Markov Chain Research Articles

Probability of a Single Current

The Riemann surface associated with counting the current between two states of an underlying Markov process is hyperelliptic. We explore the consequences of this property for the time-dependent probability of that current for Markov processes with generic transition rates. When the system is prepared in its stationary state, the relevant meromorphic differential is in particular fully characterized by the precise identification of all its poles and zeroes.

Genomic Exploration of Essential Hypertension in African-Brazilian Quilombo Populations: A Comprehensive Approach with Pedigree Analysis and Family-Based Association Studies.

Essential Hypertension (EH) is a global health issue. Despite extensive research, much of EH heritability remains unexplained. We investigated the genetic basis of EH in African-derived individuals from partially isolated quilombo populations in Vale do Ribeira (SP-Brazil). Samples from 431 individuals (167 affected, 261 unaffected, 3 unknown) were genotyped using a 650k SNP array. Estimated global ancestry proportions were 47% African, 36% European, and 16% Native American. We constructed six pedigrees using additional data from 673 individuals and created three non-overlapping SNP subpanels. We phased haplotypes and performed local ancestry analysis to account for admixture. Genome-wide linkage analysis (GWLA) and fine-mapping via family-based association studies (FBAS) were conducted, prioritizing EH-associated genes through systematic approach involving databases like PubMed, ClinVar, and GWAS Catalog. Linkage analysis identified 22 regions of interest (ROIs) with LOD scores ranging 1.45-3.03, encompassing 2363 genes. Fine-mapping (FBAS) identified 60 EH-related candidate genes and 117 suggestive/significant variants. Among these, 14 genes, including PHGDH , S100A10 , MFN2 , and RYR2 , were strongly related to hypertension harboring 29 suggestive/significant SNPs. Through a complementary approach - combining admixture-adjusted GWLA based on Markov chain Monte Carlo methods, FBAS on known and imputed data, and gene prioritizing - new loci, variants, and candidate genes were identified. These findings provide targets for future research, replication in other populations, facilitate personalized treatments, and improve public health towards African-derived underrepresented populations. Limitations include restricted SNP coverage, self-reported pedigree data, and lack of available EH genomic studies on admixed populations for independent validation, despite the performed genetic correlation analyses using summary statistics.

Influence of scalar field in massive particle motion in JNW spacetime

In this paper, we investigated the motion of massive particles in the presence of scalar and gravitational fields, particularly focusing on the Janis-Newman-Winicour (JNW) naked singularity solution. It is shown that the innermost stable circular orbit radius strongly depends on scalar coupling parameter. Additionally, we explored the radiation reaction effects on particle dynamics, incorporating a reaction term into the motion equations. Numerical simulations indicated minimal impact on particle trajectories from radiation reaction. We also examined the oscillatory motion of particles around compact objects in the JNW spacetime, focusing on radial and vertical oscillations. Our analysis indicated that the scalar field’s coupling parameter and the spacetime deformation parameter n significantly alter the fundamental frequencies of these oscillations. Furthermore, we studied quasiperiodic oscillations (QPOs) in x-ray binaries, using the relativistic precession model to analyze upper- and lower-frequency relationships. Our results indicated that increasing parameters (n and gs) shifts the frequency ratio of 3∶2 QPOs closer to the naked singularity, with n decreasing and gs increasing both frequencies. Finally, we analyzed QPO data from four selected x-ray binary systems using Markov chain Monte Carlo analysis to constrain JNW parameters. Our findings provided insights into the mass, coupling, and deformation parameter for each system, enhancing our understanding of compact object dynamics in strong gravitational fields. Published by the American Physical Society 2024

Sensitivity and Uncertainty Analysis of the GeeSEBAL Model Using High-Resolution Remote-Sensing Data and Global Flux Site Data

