Stochastic Simulation

We are most grateful to Jorge Duran, R. Dos Santos Ferreira, L. Kaas and two anonymous referees for detailed and stimulating comments on these earlier versions. We also wish to thank (without implicating) R. Boucekkine, D. de la Croix, J.H.Drèze and participants at various seminars for thoughtful questions and comments. Financial support from the IAP IV and ARC programmes is gratefully acknowledged.

In this work we present a Bio-PEPA model describing the Nuclear Factor κB (NF-κB) signalling pathway. In particular our model focuses on the dynamic response of NF-κB to an external stimulus. Each biochemical species in the pathway is represented by a specific Bio-PEPA component and the external stimulus is abstracted by time-dependent Bio-PEPA events describing the start and the end of the signal. The Bio-PEPA model is a formal intermediate representation of the pathway on which various kinds of analysis can be performed. Both stochastic and deterministic simulations are carried out to validate our model against the experimental data and in-silico experiments in the literature and to verify some properties, such as, the impact of the duration of the external stimulus and of the total NF-κB initial amount on the behaviour of some species of interest. Furthermore we use stochastic simulation to compare the behaviour of the single cell against the average behaviour of a population of cells. Finally, sensitivity analysis is considered to investigate the most influential parameters of the model. Importantly, the approach taken suggests that the sensitivity of some parameters alters with the time evolution of the pathway.

In this work we present a Bio-PEPA model describing the Nuclear Factor κB (NF-κB) signalling pathway. In particular our model focuses on the dynamic response of NF-κB to an external stimulus. Each biochemical species in the pathway is represented by a specific Bio-PEPA component and the external stimulus is abstracted by time-dependent Bio-PEPA events describing the start and the end of the signal. The Bio-PEPA model is a formal intermediate representation of the pathway on which various kinds of analysis can be performed. Both stochastic and deterministic simulations are carried out to validate our model against the experimental data and in-silico experiments in the literature and to verify some properties, such as, the impact of the duration of the external stimulus and of the total NF-κB initial amount on the behaviour of some species of interest. Furthermore we use stochastic simulation to compare the behaviour of the single cell against the average behaviour of a population of cells. Finally, sensitivity analysis is considered to investigate the most influential parameters of the model. Importantly, the approach taken suggests that the sensitivity of some parameters alters with the time evolution of the pathway.

The call for the development of geographical information systems that can handle uncertain data dates back at least twenty years. Many research groups have since worked on the design of an 'error-aware GIS', but very few -perhaps none -have reached the operational stage. Recently, the Data Uncertainty Engine (DUE) was developed to fill this gap. DUE assists users in the assessment of uncertainties in environmental data and stores these in a spatio-temporal database. Uncertain environmental data are represented in DUE as objects whose positions and attribute values may be uncertain. Uncertainty is quantified with probability distribution functions, both for numerical and categorical data types. Spatial correlation between the vertices that define an object's position or between the point values of a spatially distributed attribute at multiple locations is also accommodated for. Both expert judgement and sample data may be used to help estimate the parameters of the probability distributions. DUE must be used alongside a GIS because it cannot do standard GIS operations, such as spatial queries, overlay, or visualisation. It is an add-on that can read and write common formats and can generate multiple realisations (i.e., random draws from the probability distribution) of an uncertain object. The realisations may be used in a Monte Carlo uncertainty propagation analysis or for communicating uncertainty to a target audience with limited background in statistics. The use of DUE has now surpassed the development stage that illustrated its use with synthetic examples. It is now being used in large projects to solve real-world problems. In this paper, three examples are given. These are: (1) the modelling, storage and simulation of uncertain soil profile and pesticide properties in a project that analyses how uncertainty in these properties affects the accuracy of the estimated nationwide leaching of pesticides in the Netherlands; (2) the stochastic simulation of spatially correlated soil aluminium and iron content in a project that assesses the water quality of the river Regge catchment; and (3) the handling of positional uncertainty in the delineation of breeding bird areas in a spatial planning project in the South of the Netherlands.

The importance of the northeastern part of the greater Cairo metropolitan area is due to the presence of a nuclear power plant and the dense population and its extent towards seismic sources. This paper reviews the likely ground acceleration related to the effective seismic events initiated from the closest seismic sources to the area. For this purpose, a deterministic seismic hazard approach followed by ground stochastic simulation was performed to assess the seismic hazard in the area. Seismic sources of hazardous effects were defined. A controlling earthquake was determined, based upon an empirical relationship between the seismic moment and the rupture length of the fault during the earthquake. The soil amplification characteristics in the area were obtained by in situ ambient noise measurements with great precautions. An H/V technique has been used to estimate the fundamental frequency and amplification factors at the sites of ambient noise measurements. The values of the fundamental frequency and the corresponding amplification factor were estimated at the investigated sites within the area of interest. The maximum possible earthquake magnitude M max was estimated for the effective seismic sources surrounding the study area and the hazard parameter peak ground acceleration (PGA) calculated for given zones. The work on the estimation of PGAs will contribute to the determination of national seismic codes, giving guidance on which buildings must take seismic risk into consideration and the necessity to re-appraise the seismic risk for existing buildings.

