showed that the 10-state empirical model represented accumulated 2- to 14-day precipitation most realistically. Further, the distribution of precipitation on wet days in the catchment is related to the placement of a wet day within a wet-spell, and the 10-state models represented this realistically, while the wet/dry models did not. Although all four models accurately reproduced the annual and monthly averages in the training data, all models underestimated inter-annual and inter-seasonal variance. Even so, the 10-state empirical model performed best.We conclude that the multi-state model is a promising candidate for hydrological applications, as it simulates multi-day precipitation well, but that further development is required to improve the simulation of interannual variation.

Dynamic Analysis of the Multi-state Reliability System with Priority Repair Discipline

This paper considers a multi-state repairable system that is composed of two classes of components,one of which has a priority for repair.First,we investigate the well-posedenss of the system by applying the operator semigroup theory.Then,using Greiner’s idea and the spectral properties of the corresponding operator,we obtain that the time-dependent solution of the system converges strongly to its steady-state solution.

Multi-state supernetworks:recent progress and prospects

Supernetworks have long been adopted to address multi-dimensional choice problems, which are thorny to solve for classic singular networks. Originated from combining transport mode and route choice into a multi-modal network, supernetworks have been extended into multi-state networks to include activity-travel scheduling, centered around activity-based models of travel demand. A key feature of the network extensions is that multiple choice facets pertaining to conducting a full activity program can be modeled in a consistent and integrative fashion. Thus, interdependencies and constraints between related choice facets can be readily captured. Given this advantage of integrity, the modeling of supernetwork has become an emerging topic in transportation research. This paper summarizes the recent progress in modeling multi-state supernetworks and discusses future prospects.

A multi-state model for wind farms considering operational outage probability

As one of the most important renewable energy resources,wind power has drawn much attention in recent years.The stochastic characteristics of wind speed lead to generation output uncertainties of wind energy conversion system(WECS)and affect power system reliability,especially at high wind power penetration levels.Therefore,a more comprehensive analysis toward WECS as well as an appropriate reliability assessment model are essential for maintaining the reliable operation of power systems.In this paper,the impact of wind turbine outage probability on system reliability is firstly developed by considering the following factors:running time,operating environment,operating conditions,and wind speed fluctuations.A multistate model for wind farms is also established.Numerical results illustrate that the proposed model can be well applied to power system reliability assessment as well as solving a series of reliability-centered decision-making problems of power system scheduling and maintenance arrangements.

MAINTENANCE OF MULTI-STATE PRODUCTION SYSTEMS DETERIORATED BY RANDOM SHOCKS AND PRODUCTION

We consider the preventive maintenance of a production system that is deteriorated by random shocks and the production process itself. The degree of deterioration is modeled by discrete and finite states. Shocks arrive according to a Poisson process and deteriorate the system by random amounts. The system may deteriorate whenever it produces an item. The system is continuously monitored and repaired if the system state is at or above a predetermined level for maintenance. We analyze the lifetime, product quantity, average cost, and average profit considering revenue from the product and cost due to setup, operation, and repair. Assuming a structure of system parameters and costs, using numerical examples, we investigate the impact of production and shock arrivals on the average profit and the optimal maintenance level that maximizes the average profit. The proposed model is applicable to manufacturing tasks in which machines wear due to production, for example, press processes, milling, turning, punching, and drilling.

Reliability Analysis of Retracting Actuator with Multi-State Based on Goal Oriented Methodology

In order to conduct effective reliability analysis of retracting actuator with multi-state(success state,safety failure state and action failure state), we redefine type-3 operator in goal oriented(GO) method to describe three states of main charge of retracting actuator and improve type-15 operator in GO method to describe the logic relations of multi-state output. The quantitative and qualitative reliability analyses of retracting actuator are made based on GO method in this paper. The system state probability of retracting actuator is obtained through quantitative analysis, and its weakness is found through qualitative analysis. The analysis results show that GO method is effective to improve the reliability of retracting actuator, and this method is also feasible for reliability analysis of other complicated initiating explosive systems.

SYSTEM RELIABILITY OF ASSURED ACCURACY RATE FOR MULTI-STATE COMPUTER NETWORKS FROM SERVICE LEVEL AGREEMENTS VIEWPOINT

From the viewpoint of service level agreements, the transmission accuracy rate is one of critical performance indicators to assess internet quality for system managers and customers. Under the assumption that each arc＇s capacity is deterministic, the quickest path problem is to find a path sending a specific of data such that the transmission time is minimized. However, in many real-life networks such as computer networks, each arc has stochastic capacity, lead time and accuracy rate. Such a network is named a multi-state computer network. Under both assured accuracy rate and time constraints, we extend the quickest path problem to compute the probability that d units of data can be sent through multiple minimal paths simultaneously. Such a probability named system reliability is a performance indicator to provide to managers for understanding the ability of system and improvement. An efficient algorithm is proposed to evaluate the system reliability in terms of the approach of minimal paths.