Actual evapotranspiration (ETa) is an important component of the surface water cycle. The geeSEBAL model is increasingly being used to estimate ETa using high-resolution remote-sensing data (Landsat 4/5/7/8). However, due to surface heterogeneity, there is significant uncertainty. By optimizing the quantile values of the reverse-modelling automatic calibration algorithm (CIMEC) endpoint-component selection algorithm under extreme conditions through 212 global flux sites, we obtained the optimized quantile values of 11 vegetation types of cold- and hot-pixel endpoint components (Ts and NDVI). Based on the observation data of the global FLUXNET tower, the sensitivity of 20 parameters in the improved geeSEBAL model was determined through Sobol’s sensitivity analysis. Among them, the parameters dT and SAVI,hot were confirmed as the most sensitive parameters of the algorithm. Subsequently, we used the differential evolution Markov chain (DE-MC) method to analyse the uncertainty of the parameters in the geeSEBAL model used the posterior distribution of the parameters to modify the sensitive parameter values or ranges in the improved geeSEBAL model and to simulate the daily ETa. The results indicate that by analysing the end element components of the geeSEBAL model (Ts and NDVI), quantile numerical optimization and parameter optimization can be performed. Compared with the original algorithm, the improved geeSEBAL model has significantly improved simulation performance, as shown by higher R2 values, higher NSE values, smaller bias values, and lower RMSE values. The most suitable values of the predefined parameter Zoh were determined, and the reanalysis of meteorological data inputs (relative humidity (RH), temperature (T), wind speed (WS), and net radiation (Rn)) was also found to be an important source of uncertainty for the accurate estimation of ETa. This study indicates that optimizing the quantiles and key parameters of the model end component has certain potential for further improving the accuracy of the geeSEBAL model based on high-resolution remote-sensing data in estimating the ETa for various vegetation types.

The Effects of Vessel Traffic on the Behavior Patterns of Common Dolphins in the Tagus Estuary (Portugal).

The impact of vessels on dolphin populations has been extensively studied worldwide. The common dolphin, Delphinus delphis, has been observed in the Tagus estuary for the past two centuries, and during the last several years, these sightings seem to have increased. This area has high levels of maritime traffic throughout the year, both commercial and recreational. To understand the possible effects of vessel traffic on dolphins' behavior, land-based observations were carried out from March 2022 to March 2023. For a total of 67 events (48.9 h of dolphin sightings), differences in behavioral budgets were noted. Although "neutral reaction" was the most observed response when vessels were in the vicinity of dolphins, "negative reaction" was also common and five times more abundant than "positive reaction". The GEE model showed statistical differences between these reaction types (positive, neutral, and negative). Markov chains' analysis revealed distinct patterns in the behavioral transition probabilities, as dolphins were more likely to switch to a traveling state when vessels were nearby. This study is the first step towards understanding a potential impact source in the area since it is expected that tourism companies expand due to the increase in dolphin sightings in the estuary.

Multivariate lifetime data in presence of censoring and covariates: Use of semiparametric models under a Bayesian approach

A generalization of the popular proportional hazards model introduced by Cox (1972) is given by the class of semiparametric or transformation models to be used in the analysis of lifetime data in presence of censored data and covariates. In this study, we consider the use of semiparametric (transformation models) for the situation where there are two or more responses associated to the same individual or unit. We assume a hierarchical Bayesian analysis for semiparametric models considering the complete likelihood function obtained from the transformation models considering the unknown hazard functions as unknown latent variables and Markov Chain Monte Carlo (MCMC) methods to get the posterior summaries of interest. The dependence between multivariate responses for the same individual is captured by the introduction of another latent variable or frailty. Illustrations of the proposed methodology are presented considering two medical multivariate lifetime data sets.

Regenerative therapies for erectile dysfunction: a systematic review, Bayesian network meta-analysis, and meta-regression.

