Stochastic Model Research Articles

Unified uniaxial compressive constitutive model for C20–C120 concrete based on stochastic damage theory

The concrete uniaxial compressive stress-strain model is essential for analyzing reinforced concrete members and structures. However, models applicable to C20–C120 concrete are still relatively rare. Moreover, the previous empirical model construction methods may not reflect the physical mechanisms and randomness of concrete failure well. To this end, the database was constructed by collecting and analyzing uniaxial compressive stress-strain curve test results from different scholars. The cubic compressive strength in the database ranges from 9.9 MPa to 137.3 MPa. The adaptability of the stochastic damage model was validated using the database of test curves. Subsequently, stochastic damage models for C20–C120 concrete were calibrated based on concrete compressive strength grouping curves, and practical analysis models were suggested. The results indicate that the calculated curves closely match the test curves when the plastic strain evolution parameters η1,c and η2,c in the stochastic models are taken as 0.001–0.30 and 0.19–0.25, respectively. The adaptability of the stochastic damage model is satisfactory, but the plastic strain evolution laws vary for different concrete compressive strengths, influenced by mix proportions and the probability of failure of each component on the meso-scale. When η1,c is calculated by the empirical formula proposed in this paper and η2,c is approximated as 0.22, the calculated curves for C20–C120 concrete are consistent with the mean values of the test curves. The proposed practical analysis models provide comparable accuracy to stochastic damage models, eliminating the need for iterative calculations, making them convenient for engineering applications.

Assessing rainfall radar errors with an inverse stochastic modelling framework

Abstract. Weather radar is a crucial tool for rainfall observation and forecasting, providing high-resolution estimates in both space and time. Despite this, radar rainfall estimates are subject to many error sources – including attenuation, ground clutter, beam blockage and drop-size distribution – with the true rainfall field unknown. A flexible stochastic model for simulating errors relating to the radar rainfall estimation process is implemented, inverting standard weather radar processing methods and imposing path-integrated attenuation effects, a stochastic drop-size-distribution field, and sampling and random errors. This can provide realistic weather radar images, of which we know the true rainfall field and the corrected “best-guess” rainfall field which would be obtained if they were observed in a real-world case. The structure of these errors is then investigated, with a focus on the frequency and behaviour of “rainfall shadows”. Half of the simulated weather radar images have at least 3 % of their significant rainfall rates shadowed, and 25 % have at least 45 km2 containing rainfall shadows, resulting in underestimation of the potential impacts of flooding. A model framework for investigating the behaviour of errors relating to the radar rainfall estimation process is demonstrated, with the flexible and efficient tool performing well in generating realistic weather radar images visually for a large range of event types.

Option pricing under stochastic volatility on a quantum computer

We develop quantum algorithms for pricing Asian and barrier options under the Heston model, a popular stochastic volatility model, and estimate their costs, in terms of T-count, T-depth and number of logical qubits, on instances under typical market conditions. These algorithms are based on combining well-established numerical methods for stochastic differential equations and quantum amplitude estimation technique. In particular, we empirically show that, despite its simplicity, weak Euler method achieves the same level of accuracy as the better-known strong Euler method in this task. Furthermore, by eliminating the expensive procedure of preparing Gaussian states, the quantum algorithm based on weak Euler scheme achieves drastically better efficiency than the one based on strong Euler scheme. Our resource analysis suggests that option pricing under stochastic volatility is a promising application of quantum computers, and that our algorithms render the hardware requirement for reaching practical quantum advantage in financial applications less stringent than prior art.

Evaluating the macroeconomic impact of environmental policies in New Zealand: A New Keynesian DSGE model to sustainability

This study enhances the environmental New Keynesian framework by integrating spatial spillover effects through a dynamic stochastic general equilibrium model. The simulation results reveal that while environmental regulations can lead to welfare losses, a carbon tax levy mitigates these losses more effectively than alternative approaches in New Zealand. What is surprising is the pro-cyclical nature of environmental policies. For spillovers, shocks to capital and labor tax rates substantially curtail emissions in adjacent regions. Further simulation substantiates that higher price dispersion necessitates a reduced growth rate of emissions. These conclusions compel New Zealand to explore diverse policy options for effectively decarbonizing the economy.

