Dynamic Stochastic Model Research Articles

Poisson distributions in stochastic dynamics of gene expression: What events do they count?

The Poisson distribution is the probability distribution of the number of independent events in a given period. Although the Poisson distribution appears ubiquitously in various stochastic dynamics of gene expression, both as time-dependent distributions and stationary distributions, underlying independent events that give rise to such distributions have not been clear, especially in the presence of the degradation of gene products, which is not a Poisson process. I show that the variable following the Poisson distribution is the number of independent events where biomolecules are created, destined to survive until the end of a given time duration. This new viewpoint enables me to rederive the Poisson distribution as a time-dependent probability distribution for molecule numbers in various monomolecular reaction models of stochastic gene dynamics. Additionally, it allows me to derive an analytic form of the time-dependent probability distribution for multispecies monomolecular reaction models with species whose lifetimes follow nonexponential distributions, which is the convolution of the Poisson distribution with the multinomial distribution. This distribution is then utilized for deriving a novel series expansion form of a time-dependent distribution for a model with a stochastic production rate.

The mechanism of boreal summer SSTA phase-locking in the far eastern Pacific

In observations, the boreal winter El Niño—Southern Oscillation (ENSO) phase-locking phenomenon is evident in the central-eastern Pacific. In the far eastern equatorial Pacific (FEP) and South American coastal regions, however, the peak of sea surface temperature anomalies (SSTA) tends to occur in the boreal summer, with fewer winter peak events. By separating the direct ENSO forcing from the FEP SSTA, we found that the summer peak preference is contributed by the residual SSTA component, while the ENSO forcing provides only a small probability of winter peak. The dynamics of FEP SSTA phase-locking in observations and its biases in the climate models are investigated by adopting a linear stochastic-dynamical model. In observations, the summer phase-locking of FEP SSTA is controlled by the seasonal modulation of the SSTA damping process. In contrast, in the climate models the strength of FEP SSTA phase-locking is much smaller than observed due to the overly negative SSTA damping rate.

A model predictive control approach for energy saving optimization of an electronic assembly line

The energy-saving potential of original equipment manufacturers (OEMs) for electronic products is substantial owing to the huge market size of assembling industry in China. A semi-automatic electronic assembly line (SAEAL) for smart-phones is introduced, and its digital twin (DT) enabled energy-saving platform is developed as the hardware foundation. We propose a stochastic dynamics model via max-plus algebra to characterize the spatio-temporal nature of state transition, which provides dynamical opportunity windows for further energy-saving control strategy. Accordingly, model linearization is conducted to obtain linear state and output equations. Then, a model predictive control (MPC) approach for energy saving optimization is provided to determine the optimal start-stop control signal. The dynamics modeling and MPC approach have been applied and verified in the case of assembly line. The results show that the optimization approach could reach a proportion of 49% for the equipment sleep time of total running time and save a considerable amount of energy for normal production of OEMs.

PDEM-based multi-component and global reliability evaluation framework for steel tubular transmission towers with semi-rigid connections

The conventional analysis and design of transmission towers usually ignore the effect of semi-rigid behaviors of bolted joints and simplify the joints as the rigid or pinned connection, which might overestimate or underestimate the structural response of transmission towers and the reliability of structural components and systems. To consider the effect of semi-rigid connections on the reliability of transmission towers in this paper, a stochastic dynamic finite element model of steel tubular transmission towers with semi-rigid connections (STTTs-SRCs) is established by deriving their stiffness matrix, where the uncertainties of dimensions, material and semi-rigid connections are considered and the wind loads are simulated as stochastic processes by the dimension-reduced probabilistic simulation approach. Then, based on the equivalent extreme-value event, the multi-component and global performance functions with stress and displacement failure modes for STTTs-SRCs are established, respectively. Further, a reliability evaluation framework for STTTs-SRCs is proposed based on the probability density evolution method (PDEM). Finally, a practical engineering transmission tower is regarded as an example to demonstrate the implementation process of the proposed reliability evaluation framework. Moreover, the reliability of steel tubular transmission towers with rigid and pinned connections is compared with that of STTTs-SRCs to investigate the effect of semi-rigid connections on the reliability of transmission towers. In general, the semi-rigid connections would mainly affect the value of the multi-component failure probability, however, it would not change the location where the maximum failure probability of components occurs. Additionally, the semi-rigid connection significantly affects the global failure probability of towers for the stress failure mode while slightly affects the global failure probability of towers for the displacement failure mode. Therefore, it may be more appropriate to consider the semi-rigid connections into the analysis and design of steel tubular transmission towers.

