Probability Matrix Research Articles

Markov Chain Analysis of Ship Energy Efficiency

A formulation is presented for the assessment of the CO2 generated by ships in operation and their evolution with time, conditional on the current legislation using Markov chains. Any potential deep repair or retrofitting of the ship propulsion system or enhancement of route operational characteristics during the service life are not accounted for. The Markov transition matrix is defined based on the ship operations and CO2 history of A, B, C, D, and E carbon intensity indicator (CII) rates. The transition between different CII rate states in the survey data is used to estimate the probability of transition of the analysed ships between different CII grates. Distinct transition matrices employing the progressively tightened legislation of CII are employed and analysed. In addition, the transition matrices can be fed into risk-based models that take the CII rates as input for defining the most appropriate ship energy efficiency management plan.

Innovative Model for Assessing the Level of Failure Risk in Construction and Buildings

This research explores risk management in construction projects to prevent potential failures due to natural factors or human errors. The objective is to develop a risk assessment model for failures in construction and building projects, focusing on identification, categorization, risk level determination, and model development. The research benefits encompass theoretical contributions to construction risk management, governmental policy guidelines, operational assistance in project risk management, and enhancements in the safety and quality of construction projects. This research innovates by expanding research variables, incorporating failure risk level assessments, and utilizing technological approaches. The research methodology combines quantitative and descriptive approaches, focusing on failure risk factors from service/contractor providers, consultants, and project owners. Data is obtained through literature studies, secondary data, and primary data via questionnaires. The analysis involves factor analysis, importance index, impact probability matrix, and the Partial Least Square (PLS) method for structural analysis. The research conclusion identifies failure risk factors including financial aspects, management, equipment availability, and natural impacts such as floods and earthquakes. The risk assessment model categorizes risks into high, medium, and low, enabling appropriate anticipatory measures. This model provides guidance for stakeholders to mitigate risks, improve quality, and maintain the integrity of construction projects and buildings, supporting safety and success throughout project stages. This research makes a significant contribution to construction project risk management and construction quality improvement.

Asynchronous filtering for discrete-time T–S fuzzy sampled-data systems with improved quantization

This study delves into the asynchronous filtering problem within discrete-time Takagi–Sugeno (T–S) fuzzy sampled-data systems featuring non-periodic sampled measurements. A non-homogeneous Markov chain is utilized to capture the stochastic nature of the sampling period. The transition probability matrix of this non-homogeneous Markov process is time-varying and characterized using a multi-mode structure. To mitigate conservatism, a quantizer associated with the modes is implemented, where the quantization density is defined as the observed modes. Unlike existing approaches, there exists a discrepancy between the quantizer mode and the sampling mode, following a hidden Markov chain process. Additionally, a novel fuzzy asynchronous filter is introduced based on the observed modes to ensure the stochastic stability of the fuzzy system. Ultimately, the effectiveness of the proposed filter strategy is validated via a tunnel diode circuit model.

Trade Specialization Dynamics in a Small Open Resource-Based Developing Economy: Empirical Evidence from Botswana

ABSTRACT We analyze trade specialization dynamics in Botswana, applying the Galtonian regression and Markov matrix on the Lafay index for the period of 1998 to 2019. Galtonian regressions reveal de-specialization – Botswana gained a comparative advantage in industries for which it was initially not specialized and became less competitive in industries for which it was initially specialized. The industry hierarchy was altered only slightly due to persistence in trade specialization patterns. The Markov matrix reveals stronger upward industry mobility than downward industry mobility. De-specialization suggests slow-paced economic diversification, induced by import substitution in de-specialized industries, rather than by an expanding export base.

Optimizing doubly stochastic matrices for average consensus through swarm and evolutionary algorithms

Optimizing doubly stochastic matrices for average consensus through swarm and evolutionary algorithms

L1-gain control for 2D delayed positive continuous Markov jumping systems

This study is focused on analyzing the L1-stochastic internal stability and the design of an L1-gain controller for two-dimensional (2D) continuous positive Markov jumping systems (PMJSs) with constraints on the inputs and states. An algorithm is developed to explicitly determine the state feedback control law with the optional L1-gain performance. First, by constructing a co-positive stochastic Lyapunov function for the positive system and establishing the equation for the Markov states' mathematical expectation, several sufficient and necessary conditions for L1-stochastic internal stability are derived. This analysis indicates that 2D PMJSs with directional delays are influenced by sizes of the system matrices and magnitude of delays, and transition matrix. Second, a method for calculating the L1-gain is formulated utilizing linear programming (LP), thus, an L1-gain controller is designed to guarantee that the closed-loop system is positive and L1-stochastically internally stable, while achieving optimal L1-gain performance. Two numerical and practical examples are considered, and the influence of delays and transition probability matrices on the L1-gain is specified to validate the preceding theoretical findings.