Resource productivity and determinants of technical efficiency among cassava farmers’ in north central, Nigeria

This research analyzed resource productivity and determinants of technical efficiency among cassava farmers in North Central, Nigeria. This research employed a multi-stage sampling technique. Primary data were used based on a well-designed questionnaire. Inferential and descriptive statistics were employed for data analysis. The results of resource productivity of inputs show that cassava cuttings and fertilizer have the highest and lowest elasticities, respectively. The mean-TE (Technical Efficiency) score of 74% (0.74) indicates that an average smallholder cassava producer in the sample needs about 26% (0.26) additional inputs to get to the frontier. In the TE components, the coefficients of labour, and fertilizers are significant different from zero at 1% probability level. The coefficients of agrochemicals, land inputs are significantly different from zero at 5% probability level, while the coefficient of cassava cuttings are significant different from zero at 10% probability level. In the TIE (technical inefficiency), component the coefficients of age, credit received, members of cooperatives are significant different from zero at 1% probability level. The policy formulations should be directed towards considering technological substitutions and mechanized agriculture. Excessive labour supply, characteristics of the developing agriculture in sub-Saharan Africa, could be pushed into the secondary sector of the Nigerian economy such as the cassava processing industry, therefore generating income, employment and maintaining Nigeria in the first (1st) position in the world ranking in term of cassava output. Also, it is recommended that improved cuttings, agrochemicals, and fertilizers should be made available to cassava farmers at appropriate time to increase productivity. Furthermore, credit should be made available to cassava farmers at a single digit interest rate, devoid of cumbersome administrative procedures. Keywords: Resource productivity, technical efficiency, cassava farmers, stochastic frontier model, Nigeria

A modified variational approach to noisy cell signaling.

Signaling in cells is full of noise and, hence, described with stochastic biochemical models. Thus, an efficient computation algorithm for these fluctuating reactions is much needed. Apart from the very popular Monte Carlo simulation, methods based on probability distributions are frequently desired due to their analytical tractability and possible numerical advantages in diverse circumstances, among which the variational approach is the most notable. In this paper, new basis functions are proposed to better depict possibly complex distribution profiles, and an extra regularization scheme is supplied to the variational equation to remove occasional degeneracy-induced singularities during the evolution. The new extension is applied to four typical biochemical reaction models and restores the Gillespie results accurately but with greatly reduced simulation time. This modified variational approach is expected to work in a wide range of cell signaling networks.

Exploring bistable plankton dynamics: stochastic model analysis by SSF techniques

Exploring bistable plankton dynamics: stochastic model analysis by SSF techniques

Thinking beyond the closure assumption: Designing surveys for estimating biological truth with occupancy models