The Life-Cycle Effects of Pension Reforms: A Structural Approach

Abstract To assess the life-cycle welfare effects of pension reforms, we provide a dynamic stochastic model of saving, portfolio choice, and retirement featuring a rich characterisation of the pension system. Relying on the exogenous variation from a sequence of Italian pension reforms, we identify and estimate the model, which is then used to draw implications of alternative pension policies. The validated model predicts substantial social security wealth effects on retirement, with the offset between public pension wealth and private savings softened when households can adjust their retirement decisions. We further find important distributional effects of pension reforms, with households’ welfare decreasing more the later in the working life they face the reform. Our findings have implications for the design of pension policies and the support they might generate.

The small-bat-in-summer paradigm: Energetics and adaptive behavioural routines of bats investigated through a stochastic dynamic model.

Strong seasonality at high latitudes represents a major challenge for many endotherms as they must balance survival and reproduction in an environment that varies widely in food availability and temperature. To avoid energetic mismatches caused by limited foraging time and stochastic weather conditions, bats employ the energy-saving state of torpor during summer to save accumulated energy reserves. However, at high-latitude small-bats-in-summer face a particular challenge: as nocturnal foragers, they rely on the darkness at night to avoid predators and/or interspecific competition, but live in an environment with short, light summer nights, and even a lack of true night at the northernmost distributions of some bat species. To predict optimal behaviour in relation to latitudinal variation in diurnal cycles, we constructed a stochastic dynamic programming model of bats living at high latitudes. Using a stochastic dynamic programming framework with values that are representative for our study system, we show that individual energetic reserves are a strong driver of daytime use of torpor and night-time foraging behaviour alike, with these linked effects being both temperature- and photoperiod-dependent. We further used the model to predict survival probabilities at five locations across a latitudinal gradient (60.1° N to 70.9° N), finding that combinations of photoperiod and temperature conditions limited population distributions in the model. To verify our model results, we compared predictions for optimal decisions with our own empirical data collected on northern bats (Eptesicus nilssonii) from two latitudes in Norway. The similarities between our predictions and observations provide strong evidence that this model framework incorporates the most important drivers of diurnal decision-making in bat physiology and behaviour. Comparing empirical data and model predictions also revealed that bats facing lighter night conditions further north restrict their mass gain, which strengthens the hypothesis that predation threat is a main driver of bat nocturnality. Our model findings regarding state-dependent decisions in bats should contribute to the understanding of how bats cope with the summer challenges at high latitudes.

Experimental and Theoretical Brownian Dynamics Analysis of Ion Transport During Cellular Electroporation of E. coli Bacteria.

Escherichia coli bacterium is a rod-shaped organism composed of a complex double membrane structure. Knowledge of electric field driven ion transport through both membranes and the evolution of their induced permeabilization has important applications in biomedical engineering, delivery of genes and antibacterial agents. However, few studies have been conducted on Gram-negative bacteria in this regard considering the contribution of all ion types. To address this gap in knowledge, we have developed a deterministic and stochastic Brownian dynamics model to simulate in 3D space the motion of ions through pores formed in the plasma membranes of E. coli cells during electroporation. The diffusion coefficient, mobility, and translation time of Ca2+, Mg2+, Na+, K+, and Cl- ions within the pore region are estimated from the numerical model. Calculations of pore's conductance have been validated with experiments conducted at Gustave Roussy. From the simulations, it was found that the main driving force of ionic uptake during the pulse is the one due to the externally applied electric field. The results from this work provide a better understanding of ion transport during electroporation, aiding in the design of electrical pulses for maximizing ion throughput, primarily for application in cancer treatment.

