Markov Chain Research Articles

UTILIZING DISCRETE HIDDEN MARKOV MODELS TO ANALYZE TETRAPLOID PLANT BREEDING

In plant heredity, the phenotype is the result of observation that can be directly observed, while the genotype is the underlying hidden factor that underlies the expression of the phenotype. The genotype is an important aspect that needs to be understood to explain the pattern of trait inheritance and predict trait inheritance in subsequent generations. The discrete hidden Markov model is a model generated by pair of an unobserved Markov chain and an observation process. This model can be applied to tetraploid plant crosses by modeling genotypes as hidden state and phenotypes as the obeservation process. The probability of dominant phenotype in monohybrid, dihybrid and trihybrid crosses occurring over ten generations during that period is as follows 61,305%, 37,583%, and 23,041%. Furthermore, as more traits are crossed, the probability of dominant phenotype appearing within ten generations decreases. When the dominant phenotype occurs over ten generations, the same genotype can be obtained in monohybrid, dihybrid, and trihybrid crosses, which is heterozygous in the first and second generations, while from the third to the tenth generation it is homozygous dominant.

Quantum computing and its implications for Asian innovation ecosystems

ABSTRACT Where quantum computing is emerging as a catalyst for innovation, this paper investigates its influence on R&D efficiency and innovation outcomes across 4,500 firms in six key sectors – pharmaceuticals, finance, materials science, energy, telecommunications, and logistics – in Asia between 2015 and 2024. The study employs advanced models, including Agent-Based Modeling (ABM), Bayesian Networks, Support Vector Machines (SVM), and Markov Chains, to analyse the relationship between quantum computing investments and innovation performance. The results indicate that high-R&D sectors, such as pharmaceuticals and finance, benefit most from quantum computing due to its role in accelerating drug discovery and optimising risk management. In contrast, low-R&D sectors like telecommunications and logistics face slower adoption due to infrastructure challenges and limited resources. Government support, particularly through subsidies and tax incentives, enhances the impact of quantum computing investments on innovation outcomes, especially in high-R&D industries. This study addresses key gaps by providing empirical evidence of quantum computing’s role in driving sectoral innovation and offering actionable insights for policymakers and industry leaders.

Modeling and Performance Evaluation of a Cellular Network with OMA and NOMA Users with Batch Arrivals by Means of an M[X]/M/S/0 Model

Nowadays, efficient spectrum usage is one of the most important design principles to take into account in wireless communications due to the exponential growth of mobile devices. In that sense, solutions such as Non-Orthogonal Multiple Access (NOMA) and cognitive radio (CR) have been proposed. In essence, NOMA allows some interference level by using non-orthogonal resource allocation with a tolerable increase in receiver complexity employing successive interference cancellation (SIC). In this work, a novel mathematical model of teletraffic for users performing accessment, simultaneously, by means of Orthogonal Multiple Access (OMA) and NOMA, is developed using a Markovian process that considers bursts of arrivals to model the access schemes. This novel procedure implies a closed-form solution of the proposed system compared to other works where these parameters are estimated assuming the moment generating function obtained with approximation models. The model is validated with a discrete event simulator, considering different scenarios and simulation conditions. The simulation results are in agreement with the mathematical solution proposed.

Coupled information-epidemic spreading with consideration of self-isolation in the context of mass media

Modern social media can facilitate the diffusion of epidemic-related information during pandemics, thereby enhancing individual epidemic awareness. However, current research places less emphasis on self-isolation behaviors stimulated by such awareness, which are crucial for long-term epidemic response. Thus, we propose a coupled information-epidemic spreading model that incorporates the impact of mass media and self-isolation behaviors. Using the Microscopic Markov Chain Approach, we analyze the model, determine the epidemic threshold, and investigate parameters contributing to intertwined dynamics. Experiments show that self-isolation effectively raises the epidemic threshold and reduces outbreak scope. Besides, stronger mass media diffusion enhances self-isolation's inhibitory effect on epidemic spread. There exists a meta-critical point in information diffusion impact; only when exceeding it does information diffusion increase the epidemic threshold, but mass media presence can eliminate this point. This research underscores the critical role of mass media and self-isolation in controlling epidemics, offering valuable insights for prevention strategies.

