Mixing times of a Burnside process Markov chain on set partitions

Physics-informed band structure-integrated Continuous-time inhomogeneous Markov chains for stochastic occupancy modeling

Undecimated Wavelet Transform and Markov chain based Siamese network architecture for optimal glaucoma detection

Given a unichain Markov reward process (MRP), we provide an explicit expression for the bias values in terms of mean first passage times. This result implies a generalization of known Markov chain perturbation bounds for the stationary distribution to the case where the perturbed chain is not irreducible. It further yields an improved perturbation bound in 1-norm. As a special case, Kemeny’s constant can be interpreted as the translated bias in an MRP with constant reward − 1 , which offers an intuitive explanation why it is a constant. • Presents a new identity for the bias in Markov reward processes. • Generalizes results for Markov chain perturbation from irreducible to arbitrary chains. • Gives a new improved perturbation bound in 1-norm for the stationary distribution. • Provides a new intuitive explanation why Kemeny’s constant is a constant.

Applications of Markov chains in climate change modelling: A comprehensive review of advances, challenges, and future directions

Lie algebraic duality for some Markov processes

Accurately identifying the spatiotemporal evolution and spatial differentiation of carbon emission intensity in the transport sector is essential for formulating region-specific carbon reduction policies. This study develops an analytical framework that integrates both static and dynamic perspectives to examine spatial disparities in transport sector carbon emission intensity. From a static perspective, the Dagum Gini coefficient is employed to quantify spatial differences and their sources of transport carbon emission intensity. From a dynamic perspective, kernel density estimation is applied to depict the evolution trajectories of transport carbon emission intensity. Furthermore, the traditional Markov chain model is refined to construct a spatial Markov chain model that accounts for spatial adjacency, enabling identification of persistence and spatial spillover effects. The empirical results indicate that (1) The carbon emission intensity of the transport sector in China presents an overall declining trend with significant spatial heterogeneity among provinces. Regional disparities have expanded, with the largest gap between the eastern and western regions, where inter-regional differences contribute an average of 47.374% to total disparity, representing the main source of variation. (2) The carbon emission intensity in the national, eastern, and central regions tends to converge gradually, while the western region shows a pattern of initial convergence followed by renewed divergence. Within each region, several provinces maintain carbon emission intensity levels significantly higher than the average, forming a clear spatial gradient structure. (3) The traditional Markov chain analysis reveals evident persistence and club convergence in transport carbon emission intensity. The spatial Markov chain analysis further shows that neighboring regions strongly influence local transition probabilities, demonstrating spatial spillover and path dependence effects. Hypothesis testing confirms the necessity of incorporating spatial dependence into the analysis. Based on these findings, this study proposes that carbon reduction strategies in the transport sector should be tailored to regional disparities and spatial interdependencies, aiming to enhance overall mitigation efficiency and foster coordinated governance.

ABSTRACT This study models the spatial and spatio-temporal relative risk of Dengue transmission in Bandung using Bayesian inference. Applying the Besag-York-Mollié (BYM) framework, we evaluated separable and inseparable space-time models. Results show that Integrated Nested Laplace Approximation (INLA) produces estimates comparable to Markov chain Monte Carlo (MCMC) but is significantly faster. Evaluated via Deviance Information Criterion (DIC), the INLA-estimated inseparable spatio-temporal model performed best (DIC: 1795.190), effectively identifying high-risk areas like Arcamanik, Lengkong, and southeastern Bandung. This highlights INLA’s computational efficiency and the necessity of space-time interactions in robust disease mapping.

ABSTRACT This study investigates integrating metacognition into human–robot interaction (HRI) systems to improve reliability, efficiency, and trust. As HRI deployments expand, performance regulation under uncertainty becomes critical. Prior work has examined metacognition largely through behavioral observation, with limited system-level models that quantify operational impact. We address this gap by proposing a representative Markov chain model to evaluate metacognitive effects under deterministic and stochastic conditions. Using statistical analysis and probabilistic modeling, we measure impacts on machine accuracy and efficiency over extended operation. Experiments show metacognitive-enabled systems achieve a 59.29% reduction in errors and inefficiencies, with an 18.67% increase in execution time, indicating a favorable performance tradeoff. We further conceptualize metacognition as a quantifiable decision-regulation layer rather than an interface-level construct. The framework offers a scalable analytical basis for designing more dependable and trustworthy HRI systems in complex, information-intensive environments.

