Probability Matrix Research Articles

Detailed-level modelling of influence spreading on complex networks.

The progress in high-performance computing makes it increasingly possible to build detailed models to investigate spreading processes on complex networks. However, current studies have been lacking detailed computational methods to describe spreading processes in large complex networks. To fill this gap we present a new modelling approach for analysing influence spreading via individual nodes and links on various network structures. The proposed influence-spreading model uses a probability matrix to capture the spreading probability from one node to another in the network. This approach enables analysing network characteristics in a number of applications and spreading processes using metrics that are consistent with the quantities used to model the network structures. In addition, this study combines sub-models and offers a comprehensive look at different applications and metrics previously discussed in cases of social networks, community detection, and epidemic spreading. Here, we also note that the centrality measures based on the probability matrix are used to identify the most significant nodes in the network. Furthermore, the model can be expanded to include additional properties, such as introducing individual breakthrough probabilities for the nodes and specific temporal distributions for the links.

Mapping the Trade Direction of Indian Rice with Markov Chain Analysis

Agriculture is a cornerstone of India’s economy, with rice being a critical crop that ranks second globally, feeding over half of the world’s population and serving as a staple in Southeast Asia. This study explores the direction of India’s rice trade using Markov Chain Analysis, following an examination of the compound annual growth rate (CAGR) in rice exports to various global regions. Results reveal a 2.26 per cent CAGR in rice production, while export values surged by 16.8 per cent annually. Specifically, the CAGR for rice exports to Iraq and Iran reached 58.6 per cent and 46.47 per cent, respectively. In quantity, India’s rice exports grew by 10.82 per cent, with Iraq and Iran at 44 per cent and 34 per cent. The Transitional Probability Matrix for 2001-2022 indicates strong regional retention, with Africa maintaining 78 per cent of trade value and Asia 93.7 per cent, and similar trends in quantity, where Asia retained 92.6 per cent and Africa 89.1 per cent. These findings highlight India’s potential to diversify rice exports and strengthen its global competitive edge, urging a focus on enhancing processing, transportation, and quality standards for wider market appeal.

A novel operational reliability and state prediction method based on degradation hidden Markov model with random threshold

AbstractBearings are widely used as a common mechanical component and significantly impacts the reliability and safety of various engineering equipment. In the field of large‐scale equipment such as wind turbines, statistical data for reliability and state prediction of bearings is usually limited, leading to the inapplicability of traditional statistical methods. Besides, individual differences commonly exist among bearings, and the appropriate failure threshold for a specific bearing is difficult to be determined due to the individual uncertainty, which may induce prediction errors. To address these issues, a novel operational reliability and state prediction method based on random threshold degradation hidden Markov model was proposed in the study. The traditional hidden Markov model was improved by considering the effect of performance degradation on state transition probability matrix. Moreover, random failure thresholds of performance degradation were employed to describe individual differences between bearings. The operational reliability and state of bearings was obtained by comprehensive analysis of prediction results under different failure thresholds. Verification of the proposed operational reliability and state prediction method were conducted using PHM2012 bearing operation data. The results underscored the effectiveness of the proposed method in achieving a comparatively high accuracy in operational reliability prediction without the prerequisite of an exact failure threshold, when contrasted with several established reliability and life prediction techniques.

Convergence of the trajectories of a non-Volterra quadratic stochastic operator

In the present paper we consider non-Volterra quadratic stochastic operators defined on the two-dimensional simplex depending on a parameter \alpha . We show that such an operator has a unique fixed point and all the trajectories converge to this unique fixed point.

DUALITY: DETECTABILITY VERSUS STABILIZABILITY IN THE STOCHASTIC CONTEXT

The aim of this paper is to extend to the stochastic framework the well known duality relation between the detectability property and the stabilizability property of a finite dimensional, linear time invariant, deterministic system. We consider continuous time linear stochastic systems having the state space representation described by a system of Itˆo differential equations with periodic coefficients possibly subject to some stochastic perturbations modeled by a standard homogeneous Markov process with a finite number of states. It will be seen that in the case when the given system is affected by jump Markov perturba tions a state space representation of the dual triple may be rigorously defined if and only if the transition probability matrix of the Markov process is double stochastic (in the sense that the sums of all elements from its each row and each column are equal 1).