Modeling Emergency Traffic Using a Continuous-Time Markov Chain

This paper aims to propose a novel call for help traffic (SOS) and study its impact over Machine-to-Machine (M2M) and Human-to-Human (H2H) traffic in Internet of Things environments, specifically during disaster events. During such events (e.g., the spread COVID-19), SOS traffic, with its predicted exponential increase, will significantly influence all mobile networks. SOS traffic tends to cause many congestion overload problems that significantly affect the performance of M2M and H2H traffic. In our project, we developed a new Continuous-Time Markov Chain (CTMC) model to analyze and measure radio access performance in terms of massive SOS traffic that influences M2M and H2H traffic. Afterwards, we validate the proposed CTMC model through extensive Monte Carlo simulations. By analyzing the traffic during an emergency case, we can spot a huge impact over the three traffic types of M2M, H2H and SOS traffic. To solve the congestion problems while keeping the SOS traffic without any influence, we propose to grant the SOS traffic the highest priority over the M2M and H2H traffic. However, by implementing this solution in different proposed scenarios, the system becomes able to serve all SOS requests, while only 20% of M2M and H2H traffic could be served in the worst-case scenario. Consequently, we can alleviate the expected shortage of SOS requests during critical events, which might save many humans and rescue them from being isolated.

Star Stream Velocity Distributions in Cold Dark Matter and Warm Dark Matter Galactic Halos

The dark matter subhalos orbiting in a galactic halo perturb the orbits of stars in thin stellar streams. Over time, the random velocities in the streams develop non-Gaussian wings. The rate of velocity increase is approximately a random walk at a rate proportional to the number of subhalos, primarily those in the mass range ≈106−7 M ⊙. The distribution of random velocities in long streams is measured in simulated Milky Way–like halos that develop in representative warm dark matter (WDM) and cold dark matter (CDM) cosmologies. The radial velocity distributions are well modeled as the sum of a Gaussian and an exponential. The resulting Markov Chain Monte Carlo fits find Gaussian cores of 1−2 km s−1 and exponential wings that increase from 3 km s−1 for 5.5 keV WDM, 4 km s−1 for 7 keV WDM, to 6 km s−1 for a CDM halo. The observational prospects to use stream measurements to constrain the nature of galactic dark matter are discussed.

Learning to sample better

Abstract These lecture notes provide an introduction to recent advances in generative modeling methods based on the dynamical transportation of measures, by means of which samples from a simple base measure are mapped to samples from a target measure of interest. Special emphasis is put on the applications of these methods to Monte–Carlo (MC) sampling techniques, such as importance sampling and Markov Chain Monte–Carlo schemes. In this context, it is shown how the maps can be learned variationally using data generated by MC sampling, and how they can in turn be used to improve such sampling in a positive feedback loop.

Swarming Insects May Have Finely Tuned Characteristic Reynolds Numbers

Over the last few years, there has been much effort put into the development and validation of stochastic models of the trajectories of swarming insects. These models typically assume that the positions and velocities of swarming insects can be represented by continuous jointly Markovian processes. These models are first-order autoregressive processes. In more sophisticated models, second-order autoregressive processes, the positions, velocities, and accelerations of swarming insects are collectively Markovian. Although it is mathematically conceivable that this hierarchy of stochastic models could be extended to higher orders, here I show that such a procedure would not be well-based biologically because some terms in these models represent processes that have the potential to destabilize insect flight dynamics. This prediction is supported by an analysis of pre-existing data for laboratory swarms of the non-biting midge Chironomus riparius. I suggest that the Reynolds number is a finely tuned property of swarming, as swarms may disintegrate at both sufficiently low and sufficiently high Reynolds numbers.

Research on the Synergistic Development of China’s Pension Industry and Pension Career

To adapt to the new demographic trends and foster high-quality and sustainable population growth, this study analyzes the synergistic development of the pension industry and pension career based on the data of 31 provinces in China from 2016 to 2022, using a distance coordination model, the latest Vague set similarity measure method, new grey relational analysis, kernel density estimation, and Markov chain. The findings indicate that (1) the development levels of China’s pension industry and pension career have shown a steady upward trend, with the gap between them gradually narrowing, though the overall development of the pension career remains higher than that of the pension industry. (2) The synergistic degree of China’s pension industry and pension career is high, with the degree of synergy fluctuating but generally increasing. (3) The synergistic development degree of the pension industry and pension career has continued to rise. The increase in the synergistic development degree shows a spatial distribution pattern of “Central > East > West”. (4) The spatial distribution of synergistic development of China’s pension industry and pension career is uneven, and in the long term, regions with higher synergistic development levels tend to positively influence less developed regions.

