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To investigate the long-term prognosis of liver disease in patients with hepatitis C virus (HCV) eradication after antiviral therapy versus those with persistent HCV infection. Four hundred and eighty patients (5259 person-years [PYs]) who received interferon-based therapy and achieved sustained virologic response and 848 patients (3853 PYs) with persistent HCV infection were included. In the analysis of 1-year liver disease state transition probability matrices using Markov chain models, progression to cirrhosis from the chronic hepatitis state was observed (0.00%-0.63%) in patients with HCV eradication. Among patients with chronic hepatitis or cirrhosis and HCV eradication, hepatocellular carcinoma (HCC) development was observed in males aged ≥ 50 years (0.97%-1.96%) and females aged ≥ 60 years (0.26%-5.00%). Additionally, in patients with cirrhosis and HCV eradication, improvement to chronic hepatitis was also observed (4.94%-10.64%). Conversely, in patients with chronic hepatitis and persistent HCV infection, progression to cirrhosis was observed in males aged ≥ 30 years and female aged ≥ 40 years (0.44%-1.99%). In males aged ≥ 40 years and female aged ≥ 50 years with cirrhosis, the transition probability for HCC was relatively high (4.17%-14.02%). Under the assumption of either chronic hepatitis or cirrhosis at age 40 or 60 years as the starting condition for simulation over the next 30 or 40 years, respectively, the probability of HCC was higher in patients with persistent HCV infection than those with HCV eradication. In conclusion, HCV eradication can reduce the risk of developing cirrhosis or HCC in patients with chronic HCV infection.

In this paper, we focus on the chemical plume tracing (CPT) problem, which is a known engineering challenge. In nature, animals solve the CPT by adaptively modifying their behavior according to the environment. Therefore, we propose a CPT solution method with high engineering value by modeling the CPT algorithm of an animal. In this paper, we consider a male silkworm moth as a model. To perform CPT in a turbulent environment, the adaptive selection of the behavior plays an important role. Therefore, we performed simultaneous measurement experiments involving CPT behavior of the brain and analyzed the links between the brain's neural activity and behavioral patterns. We measured the brain's neural response in the lateral accessory lobe (LAL), which generates motion commands. We employed fuzzy inference to analyze the relationship between CPT behavior and LAL neural activity. As a result of analyzing the relationship between CPT behavior and LAL, we found that the moth modulates the behavior of the state transition probability depending on the odor frequency. We modeled the obtained phenomenon and verified its effectiveness through a constructive method. As a result, the search performance was improved compared to the conventional moth algorithm.

This article addresses a recursive parameter estimation algorithm for a hidden Markov model (HMM). The work focuses on an HMM with multiple states that are assumed to follow from a multivariate Gaussian distribution. The novelty of this study lies in a state transition probability calculation technique that simplifies the application of the backward stage of the forward–backward algorithm. For sequential observation analysis, the complexity of the created recursive algorithm for learning the HMM parameters is merely linear. Meanwhile, the classical Baum–Welch algorithm has second order complexity; therefore, it cannot be applied in online analysis situations. The properties of the proposed recursive expectation–maximization (EM) algorithm were explored by a computer simulation solving test examples and demonstrate that this algorithm can be efficiently applied to solve online tasks related to HMM parameter estimation.

In order to solve the problem of uncertainties in operation safety evaluation for terminal area airspace system, Set Pair Analysis (SPA) and Markov chain are combined to propose a dynamic evaluation model for operation safety in terminal area airspace system. In the model, firstly, on the basis of system analysis theory, the operation safety evaluation index system is established for terminal area airspace system, then based on this the conception and definition about relationship degree in SPA is adopted to describe the safety level and change characteristics of operation safety in terminal area airspace system, finally the safety state transition probability matrix is determined by Markov chain to predict the dynamic change tendency in operation safety for terminal area airspace system. The actual example on Shanghai terminal area shows that, the proposed model can accurately describe the dynamic change characteristics of operation safety for terminal area airspace system. This verifies its effectiveness and feasibility.