Abstract Occupancy models estimate distributions of imperfectly detected species, but violations of the closure assumption can bias results. However, researchers working with mobile animals may find it impossible to eliminate such violations. Here, we tested the hypothesis that occupancy models fit to realistic sampling data can generate unbiased occupancy estimates for an itinerant Wood Thrush (Hylocichla mustelina) population. In 2013 and 2014, we tracked movements of 41 breeding Wood Thrush males. We modelled territory shift probabilities using logistic exposure models and within‐territory movements using continuous‐time stochastic process models. We then constructed an individual‐based model, simulated (1000 iterations) spatiotemporal locations for individuals and simulated sampling these populations using 162 different point count protocols with variable spatial (sampling radius and point placement method), and temporal (survey length, between‐survey intervals and number of surveys) characteristics. We compared occupancy estimates with true values of instantaneous, daily and seasonal occupancy from the simulations. We parameterized continuous time stochastic process models based on movements within 34 unique territories and estimated a daily territory shift probability of 0.0099 (95% CI: 0.0060, 0.0152). Simulated data indicated that estimates of occupancy ranged from 0.18 (0.06, 1.00) to 0.80 (0.71, 0.89) depending on protocol characteristics. Occupancy estimates increased with increasing survey radius, survey length and between‐survey interval. Protocols using shorter surveys and between‐survey intervals were good estimators for instantaneous occupancy (low bias and mean‐squared error) but poor estimators for daily and seasonal occupancy; longer surveys and intervals generated unbiased estimators of daily occupancy but underestimated seasonal occupancy. Logistic regression models that ignored imperfect detection outperformed occupancy models for estimating instantaneous occupancy but not daily or seasonal occupancy. For mobile animals, occupancy of sampling sites changes in space and time. Consequently, the spatial and temporal aspects of a sampling protocol have strong, but predictable, effects on occupancy model parameter estimates. Our results demonstrate that how these factors interact is critical for designing surveys that produce occupancy estimates representative of the biological process of interest to a researcher.

Joint calibration of local volatility models with stochastic interest rates using semimartingale optimal transport

We develop and implement a non-parametric method for joint exact calibration of a local volatility model and a correlated stochastic short rate model using semimartingale optimal transport. The method relies on the duality results established in Joseph et al. (Calibration of local volatility models with stochastic interest rates using optimal transport, 2023). and jointly calibrates the whole equity-rate dynamics. It uses an iterative approach which starts with a parametric model and tries to stay close to it, until a perfect calibration is obtained. We demonstrate the performance of our approach on market data using European SPX options and European cap interest rate options. Finally, we compare the joint calibration approach with the sequential calibration, in which the short rate model is calibrated first and frozen.

Translation regulation by RNA stem-loops can reduce gene expression noise

BackgroundStochastic modelling plays a crucial role in comprehending the dynamics of intracellular events in various biochemical systems, including gene-expression models. Cell-to-cell variability arises from the stochasticity or noise in the levels of gene products such as messenger RNA (mRNA) and protein. The sources of noise can stem from different factors, including structural elements. Recent studies have revealed that the mRNA structure can be more intricate than previously assumed.ResultsHere, we focus on the formation of stem-loops and present a reinterpretation of previous data, offering new insights. Our analysis demonstrates that stem-loops that restrict translation have the potential to reduce noise.ConclusionsIn conclusion, we investigate a structured/generalised version of a stochastic gene-expression model, wherein mRNA molecules can be found in one of their finite number of different states and transition between them. By characterising and deriving non-trivial analytical expressions for the steady-state protein distribution, we provide two specific examples which can be readily obtained from the structured/generalised model, showcasing the model’s practical applicability.

An R Package for Nonparametric Inference on Dynamic Populations with Infinitely Many Types.

Fleming-Viot diffusions are widely used stochastic models for population dynamics that extend the celebrated Wright-Fisher diffusions. They describe the temporal evolution of the relative frequencies of the allelic types in an ideally infinite panmictic population, whose individuals undergo random genetic drift and at birth can mutate to a new allelic type drawn from a possibly infinite potential pool, independently of their parent. Recently, Bayesian nonparametric inference has been considered for this model when a finite sample of individuals is drawn from the population at several discrete time points. Previous works have fully described the relevant estimators for this problem, but current software is available only for the Wright-Fisher finite-dimensional case. Here, we provide software for the general case, overcoming some nontrivial computational challenges posed by this setting. The R package FVDDPpkg efficiently approximates the filtering and smoothing distribution for Fleming-Viot diffusions, given finite samples of individuals collected at different times. A suitable Monte Carlo approximation is also introduced in order to reduce the computational cost.