Advanced Millimeter-Wave Radar System for Real-Time Multiple-Human Tracking and Fall Detection.

This study explored an indoor system for tracking multiple humans and detecting falls, employing three Millimeter-Wave radars from Texas Instruments. Compared to wearables and camera methods, Millimeter-Wave radar is not plagued by mobility inconveniences, lighting conditions, or privacy issues. We conducted an initial evaluation of radar characteristics, covering aspects such as interference between radars and coverage area. Then, we established a real-time framework to integrate signals received from these radars, allowing us to track the position and body status of human targets non-intrusively. Additionally, we introduced innovative strategies, including dynamic Density-Based Spatial Clustering of Applications with Noise (DBSCAN) clustering based on signal SNR levels, a probability matrix for enhanced target tracking, target status prediction for fall detection, and a feedback loop for noise reduction. We conducted an extensive evaluation using over 300 min of data, which equated to approximately 360,000 frames. Our prototype system exhibited a remarkable performance, achieving a precision of 98.9% for tracking a single target and 96.5% and 94.0% for tracking two and three targets in human-tracking scenarios, respectively. Moreover, in the field of human fall detection, the system demonstrates a high accuracy rate of 96.3%, underscoring its effectiveness in distinguishing falls from other statuses.

Persistence of spectral projections for stochastic operators on large tensor products

Abstract It is proved that for families of stochastic operators on a countable tensor product, depending smoothly on parameters, any spectral projection persists smoothly, where smoothness is defined using norms based on ideas of Dobrushin. A rigorous perturbation theory for families of stochastic operators with spectral gap is thereby created. It is illustrated by deriving an effective slow two-state dynamics for a three-state probabilistic cellular automaton.

Investigation and calculation of the longitudinal compressive strength of unidirectional glass fiber reinforced polymer considering the fiber orientation distribution

In this study, undulations and their influence on the longitudinal compressive strength of a unidirectional glass fiber reinforced polymer (GFRP) composite are investigated theoretically and experimentally. The objective of this research is to explore the failure mechanisms in FRP and to characterize the mechanical properties of FRP as a function of fiber orientation. For this purpose, a multiscale material model is developed that considers a stochastic fiber orientation distribution (FOD) and models matrix fracture-initiated failure. The relationship between compressive strength and undulation is investigated experimentally on standardized specimens made of unidirectional GFRP. The fiber orientations are measured using X-ray computed tomography and ImageJ image analysis, resulting in a binormal distribution of fiber orientations in the series of samples tested. To examine the failure process in detail, the compression tests are simulated using finite element analysis (FEA). Both the FEA results and the measured compressive strengths confirm the model assumption of matrix fracture-initiated failure under longitudinal compressive loading. The presented analytical model realistically represents the correlation of compressive strength with the FOD.

DualGCN: Exploring Syntactic and Semantic Information for Aspect-Based Sentiment Analysis.

The task of aspect-based sentiment analysis aims to identify sentiment polarities of given aspects in a sentence. Recent advances have demonstrated the advantage of incorporating the syntactic dependency structure with graph convolutional networks (GCNs). However, their performance of these GCN-based methods largely depends on the dependency parsers, which would produce diverse parsing results for a sentence. In this article, we propose a dual GCN (DualGCN) that jointly considers the syntax structures and semantic correlations. Our DualGCN model mainly comprises four modules: 1) SynGCN: instead of explicitly encoding syntactic structure, the SynGCN module uses the dependency probability matrix as a graph structure to implicitly integrate the syntactic information; 2) SemGCN: we design the SemGCN module with multihead attention to enhance the performance of the syntactic structure with the semantic information; 3) Regularizers: we propose orthogonal and differential regularizers to precisely capture semantic correlations between words by constraining attention scores in the SemGCN module; and 4) Mutual BiAffine: we use the BiAffine module to bridge relevant information between the SynGCN and SemGCN modules. Extensive experiments are conducted compared with up-to-date pretrained language encoders on two groups of datasets, one including Restaurant14, Laptop14, and Twitter and the other including Restaurant15 and Restaurant16. The experimental results demonstrate that the parsing results of various dependency parsers affect their performance of the GCN-based models. Our DualGCN model achieves superior performance compared with the state-of-the-art approaches. The source code and preprocessed datasets are provided and publicly available on GitHub (see https://github.com/CCChenhao997/DualGCN-ABSA).

