Stochastic Modeling Framework Research Articles

Quantitative evaluation of geological uncertainty and its influence on tunnel structural performance using improved coupled Markov chain

The geo-structures embedded in the multiple variable strata could be significantly affected by the geological uncertainty. The quantitative evaluation of geological uncertainty and its influence on the structural safety of embedded tunnels are seldom studied in the past. This paper aims to analyse the effect of geological uncertainty on the structural performance of tunnel using the proposed stochastic geological modelling framework. The geological uncertainty is characterized using an improved coupled Markov chain model based on sparse limited boreholes. A mapping approach is presented to solve the mesh asymmetry problem between the simulated strata and the numerical tunnel model. The tunnel structural performance analysis is then conducted based on the combined model considering the geological uncertainty and tunnel structure. A geological uncertainty index (GUI) is proposed to quantitatively evaluate the level of uncertainty of each borehole and the whole site. The effect of the borehole layout scheme on uncertainty evaluation of factor of safety of tunnel structure is investigated by a large number of stratigraphic realizations. Boreholes collected from Norway with relatively more considerable variability and from Shanghai with relatively more minor variability are adopted as case studies to illustrate the proposed probabilistic analysis framework. The results show that the boreholes with larger GUI values and closer to tunnel locations have a greater weight to affect the embedded tunnel structural performance in uncertain geological strata.

Dynamic interdependence of advice seeking, loaning, and recovery characteristics in recovery homes

ABSTRACT Recovery homes in the US provide stable housing for over 250,000 individuals with past histories of homelessness, psychiatric comorbidity and criminal justice involvement. We need to know more about how these settings help those who remain in recovery. Our study measured advice seeking and willingness-to-loan relationships, and operationalized them as a dynamic multiplex social network—multiple, simultaneous interdependent relationships—that exist within 42 Oxford House recovery homes over time. By pooling relationship dynamics across recovery houses, a Stochastic Actor-Oriented Modeling (SAOM) framework was used to estimate a set of parameters governing the evolution of the network and the recovery attributes of the nodes simultaneously. Findings indicated that advice and loan relationships and recovery-related attitudes were endogenously interdependent, and these results were affected exogenously by gender, ethnicity, and reason for leaving the recovery houses. Prior findings had indicated that higher advice seeking in recovery houses was related to higher levels of stress with more negative outcomes. However, the current study found that recovery is enhanced over time if advice was sought from residents with higher recovery scores. Our study shows that social embedding, i.e., one’s position in relationship networks affects recovery prospects. More specifically, the formation of ties with relatively more recovered residents is an important predictor of better outcomes.

Stochastic modeling of geometrical uncertainties on complex domains, with application to additive manufacturing and brain interface geometries

We present a stochastic modeling framework to represent and simulate spatially-dependent geometrical uncertainties on complex geometries. While the consideration of random geometrical perturbations has long been a subject of interest in computational engineering, most studies proposed so far have addressed the case of regular geometries such as cylinders and plates. Here, standard random field representations, such as Karhunen–Loève expansions, can readily be used owing, in particular, to the relative simplicity to construct covariance operators on regular shapes. On the contrary, applying such techniques on arbitrary, non-convex domains remains difficult in general. In this work, we formulate a new representation for spatially-correlated geometrical uncertainties that allows complex domains to be efficiently handled. Building on previous contributions by the authors, the approach relies on the combination of a stochastic partial differential equation approach, introduced to capture salient features of the underlying geometry such as local curvature and singularities on the fly, and an information-theoretic model, aimed to enforce non-Gaussianity. More specifically, we propose a methodology where the interface of interest is immersed into a fictitious domain, and define algorithmic procedures to directly sample random perturbations on the manifold. A simple strategy based on statistical conditioning is also presented to update realizations and prevent self-intersections in the perturbed finite element mesh. We finally provide challenging examples to demonstrate the robustness of the framework, including the case of a gyroid structure produced by additive manufacturing and brain interfaces in patient-specific geometries. In both applications, we discuss suitable parameterization for the filtering operator and quantify the impact of the uncertainties through forward propagation.