Construction of a quantitative model for ski resort water demand and preliminary exploration of drainage irrigation pathways

In China, natural snowfall is insufficient, and ski resorts often require artificial snowmaking in winter and turf management in summer, which results in high overall water consumption and considered as one of the high water-consuming service industries, with an urgent need for theoretical foundations related to water management. Based on life cycle theory, we examined the characteristics of the water systems of ski resorts in winter and summer. A Monte Carlo simulation was used to construct a stochastic model to quantify the theoretical water consumption for snowmaking at ski resorts and to investigate the mechanisms by which various factors influence this consumption. We summarize the necessity of summer turf management and irrigation requirements at ski resorts, explore the interaction between ski resorts and agricultural irrigation. The results show that the theoretical water demand of ski resorts is basically consistent with the actual water consumption of ski resorts, that the constructed model is feasible, and that snowmaking water is the most important water use of ski resorts. Exploring the collection and reuse of meltwater or rainwater from ski resorts for agricultural irrigation in the spring and summer could provide more possibilities for the sustainable management of regional water resources. The research findings can provide a theoretical basis for scientifically and reasonably setting the norm of water intake for ski resorts and for developing comprehensive water resource management plans for ski resorts and agricultural irrigation.

Towards more realistic stochastic modelling of leakage in water distribution systems

ABSTRACT A new stochastic model is developed to predict leak types and sizes in water distribution systems. By linking records of actual failures in water networks with new tools for stochastic modelling, the study provides more accurate estimates of network leakage behaviour. District metered areas (DMAs) have been adopted internationally as best practice for monitoring and controlling leakage, with the infrastructure leakage index (ILI) as the main performance indicator. The leakage exponent (N1), which quantifies the relationship between leakage rate and pressure, is a key parameter in describing DMA leakage behaviour. After analysing thousands of stochastic networks for different combinations of pipe material and ILI, the study found that different pipe materials have distinct leakage exponent distributions. Iron and asbestos cement (AC) pipes display N1 values close to 0.5, polyvinyl chloride (PVC) pipes have the highest N1 values, and polyethylene (PE) lies between PVC and iron/AC. The study further showed that current guidelines linking ILI to N1 for different pipe materials depart substantially from the observed results, indicating that these guidelines may need to be updated. The study provides a tool for more realistic modelling of leakage that offers valuable insights into the behaviour of leakage in different pipe materials.

Deep learning surrogate for predicting hydraulic conductivity tensors from stochastic discrete fracture-matrix models

Deep learning surrogate for predicting hydraulic conductivity tensors from stochastic discrete fracture-matrix models

Geometry-based stochastic channel modeling of a semi-urban environment using simultaneously transmitting and reflecting reconfigurable intelligentsurface

Simultaneously Transmitting and Reflecting (STAR) Reconfigurable Intelligent Surface (RIS) demonstrates the ability to split incoming electromagnetic beams to transmit and reflect signals in a concurrent manner. Thus, compared to conventional RIS, service area coverage is extended on deploying STAR-RIS. This paper presents a geometry-based stochastic channel model (GBSM) of STAR-RIS-assisted outdoor wireless channel. For the considered semi-urban environment, STAR-RIS operates in energy-splitting mode. Channel between a base station (BS) and users (UR/UT) located on the reflect/transmit (R/T) side of STAR-RIS is characterised using a GBSM. An elliptical model incorporates the inevitable presence of scatterers in the considered semi-urban segment. Statistical properties of the wireless channel under test are analysed using space–time cross-correlation function (ST-CCF) and temporal auto-correlation function (ACF). Further, to gain holistic insight about the wireless channel behaviour, normalised Doppler power spectral density (ND-PSD) is estimated for semi-urban segment having three distinct underlying hypothesis as: (i) Wireless channel is governed by Rayleigh fading model, (ii) Wireless Channel is equipped with conventional RIS and (iii) STAR-RIS is an integral part of the considered wireless channel. Simulation results confirm that STAR-RIS performs at par with RIS, however, facilitating an additional degree of coverage. It is observed that temporal ACF and ST-CCF improves with an increase in the number of elements in STAR-RIS.