LA-ViT: A Network With Transformers Constrained by Learned-Parameter-Free Attention for Interpretable Grading in a New Laryngeal Histopathology Image Dataset.

Grading laryngeal squamous cell carcinoma (LSCC) based on histopathological images is a clinically significant yet challenging task. However, more low-effect background semantic information appeared in the feature maps, feature channels, and class activation maps, which caused a serious impact on the accuracy and interpretability of LSCC grading. While the traditional transformer block makes extensive use of parameter attention, the model overlearns the low-effect background semantic information, resulting in ineffectively reducing the proportion of background semantics. Therefore, we propose an end-to-end network with transformers constrained by learned-parameter-free attention (LA-ViT), which improve the ability to learn high-effect target semantic information and reduce the proportion of background semantics. Firstly, according to generalized linear model and probabilistic, we demonstrate that learned-parameter-free attention (LA) has a stronger ability to learn highly effective target semantic information than parameter attention. Secondly, the first-type LA transformer block of LA-ViT utilizes the feature map position subspace to realize the query. Then, it uses the feature channel subspace to realize the key, and adopts the average convergence to obtain a value. And those construct the LA mechanism. Thus, it reduces the proportion of background semantics in the feature maps and feature channels. Thirdly, the second-type LA transformer block of LA-ViT uses the model probability matrix information and decision level weight information to realize key and query, respectively. And those realize the LA mechanism. So, it reduces the proportion of background semantics in class activation maps. Finally, we build a new complex semantic LSCC pathology image dataset to address the problem, which is less research on LSCC grading models because of lacking clinically meaningful datasets. After extensive experiments, the whole metrics of LA-ViT outperform those of other state-of-the-art methods, and the visualization maps match better with the regions of interest in the pathologists' decision-making. Moreover, the experimental results conducted on a public LSCC pathology image dataset show that LA-ViT has superior generalization performance to that of other state-of-the-art methods.

A new EDA algorithm combined with Q-learning for semiconductor final testing scheduling problem

In recent years, the Semiconductor Final Testing Scheduling Problem (SFTSP), recognized as a unique multi-resource scheduling challenge, attracts increasingly attention of academia and industry in the semiconductor manufacturing process. In this paper, a novel estimation of distribution algorithm combined with Q-learning (QEDA) is proposed to solve the SFTSP. According to the characteristics of the used operation encoding, a new probability matrix update mechanism is proposed for enhancing the priority relationships among operations. Considering that the traditional EDA is not in favor of local exploitation compared with its global exploration, a reinforcement learning is designed to improve the performance of the proposed algorithm. Furthermore, for the challenge of the resource allocation in SFTSP, four actions are introduced based on the variance of individual objectives. Extensive numerical simulations and comparative experiments show that the proposed QEDA algorithm exhibits much better performance than the state-of-the-art algorithms in the literature for solving the SFTSP.

Novel Detection and Progression Markers for Diabetes Based on Continuous Glucose Monitoring Data Dynamics.