A stochastic evolutionary dynamic game model for analyzing the ride-sourcing market with limited platform reputation

Ride-sourcing services have become increasingly vital in meeting on-demand mobility needs. However, safety issues and public health concerns are obstacles for passengers' trust in ride-sourcing service providers. In this paper, we propose a stochastic evolutionary dynamic game approach to modeling and managing the ride-sourcing market with limited platform reputation, and interpret some intriguing phenomena in terms of passengers' and drivers' travel behavior, e.g. survivor bias, reciprocity, and tragedy of the commons. A stochastic state dynamic game model is formulated to capture complicated interactions among three games/states, i.e. trust game, complaint game, and rating-based game. The stationary distribution of each state and transitional probabilities are deducted from the stochastic game theory. We analyze the ride-sourcing system's evolution and reveal its intrinsic mechanism based on the model. We found that, if the governmental support for complaints is inadequate and passengers bear the high complaint costs, drivers will be more inclined to compensate passengers privately (i.e. reciprocity) to escape punishment for unqualified service. As a result, the service quality will deteriorate in the long run. To prevent the deterioration of service quality, we explore adaptive pricing strategies for the ride-sourcing platform and suggest managerial strategies for the government. This paper bridges the gap between the dynamic evolution and the mechanism of trust in ride-sourcing services, which has been seldom studied in the literature. All of the analytical results are illustrated by numerical experiments.

Vessel weather routing subject to sulfur emission regulation

The International Maritime Organization (IMO) rolled out a set of new regulations that limit the sulfur content in the fuel oil used by ships, which came into effect from 2020. This study aims to explore the operational decisions of vessels inside and outside emission control areas (ECAs) under uncertain weather conditions and scrutinizes the economics of two types of ships: fuel-switching and scrubber installation. Such operational decisions include speed, trim, and path decision. We construct a navigation grid system, in which each grid contains weather parameters and sea condition. This navigation grid system can be applied to other type of ships due to the well-established cost structure. To improve fuel consumption estimation, we train fuel consumption estimation functions with respect to weather parameters, sea conditions, and operational decisions. This study then develops a stochastic dynamic programming model to optimize the path decisions, vessel speed, and trim. To evaluate the efficiency of the developed stochastic dynamic programming model, we further conduct a case study on a Post-Panamax container vessel that operates westbound from Hamburg to Houston. We identify the path decision, speed and trim under ECAs and the uncertain weather conditions. Surprisingly, this case study demonstrates that the ship utilizing fuel-switching takes a detour trip; in contrast, the ship with a scrubber chooses the shortest path by maximizing the speed. Additionally, we observe a knock-on effect — scrubber installation lifts carbon dioxide emissions due to increased vessel speed outside the ECA region. Rich managerial insights and potential policy implications are discussed.

A stochastic dynamical model for nosocomial infections with co-circulation of sensitive and resistant bacterial strains.

Nosocomial infections (hospital-acquired) has been an important public health problem, which may make those patients with infections or involved visitors and hospital personnel at higher risk of worse clinical outcomes or infection, and then consume more healthcare resources. Taking into account the stochasticity of the death and discharge rate of patients staying in hospitals, in this paper, we propose a stochastic dynamical model describing the transmission of nosocomial pathogens among patients admitted for hospital stays. The stochastic terms of the model are incorporated to capture the randomness arising from death and discharge processes of patients. Firstly, a sufficient condition is established for the stochastic extinction of disease. It shows that introducing randomness in the model will result in lower potential of nosocomial outbreaks. Further, we establish a threshold criterion on the existence of stationary distribution and ergodicity for any positive solution of the model. Particularly, the spectral radius form of stochastic threshold value is calculated in the special case. Moreover, the numerical simulations are conducted to both validate the theoretical results and investigate the effect of prevention and control strategies on the prevalence of nosocomial infection. We show that enhancing hygiene, targeting colonized and infected patients, improving antibiotic treatment accuracy, shortening treatment periods are all crucial factors to contain nosocomial infections.