Local set stability and target control of probabilistic Boolean networks

This paper analyzes the local set stability of probabilistic Boolean networks (PBNs), including local finite-time set stability with probability one (FSSPO) and local asymptotic set stability with probability one (ASSPO). Firstly, a necessary and sufficient condition is proposed for the local FSSPO of PBNs. Then, a reachable set with probability one is constructed, based on which, the largest domain of attraction for the local FSSPO of PBNs is determined. Secondly, by constructing two parameterized sets, the transition probability matrix of PBNs is properly partitioned, and the largest domain of attraction for the ASSPO is depicted. Finally, for PBNs which are locally stable, the target control is introduced to achieve the global FSSPO and global ASSPO of PBNs, respectively.

Attribute enhanced random walk for community detection in attributed networks

Traditional community detection methods often rely solely on network topology, potentially overlooking the influence of attributes. However, community detection in attributed networks presents a unique challenge due to the complex interplay between network topology and node attributes. In this paper, we present AERW, a novel approach that integrates both network topology and node attributes for effective community detection. AERW leverages the principle of homophily by aggregating neighbor attributes within triangles to capture higher-order structural information. Then constructing a bipartite graph to effectively integrate topological and attribute information, ensuring that both aspects are equally represented in the community detection process. Next AERW utilizes hierarchical clustering applied to the probability transition matrix derived from the random walk, enabling the identification of community structures without needing prior knowledge of the number of communities. Extensive experimentation across synthetic and real-world networks underscores AERW’s efficacy, establishing it as a superior approach in community detection within attributed networks.

Floating wave energy farms: How energy calculations shape economic feasibility?

The aim of this study is to use two different methodologies for calculating the energy produced by a total wave energy farm in the Cantabrian Sea (North of Spain). First method studies the energy produced by the farm taking into account the wave energy converter power matrix and the probability matrix of sea conditions for a particular location. On the other hand, second method is a more simplified methodology in which the wave energy converter power matrix is not taken into account, but it considers the density of the water, gravity, period and height of the wave, as well as the percentage of efficiency, among others. Finally, the energy generated by the farm and the economic parameters that allow calculating its economic feasibility are studied, such as Levelized Cost of Energy, Net Present Value and Internal Rate of Return. Results indicate the importance of using a particular method for calculating the energy produced by a wave energy farm in terms of the variation of its economic feasibility. In this sense, it is shown that despite the fact that the first method is more detailed, the variations between both methods are very small, therefore the simplest model can be used in the future studies, reducing the calculation process in the future.

Lost in the Shuffle: Testing Power in the Presence of Errorful Network Vertex Labels

Two-sample network hypothesis testing is an important inference task with applications across diverse fields such as medicine, neuroscience, and sociology. Many of these testing methodologies operate under the implicit assumption that the vertex correspondence across networks is a priori known. This assumption is often untrue, and the power of the subsequent test can degrade when there are misaligned/label-shuffled vertices across networks. This power loss due to shuffling is theoretically explored in the context of random dot product and stochastic block model networks for a pair of hypothesis tests based on Frobenius norm differences between estimated edge probability matrices or between adjacency matrices. The loss in testing power is further reinforced by numerous simulations and experiments, both in the stochastic block model and in the random dot product graph model, where the power loss across multiple recently proposed tests in the literature is considered. Lastly, the impact that shuffling can have in real-data testing is demonstrated in a pair of examples from neuroscience and from social network analysis.

