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We investigate the problem of detecting the distributed targets buried in the Gaussian noise whose covariance matrix is unknown when signal mismatch occurs. The idea is to add a fictitious signal under the null hypothesis of the origin detection problem so that when signal mismatch occurs, the fictitious signal captures the mismatched signals, thus making the null hypothesis more plausible. More precisely, the fictitious signal is modeled as a Gaussian component with a covariance matrix of a stochastic factor multiplied by a rank-one matrix. The generalized likelihood ratio test (GLRT) is employed to address the modification detection problem. We present an exhaustive derivation of the detector and prove that it possesses the constant false alarm rate (CFAR) property. The performance analysis demonstrates the effectiveness of the proposed detector. When the SNR is 23 dB, as generalized cosine squared decreases from 1 to 0.83, the detection probability of the proposed GLRT-SL drops to 0.65, exhibiting the fastest decline compared to the G-ABORT-HE, which falls to 0.98, and the GW-ABORT-HE, which decreases to 0.85. [ABSTRACT FROM AUTHOR]

This paper offers several new sufficient conditions of the partial moment stability of linear hybrid stochastic systems with delay. Despite its potential applications in economics, biology and physics, this problem seems to have not been addressed before. A number of general theorems on the partial moment stability of stochastic hybrid systems are proven herein by applying a specially designed regularization method, based on the connections between Lyapunov stability and input-to-state stability, which are well known in control theory. Based on the results obtained for stochastic hybrid systems, some new conditions of the partial stability of deterministic hybrid systems are derived as well. All stability conditions are conveniently formulated in terms of the coefficients of the systems. A numerical example illustrates the feasibility of the suggested framework. [ABSTRACT FROM AUTHOR]

We consider an irreducible discrete-time Markov process with states represented as (k, i) where k is an M-dimensional vector with non-negative integer entries, and i indicates the state (phase) of the external environment. The number n of phases may be either finite or infinite. One-step transitions of the process from a state (k, i) are limited to states (n, j) such that n ≥ k−1, where 1 represents the vector of all 1s. We assume that for a vector k ≥ 1, the one-step transition probability from a state (k, i) to a state (n, j) may depend on i, j, and n − k, but not on the specific values of k and n. This process can be classified as a Markov chain of M/G/1 type, where the minimum entry of the vector n defines the level of a state (n, j). It is shown that the first passage distribution matrix of such a process, also known as the matrix G, can be expressed through a family of nonnegative square matrices of order n, which is a solution to a system of nonlinear matrix equations. [ABSTRACT FROM AUTHOR]

Numerous algorithms have been proposed to infer the underlying structure of the social networks via observed information propagation. The previously proposed algorithms concentrate on inferring accurate links and neglect preserving the essential topological properties of the underlying social networks. In this paper, we propose a novel method called DANI to infer the underlying network while preserving its structural properties. DANI is constructed using the Markov transition matrix, which is derived from the analysis of time series cascades and the observation of node-node similarity in cascade behavior from a structural perspective. The presented method has linear time complexity. This means that it increases with the number of nodes, cascades, and the square of the average length of cascades. Moreover, its distributed version in the MapReduce framework is scalable. We applied the proposed approach to both real and synthetic networks. The experimental results indicated DANI exhibits higher accuracy and lower run time compared to well-known network inference methods. Furthermore, DANI preserves essential structural properties such as modular structure, degree distribution, connected components, density, and clustering coefficients. Our source code is available on GitHub (https://github.com/AryanAhadinia/DANI). [ABSTRACT FROM AUTHOR]

In this paper, a new micromechanical hysteresis loop constitutive model of C/SiC composites with different interphases was developed considering the probabilistic‐statistical matrix fragmentation process. The lengths of matrix fragmentation were divided into three types, that is, long matrix fragments (LMFs), medium matrix fragments (MMFs), and short matrix fragments (SMFs). The distributions of the LMFs, MMFs, and SMFs with increasing tensile stress were determined using the probabilistic‐stochastic model by assuming the two‐parameter matrix strength distribution. The micro stress field of the LMFs, MMFs, and SMFs upon unloading and reloading was obtained and adopted to determine the corresponding stress‐strain relations. The interaction of matrix fragmentation lengths, especially for the LMFs with large debonding energy (LDE) and SMFs, was considered in the closed‐form constitutive model and hysteresis‐based inverse tangent modulus (ITMs) damage parameter. Synergistic effects of the fiber volumes, peak stresses, and interface debonding energy on the interface damage state, mechanical hysteresis loops, and related ITMs with small debonding energy and LDE were also analyzed. Comparisons of the mechanical hysteresis loops using the new hysteresis models considering matrix stochastic fragmentation and hysteresis models considering constant matrix fragmentation were also discussed. Experimental cyclic tensile hysteresis loops and unloading/reloading ITMs of C/(PyC)/SiC and C/(PyC+SiC)/SiC composites with different interphase thickness (i.e., t = 300, 600, 1000, and 2000 nm) were predicted using the developed constitutive model. Evolution of the unloading/reloading interface slip ratio was analyzed for different tensile peak stresses. [ABSTRACT FROM AUTHOR]

Existing methods for detecting communities in attributed social networks often rely solely on network topology, which leads to suboptimal accuracy in community detection, inefficient use of available data, and increased time required for identifying groups. This paper introduces the Dual Embedding-based Graph Convolution Network (DEGCN) to address these challenges. This new method uses graph embedding techniques in a new deep learning framework to improve accuracy and speed up community detection by combining the nodes' content with the network's topology. Initially, we compute the modularity and Markov matrices of the input graph. Each matrix is then processed through a graph embedding network with at least two layers to produce a condensed graph representation. As a result, a multilayer perceptron neural network classifies each node's community based on these generated embeddings. We tested the suggested method on three standard datasets: Cora, CiteSeer, and PubMed. Then, we compared the outcomes to many basic and advanced approaches using five important metrics: F1-score, adjusted rand index (ARI), normalized mutual information (NMI), and accuracy. The findings demonstrate that the DEGCN accurately captures community structure, achieves superior precision, and has higher ARI, NMI, and F1 scores, significantly outperforming existing algorithms for identifying community structures in medium-scale networks. [ABSTRACT FROM AUTHOR]

This work addresses the discrete-time containment control problem for first-order and second-order systems, incorporating position constraints, nonuniform time delays, and switching topologies. Projection operators are introduced to maintain agent states within the position constraints. Then, model transformation methods, along with stochastic properties of matrices, are employed to handle coupled nonlinearities stemming from position constraints and time delays. By using local information, distributed projection-based control schemes are proposed for multi-agent systems. Theoretical analysis shows that all followers ultimately converge into the convex hull spanned by leaders if the union of the communication topologies contains a directed spanning tree within each specified time interval. Finally, the theoretical results are verified by numerical simulations. • Containment control is studied for systems with constraints, delays, and switching. • A projection-based algorithm improves convergence to the leader-forming convex hull. • Model transformation is used to eliminate effects of non-uniform communication delays. • Numerical simulations validate the theoretical results. [ABSTRACT FROM AUTHOR]