Current guidelines advocate a shared decision-making process approach to erectile dysfunction management, and while there is growing interest in regenerative therapies such as stem cell therapy, platelet-rich plasma injections, and low-intensity shockwave therapy for erectile dysfunction, comparative data on the efficacy of these modalities are limited. This systematic review and network meta-analysis aims to compare stem cell therapy, platelet-rich plasma injections, and low-intensity shockwave therapy for managing erectile dysfunction and quantify their impact on the International Index of Erectile Function (IIEF). In January 2024, a systematic search of online databases was performed to identify randomized clinical trials related to stem cell therapy, platelet-rich plasma injections, and low-intensity shockwave therapy in erectile dysfunction. Eligible articles reported outcomes using the IIEF score. Data were inputted into Review Manager 5.4 for pairwise meta-analysis. Data were then used to build a network in R Studio. These networks were used to model 200 000 Markov Chains via MonteCarlo sampling. The results are expressed as standardized mean difference (SMD) with 95% credible intervals (CrI). Meta-regression was used to adjust for PDE5is use. Impact on the International Index of Erectile Function. A total of 16 studies involving 907 patients were analyzed. The standardized mean difference (SMD) vs control for stem cell therapy was 0.92 [95% CrI -0.49, 2.3]. For platelet-rich plasma, the SMD vs control was 0.83 [95% CrI 0.15, 1.5], and for low-intensity shockwave therapy, the SMD vs control was 0.84 [95% CrI 0.49, 1.2]. When stratifying low-intensity shockwave therapy by dose, the SMD vs control at 0.15mJ/mm2 was 1.1 [95% CrI 0.36, 1.9], while at 0.09mJ/mm2, it was 0.75 [95% CrI 0.26, 1.2]. Meta-regression adjusting for the administration of PDE5 inhibitors yielded non-significant results. The findings suggest that stem cells, platelet-rich plasma, and low intensity shockwave therapy, particularly at 0.15 and 0.09mJ/mm2, may offer improvements in erectile function. The strength is the robust statistical methods. Limitations are in heterogeneity in control groups and follow-up durations among included studies. Shockwave therapy and platelet-rich plasma demonstrated statistically significant improvements, though the clinical relevance and extent of their impact remain questionable. Further research is necessary to determine the efficacy of stem cell therapies for erectile function.

Fatigue life prediction of film-cooling Hole specimens with initial damage

This study investigates a Nickel-based single crystal (SX) superalloy with femtosecond laser-drilled film-cooling holes (FCHs) under varying temperatures (room temperature, 850 °C, and 980 °C), employing a novel framework for predicting fatigue life based on initial manufacturing damage quantification. For all tested anisotropic SX superalloy specimens (including smooth and FCH specimens), the initial damage state is characterized as an equivalent initial flaw size (EIFS), and an EIFS calculation model considering stress concentration is established. Subsequently, the fatigue crack paths and microstructural characteristics of the FCH specimens at different temperatures are analyzed, elucidating crack initiation mechanisms and propagation patterns. A novel incremental plasticity J-integral driving force for fatigue crack propagation is introduced. By incorporating the closure effect of small crack propagation and employing Markov Chain Monte Carlo simulations for determining crack growth rate probabilities, a more accurate expression for the crack growth rate in relation to ΔJfat − ΔJth is derived. This expression comprehensively captures crack patterns on crystallographic planes and Type I mixed mode behavior. Finally, the total fatigue life of the FCH structures, featuring a threefold dispersion zone in both room and high-temperature environments, is predicted through experimental observations and description of crack growth rates. The predicted outcomes significantly outperform those of the conventional life prediction models reliant on crystal plasticity theory.

Method of calculating stationary probability distribution in Markov chain in modeling social and economic processes

Method of calculating stationary probability distribution in Markov chain in modeling social and economic processes

Transforming landscapes: Decoding the impact of universities on urbanization using advanced modeling and perception analysis.

