Probability Matrix Research Articles

Sparse subspace clustering in diverse multiplex network model

The paper considers the DIverse MultiPLEx (DIMPLE) network model, where all layers of the network have the same collection of nodes and are equipped with the Stochastic Block Models. In addition, all layers can be partitioned into groups with the same community structures, although the layers in the same group may have different matrices of block connection probabilities. To the best of our knowledge, the DIMPLE model, introduced in Pensky and Wang (2021), presents the most broad SBM-equipped binary multilayer network model on the same set of nodes and, thus, generalizes a multitude of papers that study more restrictive settings. Under the DIMPLE model, the main task is to identify the groups of layers with the same community structures since the matrices of block connection probabilities act as nuisance parameters under the DIMPLE paradigm. The main contribution of the paper is achieving the strongly consistent between-layer clustering by using Sparse Subspace Clustering (SSC), the well-developed technique in computer vision. In addition, SSC allows to handle much larger networks than spectral clustering, and is perfectly suitable for application of parallel computing. Moreover, our paper is the first one to obtain precision guarantees for SSC when it is applied to binary data.

Building confidence: Developing image-based methods to incorporate fishery-collected data in the American lobster stock assessment

The American lobster, Homarus americanus, supports the most valuable single-species fishery in North America; however to-date, a reliable and robust method to determine age does not exist, and thus some of the more traditional catch-at-age stock assessment methods cannot be used to determine status. In lieu of this, the Atlantic States Marine Fisheries Commission’s American Lobster Stock Assessment Model uses a probabilistic growth transition matrix to determine how lobsters of different sizes will grow and recruit into the fishery. Developing and updating the growth transition matrix to reflect current growth dynamics requires estimates of molt increment and interval. Tagging studies are an inexpensive method to collect this type of information, but relying on fishing industry reported recapture data and buy-in can be challenging, resulting in varied return rates and uncertainty in measurement accuracy. Here, we report on a subset of recaptured lobsters released in the Gulf of Maine and Georges Bank regions between 2015 and 2020, where in addition to recapture locations, harvesters were encouraged to submit images of recaptured lobsters alongside a standard lobster gauge as a scale to estimate carapace length. Some fishermen were able to provide both direct measurements and images. Images were analyzed in ImageJ to estimate individual lobster carapace length (CL); and each image was assigned a quality score. For all groups, image-derived lengths were correlated with measured observations, regardless of the overall image quality, with only a slight underestimation at the maximum end of CL. This image-based method for length estimation provides high-quality length predictions regardless of image quality and can significantly increase the likelihood of harvesters contributing data with broad potential to engage commercial fisherman in collaborative science. Using this method we were able to expand the dataset of length records from this project by 251 or 33 %, providing additional data at a rate similar to tagging an additional 6000 lobsters.

Dynamics of nonlinear stochastic operators and associated Markov measures

The aim of this paper is to examine the stability of a class of nonlinear stochastic operators on a finite‐dimensional simplex. We identify a number of properties of the set of the class of stochastic operators, including the stability of each operator. We then use these operators to define non‐homogeneous Markov measures that rely on initial data and carry out an investigation into the absolute continuity and singularity of these measures.

Unsupervised detection of large-scale weather patterns in the northern hemisphere via Markov State Modelling: from blockings to teleconnections