Eradicating feral pigs from island ecosystems can assist in restoring damaged biodiversity values and protect commercial industries such as agriculture. Although many feral pig eradications have been attempted, management decisions are often led by practitioner experience rather than empirical evidence. Few interventions have been guided by population models to identify harvest intensity necessary to achieve eradication within a specified time frame, nor have they applied data on control effort and costs to evaluate the relative cost‐effectiveness of proposed control strategies. We used effort and cost data from a feral pig‐control program on Kangaroo Island, South Australia, over 17 months to derive functional‐response relationships between control effort (in hours per pig) and pig abundance for four control methods: (1) ground‐based shooting, (2) trapping with remote triggers, (3) poison baiting, and (4) thermal‐assisted aerial culling. We developed a stochastic Leslie matrix with compensatory density feedback on survival to project population trajectories from an initial population (N0) of 250 female pigs with an estimated island‐wide carrying capacity (K) of 2500 over 3 and 10 years for populations subjected to an annual harvest of 35%–95%. We built functional‐response models to calculate annual effort and cost for six cull scenarios across all harvest rates. We derived total cost and effort over 3‐ and 10‐year projections from the sum of annual cost and effort within the projection intervals. Pig populations were reduced to <10% N0 based on harvest rates >80% and 60% for culls of 3‐ and 10‐year durations, respectively. In all scenarios above, the minimum required harvest rate and the total cost to reduce population to ≤10% of N0 decreased with increasing harvest proportion, with lower total costs incurred over 3 years compared to 10 years. The simulations suggest that the most cost‐effective approach for most scenarios is to maximize annual harvest and complete eradication effort over the shortest periods. [ABSTRACT FROM AUTHOR]

Background: This article applies a variant of the Markov chain that explicitly incorporates spatial effects. It is an extension of the Markov class allowing a more complete analysis of the spatial dimensions of transition dynamics. The aim is to provide a methodology for applying the explicit model to spatial dependency analysis. Methods: Here, the question is to study and quantify whether neighborhood context affects transitional dynamics. Rather than estimating a homogeneous law, the model requires the estimation of k transition laws each dependent on spatial neighbor state. This article used published data on confirmed cases of Covid'19 in the 22 regions of Madagascar. These data were discretized to obtain a discrete state of propagation intensity. Results: The analysis gave us the transition probabilities between Covid'19 intensity states knowing the context of neighboring regions, and the propagation time laws knowing the spatial contexts. The results showed that neighboring regions had an effect on the propagation of Covid'19 in Madagascar. Conclusion: After analysis, we can say that there is spatial dependency according to these spatial transition matrices. [ABSTRACT FROM AUTHOR]

The article "Commentary: Accelerating spiking neural network simulations with PymoNNto and PymoNNtorch" published in Frontiers in Neuroinformatics compares different simulators for spiking neural networks. The study reveals that discrepancies in firing rates between simulators are due to the use of an unsuitable numerical integration method. The analysis confirms that only NEST simulator accurately simulates the model mathematically. The study also uncovers a subtle bug in NESTML and emphasizes the importance of precise benchmarks in simulation studies. [Extracted from the article]

In the present study, an effort was made to determine the effects of a porous matrix with different viscosities on the dynamic and static behaviors of rough short journal bearings taking into account the action of a squeezing film under varying loads without journal rotation. The micropolar fluid was regarded as a lubricant that contained microstructure additives in both the porous region and the film region. By applying Darcy's law for micropolar fluids through a porous matrix and stochastic theory related to uneven surfaces, a standardized Reynolds-type equation was extrapolated. Two scenarios with a stable and an alternating applied load were analyzed. The impacts of variations in viscosity, the porous medium, and roughness on a short journal bearing were examined. We inspected the dynamic and static behaviors of the journal bearing. We found that the velocity of the journal center with a micropolar fluid decreased when there was a cyclic load, and the impact of variations in the viscosity and porous matrix diminished the load capacity and pressure in the squeeze film and increased the velocity of the journal center. [ABSTRACT FROM AUTHOR]

Given a nonnegative matrix A=(Aij) , the matrix scaling problem asks whether A can be scaled to a doubly stochastic matrix D1AD2 for some positive diagonal matrices D1, D2. The Sinkhorn algorithm is a simple iterative algorithm, which repeats row-normalization Aij←Aij/∑jAij and column-normalization Aij←Aij/∑iAij alternatively. By this algorithm, A converges to a doubly stochastic matrix in limit if and only if the bipartite graph associated with A has a perfect matching. This property can decide the existence of a perfect matching in a given bipartite graph G, which is identified with the 0, 1-matrix AG. Linial et al. (2000) showed that O(n2log n) iterations for AG decide whether G has a perfect matching. Here, n is the number of vertices in one of the color classes of G. In this paper, we show an extension of this result. If G has no perfect matching, then a polynomial number of the Sinkhorn iterations identifies a Hall blocker—a vertex subset X having neighbors Γ(X) with |X|>|Γ(X)| , which is a certificate of the nonexistence of a perfect matching. Specifically, we show that O(n2log n) iterations can identify one Hall blocker and that further polynomial iterations can also identify all parametric Hall blockers X of maximizing (1−λ)|X|−λ|Γ(X)| for λ∈[0,1]. The former result is based on an interpretation of the Sinkhorn algorithm as alternating minimization for geometric programming. The latter is on an interpretation as alternating minimization for Kullback–Leibler (KL) divergence and on its limiting behavior for a nonscalable matrix. We also relate the Sinkhorn limit with parametric network flow, principal partition of polymatroids, and the Dulmage–Mendelsohn decomposition of a bipartite graph. Funding: K. Hayashi was supported by the Japan Society for the Promotion of Science [Grant JP19J22605]. H. Hirai was supported by Precursory Research for Embryonic Science and Technology [Grant JPMJPR192A]. [ABSTRACT FROM AUTHOR]

Featured Application: This study can be used for navigation operations of agricultural equipment or vehicles in farm environments. Due to the limitations of low coverage, high repetition rate, and slow convergence speed of the basic genetic algorithm (GA) in robot complete coverage path planning, the state transition matrix of the Markov chain is introduced to guide individual mutation based on the genetic mutation path planning algorithm, which can improve the quality of population individuals, enhancing the search ability and convergence speed of the genetic algorithm. The proposed improved genetic algorithm is used for complete coverage path planning simulation analysis in different work areas. The analysis results show that compared to traditional genetic algorithms, the improved genetic algorithm proposed in this paper reduces the average path length by 21.8%, the average number of turns by 6 times, the repetition rate by 83.8%, and the coverage rate by 7.76% in 6 different work areas. The results prove that the proposed improved genetic algorithm is applicable in complete coverage path planning. To verify whether the Markov chain genetic algorithm (MCGA) proposed is suitable for agricultural robot path tracking and operation, it was used to plan the path of an actual land parcel. An automatic navigation robot can track the planned path, which can verify the feasibility of the MCGA proposed. [ABSTRACT FROM AUTHOR]