Universities play a crucial role in urban economic and structural development. The government of Bangladesh has undertaken the initiative to establish a public university in each of the 64 districts. These newly founded universities have the potential to impact urban growth significantly. We aimed to project university-induced urban expansion to address this knowledge gap and identify the mechanisms driving urban growth. The classification of supervised and unsupervised methods was employed to analyze urban development for the years 2000, 2010, 2016, and 2022. We used the Cellular Automata and Markov Chain approach to forecast future urban growth and land transition capacity. Additionally, the driving factors and selection of the study area were derived from Focus Group Discussions (FGD), Key Informant Interviews (KII), Probit Model, and Perception Index (PI). The findings of this study reveal a 1.6% urban growth rate within ten years of the establishment of the university, while urban expansion accelerated to 29.78% after ten years. The predictions also indicate a sustained urban growth rate of 4.7% by 2042. Furthermore, the PI index demonstrates that the establishment of the university has resulted in high demand for rental housing, serving as one of the primary drivers of urban expansion. Moreover, the Probit model highlights strong economic capability, proximity to the town, railway station, hospital, and easy access to credit as vital facilitators behind the drivers of urban expansion. Policymakers, the scientific community, and urban planners can benefit from this study in pursuing sustainable city development through university establishment.

Cost-Effectiveness of an Ultrasound-First Strategy in the Diagnostic Evaluation of Noncalcified Lesions Recalled From Screening Digital Breast Tomosynthesis.

BACKGROUND. Ultrasound may be sufficient in the diagnostic evaluation of many noncalcified lesions recalled from screening digital breast tomosynthesis (DBT). In some scenarios, omission of diagnostic mammography can save health care costs. OBJECTIVE. The purpose of this study was to evaluate the cost-effectiveness of a strategy of performing ultrasound first versus diagnostic mammography first in the diagnostic evaluation of noncalcified lesions recalled from screening DBT. METHODS. Decision tree analysis was performed to compare ultrasound first versus diagnostic mammography first in the diagnostic evaluation of DBT-recalled noncalcified lesions from a U.S. health care system perspective with a 40-year horizon. The analysis used probabilities and prevalence information from published single-institution prospective data, additional literature-derived estimates of diagnostic test performance, and Medicare-allowable reimbursement rates. Health states were represented in a Markov chain model. For each strategy, the total cost and effectiveness (expressed in quality-adjusted life-years [QALYs]) were estimated. Cost-effectiveness was assessed through incremental cost-effectiveness ratios (ICERs) and incremental net monetary benefit, with use of a willingness-to-pay (WTP) threshold of US$100,000 per QALY gained. Deterministic sensitivity analyses were performed to estimate the impact of different input parameters, and probabilistic sensitivity analysis with Monte Carlo simulations was conducted to estimate the impact of combined uncertainty across parameters. RESULTS. In the base-case scenario, for diagnostic evaluation of DBT-recalled noncalcified lesions, a strategy of performing ultrasound first versus diagnostic mammography first resulted in more cost savings (total cost, US$17,672 vs US$18,323) and greater cost-effectiveness (QALYs, 23.1309 vs 23.1306) over the 40-year horizon. The ultrasound-first strategy resulted in an ICER of -2,170,000 (expressed as U.S. dollars per QALY) and an incremental net monetary benefit of US$681 versus the diagnostic mammography-first strategy. Therefore, performing ultrasound first was deemed the more cost-effective strategy at the WTP threshold. In deterministic sensitivity analyses, the most important driver of cost-effectiveness was lost utility from delayed diagnosis, followed by the relative sensitivities of ultrasound and diagnostic mammography. In probabilistic sensitivity analysis, ultrasound first was the better strategy in 93.0% of iterations. CONCLUSION. A strategy of performing ultrasound first, with or without diagnostic mammography, is more cost-effective than a traditional strategy of conducting diagnostic mammography first. CLINICAL IMPACT. This cost-effectiveness analysis supports the growing prioritization of ultrasound as the primary method for evaluating DBT-recalled noncalcified lesions.