Detecting recurrent weather patterns and understanding the transitions between such regimes are key to advancing our knowledge of the low-frequency variability of the atmosphere and have important implications in terms of weather and climate-related risks. We adopt an analysis pipeline inspired by Markov State Modelling and detect in an unsupervised manner the dominant winter mid-latitude Northern Hemisphere weather patterns in the Atlantic and Pacific sectors. The daily 500 hPa geopotential height fields are first classified in about 200 microstates. The weather dynamics are then represented on the basis of these microstates and the slowest decaying modes are identified from the spectral properties of the transition probability matrix. These modes are defined on the basis of the nonlinear dynamical processes of the system and not as tentative metastable states, as often done in Markov state analysis. When focusing on a shifting longitudinal window of 60∘, we find that the longitude-dependent estimate of the longest relaxation time is smaller where stronger baroclinic activity is found. In the Atlantic and Pacific sectors slow relaxation processes are mainly related to transitions between blocked regimes and zonal flow. We also find strong evidence of a dynamical regime associated with the simultaneous Atlantic-Pacific blocking. When the analysis is performed on a broader geographical region of the Atlantic sector, we discover that the slowest relaxation modes of the system are associated with transitions between dynamical regimes that resemble teleconnection patterns like the North Atlantic Oscillation and weather regimes like the Scandinavian and Greenland blocking, yet have a much stronger dynamical foundation than classical methods based e.g. on EOF analysis. Our method clarifies that, as a result of the lack of a time-scale separation in the atmospheric variability of the mid-latitudes, there is no clear-cut way to represent the atmospheric dynamics in terms of few, well-defined modes of variability. The approach proposed here can be seamlessly applied across different regions of the globe for detecting regional modes of variability, and has a great potential for intercomparing climate models and for assessing the impact of climate change on the low-frequency variability of the atmosphere.

Magic in generalized Rokhsar-Kivelson wavefunctions

Magic is a property of a quantum state that characterizes its deviation from a stabilizer state, serving as a useful resource for achieving universal quantum computation e.g., within schemes that use Clifford operations. In this work, we study magic, as quantified by the stabilizer Renyi entropy, in a class of models known as generalized Rokhsar-Kivelson systems, i.e., Hamiltonians that allow a stochastic matrix form (SMF) decomposition. The ground state wavefunctions of these systems can be written explicitly throughout their phase diagram, and their properties can be related to associated classical statistical mechanics problems, thereby allowing powerful analytical and numerical approaches that are not usually available in conventional quantum many body settings. As a result, we are able to express the SRE in terms of wave function coefficients that can be understood as a free energy difference of related classical problems. We apply this insight to a range of quantum many body SMF Hamiltonians, which affords us to study numerically the SRE of large high-dimensional systems, and in some cases to obtain analytical results. We observe that the behaviour of the SRE is relatively featureless across quantum phase transitions in these systems, although it is indeed singular (in its first or higher order derivative, depending on the nature of the transition). On the contrary, we find that the maximum of the SRE generically occurs at a cusp away from the quantum critical point, where the derivative suddenly changes sign. Furthermore, we compare the SRE and the logarithm of overlaps with specific stabilizer states, asymptotically realised in the ground state phase diagrams of these systems. We find that they display strikingly similar behaviors, which in turn establish rigorous bounds on the min-relative entropy of magic.

System reliability modeling and analysis for a marine power equipment operating in a discrete‐time dynamic environment

AbstractExploring on reliability modeling and analysis on a marine equipment in a dynamic environment is a meaningful and challenging issue, because the system commonly carries out the task at sea away from land and suffers a distinct influence of environment. Thus, a reliability model of a multi‐state repairable system operating in dynamic environment is developed by introducing the background of the marine power system in this paper. The novelty of the research lies in the modeling and computing methods are relatively innovative by employing the aggregated stochastic processes, Hadamard production and matrix‐analytic method. First, the working modes of the marine power system under several different kinds of conditions are introduced. Then, the evolution of both the system states and environment are described as discrete‐time Markov chains with multiple and different transition probability matrices. The failure probability and repair probability of components are also distinct in different environments. Furthermore, some performance indexes, especially the index relevant to the environment, are derived, respectively. Finally, the conclusion is obtained by a numerical example of the marine power system, which also illustrates the validity and applicability of the proposed model.

Finite-time asynchronous control for semi-Markov jump systems with random uncertainties and actuator faults

This article is aimed at studying the finite-time reliable asynchronous control issue for continuous semi-Markov jump systems (S-MJSs) with actuator failures and randomly occurring uncertainties (ROUs). To characterize the asynchronous phenomenon between the system mode and the controller mode, the mode detector approach via a hidden semi-Markov model (HSM) is adopted. The transition probability (TP) matrix of the HSM is nonhomogeneous, which can be provided by a polytopic structure. By resorting the mode-dependent Lyapunov function, sufficient conditions are attained to guarantee the stochastic finite-time boundedness (SFTB) and H∞ performance of the closed-loop system. Then, according to a skillful matrix inequality transforming method, the reliable asynchronous control law is constructed. Finally, a tunnel diode circuit system and a mass-spring-damper mechanical system are proposed to demonstrate the superiority, effectiveness and practicality of the developed design method.