Despite the availability of electronic navigators and automated vehicles, static wayfinding instructions remain widely used due to their resistance to signal disturbances, as well as their economic and environmental advantages over electronic signs. To investigate the impact of static wayfinding on the network cost and flow distribution, this paper presents an efficient method for updating the incident matrix and extends the stochastic user equilibrium (SUE) framework to incorporate static wayfinding instructions by using the generalized nested logit (GNL) choice model to represent user behavior. The SUE principle relaxes the assumption that users possess perfect knowledge of traffic conditions and always choose the optimal link to minimize their costs. The GNL model improves generalization performance of the cross-nested logit (CNL) model while solving the overlap problem of the multinomial logit (MNL) model. The disaggregate simplicial decomposition (DSD) algorithm is applied to solve proposed user equilibrium by iteratively finding decent directions through an auxiliary solution and determining step size using different methods. The results indicate that the self-regulated averaging (SRA) method can solve the proposed model efficiently. Additionally, increasing travel time cost on guided links and even outer links can be potential influences caused by static wayfinding instructions. The study results can assist decision-makers in quantitatively assessing the value of placing static wayfinding instructions at certain locations and choosing effective layout information. [ABSTRACT FROM AUTHOR]

In recent years, the non-invasive load monitoring (NILM) method based on sparse coding has shown promising research prospects. This type of method learns a sparse dictionary for each monitoring target device, and it expresses load decomposition as a problem of signal reconstruction using dictionaries and sparse vectors. The existing NILM methods based on sparse coding have problems such as inability to be applied to multi-state and time-varying devices, single-load characteristics, and poor recognition ability for similar devices in distributed manners. Using the analysis above, this paper focuses on devices with similar features in households and proposes a distributed non-invasive load monitoring method using Karhunen–Loeve (KL) feature extraction and an improved deep dictionary. Firstly, Karhunen–Loeve expansion (KLE) is used to perform subspace expansion on the power waveform of the target device, and a new load feature is extracted by combining singular value decomposition (SVD) dimensionality reduction. Afterwards, the states of all the target devices are modeled as super states, and an improved deep dictionary based on the distance separability measure function (DSM-DDL) is learned for each super state. Among them, the state transition probability matrix and observation probability matrix in the hidden Markov model (HMM) are introduced as the basis for selecting the dictionary order during load decomposition. The KL feature matrix of power observation values and improved depth dictionary are used to discriminate the current super state based on the minimum reconstruction error criterion. The test results based on the UK-DALE dataset show that the KL feature matrix can effectively reduce the load similarity of devices. Combined with DSM-DDL, KL has a certain information acquisition ability and acceptable computational complexity, which can effectively improve the load decomposition accuracy of similar devices, quickly and accurately estimating the working status and power demand of household appliances. [ABSTRACT FROM AUTHOR]

Accurate forecasting of high-resolution particulate matter 2.5 (PM2.5) levels is essential for the development of public health policy. However, datasets used for this purpose often contain missing observations. This study presents a two-stage approach to handle this problem. The first stage is a multivariate spatial time series (MSTS) model, used to generate forecasts for the sampled spatial units and to impute missing observations. The MSTS model utilizes the similarities between the temporal patterns of the time series of the spatial units to impute the missing data across space. The second stage is the high-resolution prediction model, which generates predictions that cover the entire study domain. The second stage faces the big N problem giving rise to complex memory and computational problems. As a solution to the big N problem, we propose a Gaussian Markov random field (GMRF) for innovations with the Matérn covariance matrix obtained from the corresponding Gaussian field (GF) matrix by means of the stochastic partial differential equation (SPDE) method and the finite element method (FEM). For inference, we propose Bayesian statistics and integrated nested Laplace approximation (INLA) in the R-INLA package. The above approach is demonstrated using daily data collected from 13 PM2.5 monitoring stations in Jakarta Province, Indonesia, for 1 January–31 December 2022. The first stage of the model generates PM2.5 forecasts for the 13 monitoring stations for the period 1–31 January 2023, imputing missing data by means of the MSTS model. To capture temporal trends in the PM2.5 concentrations, the model applies a first-order autoregressive process and a seasonal process. The second stage involves creating a high-resolution map for the period 1–31 January 2023, for sampled and non-sampled spatiotemporal units. It uses the MSTS-generated PM2.5 predictions for the sampled spatiotemporal units and observations of the covariate's altitude, population density, and rainfall for sampled and non-samples spatiotemporal units. For the spatially correlated random effects, we apply a first-order random walk process. The validation of out-of-sample forecasts indicates a strong model fit with low mean squared error (0.001), mean absolute error (0.037), and mean absolute percentage error (0.041), and a high R² value (0.855). The analysis reveals that altitude and precipitation negatively impact PM2.5 concentrations, while population density has a positive effect. Specifically, a one-meter increase in altitude is linked to a 7.8% decrease in PM2.5, while a one-person increase in population density leads to a 7.0% rise in PM2.5. Additionally, a one-millimeter increase in rainfall corresponds to a 3.9% decrease in PM2.5. The paper makes a valuable contribution to the field of forecasting high-resolution PM2.5 levels, which is essential for providing detailed, accurate information for public health policy. The approach presents a new and innovative method for addressing the problem of missing data and high-resolution forecasting. [ABSTRACT FROM AUTHOR]

Background: Traditional recombinant inbred lines (RILs) are generated from repeated self-fertilization or brother-sister mating from the F1 hybrid of two inbred parents. Compared with the F2 population, RILs cumulate more crossovers between loci and thus increase the number of recombinants, resulting in an increased resolution of genetic mapping. Since they are inbred to the isogenic stage, another consequence of the heterozygosity reduction is the increased genetic variance and thus the increased power of QTL detection. Self-fertilization is the primary form of developing RILs in plants. Brother-sister mating is another way to develop RILs but in small laboratory animals. To ensure that the RILs have at least 98% of homozygosity, we need about seven generations of self-fertilization or 20 generations of brother-sister mating. Prior to homozygosity, these lines are called pre-recombinant inbred lines (PRERIL). Phenotypic values of traits in PRERILs are often collected but not used in QTL mapping. To perform QTL mapping in PRERILs, we need the recombination fraction between two markers at generation t for t < 7 (selfing) or t < 20 (brother-sister mating) so that the genotypes of QTL flanked by the markers can be inferred. Results: In this study, we developed formulas to calculate the recombination fractions of PRERILs at generation t in self-fertilization, brother-sister mating, and random mating. In contrast to existing works in this topic, we used computer code to construct the transition matrix to form the Markov chain of genotype array between consecutive generations, the so-called recurrent equations. Conclusions: We provide R functions to calculate the recombination fraction using the newly developed recurrent equations of ordered genotype array. With the recurrent equations and the R code, users can perform QTL mapping in PRERILs. Substantial time and effort can be saved compared with QTL mapping in RILs. [ABSTRACT FROM AUTHOR]