Euclid preparation. LIII. LensMC, weak lensing cosmic shear measurement with forward modelling and Markov Chain Monte Carlo sampling

is a weak lensing shear measurement method developed for and Stage-IV surveys. It is based on forward modelling in order to deal with convolution by a point spread function (PSF) with comparable size to many galaxies, sampling the posterior distribution of galaxy parameters via Markov chain Monte Carlo, and marginalisation over nuisance parameters for each of the 1.5 billion galaxies observed by We quantified the scientific performance through high-fidelity images based on the Flagship simulations and emulation of the VIS images, realistic clustering with a mean surface number density of $ arcmin^ for galaxies, and $ arcmin^ for stars, and a diffraction-limited chromatic PSF with a full width at half maximum of $ $ and spatial variation across the field of view. measured objects with a density of $ arcmin^ in $4500 deg^2 $. The total shear bias was broken down into measurement (our main focus here) and selection effects (which will be addressed in future work). We found measurement multiplicative and additive biases of $m_1=(-3.6 $, $m_2=(-4.3 $, $c_1=(-1.78 $, and $c_2=(0.09 $; a large detection bias with a multiplicative component of $1.2 $ and an additive component of $-3 $; and a measurement PSF leakage of $ $ and $ $. When model bias is suppressed, the obtained measurement biases are close to requirement and largely dominated by undetected faint galaxies ($-5 $). Although significant, model bias will be straightforward to calibrate given its weak sensitivity on galaxy morphology parameters. is publicly available at

Imaging research on damage localization of concrete structure based on Lamb wave and Bayesian fusion algorithm

Concrete structures are critical materials in the field of industrial construction and are susceptible to invisible damage under the influence of a variety of factors. The method of increasing the number of sensors is usually used to obtain high-precision damage detection, but it increases the experimental cost and signal processing time, so it is especially important to perform high-precision and low-cost non-destructive testing for it. The article uses Bayes to combine the elliptical trajectory method with a probabilistic damage imaging algorithm, and utilizes the algorithm to achieve higher accuracy damage localization imaging results with a smaller number of sensors. The wavelet transform is used to calculate the time of flight to obtain the localization results of the elliptical trajectory method, the signal damage factor is calculated based on the amplitude information to obtain the localization results of the probabilistic damage imaging, the probability distribution of the damage location is obtained using Bayesian, and the damage localization results are obtained by solving the problem through the Markov chain Monte Carlo method. A dense sensor array based and probabilistic imaging algorithm is also used to localize the damage to the material and the results are compared with the results of the Bayesian fusion algorithm. The results show that the Bayesian fusion algorithm can obtain higher accuracy of damage localization with a significant reduction in the number of sensors, and at the same time greatly reduces the number of signals, simplifies the experimental process, and has high practical value.

On the importance of assessing topological convergence in Bayesian phylogenetic inference

Abstract Modern phylogenetics research is often performed within a Bayesian framework, using sampling algorithms such as Markov chain Monte Carlo (MCMC) to approximate the posterior distribution. These algorithms require careful evaluation of the quality of the generated samples. Within the field of phylogenetics, one frequently adopted diagnostic approach is to evaluate the effective sample size (ESS) and to investigate trace graphs of the sampled parameters. A major limitation of these approaches is that they are developed for continuous parameters and therefore incompatible with a crucial parameter in these inferences: the tree topology. Several recent advancements have aimed at extending these diagnostics to topological space. In this reflection paper, we present two case studies – one on Ebola virus and one on HIV – illustrating how these topological diagnostics can contain information not found in standard diagnostics, and how decisions regarding which of these diagnostics to compute can impact inferences regarding MCMC convergence and mixing. Our results show the importance of running multiple replicate analyses and of carefully assessing topological convergence using the output of these replicate analyses. To this end, we illustrate different ways of assessing and visualizing the topological convergence of these replicates. Given the major importance of detecting convergence and mixing issues in Bayesian phylogenetic analyses, the lack of a unified approach to this problem warrants further action, especially now that additional tools are becoming available to researchers.