Empirical research often cites observed choice responses to variation that shifts expected discounted future utilities, but not current utilities, as an intuitive source of information on time preferences. We study the identification of dynamic discrete choice models under such economically motivated exclusion restrictions on primitive utilities. We show that each exclusion restriction leads to an easily interpretable moment condition with the discount factor as the only unknown parameter. The identified set of discount factors that solves this condition is finite, but not necessarily a singleton. Consequently, in contrast to common intuition, an exclusion restriction does not in general give point identification. Finally, we show that exclusion restrictions have nontrivial empirical content: The implied moment conditions impose restrictions on choices that are absent from the unconstrained model., 39 pages

The aim of this paper is to present a review on the stochastic version of the deterministic SIR (Susceptible – Infectious - Recovery) epidemiological compartment model through the branching process approximation. The stochastic process (branching process) approximation was developed using the Continuous Time Markov Chains where the time variable is continuous and the state variable is discrete. The state random variables are the compartments: S(t), I(t) and R(t). In this review two ways of estimating the state transition probability has been provided and some stochastic thresholds of the branching process (basic reproduction number, Malthusian parameter and the average number of infections produced by an infectious individual in a single generation) have also been deduced. Finally, the probability of major and minor outbreak of the branching process (epidemic process) has been presented. The theoretical methods have also been validated with some examples of numerical simulations.

An advanced understanding of the neurophysiologic changes that occur with aging may help improve care for older, vulnerable surgical patients. The objective of this study was to determine age-related changes in cortical connectivity patterns during surgical anesthesia. This was a substudy analysis of a prospective, observational study characterizing cortical connectivity during surgical anesthesia in adult patients (n = 45) via whole-scalp (16-channel) electroencephalography. Functional connectivity was estimated using a weighted phase lag index (wPLI), which was classified into a discrete set of states through k-means analysis. Temporal dynamics were quantified by occurrence rate and state transition probabilities. The mean global connectivity state transition probability [13.4% (±8.1)] was not correlated with age (ρ = 0.100, p = 0.513). Increasing age was inversely correlated with prefrontal-frontal alpha-beta connectivity (ρ = −0.446, p = 0.002) and positively correlated with frontal-parietal theta connectivity (ρ = 0.414, p = 0.005). After adjusting for anesthetic-related confounders, prefrontal-frontal alpha-beta connectivity remained significantly associated with age (β = −0.625, 95% CI −0.99 to −0.26; p = 0.001), while frontal-parietal theta connectivity was no longer significant (β = 0.436, 95% CI −0.03 to 0.90; p = 0.066). Specific transition states were also examined. Between frontal-parietal connectivity states, transitioning from theta-alpha to theta-dominated connectivity positively correlated with age (ρ = 0.545, p = 0.001). Dynamic connectivity states during surgical anesthesia, particularly involving alpha and theta bandwidths, maybe an informative measure to assess neurophysiologic changes that occur with aging.

Probabilistic Boolean control networks (PBCNs) have received a great amount of attention in the field of opinion dynamics in social networks and gene (or genetic) regulatory networks. PBCNs have been transferred to state transition probability matrices. Using a Markov chain theory, the PBCN is investigated under a state space framework. In this paper, we address the problem of constructing a probabilistic Boolean control network from a prescribed transition probability matrix. First, an algorithm is given to obtain the realization of a PBCN. Second, because of the non-uniqueness of the logical realization of a PBCN, a modified algorithm is introduced to obtain other realizations of PBCNs. Finally, an illustrative example is given to demonstrate both the efficiency and effectiveness of the proposed algorithms. In addition, the future direction of the research is discussed.

The proper consideration of all plausible feature spaces of the hydrological cycle and inherent uncertainty in preceding developed drought indices is inevitable for comprehensive drought assessment. Therefore, this study employed the Dynamic Naive Bayesian Classifier (DNBC) for multi-index probabilistic drought assessment by integrating various drought indices (i.e., Standardized Precipitation Index (SPI), Streamflow Drought Index (SDI), and Normalized Vegetation Supply Water Index (NVSWI)) as indicators of different feature spaces (i.e., meteorological, hydrological, and agricultural) contributing to drought occurrence. The overall results showed that the proposed model was able to account for various physical forms of drought in probabilistic drought assessment, to accurately detect a drought event better than (or occasionally equal to) any single drought index, to provide useful information for assessing potential drought risk, and to precisely capture drought persistence in terms of drought state transition probability in drought monitoring. This easily produced an alternative method for comprehensive drought assessment with combined use of different drought indices.