Disentangling the Legacies of Climate and Management on Tree Growth

Legacies of past climate conditions and historical management govern forest productivity and tree growth. Understanding how these processes interact and the timescales over which they influence tree growth is critical to assess forest vulnerability to climate change. Yet, few studies address this issue, likely because integrated long-term records of both growth and forest management are uncommon. We applied the stochastic antecedent modelling (SAM) framework to annual tree-ring widths from mixed forests to recover the ecological memory of tree growth. We quantified the effects of antecedent temperature and precipitation up to 4 years preceding the year of ring formation and integrated management effects with records of harvesting intensity from historical forest management archives. The SAM approach uncovered important time periods most influential to growth, typically the warmer and drier months or seasons, but variation among species and sites emerged. Silver fir responded primarily to past climate conditions (25–50 months prior to the year of ring formation), while European beech and Scots pine responded mostly to climate conditions during the year of ring formation and the previous year, although these responses varied among sites. Past management and climate interacted in such a way that harvesting promoted growth in young silver fir under wet and warm conditions and in old European beech under drier and cooler conditions. Our study shows that the ecological memory associated with climate legacies and historical forest management is species-specific and context-dependent, suggesting that both aspects are needed to properly evaluate forest functioning under climate change.

Associating Climatic Trends with Stochastic Modelling of Flow Sequences

Water is essential to all lifeforms including various ecological, geological, hydrological, and climatic processes/activities. With the changing climate, associated El Niño/Southern Oscillation (ENSO) events appear to stimulate highly uncertain patterns of precipitation (P) and evapotranspiration (EV) processes across the globe. Changes in P and EV patterns are highly sensitive to temperature (T) variation and thus also affect natural streamflow processes. This paper presents a novel suite of stochastic modelling approaches for associating streamflow sequences with climatic trends. The present work is built upon a stochastic modelling framework (HMM_GP) that integrates a hidden Markov model (HMM) with a generalised Pareto (GP) distribution for simulating synthetic flow sequences. The GP distribution within the HMM_GP model aims to improve the model’s efficiency in effectively simulating extreme events. This paper further investigated the potential of generalised extreme value distribution (GEV) coupled with an HMM model within a regression-based scheme for associating the impacts of precipitation and evapotranspiration processes on streamflow. The statistical characteristic of the pioneering modelling schematic was thoroughly assessed for its suitability to generate and predict synthetic river flow sequences for a set of future climatic projections, specifically during ENSO events. The new modelling schematic can be adapted for a range of applications in hydrology, agriculture, and climate change.

Dynamic modeling and real-time management of a system of EV fast-charging stations

Demand for electric vehicles (EVs), and thus EV charging, has steadily increased over the last decade. Studies suggest that fast-charging facilities are crucial for the EV market. However, there is limited fast-charging infrastructure in most parts of the world to support EV travel, especially long-distance trips. The goal of this study is to develop a stochastic dynamic simulation modeling framework of a regional system of EV fast-charging stations for real-time management and strategic planning (i.e., capacity allocation) purposes. To model EV user behavior, specifically fast-charging station choices, the framework incorporates a multinomial logit station choice model that considers station charging prices, expected wait times, and detour distances. To capture the dynamics of supply and demand at each EV fast-charging station, the framework incorporates a multi-server queueing model in the simulation. The study assumes that multiple fast-charging stations are managed by a single entity (public or private) and that the demand for these stations are interrelated (through the station choice model). To manage the system of stations, this study proposes and tests dynamic demand-responsive price adjustment (DDRPA) schemes based on station queue lengths. The study applies the modeling framework to a system of EV fast-charging stations in Southern California. The computational results indicate that DDRPA strategies are an effective mechanism to balance charging demand across fast-charging stations. Specifically, compared to the no DDRPA scheme case, the quadratic DDRPA scheme reduces average wait time by 26%, increases charging station revenue (and user costs) by 5.8%, while, most importantly, increasing social welfare by 2.7% in the base scenario. Moreover, the study also illustrates that the modeling framework can evaluate the allocation of EV fast-charging station capacity, to identify stations that require additional chargers and areas that would benefit from additional fast-charging stations.