Colonization-persistence trade-offs in natural bacterial communities.

Fitness equalizing mechanisms, such as trade-offs, are recognized as one of the main factors promoting species coexistence in community ecology. However, they have rarely been explored in microbial communities. Although microbial communities are highly diverse, the coexistence of their multiple taxa is largely attributed to niche differences and high dispersal rates, following the principle 'everything is everywhere, but the environment selects'. We use a dynamical stochastic model based on the theory of island biogeography to study highly diverse bacterial communities over time across three different systems (soils, alpine lakes and shallow saline lakes). Assuming fitness equalization mechanisms, here we newly analytically derive colonization-persistence trade-offs, and report a signal of such trade-offs in natural bacterial communities. Moreover, we show that different subsets of species in the community drive this trade-off. Rare taxa, which are occasional and more likely to follow independent colonization/extinction dynamics, drive this trade-off in the aquatic communities, while the core sub-community did it in the soils. We conclude that equalizing mechanisms may be more important than previously recognized in bacterial communities. Our work also emphasizes the fundamental value of dynamical models for understanding temporal patterns and processes in highly diverse communities.

Modeling the profitability of investing in cooling systems in dairy farms under several intensities of heat stress in the Mediterranean

Heat stress (HS) in dairy cows affects dry matter intake, milk yield, reproduction, and culling rate. Cooling systems (CS) may partially revert these effects, but their profitability depends on the price of milk and effectiveness and cost of the CS. Because these effects may interact over time, stochastic dynamic models are useful tools to evaluate the effects of HS and the profitability of CS. Several HS intensity scenarios, from 1,000 to 31,000 temperature and humidity index load (THILoad, units/yr), were simulated in a stochastic dynamic dairy herd simulator, with 3 milk prices (€0.28, €0.32, and €0.36/L) and 2 initial investment costs in fans and sprinklers (€100 and €200/cow). The HS and CS scenarios simulated were modeled as a function of the THILoad to predict the technical and economic performance in 21 selected locations of the Mediterranean. The THILoad mean of the 21 selected locations was 12,530 (ranging from 6,908 to 31,424). Heat stress reduced milk yield in a range of 346 to 1,696 L/cow per year, feeding costs in a range of €63 to €266/cow per year, and pregnancy rate in a range of 1.0 to 3.0%/yr and increased culling rates in a range of 5.7 to 16.4%/yr compared with the control scenario. The implementation of CS increased milk yield in a range from 173 to 859 L/cow per year, feeding cost in a range from €26 to €139/cow per year, and pregnancy rate in a range from 0.1 to 1.0%/yr and reduced culling rate in a range from 1.0 to 3.9%/yr compared with HS scenarios. When the THILoad was ≤6,300, the implementation of CS was never profitable, from 6,300 to 11,000 was dependent on milk price and CS cost, and over 11,000 was consistently profitable. The Δnet margin (€/cow per year) for CS at an initial investment cost of €100/cow ranged from -9 to 239 and at an initial investment cost of €200/cow ranged from -24 to 225. The profitability of CS depends on the THILoad, milk price, and CS cost.