It is well documented that massive dynamic information is contained in the resting-state fMRI. Recent studies have identified recurring states dominated by similar coactivation patterns (CAPs) and revealed their temporal dynamics. However, the reproducibility and generalizability of the CAP analysis are unclear. To address this question, the effects of methodological pipelines on CAP are comprehensively evaluated in this study, including the preprocessing, network construction, cluster number and three independent cohorts. The CAP state dynamics are characterized by the fraction of time, persistence, counts, and transition probability. Results demonstrate six reliable CAP states and their dynamic characteristics are also reproducible. The state transition probability is found to be positively associated with the spatial similarity. Furthermore, the aberrant CAP states in schizophrenia have been investigated by using the reproducible method on three cohorts. Schizophrenia patients spend less time in CAP states that involve the fronto-parietal network, but more time in CAP states that involve the default mode and salience network. The aberrant dynamic characteristics of CAP states are correlated with the symptom severity. These results reveal the reproducibility and generalizability of the CAP analysis, which can provide novel insights into the neuropathological mechanism associated with aberrant brain network dynamics of schizophrenia.

When opponent players in a racket competition anticipate the course of a struck ball, they use the kinematic clues when the ball is struck as clues, including various contextual informations, such as the position when the ball is struck and the status of the game. This study proposes a measurement method of the state transition probability that shows the connection between two strokes as effective contextual information for increasing the accuracy of a player’s anticipation of the course of a struck ball. The state transition probability that is calculated by the proposed method shows the struck ball sequence pattern for a player, and whether characteristic differences can be found between players is examined. Two matches of opposing players in a soft tennis singles match competition were analyzed in this study. The two-dimensional actual coordinate data of the drop position of the ball was acquired from the target matches. The courts were divided into three sections from the left to right direction, the depth direction, and from the net towards the baseline. The striking of the ball within these sections was defined as one state, and the state transition probability matrix was measured. The result shows that the state transition probabilities of two players, namely, the characteristic differences in the struck ball sequence pattern, were observed, and their effectiveness as contextual information of the prediction clues was demonstrated.

It is the key to ensure the sustainable operation of intelligent substation to accurately predict the effective life of centralized protection measurement and control device in intelligent substation. A life prediction method based on cloud model and Markov chain is proposed. The initial state probability distribution vector is constructed by using the operation state data of the centralized protection measurement and control device and the membership function of the cloud model, then the state transition probability matrix is obtained according to the Markov chain principle, and the effective life of the protection device is predicted by the reliability criterion. The result of calculation example shows that the method can scientifically predict the effective life of the centralized protection measuring and controlling device, and can provide guidance for the status maintenance of the intelligent substation device.

Integrated information theory (IIT) proposes a measure of integrated information, termed Phi (&Phi, ), to capture the level of consciousness of a physical system in a given state. Unfortunately, calculating &Phi, itself is currently possible only for very small model systems and far from computable for the kinds of system typically associated with consciousness (brains). Here, we considered several proposed heuristic measures and computational approximations, some of which can be applied to larger systems, and tested if they correlate well with &Phi, While these measures and approximations capture intuitions underlying IIT and some have had success in practical applications, it has not been shown that they actually quantify the type of integrated information specified by the latest version of IIT and, thus, whether they can be used to test the theory. In this study, we evaluated these approximations and heuristic measures considering how well they estimated the &Phi, values of model systems and not on the basis of practical or clinical considerations. To do this, we simulated networks consisting of 3&ndash, 6 binary linear threshold nodes randomly connected with excitatory and inhibitory connections. For each system, we then constructed the system&rsquo, s state transition probability matrix (TPM) and generated observed data over time from all possible initial conditions. We then calculated &Phi, approximations to &Phi, and measures based on state differentiation, coalition entropy, state uniqueness, and integrated information. Our findings suggest that &Phi, can be approximated closely in small binary systems by using one or more of the readily available approximations (r &gt, 0.95) but without major reductions in computational demands. Furthermore, the maximum value of &Phi, across states (a state-independent quantity) correlated strongly with measures of signal complexity (LZ, rs = 0.722), decoder-based integrated information (&Phi, *, rs = 0.816), and state differentiation (D1, rs = 0.827). These measures could allow for the efficient estimation of a system&rsquo, s capacity for high &Phi, or function as accurate predictors of low- (but not high-)&Phi, systems. While it is uncertain whether the results extend to larger systems or systems with other dynamics, we stress the importance that measures aimed at being practical alternatives to &Phi, be, at a minimum, rigorously tested in an environment where the ground truth can be established.