Glucose Prediction under Variable-Length Time-Stamped Daily Events: A Seasonal Stochastic Local Modeling Framework.

Accurate glucose prediction along a long-enough time horizon is a key component for technology to improve type 1 diabetes treatment. Subjects with diabetes might benefit from supervision and control systems that accurately predict risks and trigger corrective actions early enough with improved mitigation. However, large intra-patient variability poses big challenges to glucose prediction. In previous works by the authors, clustering and local modeling techniques with seasonal stochastic models proved to be efficient, allowing for good glucose prediction accuracy for long prediction horizons. Continuous glucose monitoring (CGM) data were partitioned into fixed-length postprandial time subseries and clustered with Fuzzy C-Means to collect similar behaviors, enforcing seasonality at each cluster after subseries concatenation. Then, seasonal stochastic models were identified for each cluster and local predictions were integrated into a global prediction. However, free-living conditions do not support the fixed-length partition of CGM data since daily events duration is variable. In this work, a new algorithm is provided to overcome this constraint, allowing better coping with patient’s variability under variable-length time-stamped daily events in supervision and control applications. Besides predicted glucose, two real-time indices are additionally provided—a crispness index, indicating good representation of current glucose behavior by a single model, and a normality index, allowing for the detection of an abnormal glucose behavior (unusual according to registered historical data). The framework is tested in a proof-of-concept in silico study with ten patients over four month training data and two independent two month validation datasets, with and without abnormal behaviors, from the distribution version of the UVA/Padova simulator extended with diverse sources of intra-patient variability.

Recent declines in life expectancy: Implication on longevity risk hedging

An article published in the British Medical Journal in 2018 reveals that a number of developed countries have experienced a decline in life expectancy in recent years. Within the classical framework of stochastic mortality modeling, the observed decline in life expectancy may be attributed to noises around the fitted log-linear trends in age-specific death rates. However, the patterns of the mortality heat maps for these countries suggest that it is likely a result of a fading of waves of high mortality improvement, which previously contributed to a linear rise in life expectancy in the developed world. In this paper, we introduce an improved version of the heat wave mortality model, which has the potential to capture the cessation of the waves of high mortality improvement. The proposed model is then used to examine the impact of declines in life expectancy on index-based longevity hedges. It is found that if life expectancy declines, a simple delta hedge still performs reasonably well in the sense that the over-hedging problem is only modest.

A combined analysis of hedge effectiveness and capital efficiency in longevity hedging

By hedging longevity exposures, annuity providers can reduce both the uncertainty in future cash flows and capital charges in a cost efficient manner. We argue that a separate analysis of these two aspects cannot provide a full picture of the implications of longevity hedging, in particular when using index-based instruments.Hence, we propose a stochastic modeling framework for a joint analysis of the risk-reducing effect and the economic impact of longevity hedges in terms of hedge effectiveness and capital efficiency, respectively. In an economic capital model under Solvency II, a wide selection of customized and index-based instruments is analyzed. We show that different hedging objectives require different instruments on different index populations and discuss the accompanying trade-off between hedge effectiveness and capital efficiency. While customized hedges naturally outperform their index-based counterparts in terms of hedge effectiveness, we show that cost efficient index-based designs may be more capital efficient.

PRICING LONGEVITY-LINKED SECURITIES IN THE PRESENCE OF MORTALITY TREND CHANGES

ABSTRACTEven though the trend in mortality improvements has experienced several permanent changes in the past, the uncertainty regarding future mortality trends is often left unmodeled when pricing longevity-linked securities. In this paper, we present a stochastic modeling framework for the valuation of longevity-linked securities which explicitly considers the risk of random future changes in the long-term mortality trend. We construct a set of meaningful probability distortions which imply equivalent risk-adjusted pricing measures under which the basic model structure is preserved. Inspired by risk-based capital requirements for (re)insurers, we also establish a cost-of-capital pricing approach which then serves as the appropriate reference framework for finding a reasonable range for the market price of longevity risk. In a numerical application, we demonstrate that our model produces plausible risk loadings and show that a greater proportion of the risk loading is allocated to longer maturities when the risk of random future mortality trend changes is adequately modeled.