Sum and Tensor of Quantitative Effects

Inspired by the seminal work of Hyland, Plotkin, and Power on the combination of algebraic computational effects via sum and tensor, we develop an analogous theory for the combination of quantitative algebraic effects. Quantitative algebraic effects are monadic computational effects on categories of metric spaces, which, moreover, have an algebraic presentation in the form of quantitative equational theories, a logical framework introduced by Mardare, Panangaden, and Plotkin that generalises equational logic to account for a concept of approximate equality. As our main result, we show that the sum and tensor of two quantitative equational theories correspond to the categorical sum (i.e., coproduct) and tensor, respectively, of their effects qua monads. We further give a theory of quantitative effect transformers based on these two operations, essentially providing quantitative analogues to the following monad transformers due to Moggi: exception, resumption, reader, and writer transformers. Finally, as an application, we provide the first quantitative algebraic axiomatizations to the following coalgebraic structures: Markov processes, labelled Markov processes, Mealy machines, and Markov decision processes, each endowed with their respective bisimilarity metrics. Apart from the intrinsic interest in these axiomatizations, it is pleasing they have been obtained as the composition, via sum and tensor, of simpler quantitative equational theories.

Firn seismic anisotropy in the Northeast Greenland Ice Stream from ambient-noise surface waves

Abstract. We analyse ambient-noise seismic data from 23 three-component seismic nodes to study firn velocity structure and seismic anisotropy near the EastGRIP camp along the Northeast Greenland Ice Stream (NEGIS). Using nine-component correlation tensors, we derive dispersion curves of Rayleigh and Love wave group velocities from 3 to 40 Hz. These velocity distributions exhibit anisotropy along and across the flow. To assess these variations, we invert dispersion curves for shear wave velocities (Vsh and Vsv) in the top 150 m of the NEGIS using a Markov chain Monte Carlo approach. The reconstructed 1-D shear velocity model reveals radial anisotropy in the firn, with Vsh 12 %–15 % greater than Vsv, peaking at the critical density (550 kg m−3). We combine density data from firn cores drilled in 2016 and 2018 to create a new density parameterisation for the NEGIS, serving as a reference for our results. We link seismic anisotropy in the NEGIS to effective and intrinsic causes. Seasonal densification, wind crusts, and melt layers induce effective anisotropy, leading to faster Vsh waves. Changes in firn recrystallisation cause intrinsic anisotropy, altering the Vsv / Vsh ratio. We observe a shallower firn–ice transition across the flow (≈ 50 m) compared with along the flow (≈ 60 m), suggesting increased firn compaction due to the predominant wind direction and increased deformation towards the shear margin. We demonstrate that short-duration (9 d minimum), passive, seismic deployments and noise-based analysis can determine seismic anisotropy in firn, and we reveal 2-D firn structure and variability.

Developing a severe gust load spectrum for transport aircraft based on measured load data

PurposeDeveloping severe load spectrum of transport aircraft structures is crucial for enhancing the fatigue damage correlation between full-scale fatigue testing results and operational service. The lack of consensus on severe spectrum development methods for transport aircraft has prompted the current research, resulting in a proposed approach for a severe gust load spectrum based on the acceleration cumulative exceedance surface.Design/methodology/approachThe measured load data were analyzed using a model based on the cumulative exceedance number surface to describe the variation in exceedance numbers. An improved sampling method based on multivariate Markov Chain Monte Carlo was employed to obtain the fleet fatigue damage distribution, enabling the determination of the severity of severe spectrum and the corresponding cumulative exceedance number surface, and a severe gust load spectrum was developed based on the surface.FindingsThe method that characterizes load spectrum variation using the cumulative exceedance surface minimizes the randomness of peak-trough pairs by incorporating the correlation of load spectrum peaks and troughs. This approach reduces the variation in fleet fatigue damage, thereby lowering the requirements for the severity of severe spectrum fatigue damage.Originality/valueThe proposed methodology extends from a one-dimensional curve to a two-dimensional surface, accounting for the correlation between peak and trough values to develop a severe spectrum. This approach more accurately describes the variation in acceleration cumulative exceedance numbers, directly benefiting fatigue damage calculation. This study provides valuable references for developing severe spectrum for transport aircraft.