Intelligent Adaptive Networks for Chaos Analysis in Stochastic SIS Differential Epidemic Model with the Impact of Unpredictable Environmental Factors

In this study, an intelligent computing framework is presented to explore the influence of unpredictable environmental factors on the spread of infections. A stochastic non-linear SIS epidemic model (SISEM) is examined that incorporates a non-linear incidence rate, and impact of random fluctuations on the disease transmission. The knacks of artificial neural networks Levenberg–Marquardt (ANNLMA) technique are exploited to illustrate the behavioral complexities of stochastic non-linear SISEM, which explores the dynamics of disease transmission in a stochastic environment and provides insights into the interactions between susceptible and infectious populations. The Milstein approach of order 1 generates a dataset for the proposed ANNLMA technique by varying integrated parameters, such as the rates of recovery, death, disease transmission, noise standard deviation and the entire population, for various SISEM scenarios. The referenced dataset is randomly divided into test, validation and train sets for the weight learning of the proposed ANNLMA. The viability of the ANNLMA is measured using intensive simulation-based investigations through analysis of mean squared errors, histograms, regression and autocorrelation studies. The investigations highlighted that the ANNLMA results closely match the reference results, illustrating convergence within the 10[Formula: see text] to 10[Formula: see text] range, indicating the validity of the proposed methodology.

Stochastic measurement-based multi-cloud consolidation for efficient resource distribution

In distributed cloud systems, due to high computational complexity, existing methods cannot infinitely reduce the measurement interval to obtain the mean demand. However, considering both the unpredictability of demand and the diversity of pricing adds significant complexity to the problem. In response, we introduce an efficient algorithm called Stochastic Demand-oriented Resource consolidation based on Meta-heuristics (SDRM). The algorithm introduces the stochastic demand model and formulates a cross-cloud demand consolidation and resource scheduling problem, and tries to solve it efficiently by combining differential evolution algorithm with dynamic programming optimization. The results are provided for experiments utilizing both simulated and real-world data. It demonstrates that compared with traditional algorithms, increasing gain by up to 53%, SDRM just incurs an affordable time expense (i.e., 1.10-2.51 times that of existing algorithms). Therefore, SDRM stands as a compelling solution for resource distribution in heterogeneous cloud environments.

A stochastic SIRS epidemic model with a saturation incidence under semi-Markovian switching

A stochastic SIRS epidemic model with a saturation incidence under semi-Markovian switching

Stochastic Boolean model of normal and aberrant cell cycles in budding yeast

The cell cycle of budding yeast is governed by an intricate protein regulatory network whose dysregulation can lead to lethal mistakes or aberrant cell division cycles. In this work, we model this network in a Boolean framework for stochastic simulations. Our model is sufficiently detailed to account for the phenotypes of 40 mutant yeast strains (83% of the experimentally characterized strains that we simulated) and also to simulate an endoreplicating strain (multiple rounds of DNA synthesis without mitosis) and a strain that exhibits ‘Cdc14 endocycles’ (periodic transitions between metaphase and anaphase). Because our model successfully replicates the observed properties of both wild-type yeast cells and many mutant strains, it provides a reasonable, validated starting point for more comprehensive stochastic-Boolean models of cell cycle controls. Such models may provide a better understanding of cell cycle anomalies in budding yeast and ultimately in mammalian cells.

Stochastic Analysis for the Dual Virus Parallel Transmission Model with Immunity Delay.

In this article, the qualitative properties of a stochastic dual virus parallel transmission model with immunity delay are analyzed. First, we use Lyapunov theory to study the existence and uniqueness of the global positive solution of the proposed model. Second, the threshold values of the persistence and extinction of two viruses were obtained. Finally, the numerical simulation verifies the theoretical results. The results show that the immunity delay and the intensity of noise have important effects on the two diseases spreading in parallel.