In this paper, we propose pattern recognition for tennis tactics using ball trajectory data from the motion capture system. The purpose of the study is to adapt machine learning in order to implement feature extraction of rallies in tennis game using positions of ball bounce. We modeled this task as statistical modeling of time-series data using a Hidden Markov Model. We also conducted experiments and we verified the dispersion of the mixture component and the centroid, corresponding to two types of tennis court area division. Moreover, we implemented feature extraction of rally according to the initial state probability and the state transition probability.

An improved ant colony algorithm based on the three constraint conditions that aiming at the problem of resource scheduling in cloud computing is proposed in this paper. this method is divided into three steps: Firstly, we describe the state transition probability by using the information heuristic factor and the expected heuristic factor. Secondly, the pheromone update strategy is used to design the scheduling process. Finally, the optimal path is based on the expected execution time, network delay and network bandwidth of three constraints. Experimental results show that the proposed method has faster execution speed than the traditional ant colony algorithm, and the load balancing of the results is more satisfactory.

This paper addresses the sliding mode control problem for uncertain MIMO linear Markovian jump systems. Firstly, by using the linear matrix inequality approach, sufficient conditions are proposed to guarantee the stochastically asymptotical stability of the system on the sliding surfaces. Secondly, an equivalent control based sliding mode control is proposed, such that the closed-loop system can be driven onto the desired sliding surfaces in a finite time. Finally, combining with multi-step state transition probability, the reaching and sliding probabilities are derived for situations where the control force may not be strong enough to ensure the fully asymptotical stability. Simulation results are presented to illustrate the effectiveness of the proposed design method.

At present, submarine intelligent path planning is an essential subject due to electronic chart technology and improvement on navigation equipment when submarine sailing has been normalized. Based on hydrological environment, a new threat cost calculation method is proposed. The distance from the waypoint to the threat center and the length of the track in the threat area are added to the cost function. The pheromone update coalescing differential evolution algorithm is aimed to solve the problem that ant colony algorithm is subject to local optimization and lead to improve the performance of global search. Combined with the actual navigation status and navigation environment of the submarine, an improved strategy of state transition probability is proposed. Finally, with factors such as submarine sailing safety, concealment and endurance, simulation of submarine three-dimensional path planning under different tactical needs demonstrates that the method designed in this paper has engineering application value.

This paper studies a vehicle routing problem with compatibility constraints (VRPCC). It is originated from an application of the cold-chain logistics where different types of cold-chain products may or may not be delivered at the same time. We provide a detailed description of the VRPCC and then propose a hybrid metaheuristic algorithm for solving it. The algorithm includes an ant colony optimization process, in which the new state transition probability formula and pheromone updating rule are applied. In addition, a tabu search process is involved to further improve the solution quality. We modify several VRP benchmark data to form VRPCC instances. The performance of the hybrid algorithm is evaluated and the parameter analysis is conducted. The results demonstrate the effectiveness and efficiency of the algorithm in solving the VRPCC.

This paper represents a scheme for solving the problem that is faced by the Secondary Users for channel switching in Cognitive Radio networks. In this work, an efficient proactive channel selection and switching framework called Best Fit Channel Switching (BFCS) is proposed to minimize the amount of channel switching overhead for SUs between different channels. Based on channel usage information of PU and application specific parameters, One State Transition Probability (OSTP) and Two State Transition Probability (TSTP) are calculated. Then with the help of OSTP and TSTP a list of best channels for switching is obtained. Thus the proposed scheme enables the SUs to proactively predict the future spectrum availability status and switch to the best channel for communication when any PU arrives amidst of its current transmission. The proposed method is compared with the existing methods to evaluate its performance for parameters like channel switching cost.

1 Decomposition is an effective way to reduce power in finite-state machines (FSMs) synthesis. In this study, we proposed a fuzzy c-mean clustering based decomposition method, called FCM-D, for FSM synthesis. FCM-D partitions a set of states of FSM into a collection of c fuzzy clusters; hence a FSM is decomposed into several sub machines. The objective function is to minimize the cross state transition probability between sub machines and increase the inner state transition probability within each sub machine. We test our approach on seven benchmarks, and the experimental results show FCM-D achieved a significant reduction on dynamic power and leakage power consumption.