Reliability assessment of stochastic networks with ER connectivity and ER dependency

In stochastic networks, nodes usually function dependently and interact with other nodes through connectivity links or dependency links. In this paper, the model for stochastic networks considering sub-networks with connectivity and dependency links of Erdös-Rényi (ER) topology is proposed, which is defined as networks with arbitrary pair of nodes randomly connected/depended by a constant probability. The reliability evaluation framework for the proposed networks is developed, where both of the extended multi-valued decision diagram (MDD) method and Monte Carlo simulation (MCS) are involved. The MDD method is proposed to assess the reliability of deterministic stochastic networks with ER connectivity and dependency, where arbitrary time to failure distributions of nodes are allowed. Based on the reliability evaluation for a stochastic network with a deterministic structure, the MCS is employed to achieve the reliability analysis of corresponding stochastic networks. Numerical examples are presented to demonstrate the proposed stochastic network model and reliability evaluation framework, where the probability distributions for the reliability of stochastic networks are provided.

Stochastic challenges to interrupting helminth transmission

Predicting the effect of different programmes designed to control both the morbidity induced by helminth infections and parasite transmission is greatly facilitated by the use of mathematical models of transmission and control impact. In such models, it is essential to account for the many sources of uncertainty – natural, or otherwise – to ensure robustness in prediction and to accurately depict variation around an expected outcome. In this paper, we investigate how well the standard deterministic models match the predictions made using individual-based stochastic simulations. We also explore how well concepts which derive from deterministic models, such as ‘breakpoints’ in transmission, apply in the stochastic world. Employing an individual-based stochastic model framework we also investigate how transmission and control are affected by the migration of infected people into a defined community. To give our study focus we consider the control of soil-transmitted helminths (STH) by mass drug administration (MDA), though our methodology is readily applicable to the other helminth species such as the schistosome parasites and the filarial worms. We show it is possible to theoretically define a ‘stochastic breakpoint’ where much noise surrounds the expected deterministic breakpoint. We also discuss the concept of the ‘interruption of transmission’ independent of the ‘breakpoint’ concept where analyses of model behaviour illustrate the current limitations of deterministic models to account for the ‘fade-out’ or transmission extinction behaviour in simulations. Our analysis of migration confirms a relationship between the critical infected human migration rate scale (i.e., order of magnitude) per unit of time and the death rate of infective stages that are released into the free-living environment. This relationship is shown to determine the likelihood that control activities aim at chemotherapeutic treatment of the human host will eliminate transmission. The development of a new stochastic simulation code for STH in the form of a publicly-available open-source python package which includes features to incorporate many population stratifications, different control interventions including mass drug administration (with defined frequency, coverage levels and compliance patterns) and inter-village human migration is also described.

Evaluation of the implications of ice‐jam flood mitigation measures

AbstractIce‐jam flood risk management requires new approaches to reduce flood damages. Although many structural and non‐structural measures are implemented to reduce the impacts of ice‐jam flooding, there are still many challenges in identifying appropriate strategies to reduce the ice‐jam flood risk along northern rivers. The main purpose of this study is to provide a novel methodological framework to assess the feasibility of various ice‐jam flood mitigation measures based on risk analysis. A total of three ice‐jam flood mitigation measures (artificial breakup, sediment dredging and dike installation) were examined using a stochastic modelling framework for the potential to reduce the ice‐jam flood risk along the Athabasca River at Fort McMurray. An ensemble of hundreds of backwater level profiles was used to construct ice‐jam flood hazard maps to estimate expected annual damages, using depth‐damage curves for structural and content damages, within the downtown area of Fort McMurray. The results show that, while sediment dredging may be able to reduce a certain level of expected annual damages in the town, and artificial breakup and a dike with a crest elevation of 250 m a.s.l. can be the most effective measures to reduce the amount of expected annual damages.