2D Transdimensional Joint Inversion of Radio Magnetotelluric and Electrical Resistivity Tomography Data

Summary The joint inversion of radio magnetotelluric and electrical resistivity tomography data has the potential to reduce the uncertainties in the subsurface conductivity model. This is particularly beneficial when the datasets offer complementary information about the subsurface. However, the traditional gradient-based inversion methods pose challenges in quantifying uncertainty, as they yield a single model with limited appraisal of parameter uncertainty. The Bayesian inversion approach stands out for its capacity to provide quantitative assessments of uncertainty in the inverted model parameters. This is accomplished by generating an ensemble of models, leading to a posterior distribution that encapsulates both prior information concerning model parameters and the dataset information. We have implemented a transdimensional Markov chain Monte Carlo algorithm to perform the joint inversion of radio magnetotelluric and electrical resistivity tomography data. Through synthetic data studies, we illustrate how the inclusion of two complementary datasets can effectively reduce uncertainties in model parameters and how the model parameter uncertainties can be quantified. Subsequently, the developed algorithm is tested using exemplary field data from a waste site near Roorkee, India. Intensive prior geoelectric and transient electromagnetic as well as radio magnetotelluric studies investigated possible waste water seepage with a potential to contaminate the shallow aquifers. The derived subsurface structure from our transdimensional Bayesian results compare well with the deterministic results for the exemplary profile, but in addition provide comprehensive uncertainty estimates.

Explainable artificial intelligence (XAI) to find optimal in-silico biomarkers for cardiac drug toxicity evaluation

The Comprehensive In-vitro Proarrhythmia Assay (CiPA) initiative aims to refine the assessment of drug-induced torsades de pointes (TdP) risk, utilizing computational models to predict cardiac drug toxicity. Despite advancements in machine learning applications for this purpose, the specific contribution of in-silico biomarkers to toxicity risk levels has yet to be thoroughly elucidated. This study addresses this gap by implementing explainable artificial intelligence (XAI) to illuminate the impact of individual biomarkers in drug toxicity prediction. We employed the Markov chain Monte Carlo method to generate a detailed dataset for 28 drugs, from which twelve in-silico biomarkers of 12 drugs were computed to train various machine learning models, including Artificial Neural Networks (ANN), Support Vector Machines (SVM), Random Forests (RF), XGBoost, K-Nearest Neighbors (KNN), and Radial Basis Function (RBF) networks. Our study’s innovation is leveraging XAI, mainly through the SHAP (SHapley Additive exPlanations) method, to dissect and quantify the contributions of biomarkers across these models. Furthermore, the model performance was evaluated using the test set from 16 drugs. We found that the ANN model coupled with the eleven most influential in-silico biomarkers namely dVmdtrepol,dVmdtmax,APD90,APD50,APDtri,CaD90,CaD50,Catri,CaDiastole,qInward,andqNet\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\frac{dVm}{dt}_{repol}, \\frac{dVm}{dt}_{max}, {APD}_{90}, {APD}_{50}, {APD}_{tri}, {CaD}_{90}, {CaD}_{50}, {Ca}_{tri}, {Ca}_{Diastole}, qInward, and qNet$$\\end{document} showed the highest classification performance among all classifiers with Area Under the Curve (AUC) scores of 0.92 for predicting high-risk, 0.83 for intermediate-risk, and 0.98 for low-risk drugs. We also found that the optimal in silico biomarkers selected based on SHAP analysis may be different for various classification models. However, we also found that the biomarker selection only sometimes improved the performance; therefore, evaluating various classifiers is still essential to obtain the desired classification performance. Our proposed method could provide a systematic way to assess the best classifier with the optimal in-silico biomarkers for predicting the TdP risk of drugs, thereby advancing the field of cardiac safety evaluations.