In order to deal with the problem such as slow convergent speed and local optimum existing in traditional ant colony algorithm (ACO) for mobile robot path planning, an improved ant colony algorithm is proposed, and the improvement includes state transition probability and dynamic pheromone evaporation coefficient. Simulation results show that this method is superior to the traditional ant colony algorithm, and therefore it can effectively improve the quality of the path planning of the robot.

NPC in game is an important factor to increase the fun of the game by cooperating with player or confrontation with player. NPC's behavior patterns in the previous games are limited. Also, there is not much difference in NPC's ability among the existing games because it's designed to FSM. Therefore, players who have matched with NPCs which have the characteristics may have difficulty to play.This paper is for improving the problem and production and evaluation of the game NPC behavior model based on wolves hunting model in real life. To achieve it, first, the research surveys and studies behavior states for wolves to capture prey in the real world. Secondly, it is implemented using the Unity3D engine. Third, this paper compares the implemented state transition probability to state transition probability in real world, state transition probability in general game. The comparison shows that the number of state transitions of NPCs increases, proportions of implemented NPC behavior patterns converges to probabilities of state transition in real-world. This means that the aggressive behavior pattern of NPC implemented is similar to the wolf hunting behavior pattern of the real world, and it can thereby provide more player experience. Keywords : Artificial Intelligence(인공 지능), Behavior Pattern of NPC(NPC 행동 패턴), Hunting Model(사냥 모델), Player Experience(플레이어 경험)

Combined with grey model and the characteristics of the Markov chain, based on the grey prediction model, calculating the state transition probability, grey Markov chain model is established. The results show that the grey Markov chain model has higher prediction accuracy than GM (1, 1) model, can offer references for passenger flow organization.

A novel method for electrical equipments condition assessment is proposed based on Markov prediction. Firstly, the condition representation parameters are induced according to the general volt-ampere characteristics, which can be identified by least square method. Secondly, the number of samples falling into different intervals is counted and the state transition probability matrix is calculated. Last, the distribution of parameters in future detection periods is predicted and the equipments condition is assessed by the ratio of the length of current operation time and the estimated life. Take a single phase two-winding transformer as an example, Monte Carlo simulation is used to generate the leakage inductance data and the electrical data is derived by PSCAD. The equipment condition assessment results verify the effectiveness and feasibility of this proposed method.

To solve the charge planning problem involving charges and the orders in each charge, a traveling salesman problem based charge planning model and the improved cross entropy algorithm are proposed. Firstly, the charge planning problem with unknown charge number is modeled as a traveling salesman problem. The objective of the model is to minimize the dissimilarity costs between each order and its charge center order, the open order costs, and the unselected order costs. Secondly, the improved cross entropy algorithm is proposed with the improved initial state transition probability matrix which is constructed according to the differences of steel grades and order widths between orders. Finally, an actual numerical example shows the effectiveness of the model and the algorithm.

Football is one of the most popular sports in the world, in which is the largest number of people participate, especially four years of a world cup will stimulate the upsurge of the fans all over the world. While the people are enjoying the game, they will pay more attention to the competition result, and because the foot matches could bring the tremendous economic benefits. Thus, it becomes very important to stimulate the football matches process and predict the competition results. The paper is studied from the two aspects. On the one hand, in this paper, the data mining technology is used to analyze the present situation of a football team and present the competition results on the basis of predicting the trend of development. On the other hand, the homogeneous Markov chain is introduced into the football match and the state transition probability matrix is established to obtain the main impacting data. Meanwhile, the paper uses the homogeneous Markov model to predict the future development of the football match and get the reasonable conclusions, that is, the situation of a good football match is stable. This method can be used to not only predict the competition result of the football match, but also to predict the competition results of the other matches.

Firstly a GM(1,1) is built to get the dynamic base line for the coal bed methane dynamic productivity of coal mine area. Secondly on the basis of the GM(1,1), Markov chain is applied to achieve state transition probability matrix. Thirdly the coal bed methane dynamic productivity of coal mine area interval is forecasted and analyzed in the form of probability by the system state classification, the calculation of the residue between true value and model fitting value and the standardization of deviation of the residue. It's proved in theory and practice that the forecast results not only are more reliable but also can help the decision maker with grasping the coal bed methane dynamic productivity of coal mine area development tendency in general and making proper decision. Results show that the Grey Markov Model has higher accuracy than that of GM(1,1) model.