Benefits of Stochastic Optimization for Scheduling Energy Storage in Wholesale Electricity Markets

We propose a two-stage stochastic model for optimizing the operation of energy storage. The model captures two important features: uncertain real-time prices when day-ahead operational commitments are made; and the price impact of charging and discharging energy storage. We demonstrate that if energy storage has full flexibility to make real-time adjustments to its day-ahead commitment and market prices do not respond to charging and discharging decisions, there is no value in using a stochastic modeling framework, i.e., the value of stochastic solution is always zero. This is because in such a case the energy storage behaves purely as a financial arbitrageur day ahead, which can be captured using a deterministic model. We show also that prices responding to its operation can make it profitable for energy storage to “waste” energy, for instance by charging and discharging simultaneously, which is normally sub-optimal. We demonstrate our model and how to calibrate the price-response functions from historical data with a practical case study.

Stochastic short-term integrated electricity procurement and production scheduling for a large consumer

This paper addresses the problem faced by large electricity consumers to simultaneously determine the optimal day-ahead electricity procurement and the optimal energy-aware production schedule. The inherent uncertainty of the problem, due to the bidding process in the day-ahead market, is dealt with by means of the stochastic programming modeling framework. In particular, a two-stage problem is formulated with the aim of establishing the optimal bidding strategy and the optimal production schedule hedging against price uncertainty. The optimal integrated solution is defined to minimize the overall cost and to control the risk of high cost scenarios due to uncertain price peaks. The stochastic model is solved with a scenario-decomposition approach. Extensive numerical experiments have been carried out to assess the performance of the proposed decision approach. The results collected when considering an industrial relevant case-study show the superiority of the proposed methodology in comparison with a deterministic approach.

Theoretical study of the impact of adaptation on cell-fate heterogeneity and fractional killing

Fractional killing illustrates the cell propensity to display a heterogeneous fate response over a wide range of stimuli. The interplay between the nonlinear and stochastic dynamics of biochemical networks plays a fundamental role in shaping this probabilistic response and in reconciling requirements for heterogeneity and controllability of cell-fate decisions. The stress-induced fate choice between life and death depends on an early adaptation response which may contribute to fractional killing by amplifying small differences between cells. To test this hypothesis, we consider a stochastic modeling framework suited for comprehensive sensitivity analysis of dose response curve through the computation of a fractionality index. Combining bifurcation analysis and Langevin simulation, we show that adaptation dynamics enhances noise-induced cell-fate heterogeneity by shifting from a saddle-node to a saddle-collision transition scenario. The generality of this result is further assessed by a computational analysis of a detailed regulatory network model of apoptosis initiation and by a theoretical analysis of stochastic bifurcation mechanisms. Overall, the present study identifies a cooperative interplay between stochastic, adaptation and decision intracellular processes that could promote cell-fate heterogeneity in many contexts.

Modelling COVID 19 in the Basque Country from introduction to control measure response

In March 2020, a multidisciplinary task force (so-called Basque Modelling Task Force, BMTF) was created to assist the Basque health managers and Government during the COVID-19 responses. BMTF is a modelling team, working on different approaches, including stochastic processes, statistical methods and artificial intelligence. Here we describe the efforts and challenges to develop a flexible modeling framework able to describe the dynamics observed for the tested positive cases, including the modelling development steps. The results obtained by a new stochastic SHARUCD model framework are presented. Our models differentiate mild and asymptomatic from severe infections prone to be hospitalized and were able to predict the course of the epidemic, providing important projections on the national health system’s necessities during the increased population demand on hospital admissions. Short and longer-term predictions were tested with good results adjusted to the available epidemiological data. We have shown that the partial lockdown measures were effective and enough to slow down disease transmission in the Basque Country. The growth rate lambda was calculated from the model and from the data and the implications for the reproduction ratio r are shown. The analysis of the growth rates from the data led to improved model versions describing after the exponential phase also the new information obtained during the phase of response to the control measures. This framework is now being used to monitor disease transmission while the country lockdown was gradually lifted, with insights to specific programs for a general policy of “social distancing” and home quarantining.

