Abstract This paper extends the traditional group self-annuitisation framework by explicitly incorporating mortality heterogeneity among participants. Heterogeneity stems from multiple factors that lead individuals to age at different paces, despite being born in the same year. Ageing is modelled as a finite-state continuous-time Markov process where each state represents a distinct phase of physiological deterioration, and transitions capture the stochastic progression towards death. Benefits are differentiated by ageing state and, after issue, they are dynamically adjusted in response to the realised evolution of both ageing and mortality. Our design is novel in its use of the Markov ageing framework within a risk-sharing scheme and in how benefits are updated. Indeed, both benefits and their respective adjustment coefficients are state-specific. Through the explicit modelling of cross-subsidies across states, the design ensures that actuarial equivalence between benefits and available resources is preserved both at the pool level and within each ageing state. However, we find that benefit adjustments based on actuarial equivalence may display undesirable patterns in some ageing classes, when their size shrinks substantially; this happens, in particular, in the younger ageing states, which are likely to empty out. To contrast such effects, we introduce a design preserving a target level of differentiation across states that mitigates the unfavourable impact of a declining size for younger ages. In our analysis, we point out that such a design (which is desirable in many respects) implies solidarity effects across states. Such effects can be identified by comparing benefit amounts under the two assumptions (i.e., benefits adjusted according to actuarial equivalence or so to preserve a predefined level of differentiation). The proposed framework is tested using Australian mortality data.

Addressing the challenge of balancing prediction accuracy and interpretability in smartphone battery life forecasting, this study constructs a physically-driven continuous-time dynamical model and a dynamically calibrated Time-to-End-of-Life (TTE) prediction system. The study first decomposes battery output power into external loads and internal losses based on the law of energy conservation, coupling it with a first-order lumped-parameter thermal model. To address user behavior randomness, a continuous-time Markov chain simulation mode switching is introduced, utilizing an Unscented Kalman Filter (UKF) for online parameter calibration. Empirical results demonstrate that this model accurately describes the evolution trajectory of the state of charge (SOC) under various load and temperature conditions. Specifically, the framework achieves precise runtime estimation across diverse scenarios—predicting TTE from 10.69 hours in compute-heavy modes to 23.46 hours in light-load modes—and identifies CPU operations as the primary energy consumption driver, while revealing GPS impact is negligible. This study provides a systematic quantitative solution for energy efficiency management and high-precision runtime prediction in mobile devices.

This paper presents the design, modeling, and analysis of a dynamic channel allocation method for IoT systems with a finite number of nodes and heterogeneous data traffic types. The proposed method effectively supports both real-time and non-real-time data transmission over a sample IoT networking scenario. The proposed dynamic channel allocation method was analytically modeled using a 2-dimensional continuous-time Markov chain, and its performance was evaluated in a sample IoT network scenario involving a finite number of IoT nodes. Additionally, a discrete event simulation model of the proposed model was developed. The analytical model results of the proposed channel allocation method were verified by comparing them with the simulation model results. In a network scenario with 12 channels, 1000 real-time and non-real-time users, and a total load of 10, the throughput was obtained as 4.534 for non-real-time nodes and 3.477 for real-time nodes. Furthermore, under the same load, the channel utilization is 18.892% for non-real-time nodes and 43.474% for real-time nodes. Thus, it has been demonstrated that the developed dynamic channel allocation method offers significant performance in IoT applications, particularly in the efficient transmission of heterogeneous data traffic.

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.

In this paper, we propose two approaches to derive the discrete Poincaré inequality for the B-schemes, a family of finite volume discretization schemes, for the one-dimensional Fokker-Planck equation in full space. We study the properties of the spatially discretized Fokker-Planck equation in the viewpoint of a continuous-time Markov chain. The first approach is based on Gamma-calculus, through which we show that the Bakry-Émery criterion still holds in the discrete setting. The second approach employs the Lyapunov function method, allowing us to extend a local discrete Poincaré inequality to the full space. The assumptions required for both approaches are roughly comparable with some minor differences. These methods have the potential to be extended to higher dimensions. As a result, we obtain exponential convergence to equilibrium for the discrete schemes by applying the discrete Poincaré inequality.