Structured multi-view k-means clustering

K-means is a very efficient clustering method and many multi-view k-means clustering methods have been proposed for multi-view clustering during the past decade. However, since k-means have trouble uncovering clusters of varying sizes and densities, these methods suffer from the same performance issues as k-means. Improving the clustering performance of multi-view k-means has become a challenging problem. In this paper, we propose a new multi-view k-means clustering method that is able to uncover clusters in arbitrary sizes and densities. The new method simultaneously performs three tasks, i.e., sparse connection probability matrices learning, prototypes aligning, and cluster structure learning. We evaluate the proposed new method by 5 benchmark datasets and compare it with 11 multi-view clustering methods. The experimental results on both synthetic and real-world experiments show the superiority of our proposed method.

Devising an analytical method for solving the eighth-order Kolmogorov equations for an asymmetric Markov chain

The object of research is a complex system of three subsystems, which function independently of each other and are in a working or failed state. There is a need to analytically model and manage the Markov random process in the system, varying the intensity of their development-restoration and degradation-destruction flows. In the study, an analytical method for solving Kolmogorov equations of the eighth order for an asymmetric Markov chain was devised. The corresponding Kolmogorov equations of the eighth order have an ordered transition probability matrix. The distribution of the eight roots of this equation in the complex plane has central symmetry. The results are analytical solutions for the probabilities of the eight states of the Markov chain in time in the form of ordered determinants with respect to the indices of the eight roots and the indices of the eight states, including the column vector of the initial conditions. Symmetry has been established in the distribution on the complex plane of eight real, negative roots of the characteristic Kolmogorov equation centered at the point defined as Re ϑ = –a7/8, where a7 is the coefficient of the characteristic equation of the eighth degree at the seventh power. Formulas expressing eight roots of the characteristic Kolmogorov equation have been heuristically derived, one of which is zero, due to the intensities of failures and recovery of three subsystems, the eight states of which in general make up an asymmetric Markov chain. For structures consisting of three independently functioning processes, the random process of the transition of the structure through eight possible states with a known initial state is determined in time. An analytical solution to Kolmogorov differential equations of the eighth order for an asymmetric state graph is proposed in harmonic form for the purpose of analysis and synthesis of a random Markov process in a triple system.

New method for stability of probabilistic Boolean networks with inequality constraints

This paper studies the stability of probabilistic Boolean networks (PBNs) with state inequality constraints by establishing a new algebraic representation. On one hand, combining with the semi-tensor product (STP) of matrices and the law of total expectation, the algebraic representation of PBNs is established. On the other hand, based on the STP of matrices, an algorithm is proposed to determine the solution set of the state inequality constraints. Then, based on the algebraic representation and the inequality constrained solution set, a new form of transition probability matrix is constructed for PBNs. Finally, by the proposed transition probability matrix, new criteria are proposed for the finite-time stability with positive probability of PBNs. Several simulation examples are used to illustrate the effectiveness of the obtained results.

Coherent Set Identification Via Direct Low Rank Maximum Likelihood Estimation

We analyze connections between two low rank modeling approaches from the last decade for treating dynamical data. The first one is the coherence problem (or coherent set approach), where groups of states are sought that evolve under the action of a stochastic transition matrix in a way maximally distinguishable from other groups. The second one is a low rank factorization approach for stochastic matrices, called direct Bayesian model reduction (DBMR), which estimates the low rank factors directly from observed data. We show that DBMR results in a low rank model that is a projection of the full model, and exploit this insight to infer bounds on a quantitative measure of coherence within the reduced model. Both approaches can be formulated as optimization problems, and we also prove a bound between their respective objectives. On a broader scope, this work relates the two classical loss functions of nonnegative matrix factorization, namely the Frobenius norm and the generalized Kullback–Leibler divergence, and suggests new links between likelihood-based and projection-based estimation of probabilistic models.