Effect of update rule transition triggered by Q-learning algorithm in evolutionary prisoner's dilemma game involving extortion

Most studies have shown that the heterogeneity of update rules has an important impact on evolutionary game dynamics. In the meanwhile, Q-learning algorithm has gained attention and extensive study in evolutionary games. Therefore, a mixed stochastic evolutionary game dynamic model involving extortion strategy is constructed by combining imitation and aspiration-driven updating rules. During the evolution of the model, individuals will use the Q-learning algorithm which is a typical self-reinforcement learning algorithm to determine which update rule to adopt. Herein, through numerical simulation analyses, it is found that the mixed stochastic evolutionary game dynamic model affected by the Q-learning algorithm ensures the survival of cooperators in the grid network. Moreover, the cooperators cannot form a cooperation cluster in the grid network but will form a chessboard-like distribution with extortioners to protect cooperators from the invasion of defectors. In addition, a series of results show that, before the evolution turns into steady state, our model increases the number of nodes utilizing the average aspiration-driven update rule, thereby promoting the emergence of chessboard-like distribution. Overall, our study may provide some interesting insights into the development of cooperative behavior in the real world.

Hierarchical optimal allocation of BESS using APT-FPSO based on stochastic programming model considering voltage sensitivity and eigenvalues analyses

Integration of energy storage systems (ESSs) to microgrids (MGs) due to the growing penetration of intermittent energy resources is a great motivation to develop studies in the context of optimal sizing and placement of these systems. In this paper, a multi-objective bi-level optimization problem is addressed based on the stochastic nature and dynamic model of power system elements.As a preliminary step, the optimal size and capacity of the battery energy storage system (BESS) are determined to minimize frequency fluctuations. This level has been performed based on three approaches considering the daily intra-hour stochastic data. In the secondary level, the dynamic behaviour of all MG elements has been considered and correspondingly a dynamic objective function based on system eigenvalues and voltage sensitivity index (VSI) has been developed. According to the proposed objective function, the secondary step for sizing and placement of the battery units has been performed by adaptive particularly tuneable fuzzy particle swarm optimization (APT-FPSO) algorithm to reduce power losses, improve the voltage profile/ stability, and mitigate low-frequency fluctuations. Finally, the effectiveness of the proposed approach is evaluated using time-domain simulations, voltage sensitivity studies, and eigenvalue analysis.

Probabilities Are Not Enough: Formal Controller Synthesis for Stochastic Dynamical Models with Epistemic Uncertainty

Capturing uncertainty in models of complex dynamical systems is crucial to designing safe controllers. Stochastic noise causes aleatoric uncertainty, whereas imprecise knowledge of model parameters leads to epistemic uncertainty. Several approaches use formal abstractions to synthesize policies that satisfy temporal specifications related to safety and reachability. However, the underlying models exclusively capture aleatoric but not epistemic uncertainty, and thus require that model parameters are known precisely. Our contribution to overcoming this restriction is a novel abstraction-based controller synthesis method for continuous-state models with stochastic noise and uncertain parameters. By sampling techniques and robust analysis, we capture both aleatoric and epistemic uncertainty, with a user-specified confidence level, in the transition probability intervals of a so-called interval Markov decision process (iMDP). We synthesize an optimal policy on this iMDP, which translates (with the specified confidence level) to a feedback controller for the continuous model with the same performance guarantees. Our experimental benchmarks confirm that accounting for epistemic uncertainty leads to controllers that are more robust against variations in parameter values.

Dynamical behavior and density function of a stochastic model of HPV infection and cervical cancer with a case study for Xinjiang, China

In this article, combining the transmission features of HPV infection and secondary cervical cancer in Xinjiang, China, a stochastic dynamical model for the HPV infection and secondary cervical cancer with environmental white noise is proposed. Firstly, the stochastic extinction of disease is investigated. A sufficient criterion for the asymptotic behavior of any positive solution of stochastic model revolving around the disease-free equilibrium of corresponding deterministic model is established. Secondly, a threshold criterion for the existence of unique ergodic stationary distribution is obtained by means of the auxiliary function. Furthermore, a new technique of partitioned matrix for the calculation of probability density function is proposed, the expression of a log-normal density function around the quasi-endemic equilibrium of stochastic model is calculated. Lastly, the best-fit parameter values in our model are identified by the MCMC algorithm on the basis of the cervical cancer data in Xinjiang province, China. The basic reproduction number is estimated as 1.3496 (95% CnI: (1.3458, 1.3716)). Then, to determine the key parameters of the model, the sensitivity analysis is explored. Some possible interventions and control measures are provided to reduce the HPV infection spread and cervical cancer in Xinjiang of China.