Latent Markov time-interaction processes

We present parametric and semiparametric latent Markov time-interaction processes, that are point processes where the occurrence of an event can increase or reduce the probability of future events. We first present time-interaction processes with parametric and nonparametric baselines, then we let model parameters be modulated by a discrete state continuous time latent Markov process. Posterior inference is based on a novel and efficient data augmentation approach in the Markov Chain Monte Carlo framework. We illustrate with a simulation study; and an original application to terrorist attacks in Europe in the period 2001-2017, where we find two distinct latent clusters for the hazard of occurrence of terrorist events, negative association with GDP growth, and self-exciting phenomena.

Research on Complete Coverage Path Planning of Agricultural Robots Based on Markov Chain Improved Genetic Algorithm

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.

A multi-phase mission success evaluation approach for maritime autonomous surface ships considering equipment performance degradation and system composition changes

With the development of Maritime Autonomous Surface Ships (MASSs), the mission success assessment problem cannot be ignored because of potential security issues of MASSs. This paper addresses the issue of performance degradation at different stages, the problem of state dependence in multi-stage missions of MASSs, and the correlation problem between missions of stages. Based on the coupling of the reliability model of each single-stage mission system, a multi-stage mission success evaluation method for MASSs is proposed. By leveraging the ability of the conditional probability tables in Bayesian networks to express the complex relationships between the nodes, the dynamic Bayesian network model of stages is constructed based on the fault tree. Based on the Markov process, the problem of state dependence on shared equipment between stages is solved. Considering the complex relationship between multi-stage missions, the virtual node is introduced, and the multi-state Bayesian network is combined to realize the coupling of the reliability evaluation results of each single-stage mission. It is applied to the multi-stage mission success evaluation of the MASS to obtain the success probability of MASSs and the key equipment of each stage. The results show that evaluation results are more suitable for engineering practice.

Heterogeneous Mediation Analysis for Cox Proportional Hazards Model With Multiple Mediators.

This study proposes a heterogeneous mediation analysis for survival data that accommodates multiple mediators and sparsity of the predictors. We introduce a joint modeling approach that links the mediation regression and proportional hazards models through Bayesian additive regression trees with shared typologies. The shared tree component is motivated by the fact that confounders and effect modifiers on the causal pathways linked by different mediators often overlap. A sparsity-inducing prior is incorporated to capture the most relevant confounders and effect modifiers on different causal pathways. The individual-specific interventional direct and indirect effects are derived on the scale of the logarithm of hazards and survival function. A Bayesian approach with an efficient Markov chain Monte Carlo algorithm is developed to estimate the conditional interventional effects through the Monte Carlo implementation of the mediation formula. Simulation studies are conducted to verify the empirical performance of the proposed method. An application to the ACTG175 study further demonstrates the method's utility in causal discovery and heterogeneity quantification.

Within-chain parallelization-Giving Stan Jet Fuel for population modeling in pharmacometrics.

Stan is a powerful probabilistic programming language designed mainly for Bayesian data analysis. Torsten is a collection of Stan functions that handles the events (e.g., dosing events) and solves the ODE systems that are frequently present in pharmacometric models. To perform a Bayesian data analysis, most models in pharmacometrics require Markov Chain Monte Carlo (MCMC) methods to sample from the posterior distribution. However, MCMC is computationally expensive and can be time-consuming, enough so that people will often forgo Bayesian methods for a more traditional approach. This paper shows how to speed up the sampling process in Stan by within-chain parallelization through both multi-threading using Stan's reduce_sum() function and multi-processing using Torsten's group ODE solver. Both methods show substantial reductions in the time necessary to sufficiently sample from the posterior distribution compared with a basic approach with no within-chain parallelization.