Impact of Urban Expansion on Carbon Emissions in the Urban Agglomerations of Yellow River Basin, China

Continued urban expansion (UE) has long been regarded as a huge challenge for climate change mitigation. However, much less is known about how UE affects carbon emissions (CEs), especially in the urban agglomerations of the Yellow River Basin (UAYRB), China. In this regard, this study introduced kernel density analysis, the Gini coefficient, and Markov chains to reveal the UE patterns and carbon emissions intensity (CEI) in the UAYRB at the county level, and explored the spatial heterogeneity of the impact of UE on CEI with the geographically and temporally weighted regression model. The results show that both CEI and UE in the UAYRB showed a steady growing trend during the study period. The kernel density of CEI and UE revealed that CEI in the UAYRB was weakening, while the UE rate continuously slowed down. The Gini coefficients of both CEI and UE in the UAYRB region were at high levels, indicating obvious spatial imbalance. The Markov transfer probability matrix for CEI with a time span of five years showed that CEI growth will still occur over the next five years, while that of UE was more obvious. Meanwhile, counties with a regression coefficient of UE on CEI higher than 0 covered the majority, and the distribution pattern remained quite stable. The regression coefficients of different urban landscape metrics on CEI in the UAYRB varied greatly; except for the landscape shape index, the regression coefficients of the aggregation index, interspersion and juxtaposition index, and patch density overall remained positive. These findings can advance the policy enlightenment of the high-quality development of the Yellow River Basin.

Numerical solution for stochastic Volterra-Fredholm integral equations with delay arguments

We present a method for computing the stochastic operational matrix of integration to advance the study of stochastic Volterra-Fredholm integral equations (SVFIEs) based on delay arguments. First, the method evaluates the combined effects of the delay and its parameters on the accuracy improvement of the convergence rate. Our results can be applied to SVFIEs, with the operational delay matrices of the block pulse function simplified to algebraic ones. Numerical calculations were performed on a PC using Python 3 programs. Results also demonstrate the accuracy of approximate solutions; arithmetic operations are carried out without the need for derivation or integration.

An adaptive transition probability matrix with quality seeds for cellular automata models

ABSTRACT The cellular automata (CA) model is the predominant method for predicting land use and land cover (LULC) changes. The accuracy of this model critically depends on well-defined transition rules, which encapsulate the local dynamics of complex systems and facilitate the manifestation of organized global patterns. While current studies largely concentrate on land use transition matrices as core elements of these rules, exclusive reliance on these matrices is insufficient for capturing the full spectrum of land use change potential. Addressing this gap, our research introduces the adaptive transition probability matrix with quality seeds (ATPMS) model, which incorporates both the Markov model and the genetic algorithm (GA) into the traditional CA framework. Furthermore, an artificial neural network (ANN) is utilized to determine land suitability. Implemented in Beijing, Wuhan, and the Pearl River Delta (PRD), our results indicate that the ATPMS-ANN-CA model surpasses the standard Markov-ANN-CA model in various validation metrics, displaying improvements in overall accuracy (OA) by 0.03% to 0.74% and figure of merit (FoM) by 3.67% to 63.14%. Additionally, the ATPMS-ANN-CA model excels in providing detailed landscape analysis.

An iterated greedy algorithm with acceleration of job allocation probability for distributed heterogeneous permutation flowshop scheduling problem