Respiratory syncytial virus (RSV) causes substantial disease burden worldwide, disproportionately affecting infants and young children. Higher susceptibility to RSV infections in young children, interacting with age-varying contact patterns and risk of disease progression, could drive the age-related variations in disease burden, though the extent of the susceptibility differences, and their influence on transmission dynamics and immunisation impact remains unclear. We developed an age-structured deterministic transmission model that integrated virological surveillance data, hospitalisations, and infection rates from the UK. We estimated age-dependent susceptibility coefficients for the 0- < 5years, 5-59year and ≥ 60years by integrating a profile likelihood approach with Markov Chain Monte Carlo (MCMC)-based calibration. Models were fitted to weekly RSV-positive cases in Scotland and infection rate estimates for the UK population. Age-specific infection-hospitalisation ratios (IHRs) were derived by combining modelled infections with RSV-associated hospitalisations. We evaluated multiple paediatric immunisation scenarios by estimating infections and hospitalisations averted, and the number of individuals needed to immunise (NNI) to prevent one RSV hospitalisation at varying coverage and efficacy. We estimated a susceptibility coefficient of 0.38 (95% CI 0.36-0.38) for 5-59years, and 0.38 (0.20-0.40) for ≥ 60years, relative to those under 5years. The overall annual infection rate was 51.8%, with peaked in children aged 12-23months (71.1%) and 0-2months (63.7%) using the best-fitting model, showing a substantial shift in the age distribution compared to the base model. IHRs showed a U-shaped distribution, with the highest rates in infants aged 0-2months and adults aged 75 and above. This model also projected a greater impact from immunisation programmes compared to the base model. For instance, an infant immunisation programme with 80% coverage and 80% efficacy against hospitalisation was projected to prevent 15.2% of hospitalisations, compared to 8.9% in the base model. Broader programmes, such as targeting 0-4-year-olds, resulted in larger reductions in hospitalisations (27.1%), while NNI increased as the programme expanded. The increased RSV susceptibility in children under 5years drives higher baseline transmission rates and disease burden in this subgroup, thereby influencing immunisation programme impact and efficiency.

This study develops and evaluates a hybrid Compliance–AI cybersecurity model for unified protection of traditional banking and decentralized finance (DeFi) systems in Brazil. Using publicly available data from the NIST Cybersecurity Framework, DeFi exploit repositories (REKT and DeFiLlama), Elliptic crypto-transaction graphs, IEEE-CIS fraud data, DARPA Transparent Computing datasets, and Monte Carlo–simulated cross-domain attack scenarios, the research applies hierarchical clustering, supervised learning, Markov chain modeling, and stochastic simulation. Results show that 45% of banking controls are transferable or hybridizable to DeFi, that embedding machine-readable compliance features improves ROC–AUC from 0.842 to 0.914 and reduces false positives by nearly 47%, and that bidirectional orchestration lowers escalation probability by over 54%. Monte Carlo analysis further indicates a 62% reduction in tail financial risk under the hybrid architecture. The study recommends machine-readable regulation, compliance-aware AI deployment, orchestrated enforcement layers, and expanded RegTech and SupTech adoption to strengthen systemic financial cybersecurity. Keywords: Compliance–AI Integration, Financial Cybersecurity, Decentralized Finance, Machine-Readable Regulation, Systemic Cyber Risk.

Mosquitoes are vectors of diseases globally, making development of models that better explain mosquito abundance imperative. Mosquito population dynamics are particularly sensitive to local weather conditions, and mosquito-borne disease outbreaks can be spatially concentrated. There is a need for improved modeling studies to address whether spatial variation in disease outbreaks is driven by spatial variation in weather conditions, especially in dry and hot environments. In the present study, we built a climate-driven model of mosquito population dynamics and compared whether predictions of mosquito abundance at the county scale were improved by accounting for subcounty weather variation. Using a 5-year time series of weekly Culex quinquefasciatus abundance data collected for each zip code in Maricopa County, USA, we assessed how local variation in weather could explain and predict mosquito population dynamics. We built a mechanistic model of mosquito population dynamics influenced by daily maximum temperature and 30-day accumulated precipitation. We grouped zip codes on the basis of similar patterns of temperature and precipitation using functional clustering. We compared two approaches: one using county-level average weather and another using data from the identified weather clusters. We used Markov chain Monte Carlo simulations to fit the mechanistic model using averaged weather data in each cluster, then compared the model fit with observed data between the county-level model and the model on the basis of weather-based clusters. Simple, weather-forced modeling accurately estimated detailed Cx. quinquefasciatus abundance trajectories throughout the 5-year period. Modeling mosquito abundances in the subcounty spatial clusters demonstrated that the same effects of temperature and precipitation on population growth rates could explain small-scale changes in mosquito abundances. However, when we aggregated the subcounty model fits to the county-scale, the resulting fits were more precise but sometimes overly confident, leading to lower overall accuracy and predictive performance. Our study demonstrated the importance of collecting fine-scale mosquito abundance data to improve our understanding and the predictability of mosquito population dynamics. The strong performance of both the cluster-based and county-level models illustrated the value of spatially sensitive modeling in this application. We anticipate that such modeling efforts will aid in using weather forecasts to predict increases in mosquito populations, thereby aiding in efforts to control the spread of infectious disease.