The purpose of this article is to develop the receding horizon (RH) estimation for multi‐rate sampled systems with measurement delays and packet losses in the measurements. An event‐triggered transmission scheme is introduced to remove measurements that are unnecessary for the design of the estimator. The stochastic diagonal matrixes are introduced to represent the phenomenon of packet losses, where each component is subject to an individual Bernoulli process. The original system is firstly transformed into a delay‐free one by using the reorganized observation method. Further, a batch form and an iterative form of RH estimation are proposed by minimizing a given cost function that includes some terminal weighting terms based on the new system. The stability of the proposed RH estimation is guaranteed by the natural assumptions and a simulation instance is given to verify the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This article examines the stability properties of linear stochastic difference equations with delays. For this purpose, a novel approach is used that combines the theory of inverse-positive matrices and the asymptotic methods developed by N.V. Azbelev and his students for deterministic functional differential equations. Several efficient conditions for p-stability and exponential p-stability (2 ≤ p < ∞) of systems of linear Itô-type difference equations with delays and random coefficients are found. All results are conveniently formulated in terms of the coefficients of the equations. The suggested examples illustrate the feasibility of the approach. [ABSTRACT FROM AUTHOR]

The fact that the famous basic reproduction number R 0 , i.e., the largest eigenvalue of the next generation matrix F V − 1 , sometimes has a probabilistic interpretation is not as well known as it deserves to be. It is well understood that half of this formula, − V , is a Markovian generating matrix of a continuous-time Markov chain (CTMC) modeling the evolution of one individual on the compartments. It has also been noted that the not well-enough-known rank-one formula for R 0 of Arino et al. (2007) may be interpreted as an expected final reward of a CTMC, whose initial distribution is specified by the rank-one factorization of F. Here, we show that for a large class of ODE epidemic models introduced in Avram et al. (2023), besides the rank-one formula, we may also provide an integral renewal representation of R 0 with respect to explicit "age kernels" a (t) , which have a matrix exponential form.This latter formula may be also interpreted as an expected reward of a probabilistic continuous Markov chain (CTMC) model. Besides the rather extensively studied rank one case, we also provide an extension to a case with several susceptible classes. [ABSTRACT FROM AUTHOR]

The Shaanxi section is the central region of the Loess Plateau. Its unique wetland environment plays an indispensable role in regional ecological environment security. Clarifying the characteristics of wetland changes in the region is an important prerequisite for wetland management and protection. This study, based on the remote sensing data of the Shaanxi section of the Loess Plateau, analyzed the changes in the wetland area and type transfer in this region in 1980, 1990, 2000, 2010 and 2020 using the wetland dynamic degree model, the Markov transfer matrix, the landscape pattern index, and centroid analysis. The results showed that, from 1980 to 2020, the total wetland area and natural wetland area in the Shaanxi section of the Loess Plateau continued to shrink, decreasing by 79.35 km2 and 80.50 km2, respectively, while the artificial wetland area increased by 1.14 km2. Among the regions, Xi'an experienced the most significant reduction, with a total decrease of 83.04 km2 over 40 years, followed by Xianyang City, where the wetland area decreased by 6.50 km2. In contrast, the wetland areas of Yulin City, Weinan City, Yan'an City, Baoji City and Tongchuan City increased slightly. From 1980 to 2020, the change in the wetland types in the Shaanxi section of the Loess Plateau was mainly characterized by transfers between beach lands and river canals. River canals are the primary type of wetland in this region. The degree of fragmentation is the highest in reservoir potholes, while marshes have the largest clumpiness index. Over the same period, the centroid of the wetlands in the Shaanxi section of the Loess Plateau moved from south to north as a whole, although, between 1990 and 2000, the centroid position remained relatively stable. These results provide a theoretical basis and data support for wetland monitoring and protection in the Shaanxi section of the Loess Plateau and also provide a reference for the protection and sustainable development of other inland wetland resources in arid and semi-arid regions. [ABSTRACT FROM AUTHOR]

Understanding the regional disparities, dynamic evolution, and convergence–divergence characteristics of global agricultural energy efficiency is crucial for enhancing agricultural energy efficiency, ensuring food security, and responding to global green development trends. This paper utilizes 2002–2021 panel data from 144 countries globally, employing the epsilon-based measure–global Malmquist–Luenberger (EBM-GML) model to estimate agricultural energy efficiency, considering unexpected output. The Dagum Gini coefficient, kernel density estimation, spatial Markov matrix, and spatial convergence model are employed to explain the spatial patterns and evolving trends of global and regional agricultural energy efficiency at three levels: regional disparities, dynamic evolution, and convergence. The results indicate significant spatial heterogeneity in global agricultural energy efficiency, with Europe exhibiting the highest efficiency, followed by Asia and the Americas, while Oceania and Africa demonstrate the lowest efficiency. Agricultural energy efficiency globally and in each region continues to improve, with increasing regional disparities, and difficulties in grade transitions in agricultural energy efficiency across regions. Each region exhibits β-convergence characteristics, but the convergence rates vary, and various factors influence growth rates of agricultural energy efficiency differently across regions. Therefore, countries should tailor their strategies based on local conditions, considering their own resource endowments and developmental stages, and strengthen international exchanges and cooperation. [ABSTRACT FROM AUTHOR]