Simulation of unmanned aerial vehicle (UAV) flight environment is one of the key technologies in three-dimensional path planning. We adopt efficient intelligent algorithm for path planning in the simulation environment. Basic ant colony algorithm is easy to reach local optimum prematurely with slow convergence speed and long computing time. In this paper, information of the shortest distance is sent to the system for controlling, and optimize the node selection method by improving the calculation of state transition probability. In addition, the local updating rules are improved in order to improve the efficiency of the algorithm. The simulation results show that the improved ant colony algorithm is used to meet the requirements of the unmanned aerial vehicle flight track.

Cyber deception may be an effective solution to exposing and defeating malicious users of information systems. Malicious users of an information system include cyber intruders, advanced persistent threats, and malicious insiders. Once such users gain unobstructed access to, and use of, the protected information system, it is difficult to distinguish between legitimate and illegitimate users.

Due to the uncertainties that exist in the running of the analog circuits, the traditional hidden Markov model (HMM) approach is improved through replacing the state transition probability (STP) matrix of the traditional model by time-varying one. An updating control factor is introduced for avoiding the excess updating of the STP in the initial stage of each state. The experimental results indicate that the improved HMM has better fault recognition and diagnosis capability.

Product quality is very important because many faults have a real impact on users directly. It is significative that Markov chain theory is applied in product quality prediction. A new method of state transition probability matrix in Markov chain is used to provide fault diagnosis and quality prediction in this paper. The aim of this study is to deliver a quality prediction method for mechanical and electrical product by using the data collection and analysis techniques. Firstly, a new approach of fault diagnosis was presented by using the theory of state transition probability matrix. Then, Markov chain theory is used to build the mathematical patterns in the quality prediction with the state transition probability matrix. Finally, we illustrate the veracity rationality and science of the approved method using a numerical example of ball valves.

Attribute reduction problem (ARP) in rough set theory (RST) is an NPhard one, which is difficult to be solved via traditionally analytical methods. In this paper, we propose an improved approach to ARP based on ant colony optimization (ACO) algorithm, named the improved ant colony optimization (IACO). In IACO, a new state transition probability formula and a new pheromone traps updating formula are developed in view of the differences between a traveling salesman problem and ARP. The experimental results demonstrate that IACO outperforms classical ACO as well as particle swarm optimization used for attribute reduction.

This paper addresses detection of oestrus in dairy cows using automata-based modelling and diagnosis. Measuring lying/standing behaviour of the cows by a sensor attached to the cows hindleg, lying/standing behaviour is modelled as a stochastic automaton. The paper introduces a cow's lying-balance as a biologically inspired quantity describing how much the cow has been resting for a preceding period. A dynamic lying-balance model is identified from real data and the lying balance is used as input, together with lying/standing sensor measurements. Using different automata models for oestrus and non-oestrus conditions, with state transition probability densities identified from observations, diagnosis theory for stochastic automata is employed to obtain diagnoses of oestrus. The oestrus cases are detected using consistency based diagnosis on real data.

A new grey forecasting model based on BP neural network and Markov chain was proposed. In order to combine the grey forecasting model with neural network, an important theorem that the grey differential equation is equivalent to the time response model, was proved by analyzing the features of grey forecasting model(GM(1,1)). Based on this, the differential equation parameters were included in the network when the BP neural network was constructed, and the neural network was trained by extracting samples from grey system’s known data. When BP network was converged, the whitened grey differential equation parameters were extracted and then the grey neural network forecasting model (GNNM(1,1)) was built. In order to reduce stochastic phenomenon in GNNM(1,1), the state transition probability between two states was defined and the Markov transition matrix was established by building the residual sequences between grey forecasting and actual value. Thus, the new grey forecasting model(MNNGM(1,1)) was proposed by combining Markov chain with GNNM(1,1). Based on the above discussion, three different approaches were put forward for forecasting China electricity demands. By comparing GM(1, 1) and GNNM(1,1) with the proposed model, the results indicate that the absolute mean error of MNNGM(1,1) is about 0.4 times of GNNM(1,1) and 0.2 times of GM(1,1), and the mean square error of MNNGM(1,1) is about 0.25 times of GNNM(1,1) and 0.1 times of GM(1,1).