A Stochastic Dynamical Model of Slope Creep and Failure

AbstractWe propose a stochastic dynamical model to simulate slope secondary and tertiary creep phenomena. The slope secondary creep is represented by the Kesten process defined as a stochastic affine auto‐regressive process involving both multiplicative and additive random variables. The Kesten process can realistically capture the co‐existence of a background deformation and intermittent displacement bursts, which are together well characterized by an inverse gamma velocity distribution. The slope tertiary creep is modeled by a nonlinear stochastic dynamical equation embodying a nonlinear feedback mechanism and a nonlinear random effect, which can mimic the development of slow or catastrophic landslides. For catastrophic landslides, the probability density function of slope velocities tends to deviate from the inverse gamma distribution by populating the “dragon‐king” regime, although sometimes they may grow undetectably in the “black‐swan” regime. Our model provides a quantitative framework to understand, simulate, and interpret complex landslide displacement time series.

Modeling stock-oil co-dependence with Dynamic Stochastic MIDAS Copula models

Stock and oil relationship is usually time-varying and depends on the current economic conditions. In this study, we propose a new Dynamic Stochastic Mixed data sampling (DSM) copula model, that decomposes the stock-oil relationship into a short-run dynamic stochastic component and a long-run component, governed by related macro-finance variables. Inference and prediction is carried out using a novel Bayesian estimation strategy, that can efficiently estimate the latent states and delivers an estimate of the log marginal likelihood used for model comparison. We find that inflation/interest rate, uncertainty and liquidity factors are the main drivers of the long-run co-dependence. We show that the multi-step-ahead variance covariance forecasts constructed using the proposed approach are closer to the true values as compared to the benchmark model. Finally, investment portfolios, based on the proposed DSM copula model, are more accurate and produce better economic outcomes as compared to other alternatives.

Applying the AD-AS Model to the Housing Market of Post-Socialist Economies

We propose applying the standard aggregate demand and aggregate supply model (AD-AS) to the housing market. It is a very simple and intuitive tool that can help shed light on the major forces at play in the market and that can supplement the use of the general equilibrium and dynamic stochastic equilibrium models (DSGE). The latter models are very sophisticated and aim to cover many aspects of the economy, but they require a significant number of long time series to estimate the model parameters. However, in many countries, such as post-socialist countries, the time series are short. Those models moreover cover only real house prices, but in certain situations we should consider real and nominal prices at the same time.

An exploratory assessment of the Bering-Chukchi-Beaufort Seas stock of bowhead whales using a stochastic population dynamics model

The stochastic population dynamics model used by Aboriginal Whaling Management Procedure developers is revised to correct weaknesses related to uncertainty parameterisation and replacement yield estimation. Two variants of this model, along with the standard deterministic version, are used to assess the Bering-Chukchi-Beaufort Seas stock of bowhead whales. The variants differ with respect to the magnitude and complexity of the stochastic variation they introduce into natural mortality and birth/calf survival processes. An allowable catch statistic, E (Q0), is defined for appropriate use with stochastic model assessments. Using the same assessment methods, likelihood and priors as IWC (1999a), 5th percentiles of E (Q0) were found to be 117, 106 and 91 for the deterministic, simpler stochastic and extreme stochastic models, respectively. Bayes factor results show that there is no evidence suggesting that either stochastic model should be favoured over any simpler alternative, and the deterministic model yielded the best fit overall. The E (Q0) estimates confirm and strengthen past IWC Scientific Committee inference that under current bowhead subsistence hunting levels the stock should continue to increase towards stabilisation above its maximum sustainable yield level.