Massively parallel algorithms leveraging graphics processing units (GPUs) have significantly accelerated inference in statistical phylogenetics, with applications in understanding pathogen evolution, population dynamics, natural selection, and evolutionary timescales using ancient genomes. Continued advancements in GPU hardware necessitate innovative algorithms to fully exploit their potential. Here, we introduce three novel algorithms that accelerate matrix multiplication operations using tensor cores on NVIDIA GPUs to calculate the observed sequence data likelihood and the gradient of the log-likelihood with respect to branch-length-specific parameters under continuous-time Markov chain models of evolution. The algorithms presented in this paper deliver 2 to 3-fold gains in performance for amino acid and codon models compared to existing GPU-based massively parallel algorithms. Notably, these performance gains are accompanied by a ~2-fold reduction in energy usage, demonstrating the potential of these algorithms to lower the carbon footprint of evolutionary computing. We make our new algorithms available to the broader phylogenetics community through the high-performance, open source library BEAGLE v4.0.0.

The paper develops a coarse-grained framework for computing mean extinction times in multi-metastable systems modeled as one-step continuous-time Markov chains with an absorbing state. At the microscopic level, backward equations on finite corridors are solved to obtain closed-form series for committors, mean first-passage times, and intrawell (basin) waiting times. A renewal–reward construction then yields effective interwell transition rates written as a success probability divided by a mean cycle duration, providing an interpretable effective rate constant. These rates define a reduced Markov chain on the wells together with extinction; mean extinction times follow from a linear system, and the associated fundamental matrix quantifies pre-extinction residence times in each coarse state. This framework makes explicit how multiple escape pathways and intrawell dwell times contribute to extinction statistics in finite systems. The method is illustrated on a double-well landscape with an extinction state, using a reversible potential-to-rates mapping for the numerical example. Comparisons of alternative intrawell models and validation against exact one-step computations demonstrate accuracy at finite system sizes, including regimes where diffusion approximations are unreliable. The resulting formulas require only local rate data, remain numerically stable under strong bias, and extend directly to multiple wells and flexible boundary conditions.

In a recent article, we mathematically extended conventional discrete-time finite Markov chains, characterized by an $N \times N$ transition probability matrix, to discrete-time finite fuzzy Markov chains capable of modeling fuzzy states and fuzzy events, which frequently arise in fields such as biomedicine. This advancement is built upon the theory of stochastic fuzzy discrete event systems (SFDESs) and the supervised learning algorithm for FDESs, previously published by the authors. The fuzzy Markov chain is represented by a single-event SFDES comprising $N^{2}$ FDES, each with its own occurrence probability and an associated $N \times N$ event transition matrix, which is automatically learned using the aforementioned learning algorithm. Additionally, each FDES is associated with a set of fuzzy sets that fuzzify the random variable values and are required to satisfy specific constraints. Manually designing these fuzzy sets can be challenging, especially for modelers with little or no prior knowledge of fuzzy set theory. To overcome this challenge, we develop stochastic gradient descent-based algorithms that simultaneously learn constrained Gaussian fuzzy sets and the event transition matrices. To reduce the complexity of parameter learning, the Gaussian fuzzy sets are designed such that their means are computed directly from the terminal points of the subintervals that divide the ranges of the random variables, rather than being learned. Furthermore, dependencies between the Gaussian fuzzy sets for each random variable are introduced, reducing the number of standard deviations to be learned to $N$ for all Gaussian fuzzy sets in an FDES, while the remaining standard deviations are computed based on these dependencies. In addition, we establish that these new algorithms are fully applicable to continuous-time finite fuzzy Markov chains, extending their utility to a broader range of applications. An illustrative example is provided to demonstrate the effectiveness of the learning algorithms. These new algorithms make fuzzy Markov chains more accessible to modelers, regardless of their familiarity with fuzzy sets, while enhancing the overall practicality of the approach.