Develop a diabetes diagnostic tool based on two markers of continuous glucose monitoring (CGM) dynamics: CGM entropy rate (ER) and Poincaré plot (PP) ellipse area (S). 5,754 daily CGM profiles from 843 individuals with type 1, type 2 diabetes, or healthy individuals with or without islet autoantibody status were used to compute two individual dynamic markers: ER (in bits per transition; BPT) of daily probability matrices describing CGM transitions between eight glycemic states, and the area S (mg2/dL2) of individual CGM PP ellipses using standard PP descriptors. The Youden's index was used to determine "optimal" cut-points for ER and S for health vs. diabetes (case 1); type 1 vs. type 2 (case 2); and low vs. high type 1 immunological risk (case 3). The markers' discriminative power was assessed through the area under the receiver operating characteristics curves (AUC). Optimal cut-off points were determined for ER and S for each of the three cases. ER and S discriminated case 1 with AUC = 0.98 (95% CI: 0.97-0.99) and AUC = 0.99 (95% CI: 0.99-1.00), respectively, (cut-offs ERcase1 = 0.76 BPT, Scase1 = 1993.91 mg2/dL2), case 2 with AUC = 0.81 (95% CI, 0.77-0.84) and AUC = 0.76 (95% CI, 0.72-0.81), respectively (ERcase2 = 1.00 BPT, Scase2 = 5112.98 mg2/dL2), and case 3 with AUC = 0.81 (95% CI, 0.77-0.84) and AUC = 0.76 (95% CI, 0.72-0.81), respectively (ERcase3 = 0.52 BPT, Scase3 = 923.65 mg2/dL2). CGM dynamics markers can be an alternative to fasting plasma glucose or glucose tolerance testing and identifying individuals at higher immunological risk of progressing to type 1 diabetes.

Quantum No-signalling Correlations and Non-local Games

We introduce and examine three subclasses of the family of quantum no-signalling (QNS) correlations introduced by Duan and Winter: quantum commuting, quantum and local. We formalise the notion of a universal TRO of a block operator isometry, define an operator system, universal for stochastic operator matrices, and realise it as a quotient of a matrix algebra. We describe the classes of QNS correlations in terms of states on the tensor products of two copies of the universal operator system and specialise the correlation classes and their representations to classical-to-quantum correlations. We study various quantum versions of synchronous no-signalling correlations and show that they possess invariance properties for suitable sets of states. We introduce quantum non-local games as a generalisation of non-local games. We define the operation of quantum game composition and show that the perfect strategies belonging to a certain class are closed under channel composition. We specialise to the case of graph colourings, where we exhibit quantum versions of the orthogonal rank of a graph as the optimal output dimension for which perfect classical-to-quantum strategies of the graph colouring game exist, as well as to non-commutative graph homomorphisms, where we identify quantum versions of non-commutative graph homomorphisms introduced by Stahlke.

Research on a global periodic climate prediction method based on improved BP neural network

Climate prediction has a wide social demand, but due to the complexity of climate system formation and the uniqueness of Chinas terrain, accurate prediction is extremely complex and difficult. Therefore, this article proposes a global periodic climate prediction method based on an improved BP neural network. Firstly, based on historical meteorological data, establish a climate model and summarize and analyze the characteristics of the patterns; Then, based on the BP neural network, considering the relationship between adjacent days, rolling sampling of historical data is carried out according to seasonal and meteorological factors in the sampling interval, establishing a multi-state transition probability matrix, and constructing an annual time series forecasting model; Finally, taking precipitation prediction as an example, an example was used to simulate the annual precipitation situation. The calculation results have verified the effectiveness of the proposed method, indicating that it can simulate climate conditions well and provide guidance for climate governance and engineering construction.

A Reliability Assessment Method for Complex Systems Based on Non-Homogeneous Markov Processes.

The Markov method is a common reliability assessment method. It is often used to describe the dynamic characteristics of a system, such as its repairability, fault sequence and multiple degradation states. However, the "curse of dimensionality", which refers to the exponential growth of the system state space with the increase in system complexity, presents a challenge to reliability assessments for complex systems based on the Markov method. In response to this challenge, a novel reliability assessment method for complex systems based on non-homogeneous Markov processes is proposed. This method entails the decomposition of a complex system into multilevel subsystems, each with a relatively small state space, in accordance with the system function. The homogeneous Markov model or the non-homogeneous Markov model is established for each subsystem/system from bottom to top. In order to utilize the outcomes of the lower-level subsystem models as inputs to the upper-level subsystem model, an algorithm is proposed for converting the unavailability curve of a subsystem into its corresponding 2×2 dynamic state transition probability matrix (STPM). The STPM is then employed as an input to the upper-level system's non-homogeneous Markov model. A case study is presented using the reliability assessment of the Reactor Protection System (RPS) based on the proposed method, which is then compared with the models based on the other two contrast methods. This comparison verifies the effectiveness and accuracy of the proposed method.