Simple Summary: In scRNA-seq analysis, diffusion-based approaches help identify the connections between cells, allowing us to observe the progression of individual cells as they change phenotypes within a mathematical space known as a manifold. Recently, these approaches have been used as a reference for imputation, a technique that addresses missing data, a common challenge in scRNA-seq analysis. For example, MAGIC is a popular diffusion-based imputation method, and it has shown success in uncovering gene–gene interactions related to phenotypic transitions that would not be possible without imputation. However, previous evaluations have not adequately compared the impact of different parameter settings on MAGIC, particularly over-smoothing issues. To address this, we developed sc-PHENIX, which utilizes a similar diffusion approach as MAGIC but incorporates a PCA-UMAP initialization step, whereas MAGIC only uses PCA. We compared sc-PHENIX and MAGIC in terms of imputation accuracy, visualization, biological insights, and preservation of data structure. Our findings show that sc-PHENIX outperforms MAGIC across various common parameters such as "diffusion time" (t), the number of nearest neighbors (knn), and PCA dimensions. It effectively captures and preserves the global, local, and continuous data structures, leading to more reliable imputation and potentially uncovering new biological insights in diverse datasets. Single-cell transcriptomics (scRNA-seq) is revolutionizing biological research, yet it faces challenges such as inefficient transcript capture and noise. To address these challenges, methods like neighbor averaging or graph diffusion are used. These methods often rely on k-nearest neighbor graphs from low-dimensional manifolds. However, scRNA-seq data suffer from the 'curse of dimensionality', leading to the over-smoothing of data when using imputation methods. To overcome this, sc-PHENIX employs a PCA-UMAP diffusion method, which enhances the preservation of data structures and allows for a refined use of PCA dimensions and diffusion parameters (e.g., k-nearest neighbors, exponentiation of the Markov matrix) to minimize noise introduction. This approach enables a more accurate construction of the exponentiated Markov matrix (cell neighborhood graph), surpassing methods like MAGIC. sc-PHENIX significantly mitigates over-smoothing, as validated through various scRNA-seq datasets, demonstrating improved cell phenotype representation. Applied to a multicellular tumor spheroid dataset, sc-PHENIX identified known extreme phenotype states, showcasing its effectiveness. sc-PHENIX is open-source and available for use and modification. [ABSTRACT FROM AUTHOR]

The need to replace nonrenewable sources is a global challenge, especially for emerging countries with financial constraints to invest in energy transition. In Brazil, electrical generation is predominantly renewable, since the hydraulic source is responsible for more than half of the domestic electricity supply. Other alternative sources, such as biomass, solar, and wind, complement the renewable portion of the Brazilian electrical matrix. However, periods of drought and climate disturbances threaten the stability of the electrical system and increase dependence on thermal generation. Based on the global movement to intensify the use of renewable sources, which are volatile and influenced by climate variations, the objective of this research is to predict electricity generation using the Heston model. This model, originally applied to predict option prices, assumes nonconstant volatility and has the ability to estimate the average value including the stochastic volatility process. The database is made up of monthly values of the volume of electrical energy generation from biomass, coal, fuel oil, hydraulic, industrial waste, natural gas, nuclear, solar, and wind sources. Compared to the Black‐Scholes model, the chosen method proved to be superior in predicting the generation from coal, hydropower, and solar energy, according to the MAE, MAPE, and RMSE statistics. We conclude that a financial model can be effectively applied to the energy sector and the Heston model can be a useful instrument to assist in the planning and management of the national electrical system. One suggestion for the Brazilian case is to encourage the use of alternative energies and low‐carbon sources, such as solar, wind, and natural gas, providing greater energy security and a more reliable electrical system. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Agricultural ecological efficiency is an important tool with which to measure the coordination of the sustainable development of agricultural economies and ecological environments. In this paper, a super-efficiency slacks-based measures model was used to measure the agricultural ecological efficiency in Hebei Province. The characteristics of spatial and temporal evolution patterns were explored using a spatial Markov transfer matrix. The results showed that (i) based on measurements, the agricultural ecological efficiency in Hebei Province showed regional differences in four regions (eastern, northern, central and southern Hebei) and 141 counties; (ii) from the perspective of evolutionary characteristics of agricultural ecological efficiency, the overall development of in Hebei Province was good, with more concentrated spatial distribution and more obvious direction, while the type of transfer of agricultural ecological efficiency in Hebei Province showed strong stability that was significantly affected by geographical neighborhood conditions and the club convergence phenomenon; (iii) from the perspective of the long-term evolutionary trend of agricultural ecological efficiency, the areas adjacent to counties with low efficiency had limited potential for improvement, and the areas adjacent to counties with high grade had great potential. However, it was difficult to achieve large-scale improvement in agricultural ecological efficiency in Hebei Province, whether the impact of geospatial backgrounds was considered or not. [ABSTRACT FROM AUTHOR]

Markov Decision Process Tayloring for Approximation Design Optimal control problems are difficult to solve for problems on large state spaces, calling for the development of approximate solution methods. In "A Low-rank Approximation for MDPs via Moment Coupling," Zhang and Gurvich introduce a novel framework to approximate Markov decision processes (MDPs) that stands on two pillars: (i) state aggregation, as the algorithmic infrastructure, and (ii) central-limit-theorem-type approximations, as the mathematical underpinning. The theoretical guarantees are grounded in the approximation of the Bellman equation by a partial differential equation (PDE) where, in the spirit of the central limit theorem, the transition matrix of the controlled Markov chain is reduced to its local first and second moments. Instead of solving the PDE, the algorithm introduced in the paper constructs a "sister"' (controlled) Markov chain whose two local transition moments are approximately identical with those of the focal chain. Because of this moment matching, the original chain and its sister are coupled through the PDE, facilitating optimality guarantees. Embedded into standard soft aggregation, moment matching provides a disciplined mechanism to tune the aggregation and disaggregation probabilities. We introduce a framework to approximate Markov decision processes (MDPs) that stands on two pillars: (i) state aggregation, as the algorithmic infrastructure, and (ii) central-limit-theorem-type approximations, as the mathematical underpinning of optimality guarantees. The theory is grounded in recent work by Braverman et al. [Braverman A, Gurvich I, Huang J (2020) On the Taylor expansion of value functions. Oper. Res. 68(2):631–65] that relates the solution of the Bellman equation to that of a partial differential equation (PDE) where, in the spirit of the central limit theorem, the transition matrix is reduced to its local first and second moments. Solving the PDE is not required by our method. Instead, we construct a "sister" (controlled) Markov chain whose two local transition moments are approximately identical with those of the focal chain. Because of this moment matching, the original chain and its sister are coupled through the PDE, a coupling that facilitates optimality guarantees. Embedded into standard soft aggregation algorithms, moment matching provides a disciplined mechanism to tune the aggregation and disaggregation probabilities. Computational gains arise from the reduction of the effective state space from N to N 1 2 + ϵ is as one might intuitively expect from approximations grounded in the central limit theorem. Funding: This work was supported by the National Science Foundation [Grant CMMI-1662294]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/opre.2022.2392. [ABSTRACT FROM AUTHOR]

We study a semismooth Newton-type method for the nearest doubly stochastic matrix problem where the nonsingularity of the Jacobian can fail. The optimality conditions for this problem are formulated as a system of strongly semismooth functions. We show that the nonsingularity of the Jacobian does not hold for this system. By exploiting the problem structure, we construct a modified two step semismooth Newton method that guarantees a nonsingular Jacobian matrix at each iteration, and that converges to the nearest doubly stochastic matrix quadratically. Funding: This work was supported by Canadian Network for Research and Innovation in Machining Technology. The research of H. Hu, H. Im, and H. Wolkowocz was supported by The Natural Sciences and Engineering Research Council of Canada. The research of X. Li was supported by the National Natural Science Foundation of China [No. 11601183] and Natural Science Foundation for Young Scientist of Jilin Province [No. 20180520212JH]. [ABSTRACT FROM AUTHOR]