Abstract Fragmentation population-balance equations describe how particle-size distributions evolve under breakage and daughter fragment redistribution. By log-size we mean the logarithmic internal coordinate ξ = ln( x / x 0 ), where x is a size-like variable taken proportional to a conserved mass. From a standard self-similar fragmentation class we derive an exact conservative transport equation in ξ for the normalized mass fraction : a state-dependent pure-jump master equation (nonlocal internal-coordinate mass transfer). We also give an explicit Gorini–Kossakowski–Sudarshan–Lindblad (GKSL) factorization whose diagonal sector reproduces this master equation, used here as an optional structure-preserving operator representation and constrained parameterization for inverse modeling. In a controlled small-jump regime, the nonlocal jump transport reduces to a drift–diffusion (Fokker–Planck) operator in log-size space. Under detailed-balance conditions this operator admits the standard symmetrization to a self-adjoint Schrödinger-type spectral problem, motivating compact parametric hypothesis classes for distribution shapes. We then present two inverse routes: (i) time-resolved parametric fitting of transport/spectral parameters, and (ii) a regularized steady inversion that reconstructs an effective potential from a measured steady PSD. We include numerical benchmarks: forward simulation of the jump transport model (continuous-time Markov chain discretization) and its drift–diffusion reduction, quantitative discrepancy metrics, and inverse parameter recovery on an Airy half-line synthetic benchmark under multiplicative noise.

Guaranteed annuity options (GAOs) allow policyholders to convert accumulated funds into life annuities at maturity at a guaranteed minimum rate. Thus, insurers are exposed to both investment and longevity risks. Accurate valuation of these long-term, survival-contingent contracts is essential for solvency assessment and risk management. Many existing approaches assume independence between interest rate and mortality risks. This paper develops a computationally efficient pricing framework for GAOs that jointly models interest and mortality rates as correlated stochastic processes with regime-switching dynamics governed by a finite-state continuous-time Markov chain. Model parameters are estimated using U.S. interest rates and cohort mortality data via quasi-maximum likelihood estimation. A semi-analytic valuation formula is derived based on the joint distribution of the underlying processes. Numerical results show that incorporating correlation and regime-switching materially increases GAO prices relative to conventional one-state models. The proposed semi-analytic approach delivers substantial computational advantages over standard Monte Carlo simulations. Sensitivity analysis further identifies the parameters most relevant for long-horizon pricing and solvency considerations. This highlights the practical relevance of the framework for managing longevity-linked guarantees under economic and demographic uncertainty.

Growing global data volumes and the increasing frequency of climate-related and geopolitical threats highlight the need for ultra-resilient backup infrastructures. This paper proposes a novel Satellite-RAID architecture, named O-RAID, in which clusters of satellites operate as a distributed redundant array of independent disks (RAID), enabling large-scale cold and warm backup storage in Earth's orbit. Unlike previous work on space-based computing or satellite cloud relays, this research presents a formal design for orbital storage redundancy, inter-satellite parity exchange, latency-tolerant RAID protocols and power provisioning using a geostationary solar-energy beam. To establish a foundation for quantifying system resilience, we develop a reliability framework based on a Continuous-Time Markov Chain (CTMC) model, defining the states and transition rates for future survivability analysis of an orbital RAID equivalent. The paper provides a comprehensive analysis of the system architecture, its core components and the mathematical underpinnings for erasure coding and communication. An in-depth examination of system feasibility, survivability simulations, key constraints and communication overhead is presented, concluding that orbital backup storage presents a viable and promising paradigm for national archives, disaster-resilient storage and long-term scientific data preservation with technical readiness projected by 2035.

Neural barcoding representing cortical spatiotemporal dynamics based on continuous-time Markov chains.

A partition method for bounding continuous-time Markov chain models of general reaction network.

Quantifying the risk of long-term chikungunya persistence in Miami-Dade county.

Resilience Analysis of Four-state Engineering Systems Under the Framework of Continuous-time Markov Chain Model

Mask-based privacy-preserving adaptive bipartite fuzzy consensus control for stochastic nonlinear multi-agent systems under markovian switching topologies.