On G-majorization of vectors

A real matrix [Formula: see text] is row generalized stochastic if the sum of absolute value of entries in each row is less than or equal to one and there is a fixed [Formula: see text] such that the sum of all entries in each row is [Formula: see text]. For vectors [Formula: see text] (respectively, [Formula: see text]), it is said that [Formula: see text] is right (respectively, left) generalized matrix majorized by [Formula: see text] (denoted by [Formula: see text] (respectively, [Formula: see text])) if [Formula: see text] (respectively, [Formula: see text]) for some [Formula: see text]-by-[Formula: see text] row generalized stochastic matrix [Formula: see text]. In this paper, we have found all vectors such as [Formula: see text] that are right-majorized by [Formula: see text] and we have found all vectors such as [Formula: see text] that are left-majorized by [Formula: see text] and we describe all equivalence classes [Formula: see text] and [Formula: see text].

Analyzing vehicle path optimization using an improved genetic algorithm in the presence of stochastic perturbation matter

By analyzing the influence of stochastic perturbation matters on vehicle path optimization, a perturbation scheduling model for logistics and distribution with a carbon tax mechanism is established under the premise of time window variation and load capacity constraints. Herein, we propose an enhanced Genetic Algorithm (GA) based on a Gaussian matrix mutation (GMM) operator, which maintains the diversity of the population while speeding up the algorithm’s convergence. The model builds a Gaussian probability matrix using the site positional order distribution characteristics implied in the original site data information, and applies the Gaussian probability matrix to individual gene mutations using a roulette-wheel-selection method; thus, the study guarantees the genetic diversity of the population while guiding it to evolve in the high-fitness direction. Finally, an experimental simulation is performed using data obtained from a commercial supermarket, thereby verifying the effectiveness of the proposed algorithm and comparing it with other algorithms. The results reveal that compared with the classical GA, the average convergence speed of the improved GA can be increased by 50–60% and the consumed algorithm time can be reduced by 48% while maintaining the difference in solution accuracy within 1%.

Multi-perspective API call sequence behavior analysis and fusion for malware classification

The growing variety of malicious software, i.e., malware, has caused great damage and economic loss to computer systems. The API call sequence of malware reflects its dynamic behavior during execution, which is difficult to disguise. Therefore, API call sequence can serve as a robust feature for the detection and classification of malware. The statistical analysis presented in this paper reveals two distinct characteristics within the API call sequences of different malware: (1) the API existence feature caused by frequent calls to the APIs with some special functions, and (2) the API transition feature caused by frequent calls to some special API subsequence patterns. Based on these two characteristics, this paper proposes MINES, a Multi-perspective apI call sequeNce bEhavior fuSion malware classification Method. Specifically, the API existence features from different perspectives are described by two graphs that model diverse rich and complex existence relationships between APIs, and we adopt the graph contrastive learning framework to extract the consistent shared API existence feature from two graphs. Similarly, the API transition features of different hops are described by the multi-order transition probability matrices. By treat each order as a channel, a CNN-based contrastive learning framework is adopted to extract the API transition feature. Finally, the two kinds of extracted features are fused to classify malware. Experiments on five datasets demonstrate the superiority of MINES over various state-of-the-arts by a large margin.

Assessing and gauging the carbon emission efficiency in China in accordance with the sustainable development goals

In light of the growing urgency of climate change, carbon emissions reduction has emerged as a pivotal concern within global governance. In this paper, we take carbon emission efficiency (CEE) as the research object to characterize the relationship between economic, social, and environmental development in the context of the Sustainable Development Goals (SDGs). According to the regional division standard of eight comprehensive economic zones in China, this paper analyzed the spatial differences, evolutionary characteristics, and influencing factors of CEE in 257 Chinese cities over the period 2003–2019. The analysis conducted the Dagum Gini Coefficient, Markov Transition Probability Matrix, and geographically and temporally weighted regression model (GTWR). The results demonstrate that: (1) The CEE of Chinese cities exhibits an upward trajectory. (2) The inter-differences among the eight comprehensive economic zones represent the primary spatial source of CEE divergence. (3) The CEE of Chinese cities is a staged process of gradual enhancement with spatial spillover effects. (4) Environmental regulation, energy consumption intensity, and green finances are significant factors affecting CEE, and the direction and intensity of their influence have distinct spatial heterogeneity. Ultimately, this paper proposes measures to narrow the development gap between regions and enhance the CEE across the region. Meanwhile, implementing regional refinement management and formulating differentiated regional sustainable development planning.