A Conceptual Model for Health Impact Assessment of Personalized Prevention Policies

Abstract Background Personalized prevention and pharmacogenomics are emerging fields in global health, promoting tailored approaches to disease prevention and individualized drug therapy, based on the individuals’ genetic profile. However, adoption of these technologies in public health is challenged by the possibility of health disparities. Health Impact Assessment (HIA) is a useful tool to address this issue, by examining how policies differentially impact population groups, guiding stakeholders to more equitable and inclusive outcomes. Solid frameworks for assessing health impacts are needed to avoid heterogeneity when accounting for equity outcomes in HIA. This study tested a conceptual model for HIA in personalized medicine, using a case study in pharmacogenetics to map potential impacts and outcomes, with a focus on health equity. Methods A conceptual model for a HIA was developed to map expected impacts and outcomes of a health policy, aimed at enforcing DPYD genotype-guided dosing to prevent fluoropyrimidine toxicity in colorectal cancer patients. The conceptual model was developed based on literature reviews and consultation with stakeholders. Identification of relevant impacts guided selection of indicators and quantitative impact assessment using a Markov chain model. Results Impact pathways were identified using a three-tiered reference framework encompassing individual and population perspectives, organizational factors, and overarching health system considerations. The final diagram outlined key outcomes in four categories: health, organizational, economic and equity. HIA projections using this model were obtained for the DPYD testing policy. Conclusions In the rise of personalized medicine and pharmacogenomics, health inequalities challenges need to be addressed before implementation in healthcare. This study provided a novel HIA conceptual model for personalized prevention policies based on genomic information, with an emphasis on equity. Key messages • HIA is an adequate tool to evaluate potential health inequalities resulting from personalized medicine policies in healthcare. • This study provides a validated framework for HIA of personalized prevention policies grounded in genomic data.

Variational Bayesian Monte Carlo simulation for rare event assessment

Estimating rare events in structural engineering demands intensive computational resources, and the complexity of the performance function poses challenges to accurate probability estimation. To efficiently conduct the structural reliability analysis on rare events, we propose a novel variational Bayesian Monte Carlo (VBMC)-based subset simulation (SS) method. The proposed approach can be divided into two aspects: the Monte Carlo simulation (MCS) is first applied to estimate the first-layer unconditional failure probability, then VBMC is employed to estimate subsequent conditional failure probabilities. Finally, the original small failure probability is obtained by the product of the first-layer unconditional failure probability and a series of conditional failure probabilities. The proposed approach inherits the merits of SS as well as VBMC, which converts the tricky rare event estimation into a series of high-frequency event estimations and leverages VBMC instead of the canonical Markov chain to produce the independent and informative next-generation failure-conditional samples. Four case studies, including high-dimensional and discrete state space scenarios, are performed to illustrate the feasibility and generality of the proposed method.

A stochastic analysis of the dynamic space utilization in warehouses

Improving the volume space utilization of modern warehouses is a critical objective in warehouse layout design, making the accurate estimation of space utilization across different layouts essential. However, the dynamic demand and replenishment processes of heterogeneous stock keeping units (SKUs) in modern warehouses present significant challenges in accurately assessing space utilization. Traditional models have relied on deterministic frameworks that assume constant demand and production processes, which do not fully capture the heterogeneity and stochasticity in demand arrivals, sizes, and replenishment times encountered in practical scenarios. This study aims to develop a framework for computing volume space utilization in modern block stacking warehouses, incorporating both heterogeneity and stochasticity. We investigate two models in warehouse scenarios: the lost sale model, where excess demand is lost, and the backorder model, where unmet demand is backlogged. For each model, we derive the closed-form expressions of three key types of space wastes that characterize the space utilization of warehouses: honeycombing, aisle, and top-of-lane space wastes, using a continuous-time Markov chain analytical framework. Utilizing these expressions, we analyze the tradeoffs among these wastes and identify the optimal lane depth that maximizes space utilization. Our case studies show that, in a stochastic environment, the proposed computational framework allows for a more accurate estimation of space utilization, and the application of the obtained optimal lane depth can achieve significantly higher space utilization than deterministic methods found in the literature. This underscores the importance of incorporating stochasticity and heterogeneity of demand and replenishment in layout design. Additionally, by investigating the sensitivity of space utilization to varying demand processes and replenishment strategies, we provide managerial insights for adapting warehouse layout designs in response to changes in SKUs' demand and replenishment patterns.