A markov chain based photovoltaic power simulation method

Photovoltaic power generation has volatility and randomness, which affects the safety and reliability of the power system. In order to achieve accurate simulation of photovoltaic output, this paper proposes a photovoltaic power timing simulation method based on rolling sampled Markov chain model. Firstly, establish a photovoltaic output model and analyze the actual output characteristics; Then, based on the first-order Markov chain model, the relationship between adjacent days is considered, and a multistate transition probability matrix is established to construct an annual time series output model; Finally, based on the annual output data of a photovoltaic power station and historical meteorological monitoring data, an example is simulated to verify the effectiveness of the proposed method.

Influence of geological uncertainty on longitudinal deformation of tunnel based on improved coupled Markov chain

The complex geological condition encountered during excavation is the key challenge for tunneling projects. Therefore, tunnel design and construction require a comprehensive understanding of the subsurface geology. This study aims to reveal the effect of geological uncertainty on tunnel longitudinal deformation based on a reconstruction geological model using the improved coupled Markov chain method. The improved coupled Markov chain method makes the predicted results more suitable for the possible stratigraphic distribution by optimizing the transition probability matrix, and breaks through the limitations of non-coaxial predicted cell updating in traditional methods. A mapping method was proposed to establish a matching relationship between the irregular grids of the geological model and the numerical tunnel model. Then, a long tunnel in Shenzhen was selected as a case study to demonstrate the effectiveness of the proposed framework. The correlation coefficient was used to verify the relationship between tunnel deformation and the surrounding stratum with different tunnel cover depths. The geological uncertainty of various strata was quantitatively measured based on the proposed geological uncertainty index. The three-dimensional strata surrounding the tunnel were reconstructed based on exceedance probabilities for adverse geological conditions. Quantitative analysis was conducted on the tunnel vertical convergence during the excavation process.

Forecasting Freight on Board for Gonggong Export in Batam Using Markov Chain

As an archipelagic country, Indonesia has great potential in the fisheries sector. As a free trade zone, Batam is important in exporting fishery products. One of the fishery export products in Batam City is gonggong snails. It is a favorite seafood item in Riau Islands Province and has high economic value. However, previous studies focused more on the content of gonggong snails and their industrial feasibility; there has been no specific research on the analysis of gonggong snail exports in Batam City, even though gonggong snails are one of Batam City's export products. In this research, we will forecast the freight on board (FoB) value for gonggong exports in Batam City using a discrete-time Markov chain with two states: above and below the moving average. There are several types of moving averages, including simple moving averages and weighted moving averages. An initial analysis will determine the moving averages' type and duration following the Gonggong export FOB data in Batam. The data used is the Gonggong export FoB data for Batam City from January 2020 to November 2023. Based on this data, the transition probability matrix will be calculated based on the number of export transitions below and above the Weighted Moving Average 6 (WMA 6) value. Limiting probability from the Markov chain will be used to predict the long-term FOB value of fishery product exports up to steady-state conditions. It was found that steady-state conditions would be reached after 17 months, with a probability of FOB exports below WMA6 of 55.06% and FOB exports above WMA6 of 44.94%.

Consistent graph learning for multi-view spectral clustering

Given the heterogeneous information of multiple views and the possible noise embedded in multi-view data, it is difficult to directly learn a consistent representation from multiple graphs to depict the intrinsic structure of all views. We propose a consistent graph learning method by exploiting both the high-order correlations underlying multiple views and the global structure of each single view. First, we calculate a transition probability matrix from each view. Second, a tensor is constructed by stacking each transition matrix as its frontal slice and then decomposed into the latent and error tensors. For the latent tensor, after rotated, a weighted tensor nuclear norm is used to encourage the rotate tensor to fully exploit the high-order correlations underlying multiple views. Furthermore, each frontal slice of the latent tensor is regularized by the nuclear norm to capture the global structure of each single view, and is restricted by probability constraints. Besides, we adopt the Frobenius-norm-based regularization to directly learn a common affinity matrix from the latent tensor. The established model is readily optimized by the alternating Lagrangian method. Extensive experiments on six real world datasets demonstrate that our method outperforms state-of-the-art methods.