Aims: This study aimed to evaluate whether voluntary and mandatory prescription drug monitoring program (PDMP) use in Victoria, Australia, had an impact on prescribing behaviour, focusing on individual patients' prescribed opioid doses and transition to prescribing of nonmonitored medications. Methods: This was a retrospective cross‐sectional study using routinely collected primary healthcare data. A 90‐day moving average prescribed opioid dose in oral morphine equivalents was used to estimate opioid dosage. A Markov transition matrix was used to describe how patients prescribed medications transitioned between opioid dose groups and other nonopioid treatment options during 3 transition periods: transition between 2 control periods prior to PDMP implementation (T1 to T2); during the voluntary PDMP implementation (T2 to T3); and during mandatory PDMP implementation (T3 to T4). Results: Among patients prescribed opioids in our study, we noted an increased probability of transitioning to not being prescribed opioids during the mandatory PDMP period (T3 to T4). This increase was attributed mainly to the ceasing of low‐dose opioid prescribing. Membership in an opioid dose group remained relatively stable for most patients who were prescribed high opioid doses. For those who were only prescribed nonmonitored medications initially, the probability of being prescribed opioids increased during the mandatory PDMP when compared to other transition periods. Conclusion: The introduction of PDMP mandates appeared to have an impact on the prescribing for patients who were prescribed low‐dose opioids, while its impact on individuals prescribed higher opioid doses was comparatively limited. [ABSTRACT FROM AUTHOR]

This paper focuses on optimizing the green multimodal transportation path under the condition of transit time subjected to random distribution with dynamic changes. The study utilizes the transition matrix of a homogeneous Markov chain and the theory of time-space network to simulate the transit time subjected to random distribution with dynamic changes. A time-space network path optimization model is established and solved using a commercial solver. The solutions are compared under different transit time scenarios and carbon tax rates. It is observed that the reliability of the same solution decreases in a transportation environment with higher randomness. Additionally, new solutions that did not appear in a single situation are generated under dynamic changes in transit time. As the carbon tax rate increases, the transportation strategy gradually shifts away from road transportation. Furthermore, the time-space network model may yield better solutions compared to the physical network model. The choice of different types of distributions to simulate transit times also influences the solution results. [ABSTRACT FROM AUTHOR]

The Mara River basin (MRB) has a world-famous ecosystem, but the vegetation has been damaged due to economic development in recent years, and there is little known about the area that will experience severe vegetation damage in the future. Based on the vegetation vulnerability system, principal component analysis, and three Shared Socio-Economic Pathways (SSP1-2.6, SSP2-4.5, SSP5-8.5), vegetation vulnerability was calculated for the base period (2010–2019), near future period (2020–2059) and distinct future period (2060–2099) in the MRB. The spatial cluster of vegetation vulnerability was revealed by spatial correlation analysis, and the transition of vegetation vulnerability of different periods was analyzed by stochastic matrix. The results showed that for all periods, the vulnerability showed a high–high cluster in the east, and a low–low cluster midstream and downstream. From the stochastic matrix, the area of high vulnerability increased the least under the SSP1-2.6, while it increased the most under the SSP5-8.5. The vegetation vulnerability upstream increased the most from the base period to the near future period and distinct future period in the MRB. By comparing the vegetation vulnerability under different scenarios and pointing out the areas with the highest vulnerability increase, this study can better provide comprehensive decision-making for vegetation protection in the MRB. [ABSTRACT FROM AUTHOR]

This paper provides a nonparametric test for deciding the dimensionality of a policy shock as manifest in the abnormal change in asset returns' stochastic covariance matrix, following the release of a macroeconomic announcement. We use high-frequency data in local windows before and after the event to estimate the covariance jump matrix and then test its rank. We find a one-factor structure in the covariance jump matrix of the yield curve resulting from the Federal Reserve's monetary policy shocks before the 2007–2009 financial crisis. The dimensionality of policy shocks increased afterwards because of the use of unconventional monetary policy tools. [ABSTRACT FROM AUTHOR]

Consider a sequence (X n) n ≥ 1 of i.i.d. 2 × 2 stochastic matrices with each X n distributed as μ. This μ is described as follows. Let (C n , D n) T denote the first column of X n and for a given real r with 0 < r < 1 , let r − 1 C n and r − 1 D n each be Bernoulli distributions with parameters p 1 and p 2 , respectively, and 0 < p 1 , p 2 < 1 . Clearly, the weak limit of the sequence μ n , namely λ , is known to exist, whose support is contained in the set of all 2 × 2 rank one stochastic matrices. In a previous paper, we considered 0 < r ≤ 1 2 and obtained λ explicitly. We showed that λ is supported countably on many points, each with positive λ -mass. Of course, the case 0 < r ≤ 1 2 is tractable, but the case r > 1 2 is very challenging. Considering the extreme nontriviality of this case, we stick to a very special such r, namely, r = 5 − 1 2 (the reciprocal of the golden ratio), briefly mention the challenges in this nontrivial case, and completely identify λ for a very special situation. [ABSTRACT FROM AUTHOR]

The paper suggests new simple proofs of two known theorems on the ergodicity coefficient of a stochastic matrix. [ABSTRACT FROM AUTHOR]

Importance: The prevalence of obesity among United States adults has increased from 30.5% in 1999 to 41.9% in 2020. However, despite the recognition of long-term weight gain as an important public health issue, there is a paucity of studies studying the long-term weight gain and building models for long-term projection. Methods: A retrospective, cross-sectional cohort study using the publicly available National Health and Nutrition Examination Survey (NHANES 2017–2020) was conducted in patients who completed the weight questionnaire and had accurate data for both weight at time of survey and weight ten years ago. Multistate gradient boost modeling classifiers were used to generate covariate dependent transition matrices and Markov chains were utilized for multistate modeling. Results: Of the 6146 patients that met the inclusion criteria, 3024 (49%) of patients were male and 3122 (51%) of patients were female. There were 2252 (37%) White patients, 1257 (20%) Hispanic patients, 1636 (37%) Black patients, and 739 (12%) Asian patients. The average BMI was 30.16 (SD = 7.15), the average weight was 83.67 kilos (SD = 22.04), and the average weight change was a 3.27 kg (SD = 14.97) increase in body weight (Fig. 1). A total of 2411 (39%) patients lost weight, and 3735 (61%) patients gained weight (Table 1). We observed that 87 (1%) of patients were underweight (BMI < 18.5), 2058 (33%) were normal weight (18.5 ≤ BMI < 25), 1376 (22%) were overweight (25 ≤ BMI < 30) and 2625 (43%) were obese (BMI > 30). From analysis of the transitions between normal/underweight, overweight, and obese, we observed that after 10 years, of the patients who were underweight, 65% stayed underweight, 32% became normal weight, 2% became overweight, and 2% became obese. After 10 years, of the patients who were normal weight, 3% became underweight, 78% stayed normal weight, 17% became overweight, and 2% became obese. Of the patients who were overweight, 71% stayed overweight, 0% became underweight, 14% became normal weight, and 15% became obese. Of the patients who were obese, 84% stayed obese, 0% became underweight, 1% became normal weight, and 14% became overweight. Conclusions: United States adults are at risk of transitioning from normal weight to becoming overweight or obese. Covariate dependent Markov chains constructed with gradient boost modeling can effectively generate long-term predictions. [ABSTRACT FROM AUTHOR]