An effective method to calculate atomic movements in 3D objects with tuneable stochasticity (3DO-SKMF)

We present an effective computer simulation method, called 3D object stochastic kinetic modelling framework (3DO-SKMF), to calculate atomic movements in 3D objects including surface segregation and Gibbs–Thomson effect (surface curvature). Objects with any kind of shapes can easily be considered thanks to the flexibility and versatility of the model and code. Accordingly, the model and the computer code can be used in a wide variety of applications: nanoparticles, nanorods, nanotubes, nanopillars, etc. To increase the versatility of the model, it includes stochastic noise in a tuneable manner. This means that if the noise level is zero, the model is completely deterministic (mean-field), whereas by increasing the noise level the result gets closer and closer to that obtained by a kinetic Monte Carlo calculation. This allows us to calculate processes with activation barriers. Besides demonstrating the capabilities of the model, we also reproduce an experimental result showing decomposition of Ag–Cu nanoparticles. Program summaryProgram title: 3DO-SKMFCPC Library link to program files:http://dx.doi.org/10.17632/776b7txmhv.1Licensing provisions: CC BY NC 3.0Programming language: ISO CNature of problem: Atomistic simulation of nano-objects with free surfaces by calculating occupation probabilities. The model includes surface segregation and Gibbs–Thomson effect (surface curvature).Solution method: Numerical solution of a system of differential equations with taking into account the conservation of matter. The number of equations is equal to the number of lattice sites in a 3D lattice.Additional comments including restrictions and unusual features: The model contains parameters that can be determined from macroscopic measurements, still in the background it follows an atomistic approach. Note that the provided code is written for nanospheres (hollow and solid), nanowires and nanotubes, however objects with any kind of shapes can easily be considered. Due to the flexibility of the code, with minor change of initialization, any 3D object can be simulated. The published code uses the face centred cubic lattice (fcc), its modification for other lattices is, however, straightforward.

Predicting the second wave of COVID-19 in Washtenaw County, MI

The COVID-19 pandemic has highlighted the patchwork nature of disease epidemics, with infection spread dynamics varying wildly across countries and across states within the US. To explore this issue, we study and predict the spread of COVID-19 in Washtenaw County, MI, which is home to University of Michigan and Eastern Michigan University, and in close proximity to Detroit, MI, a major epicenter of the epidemic in Michigan. We apply a discrete and stochastic network-based modeling framework allowing us to track every individual in the county. In this framework, we construct contact networks based on synthetic population datasets specific for Washtenaw County that are derived from US Census datasets. We assign individuals to households, workplaces, schools, and group quarters (such as prisons or long term care facilities). In addition, we assign casual contacts to each individual at random. Using this framework, we explicitly simulate Michigan-specific government-mandated workplace and school closures as well as social distancing measures. We perform sensitivity analyses to identify key model parameters and mechanisms contributing to the observed disease burden in the three months following the first observed cases of COVID-19 in Michigan. We then consider several scenarios for relaxing restrictions and reopening workplaces to predict what actions would be most prudent. In particular, we consider the effects of 1) different timings for reopening, and 2) different levels of workplace vs. casual contact re-engagement. We find that delaying reopening does not reduce the magnitude of the second peak of cases, but only delays it. Reducing levels of casual contact, on the other hand, both delays and lowers the second peak. Through simulations and sensitivity analyses, we explore mechanisms driving the magnitude and timing of a second wave of infections upon re-opening. We find that the most significant factors are workplace and casual contacts and protective measures taken by infected individuals who have sought care. This model can be adapted to other US counties using synthetic population databases and data specific to those regions.

A Stochastic Modelling Framework for Single Cell Migration: Coupling Contractility and Focal Adhesions

The interaction of the actin cytoskeleton with cell–substrate adhesions is necessary for cell migration. While the trajectories of motile cells have a stochastic character, investigations of cell motility mechanisms rarely elaborate on the origins of the observed randomness. Here, guided by a few fundamental attributes of cell motility, I construct a minimal stochastic cell migration model from ground-up. The resulting model couples a deterministic actomyosin contractility mechanism with stochastic cell–substrate adhesion kinetics, and yields a well-defined piecewise deterministic process. Numerical simulations reproduce several experimentally observed results, including anomalous diffusion, tactic migration and contact guidance. This work provides a basis for the development of cell–cell collision and population migration models.