Distributed manufacturing paradigm is becoming one of the dominant manufacturing models today. Heterogeneities between factories exist in fact due to the differences in process flexibility and machine performance. Most research focuses on identical distributed factories and overlooks the influence of heterogeneous factories on the subproblem of job allocation. This paper investigates a distributed heterogeneous permutation flowshop scheduling problem (DHPFSP) to minimize the makespan, and a mixed-integer linear programming (MILP) model is established. Building upon a special phenomenon of job assignment to a specific heterogeneous factory in DHPFSP, an iterated greedy algorithm with acceleration of job allocation probability (IGP) is proposed. To utilize this phenomenon, a job allocation probability matrix is introduced to describe the trend of job allocation, and a fast pass strategy with job allocation probability is suggested to speed up the algorithm search process. Furthermore, to generate a high-quality initial solution quickly for IGP, an NEH-based heuristic framework for distributed heterogeneous factory environment (NEHDHF) is proposed. In NEHDHF, several distinct initial job sequence generation strategies and a new first-f job allocation strategy are proposed for obtain a better initial solution. In computational experiments, there are 720 test instances designed and publicized. The IGP achieves 535 best solutions out of 720 instances. Statistically sound results demonstrate the effectiveness of the presented algorithms for the considered problem.

A hybrid estimation of distribution algorithm for solving assembly flexible job shop scheduling in a distributed environment

This paper proposes a novel distributed assembly flexible job shop scheduling problem (DAFJSP), which involves three stages: production stage, assembly stage, and delivery stage. The production stage is accomplished in a few flexible job shops, the assembly stage is accomplished in a few single-machine factories, and the delivery stage is to deliver the obtained products to the corresponding customers. To address the problem, a hybrid estimation of distribution algorithm based on differential evolution operator and variable neighborhood search (HEDA-DEV) is proposed with the goal of minimizing the total cost and tardiness. Firstly, a new multidimensional coding method is designed based on the features of the DAFJSP. Secondly, two mutation operators and the similarity coefficient based on the probability matrix are put forward to implement the dynamic mutation. Thirdly, five types of neighborhood structures satisfying cooperative search strategies are employed to adequately improve the local exploitation ability. Finally, the comparison experiment results suggest that the proposed HEDA-DEV has competitive performance compared to the selected efficient algorithms. Moreover, a real case study is used to demonstrate that HEDA-DEV is an effective method for solving DAFJSP.

Regular dynamics in a quadratic model

In the present paper, we consider a convex combination of non‐Volterra quadratic stochastic operators defined on a finite‐dimensional simplex depending on a parameter and study their trajectory behaviors. We showed that in the case depending on the parameter and an initial point, the trajectories of such operator converge to a fixed point. For , any trajectory of the operator converges to the center of the simplex.

Cloud Migration Strategies: Ensuring Seamless Integration and Scalability in Dynamic Business Environments

The migration of a company's information systems to a cloud platform is a crucial part of the transformation of IT infrastructure. However, due to the mixture of business goals and limitations in existing IT systems, the selection and realization of these goals is not a simple one. In this paper, we present a model describing the possibility of migrating business information systems into a cloud environment by following the stochastic model approach. By properly identifying and defining various process aspects, it is relatively simple to adapt analysis and limit the transition probability matrix to well-known stochastic models. Careful manipulation of such a matrix allows using standard formulas for scaling discrete event systems to solve cloud migration problems. A detailed case study with simulation results, pointing to some of the practical limitations of the model, is presented at the end of this paper.

Математическая модель сопутствующей деятельности пилота и ее применение для объективной оценки его состояния и профессиональной подготовки

<p>A new approach to analysis and diagnostics of the pilots’ activities is presented, which makes it possible to compare both different options of the aircraft cockpit information and control field and the professional training of flight personnel from the viewpoint of application effectiveness. A mathematical model of the associated activities in use represents the pilot work via the matrix of transition probabilities, where transitions occur between the operations he performs. The approach under consideration is based on the convolution of the applied Markovian processes, which are created using the pilot activity protocols, into the quantum representations, making it possible to reveal the structure of these processes by the quantum spectral analysis. Application of the quantum filtering makes it possible to obtain quantitative diagnostic assessments of the pilot activity. Analysis of the experimental results for pilots of various training levels is given to demonstrate the possibility for assessing their professional skills as well as the prospects for using the proposed methods.</p>

Ideal lattices in semigroup of doubly stochastic matrices

In this paper, we illustrate the rule for finding number of idempotents in the doubly stochastic matrix semigroup [Formula: see text] and also locate the idempotents in the case of [Formula: see text] and [Formula: see text]. Further, we describe idempotent generated ideals of these semigroups and it is shown that the idempotent generated ideals form a lattice.