Topology sensing of FANET under missing data

The topological structure of a flying ad hoc network (FANET) is crucial to understand, explain, and predict the behavior of unmanned aerial vehicle (UAV) swarms. Most studies focusing on topology sensing use perfect observations and complete datasets. However, the received signal dataset, being non-cooperative, commonly encounters instances of missing data, causing the performance of the existing algorithms to degrade. We investigate the issue of topology sensing of FANET based on external observations and propose a topology sensing method for FANET with missing data while introducing link-prediction methods to correct the topology inference results. First, we employ multi-dimensional Hawkes processes to model the communication event sequence in the network. Subsequently, to solve the problem in which the binary decision threshold is difficult to determine and cannot be adapted to the application scenario, we propose an extended multi-dimensional Hawkes model suitable for FANET and use the maximum likelihood estimation method for topology inference. Finally, to solve the problem of the low accuracy of inference results owing to missing data, we perform community detection on the observation network and combine the community detection and inference results to construct a mixed connection probability matrix, based on which we perform topology correction. The results of the analysis show that the topology sensing method proposed in this study is robust against missing data, indicating that it is an effective solution for solving this problem.

Forecasting Using the Markov Chain Transition Matrix for Exchange Rate Fluctuations

The current research is preparing an economic statistical study on exchange rate fluctuations for the period from ( 1996 to mid-2005 ) according to the well-known phrase: (The present is the past and the future is the present ). It is a modest attempt to crystallize this type of price in a scientific-statistic method by adopting the matrix of transitional probabilities in Markov chains, as these chains are among the models that are relied upon in the process of forecasting when the data are in the present time and in three cases: - High - Low - Stability. Between the past, the present and the future, the researcher was able to reach in his research to the analysis by applying the method of the greatest places, and to achieve the main purpose of this research, the researcher dealt with four chapters as follows: The first chapter dealt with the problem of research, its importance, need, purpose and determination of its terms. The second chapter reviewed the previous studies published on the subject, as well as the theoretical aspect, in which the matrix of transitional and stable possibilities, the state of stability and independence of the Markov chains, and the estimation of transitional possibilities in the greatest possible way were presented. As for the third chapter, it included the practical aspect and the field application. The data related to the research procedures were collected from the date of (17/10/2003 to 30/6/2005), in which the Iraqi currency was exchanged from the old to the currency currently in circulation, and in which the situation of the Iraqi market suggested great relative stability at the time. Finally, the fourth chapter of this research included the conclusions reached by the researcher from which it came: The market was characterized by a state of stability after the rise in the exchange rate against the dollar, which confirmed the accuracy of the results of the matrix of transitional possibilities, which was reflected on the local stock exchange, as well as the development of recommendations that can be used by the relevant parties.

Analytic computation for stationary distributions of D-BMAP/D -MSP(a,b)/1 queueing system

ABSTRACT This paper analyses single server correlated batch arrival and correlated batch service queue with innumerable waiting space in discrete-time. The arrival and service processes are governed by discrete batch Markovian arrival process and discrete Markovian service process with general bulk service rule, respectively. Observing two consecutive random epochs, we construct general structure transition probability matrix and it is then reblocked to the desired M/G/1 structure. The UL-type RG-factorization approach combined with spectral expansion method is adopted to unravel the queue length distribution at random epoch. The relationships are undertaken to obtain the queue length distributions at pre-arrival, outside observer's, intermediate and post-departure epochs. Our most challenging effort is to derive the probability mass functions of waiting time and service batch size for arbitrary customer in an arriving batch. We address the warehouse management process for finished products from dealer to retailer as a potential practical use of our batch queue with correlation in both arrival and service, and provide the effect of our queueing behaviour in this application based on our analytical and computational investigation. Based on the implementation of parametrized numeric experiments with numerous categories, we impart our computational results to validate the analytical findings reported in this investigation.