We model an epidemic spread process involving nodes that (a) experience non-trivial asymptomatic infectious periods and (b) adapt by avoiding contacts with symptomatic infectious nodes. These modeling choices reflect ample evidence that infectious individuals are often mistakenly perceived as safe contacts due to lack of symptoms and that individuals adapt to an epidemic by avoiding contacts deemed to be of risk. We capture these choices in the [Formula: see text] (Susceptible-Asymptomatic Infected-Symptomatic Infected-Susceptible) model, where we explicitly distinguish between asymptomatic and symptomatic infectious individuals. We adopt an individual-based mean-field epidemic modeling approach and formulate the system of differential equations via continuous-time Markov chain analysis. We first consider non-adaptive homogeneous and heterogeneous mixing scenarios over arbitrary static contact networks. We derive the expression for the basic reproduction number, [Formula: see text], and establish that under otherwise similar conditions the individual infection probabilities at the metastable state of [Formula: see text] dominate those in the conventional SIS model. Then, we focus on a contact-adaptive setting, where nodes avoid interactions with known infectious neighbors or reconnect with neighbors who have recovered, to study how the time-varying contact network, asymptomatic infections and their combinations affect the epidemic spread dynamics. Overall, asymptomatic infections restrict nodes' capacity to adapt (link breaking), resulting in higher link density and consequently higher epidemic prevalence. Besides, in their presence, the retarding effect of the link-breaking mechanism on epidemic prevalence is considerably mitigated. We numerically analyze how the effective link-breaking rate and the size of the asymptomatically infected population affect the link density and, ultimately, the epidemic prevalence. The epidemic threshold appears to scale inversely with the population of asymptomatic nodes, namely the epidemic starts to spread at lower infection rates when the number of asymptomatic infections is higher.

Self-cleansing intrusion-tolerant systems mitigate attacker intrusions and control through periodic recovery, thereby enhancing both availability and security. However, vulnerabilities in the control link render these systems susceptible to request forgery attacks. Furthermore, existing research on the modeling and performance analysis of such systems remains insufficient. To address these issues, this paper introduces an authentication mechanism to fortify control link security and employs Generalized Stochastic Petri Nets for system evaluation. We constructed Petri net models for three distinct scenarios: a traditional system, a system compromised by forged controller requests, and a system fortified with authentication mechanism. Subsequently, isomorphic Continuous-Time Markov Chains were derived to facilitate theoretical analysis. Quantitative evaluations were performed by deriving steady-state probabilities and conducting simulations on the PIPE platform. To further assess practicality, we conduct scalability analysis under varying system scales and parameter settings, and implement a prototype in a virtualized testbed to experimentally validate the analytical findings. Evaluation results indicate that authentication mechanism ensures the reliable execution of cleansing strategies, thereby improving system availability, enhancing security, and mitigating data leakage risks.

A military system consisting of four autonomous subsystems (a tetrasystem) is considered: air, land, sea, and drone. During combat, each subsystem is subject to a stream of random events involving losses and restorations. The dynamics of random processes is studied using a continuous-time Markov chain with sixteen asymmetric possible states. The corresponding mathematical model of the random processes is constructed in the form of sixteenth-order Kolmogorov differential equations. Formulas are found for the sixteen roots of the characteristic Kolmogorov equation, expressed in terms of the intensities of the tetrasystem's loss and restoration flows. The analytical solution to the Kolmogorov differential equations for the tetrasystem is represented in the form of ordered matrices and sixteenth-order determinants, which allows for a compact description of a large volume of initial data, overcomes limitations associated with the problem's dimensionality, and ensures adaptability to computer technologies, including the problem of verification.

Microtubules (MTs) are dynamic protein filaments essential for intracellular organization and transport, particularly in long-lived cells such as neurons. The plus and minus ends of neuronal MTs switch between growth and shrinking phases, and the nucleation of new filaments is believed to be regulated in both healthy and injury conditions. We propose stochastic and deterministic mathematical models to investigate the impact of filament nucleation and length-regulation mechanisms on emergent properties such as MT lengths and numbers in living cells. We expand our stochastic continuous-time Markov chain model of filament dynamics to incorporate MT nucleation and capture realistic stochastic fluctuations in MT numbers and tubulin availability. We also propose a simplified partial differential equation (PDE) model, which allows for tractable analytical investigation into steady-state MT distributions under different nucleation and length-regulating mechanisms. We find that the stochastic and PDE modeling approaches show good agreement in MT length distributions, and that both MT nucleation and the catastrophe rate of large-length MTs regulate MT length distributions. In both frameworks, multiple mechanistic combinations achieve the same average MT length. The models proposed can predict parameter regimes where the system is scarce in tubulin, the building block of MTs, and suggest that low filament nucleation regimes are characterized by high variation in MT lengths, while high nucleation regimes drive high variation in MT numbers. These mathematical frameworks have the potential to improve our understanding of MT regulation in both healthy and injured neurons.