Detecting Overlapping Communities Based on Influence-Spreading Matrix and Local Maxima of a Quality Function

Community detection is a widely studied topic in network structure analysis. We propose a community detection method based on the search for the local maxima of an objective function. This objective function reflects the quality of candidate communities in the network structure. The objective function can be constructed from a probability matrix that describes interactions in a network. Different models, such as network structure models and network flow models, can be used to build the probability matrix, and it acts as a link between network models and community detection models. In our influence-spreading model, the probability matrix is called an influence-spreading matrix, which describes the directed influence between all pairs of nodes in the network. By using the local maxima of an objective function, our method can standardise and help in comparing different definitions and approaches of community detection. Our proposed approach can detect overlapping and hierarchical communities and their building blocks within a network. To compare different structures in the network, we define a cohesion measure. The objective function can be expressed as a sum of these cohesion measures. We also discuss the probability of community formation to analyse a different aspect of group behaviour in a network. It is essential to recognise that this concept is separate from the notion of community cohesion, which emphasises the need for varying objective functions in different applications. Furthermore, we demonstrate that normalising objective functions by the size of detected communities can alter their rankings.

Applying Theorem of Ross to Transition Probability Matrix in Energy Options Pricing after Political Tensions and Russia-Ukraine Conflict

Probability Matrix, it is necessary to obtain energy options pricing. The paper found the true probabilities of transition from the current state of the market to other states. The energy options pricing including effects of Political tensions is proposed. The methods are based on true probabilities of transition to the next state of the energy market. It can be used to predict the movement of the underlying asset of energy options (oil and gas derivatives pricing). For example, one strategy might be to compare the energy sources at the beginning 2022 (before 24.02.2024) with the current state of the market. The results show that this matrix can be implemented in energy options pricing, which represents the true probabilities of transition from the current state of the market to modern state. Practical implementation is an investment strategy in oil and gas futures that should include the median of a given distribution with the current state of the market after beginning of Russia-Ukraine conflict. The absence of arbitrage opportunities is a fundamental principle underlying modern financial pricing theory. This concept is peculiar to the statement of the fundamental theorem of asset pricing. The results prove idea that at a fixed point in time is the information about some market quotations of American Call options can be determined. The results have a set of quotes that are available in both directions: both for strikes and for periods to maturity.

Stochastic \({p}\)th Root Approximation of a Stochastic Matrix: A Riemannian Optimization Approach

Stochastic \({p}\)th Root Approximation of a Stochastic Matrix: A Riemannian Optimization Approach

Spectral Properties of Mimetic Operators for Robust Fluid–Structure Interaction in the Design of Aircraft Wings

This paper presents a comprehensive study on the spectral properties of mimetic finite-difference operators and their application in the robust fluid–structure interaction (FSI) analysis of aircraft wings under uncertain operating conditions. By delving into the eigenvalue behavior of mimetic Laplacian operators and extending the analysis to stochastic settings, we develop a novel stochastic mimetic framework tailored for addressing uncertainties inherent in the fluid dynamics and structural mechanics of aircraft wings. The framework integrates random matrix theory with mimetic discretization methods, enabling the incorporation of uncertainties in fluid properties, structural parameters, and coupling conditions at the fluid–structure interface. Through spectral and localization analysis of the coupled stochastic mimetic operator, we assess the system’s stability, sensitivity to perturbations, and computational efficiency. Our results highlight the potential of the stochastic mimetic approach for enhancing reliability and robustness in the design of aircraft wings, paving the way for optimization algorithms that integrate uncertainties directly into the design process. Our findings reveal a significant impact of stochastic perturbations on the spectral radius and eigenfunction localization, indicating heightened system sensitivity. The introduction of randomized singular value decomposition (RSVD) within our framework not only enhances computational efficiency but also preserves accuracy in low-rank approximations, which is critical for handling large-scale systems. Moreover, Monte Carlo simulations validate the robustness of our stochastic mimetic framework, showcasing its efficacy in capturing the nuanced dynamics of FSI under uncertainty. This study contributes to the fields of numerical methods and aerospace engineering by offering a rigorous and scalable approach for conducting uncertainty-aware FSI analysis, which is crucial for the development of safer and more efficient aircraft.