A Markov Process Model of Joint Liability and Loan Repayment for Sustainable Microfinance

Globally, land use land cover (LULC) changes are recognized as a key factor contributing to environmental changes. Understanding the LULC changes in river basin areas is essential for river basin management. The present study aims to analyze LULC changes from 1994 to 2024 in the lower part of the Mahananda River basin and predict future LULC scenarios for 2034. The study cast off Landsat imagery and random forest (RF) classification technique for past LULC classification, while the Cellular Automata Markov Chain (CA-MA) model was employed for future LULC prediction. Furthermore, a statistical technique, Receiver Operating Characteristics (ROC), was utilized for CA-MC model validation. Results highlight a substantial reduction of vegetation cover of 2249.7 km2 and barren land by 1774.08 km2, while cultivated lands, settlement, and water body increased by 3389.75 km2, 831.81 km2, and 440.8 km2, respectively, over the last three decades, revealing the influences of both natural disturbance and anthropogenic activities. The LULC classification's accuracy was assessed using Kappa coefficient and these values are above 80%, indicating that the LULC classifications in this study are highly reliable. The prediction results reveal a further decrease of vegetation cover at 503.53 km2, a continuous increase of cultivation land at 4725.29 km2, and a settlement area of 919.85 km2 over the future decades. The ROC value of 0.71 suggests that the CA-MC model performs reliably in predicting future LULC scenarios, demonstrating acceptable model accuracy. These comprehensive assessments aid in the creation of suitable land management plans and policies to accomplish or uphold sustainable development in the Mahananda River basin.

Abstract Random walks in a finite Abelian group G are studied. They use Markov chains with doubly stochastic transition matrices, in a Birkhoff subpolytope B ( G ) associated with the group G . It is shown that all future probability vectors belong to a polytope which does not depend on the transition matrices, and which shrinks during time evolution. Various quantities are used to describe the probability vectors: the majorization preorder, Lorenz values and the Gini index, entropic quantities, and the total variation distance. The general results are applied to the additive group Z ( d ) , and to the Heisenberg–Weyl group H W ( d ) / Z ( d ) . A physical implementation of random walks in Z ( d ) that involves a sequence of non-selective projective measurements, is discussed. A physical implementation of random walks in the Heisenberg–Weyl group H W ( d ) / Z ( d ) using a sequence of non-selective positive operator-valued measure measurements with coherent states, is also presented.

Abstract We present a 5 yr X-ray spectral and timing analysis of the optically selected tidal disruption event (TDE) AT2019teq, which displays extreme variability, including order-of-magnitude changes in flux on minute-to-day timescales, and a rare late-time emergence of hard X-ray emission leading to the longest-lived corona in a known TDE. In one epoch, we detect submillihertz quasiperiodic oscillations with significance tested via Markov Chain Monte Carlo based red-noise simulations ( p ≤ 0.03). AT2019teq exhibits a clear spectral evolution from a soft (blackbody-dominated) state to a hard (power-law-dominated) state, with a late-time radio brightening that may be associated with the state transition. We identify similarities between AT2019teq’s evolution and X-ray binary soft-to-hard state transitions, albeit at higher luminosity and much faster timescales. We use the presence of both the disk-dominated and corona-dominated states to apply multiple mass estimators from X-ray spectral and variability properties. These techniques are mutually consistent within 2 σ and systematically yield a lower BH mass ( log ( M BH / M ⊙ ) = 5.67 ± 0.09 ) than inferred from host galaxy scaling ( log ( M BH / M ⊙ ) = 6.14 ± 0.19 ).