One usually studies the random walk model of a cat moving from one room to another in an apartment. Imagine now that the cat also has the possibility to go from one apartment to another by crossing some corridors, or even from one building to another. That yields a new probabilistic model for which each corridor connects the entrance rooms of several apartments. This article computes the determinant of the stochastic matrix associated to such random walks. That new model naturally allows to compute the determinant of a large class of matrices. Two examples involving digraphs and hyperplane arrangements are provided. [ABSTRACT FROM AUTHOR]

A flexible extended Krylov subspace method (F -EKSM) is considered for numerical approximation of the action of a matrix function f (A) to a vector b, where the function f is of Markov type. F -EKSM has the same framework as the extended Krylov subspace method (EKSM), replacing the zero pole in EKSM with a properly chosen fixed nonzero pole. For symmetric positive definite matrices, the optimal fixed pole is derived for F -EKSM to achieve the lowest possible upper bound on the asymptotic convergence factor, which is lower than that of EKSM. The analysis is based on properties of Faber polynomials of A and (I − A / s) − 1 . For large and sparse matrices that can be handled efficiently by LU factorizations, numerical experiments show that F -EKSM and a variant of RKSM based on a small number of fixed poles outperform EKSM in both storage and runtime, and usually have advantages over adaptive RKSM in runtime. [ABSTRACT FROM AUTHOR]

This paper addresses the secure consensus control problem for a class of continuous-time two-time-scale Markov jump multi-agent systems under hybrid cyber-attacks, which suffers from both the denial-of-service attacks and deception attacks. Firstly, to make the constructed model fit the practice better, the dynamic of each agent is represented by a two-time-scale system and the transition rate matrix of the Markov chain is assumed to be partially unknown. Then, a secure consensus protocol is designed to deal with the hybrid cyber-attacks and guarantee the average consensus can be achieved with a prescribed H ∞ performance. Based on the stochastic analysis approach and Lyapunov stability method, some sufficient conditions are given in the form of linear matrix inequalities. Furthermore, the desired secure consensus protocol gains can be obtained by solving a convex optimization problem. Finally, an illustrative example is utilized to demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In networks, the Markov clustering (MCL) algorithm is one of the most efficient approaches in detecting clustered structures. The MCL algorithm takes as input a stochastic matrix, which depends on the adjacency matrix of the graph network under consideration. Quantum clustering algorithms are proven to be superefficient over the classical ones. Motivated by the idea of a potential clustering algorithm based on quantum Markov chains, we prove a clustering property for quantum Markov chains (QMCs) on Cayley trees associated with open quantum random walks (OQRW). [ABSTRACT FROM AUTHOR]

This work uses the collocation approximation method to solve a specific type of backward stochastic Volterra integral equations (BSVIEs). Using Newton's method, BSVIEs can be solved using block pulse functions and the corresponding stochastic operational matrix of integration. We present examples to illustrate the estimate analysis and to demonstrate the convergence of the two approximating sequences separately. To measure their accuracy, we compare the solutions with values of exact and approximative solutions at a few selected locations using a specified absolute error. We also propose an efficient method for solving a triangular linear algebraic problem using a single integral equation. To confirm the effectiveness of our method, we conduct numerical experiments with issues from real-world applications. [ABSTRACT FROM AUTHOR]

This paper proposes a frequency domain-based analytical framework for seismic performance of viscously damped outrigger systems. Based on a core–outrigger–damper–column simplified model, the global dynamic stiffness matrix is assembled from the core modeled as a Timoshenko beam, damped outriggers as complex rotational stiffness comprising outriggers, dampers, and perimeter columns, and inherent damping using Leung's theory and modal damping construction. A general numerical method combining Wittrick-Williams algorithm and Newtonian iteration is developed to study the dynamic characteristic of such systems with multiple damped outriggers. The fast Fourier transformation (FFT) and the inverse Fourier transformation (IFFT) are then integrated with the principle of potential energy to obtain the equivalent nodal force and thus the time history response by transformations between time and frequency domains. Finally, the stochastic analysis is conducted via the transfer function resulting from the global stiffness matrix with the stochastic seismic excitation following Kanai-Tajimi spectrum. The proposed approach is verified by comparison with the finite element method through a case study of a tall building implemented with viscously damped outriggers. This study shows that the proposed analytical framework could serve as a powerful tool for evaluating the performance of viscously damped outrigger systems. [ABSTRACT FROM AUTHOR]

Over the past few decades, the growth of population and the development of the economy have had a significant impact on the way land is used and covered (LULC) in the Nile Nyabarongo River basin. However, there is limited knowledge about the patterns of land use and the mechanisms that drive changes in these patterns because of human activities. Therefore, it is crucial to examine how land use and cover are shifting in this area, identify the factors responsible for these changes, and forecast future patterns. This study sought (1) to evaluate the changes in LULC from 1990 to 2020 and (2) to predict future fluctuations until 2060. By analyzing the LULC data for the years 1990, 2000, 2010, and 2020, this study simulated the future LULC patterns of the area for the next 30 years using the LULC transition matrix and the Markov chain model. The study classified the LULC into five categories: forestland, grassland, cropland, settlement, and water. The results revealed that there will be significant changes in the LULC of the study area from 2030 to 2060. The forest area is projected to decrease by 801.7 km, 771.6 km, and 508.2 km, while the cropland area will expand by 6307.2 km, 6249.2 km, and 6420.6 km during this period. The grassland area will experience a small increase of 761.1 km, 802.4 km, and 859.1 km, and the settlement area will also grow by 355.2 km, 407.4 km, and 453.2 km. In contrast, the water area will decrease by 55.9 km, 50.5 km, and 40 km. The ongoing pattern of LULCC is expected to persist over the next three decades, with an increase in cropland area and grassland. This study's findings can provide valuable insights for land use planners and water resource managers in developing fair land use and water resource management policies for the entire region, enabling them to make well-informed decisions. [ABSTRACT FROM AUTHOR]