Forecasting Constraint on the f(R) Theory with the CSST SN Ia and BAO Surveys

Abstract The $f(R)$ modified gravity theory can explain the accelerating expansion of the late Universe without introducing dark energy. In this study, we predict the constraint strength on the $f(R)$ theory using the mock data generated from the China Space Station Telescope (CSST) Ultra-Deep Field (UDF) Type Ia supernova (SN Ia) survey and wide-field slitless spectroscopic baryon acoustic oscillation (BAO) survey. We explore three popular $f(R)$ models, and introduce a parameter $b$ to characterize the deviation of the f(R) theory from the $\Lambda$CDM theory. The Markov Chain Monte Carlo (MCMC) method is employed to constrain the parameters in the $f(R)$ models, and the nuisance parameters and systematical uncertainties are also considered in the model fitting process. Besides, we also perform model comparisons between the $f(R)$ models and the $\Lambda$CDM model. We find that the constraint accuracy using the CSST SN Ia+BAO dataset alone is comparable to or even better than the result given by the combination of the current relevant observations, and the CSST SN Ia+BAO survey can distinguish the $f(R)$ models from the $\Lambda$CDM model. This indicates that the CSST SN Ia and BAO surveys can effectively constrain and test the $f(R)$ theory.

Medium- and Long-Term Power System Planning Method Based on Source-Load Uncertainty Modeling

In order to consider the impact of source-load uncertainty on traditional power system planning methods, a medium- and long-term optimization planning method based on source-load uncertainty modeling and time-series production simulation is proposed. First, a new energy output probability model is developed using non-parametric kernel density estimation, and the spatial correlation of the new energy output is described using pair-copula theory to model the uncertainty analysis of the new energy output. Secondly, a large number of source-load scenarios are generated using the Markov chain Monte Carlo simulation method, and the optimal selection method for discrete state numbers is provided, and then the scenario reduction is carried out using the fast forward elimination technology. Finally, the typical time-series curves of the source-load uncertainty characteristics obtained are incorporated into the optimization planning method together with various flexible resources, such as the demand-side response and energy storage, and the rationality of the planning scheme is judged and optimized based on key indicators such as the cost, wind–light abandonment rate, and loss-of-load rate. Based on the above methods, this paper offers an example of the power supply planning scheme for a certain region in the next 30 years, providing effective guidance for the development of new energy in the region.

On control charts based on generalized multiple dependent state sampling

ABSTRACT We clarify the use of the widely used multiple dependent state sampling (MDSS) technique and its generalization (GMDSS) with control charts. We show that these rules are simple modifications of well-known supplementary runs rules. The MDSS and GMDSS rules are inefficient; however, they do not distinguish between the upper and lower warning regions. We show that the application of the more conventional supplementary runs rules, i.e. those side-sensitive with respect to the warning regions, provides significantly better performance than the MDSS and GMDSS techniques. In addition, we show that a commonly used expression for determining the average run length of the GMDSS method is incorrect and provide a Markov chain alternative approach.

Nonlinear Dynamics for the Ising Model

We introduce and analyze a natural class of nonlinear dynamics for spin systems such as the Ising model. This class of dynamics is based on the framework of mass action kinetics, which models the evolution of systems of entities under pairwise interactions, and captures a number of important nonlinear models from various fields, including chemical reaction networks, Boltzmann’s model of an ideal gas, recombination in population genetics and genetic algorithms. In the context of spin systems, it is a natural generalization of linear dynamics based on Markov chains, such as Glauber dynamics and block dynamics, which are by now well understood. However, the inherent nonlinearity makes the dynamics much harder to analyze, and rigorous quantitative results so far are limited to processes which converge to essentially trivial stationary distributions that are product measures. In this paper we provide the first quantitative convergence analysis for natural nonlinear dynamics in a combinatorial setting where the stationary distribution contains non-trivial correlations, namely spin systems at high temperatures. We prove that nonlinear versions of both the Glauber dynamics and the block dynamics converge to the Gibbs distribution of the Ising model (with given external fields) in times O(nlogn)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$O(n\\log n)$$\\end{document} and O(logn)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$O(\\log n)$$\\end{document} respectively, where n is the size of the underlying graph (number of spins). Given the lack of general analytical methods for such nonlinear systems, our analysis is unconventional, and combines tools such as information percolation (due in the linear setting to Lubetzky and Sly), a novel coupling of the Ising model with Erdős-Rényi random graphs, and non-traditional branching processes augmented by a “fragmentation” process. Our results extend immediately to any spin system with a finite number of spins and bounded interactions.