Respiratory syncytial virus (RSV) causes recurrent infections throughout life. Yet, the form and durability of antibody-mediated protection induced by infection remained poorly understood. We conducted a longitudinal cohort study in Taizhou City, China. Participant age distribution approximately reflected the age structure of population in Taizhou. Blood samples were collected at baseline (March 12, 2023) and four follow-up visits (May 7-26, 2023, August 13-23, 2023, November 12, 2023, and June 2-3, 2024). Serum-specific RSV pre-fusion F (PreF) protein antibody titres were measured for all samples, and neutralising antibodies against RSV strain A2 and RSV strain B were assessed in a subset. Using a Bayesian inference framework and reversible-jump Markov Chain Monte Carlo, we recovered individual infection histories, estimated population-level RSV incidence, and characterised antibody dynamics from longitudinal PreF titres. We also estimated the correlates of protection (COP) by quantifying the relationship between PreF antibody titres and infection risk. A total of 508 individuals were included. Over the study period, two RSV epidemic waves were observed: the first wave between May and November 2023 and the second from February to May 2024. We estimated seasonal RSV infection rates of 4-7% in the community-based population. Post-infection immunity responses were most robust in young children ≤ 5years and weakest in adults ≥ 75years, with peak fold rises in antibody titres of 29.4 and 5.4, respectively. The post-infection antibody titres declined substantially, with fourfold rises sustained for an average of 128days (95% credible interval of 21-281). The probability of protection given exposure increased with higher PreF titres across all age groups. However, the predictive performance of PreF titres as a COP varied markedly by age: titres strongly predicted protection in young children but showed weaker discrimination in older children and adults, and minimal predictive value in the oldest adults. These results revealed age-related differences in the durability and protective value of natural infection-elicited RSV PreF antibody responses, emphasising the importance of age-specific prevention strategies.

The study concentrates on improving the dependability and operational efficacy of LoRa-based Wireless Sensor Networks (WSNs), which are extensively utilized in IoT applications, especially for long-range private networks. It seeks to deal with the problems that arise when a single node or communication line fails, which can have a big effect on network performance. The research utilizes a Markovian matrix theoretical framework to examine and simulate the behavior of LoRa-based Wireless Sensor Networks (WSNs), incorporating states such as Sleep (S), Idle (I), Transmit (T), and Receive (R) mode. A Python software program was created to put this model into action, allowing for testing and simulation with 50 fake data sets. The method stresses that the network should always be running, that sensor nodes should be replaced quickly, and that the network should be able to handle failures of individual nodes. The simulations indicate that using the Markov chain model in conjunction with detailed step-by-step math computation may yield a more accurate analysis of the data sets. The methodology also helps you evaluate protocols, change control, look at scalability, and make informed choices about how to build a network. This work offers practical benefits for the design, deployment, and maintenance of LoRa-based WSNs in real-world IoT scenarios. It supports network administrators and engineers in predicting power consumption, designing resilient protocols, scaling networks efficiently, and implementing adaptive control measures to ensure continuous and dependable operation. The integration of Markov chain mathematical modeling with Python-based simulation provides a robust solution for ensuring reliable operation of LoRa-based WSNs. The approach mitigates the impact of node failures, supports rapid recovery, and maintains network integrity.

Common deep learning approaches for antibody engineering focus on modeling the marginal distribution of sequences. By treating sequences as independent samples, however, these methods overlook affinity maturation as a rich and largely untapped source of information about the evolutionary process by which antibodies explore the underlying fitness landscape. In contrast, classical phylogenetic models explicitly represent evolutionary dynamics but lack the expressivity to capture complex epistatic interactions. We bridge this gap with CoSiNE, a continuous-time Markov chain parameterized by a deep neural network. Mathematically, we prove that CoSiNE provides a first-order approximation to the intractable sequential point mutation process, capturing epistatic effects with an error bound that is quadratic in branch length. Empirically, CoSiNE outperforms state-of-the-art language models in zero-shot variant effect prediction by explicitly disentangling selection from context-dependent somatic hypermutation. Finally, we introduce Guided Gillespie, a classifier-guided sampling scheme that steers CoSiNE at inference time, enabling efficient optimization of antibody binding affinity toward specific antigens.

To optimize vedolizumab therapy for Crohn's disease, this study aimed to construct a pharmacokinetic/pharmacodynamic (PK/PD) model by applying model-based meta-analysis (MBMA) methods to summary-level clinical data (SLD) and to evaluate a model-informed precision dosing (MIPD) approach based on the model. We used the results of previously reported PK analysis. For PD analysis, summary-level Crohn's Disease Activity Index (CDAI) data were extracted from Phase III trials. Following covariate analysis, the final model was fitted using the Markov chain Monte Carlo Bayesian method (four chains; burn-in 10 000; 100 000 sampling) in NONMEM. The final model was leveraged for empirical Bayes estimation in an MIPD case study. The posterior estimates of the final model indicated adequate between-chain mixing and acceptable precision ($\hat{R}$<1.01; most achieved bulk and tail effective sample size > 1000 with lowest values of 541 and 820, respectively). In the case study, the MIPD approach based on the final model accurately predicted the time course of the CDAI with minimal. PK/PD modelling by applying MBMA methods to SLD is feasible when access to individual patient data (IPD) is restricted. The MIPD approach demonstrated promising predictive accuracy. Future confirmatory studies using IPD are warranted to establish impact on patient outcomes.