A multi-agent system is a system of multiple interacting entities, known as intelligent agents, who possibly have different information and/or diverging interests. The agents could be robots, humans, or human teams. Opinion dynamics is a process of individual opinions in which a group of interacting agents continuously fuse their opinions on the same issue based on established rules to reach a consensus at the final stage. Historically, the idea of reaching consensus through repeated averaging was introduced by DeGroot for a structured time-invariant and synchronous environment. Since then, consensus, which is the most ubiquitous phenomenon of multi-agent systems, has become popular in various scientific fields such as biology, physics, control engineering, and social science. To some extent, a Krause mean process is a general model of opinion sharing dynamics in which the opinions are represented by vectors. In this paper, we represent opinion sharing dynamics by means of Krause mean processes generated by diagonally primitive cubic doubly stochastic matrices, and then we establish a consensus in the multi-agent system. [ABSTRACT FROM AUTHOR]

The k-matching polytope of a graph is the convex hull of all its matchings of a given size k when they are considered as indicator vectors. In this paper, we prove that the k-matching polytope of a bipartite graph is normal, that is, every integer point in its t-dilate is the sum of t integers points of the original polytope. This generalizes the known fact that Birkhoff polytopes are normal. As a preliminary result, we prove that for bipartite graphs the k-matching polytope is equal to the fractional k -matching polytope, having thus the H -representation of the polytope. This generalizes the Birkhoff-Von Neumann Theorem which establish that every doubly stochastic matrix can be written as a convex combination of permutation matrices. [ABSTRACT FROM AUTHOR]

The Flow matrix is a novel method to describe and extrapolate transitions among categories. The Flow matrix extrapolates a constant transition size per unit of time on a time continuum with a maximum of one incident per observation during the extrapolation. The Flow matrix extrapolates linearly until the persistence of a category shrinks to zero. The Flow matrix has concepts and mathematics that are more straightforward than the Markov matrix. However, many scientists apply the Markov matrix by default because popular software packages offer no alternative to the Markov matrix, despite the conceptual and mathematical challenges that the Markov matrix poses. The Markov matrix extrapolates a constant transition proportion per time interval during whole-number multiples of the duration of the calibration time interval. The Markov extrapolation allows at most one incident per observation during each time interval but allows repeated incidents per observation through sequential time intervals. Many Markov extrapolations approach a steady state asymptotically through time as each category size approaches a constant. We use case studies concerning land change to illustrate the characteristics of the Flow and Markov matrices. The Flow and Markov extrapolations both deviate from the reference data during a validation time interval, implying there is no reason to prefer one matrix to the other in terms of correspondence with the processes that we analyzed. The two matrices differ substantially in terms of their underlying concepts and mathematical behaviors. Scientists should consider the ease of use and interpretation for each matrix when extrapolating transitions among categories. [ABSTRACT FROM AUTHOR]

Human activities are prone to be the main drivers of land use land cover (LULC) changes, which have cascading effects on the environment and ecosystem services. The main objective of this study is to assess the historical spatiotemporal distributions of LULC changes as well as estimated future scenarios for 2035 and 2045 by considering the explanatory variables of LULC changes in Zanjan province, Iran. The LULC time-series technique was applied using three Landsat images for the years 1987, 2002, and 2019. Multi-layer Perceptron Artificial Neural Network (MLP-ANN) is applied to model the relationships between LULC transitions and explanatory variables. Future land demand was calculated using a Markov chain matrix and multi-objective land optimization in a hybrid simulation model. Validation of the model's outcome was performed using the Figure of Merit index. The residential area in 1987 was 6406.02 ha which increased to 22,857.48 ha in 2019 with an average growth rate of 3.97%. Agriculture increased annually by 1.24% and expanded to 149% (890,433 ha) of the area occupied in 1987. Rangeland showed a decline concerning its area, with only about 77% (1,502,201 ha) of its area in 1987 (1,166,767 ha) remaining in 2019. Between 1987 and 2019, the significant net change was a conversion from rangeland to agricultural areas (298,511 ha). Water bodies were 8 ha in 1987, which increased to 1363 ha in 2019, with an annual growth rate of 15.9%. The projected LULC map shows the rangeland will further degrade from 52.43% in 2019 to 48.75% in 2045, while agricultural land and residential areas would be expanded to 940,754 ha and 34,727 ha in 2045 from 890,434 ha and 22,887 ha in 2019. The findings of this study provide useful information for the development of an effective plan for the study area. [ABSTRACT FROM AUTHOR]

Land use change models have been widely used to predict the changes in the future and provide different scenarios under different policies. However, most models commonly compare the transition proportions of change relying on the gross change, which generally fails to represent the inherent dominant transition of land categories. In this paper, Markov chain was used to obtain the dominant transition as global transition probability of each land use cell by separating the systematic information from random information. The dominant transition is transformed into transition probability and then combined with WLC (weighted linear combination) to calculate the new suitability map for cellular automata (CA) simulation. Thus, an improved CA model coupled with dominant transition and Markov chain was designed to improve the performance of simulating land use changes. Choosing Changping District of Beijing, China as the study area, this paper mined the driving factors and conversion relationship revealed by land use patterns in 1988 and 1995. Some land use types have the large area and result in large transition, but the expected transition is not exceptionally large, which used to revise the probability to simulate the land use status in 2000. The predictive power of the model was evaluated by Kappa index and fractal dimension, which reached the higher simulation accuracy and landscape index similarity. The improved model provides an effective and useful method to extract dominant transition to overcome some limitation of CA–Markov model. And the dominant transition information provides a possibility for ecologically risk identification. [ABSTRACT FROM AUTHOR]

Let Mn;m be the set of all n-by-m real matrices, and let Rn be the set of all n-by-1 real vectors. An n-by-m matrix R = [rij] is called g-row substochastic if... if there exists an n-by-n upper triangular g-row substochastic matrix R such that x = Ry. Define the relation ~sgut as follows. x ~sgut y if and only if x is sgut-majorized by y and y is sgut-majorized by x. This paper characterizes all (strong) linear preservers of ~sgut on Rn. [ABSTRACT FROM AUTHOR]

Wind power prediction is an important research topic in the wind power industry and many prediction algorithms have recently been studied for the sake of achieving the goal of improving the accuracy of short-term forecasting in an effective way. To tackle the issue of generating a huge transition matrix in the traditional Markov model, this paper introduces a real-time forecasting method that reduces the required calculation time and memory space without compromising the prediction accuracy of the original model. This method is capable of obtaining the state probability interval distribution for the next moment through real-time calculation while preserving the accuracy of the original model. Furthermore, the proposed Markov-based Back Propagation (BP) neural network was optimized using the Particle Swarm Optimization (PSO) algorithm in order to effectively improve the prediction approach with an improved PSO-BP neural network. Compared with traditional methods, the computing time of our improved algorithm increases linearly, instead of growing exponentially. Additionally, the optimized Markov-based PSO-BP neural network produced a better predictive effect. We observed that the Mean Absolute Percentage Error (MAPE) and Mean Absolute Error (MAE) of the prediction model were 12.7% and 179.26, respectively; compared with the existing methods, this model generates more accurate prediction results. [ABSTRACT FROM AUTHOR]