This paper examines some connections between Orphic cosmological
ideas, particularly the Cosmic Egg, and Greek alchemical traditions.
Beginning with the seventh-century Byzantine alchemist Christianos, who systematically employed eggs as symbols for elemental quadripartition in his combinatorial analysis of alchemical procedures, this study traces how the Orphic Cosmic Egg – representing universal unity composed of four elements – possibly influenced other alchemical works. Analysis of alchemical texts, manuscript iconography, and a specific Orphic cosmogony – the one from the Clementine Homilies – reveals possible traces of connections between Orphic religious thought and early alchemical practices.

Chlorinated organic compounds are widespread aquifer contaminants. They are known to be dense non-aqueous phase liquids (DNAPLs). Therefore, they are denser than water and immiscible with other fluids. Their migration into the environment in variably saturated zones can cause severe damage. For this reason, optimizing those actions that minimize the negative impact of these compounds in the subsurface is essential. This paper presented a numerical model simulating the freeproduct DNAPL migration and extraction through a purpose-designed pumping well in a potential emergency scenario. The numerical simulations were performed using CactusHydro, a numerical code that uses a high-resolution shock-capturing flux conservative method to resolve the non-linear coupled partial differential equations of a three-phase immiscible fluid flow recently proposed in the literature, including the contaminant extraction at the base of the aquifer. We investigated the temporal (and spatial) evolution of its migration in the Parma (Northern Italy) porous alluvial aquifer following the saturation contour profiles of the three-phase fluid flow in variably saturated zones. The results indicated that this numerical approach can simulate the contaminant migration in the subsurface and the pumping of the free-product from a well screened at the base of the aquifer system. Moreover, the simulation showed the possibility of recovering about two-thirds of the free-product, in agreement with the scientific literature.

Machine learning (ML) frameworks rely heavily on pseudorandom number generators (PRNGs) for tasks such as data shuffling, weight initialization, dropout, and optimization. Yet, the statistical quality and reproducibility of these generators-particularly when integrated into frameworks like PyTorch, TensorFlow, and NumPy-are underexplored. In this paper, we compare the statistical quality of PRNGs used in ML frameworks (Mersenne Twister, PCG, and Philox) against their original C implementations. Using the rigorous TestU01 BigCrush test suite, we evaluate 896 independent random streams for each generator. Our results challenge claims of statistical robustness, revealing that even generators labelled "crush-resistant" (e.g., PCG, Philox) may fail certain statistical tests. Surprisingly, we can observe some differences in failure profiles between the native and frameworkintegrated versions of the same algorithm, highlighting some implementation differences that may exist. Mersenne Twister implementation in Pytorch and Numpy does not have the exact same failure profile as the original implementation in C. In addition, this is also the case for the TensorFlow implementation of Philox.

This paper builds, estimates. and simulates a world trade model to provide a quantitative analysis of the behavior of the U.S. trade deficit. A key feature of this model is that international trade imbalances add up to zero. The analysis estimates income and price elasticities for bilateral import equations, tests for the properties of the error term, for parameter constancy, and for the choice of dynamic specification. The paper also re­examines the structural asymmetries in elasticities noted by Houthakker and Magee and tests whether the Marshall-Lerner condition holds. The reliability of the model as a whole is assessed with residual-based stochastic simulations. The paper finds that changes in relative prices account for the bulk of the deterioration of the U.S. trade account, that reliance on either foreign or domestic growth to eliminate the U.S. external imbalances entails significant changes in real income, and that the speed with which U.S. net exports respond to exchange ...

With the growth of public environmental awareness and the improvement in national and EU legislation regarding the environment, monitoring assumed great importance in the frame of all managerial activities related to territories. In particular, recently, a number of public environmental agencies have invested great resources in planning and operating improvements on existing monitoring networks within their regions. In this framework, and, at the light of the Water Framework Directive, the optimal monitoring of the qualitative and quantitative state of groundwater becomes a priority, particularly, when severe economic constraints must be imposed and the territory to be monitored is quite wide. There are a lot of reasons justifying the optimal extension of a monitoring network. In fact, a modest coverage of the monitored area often makes impossible to provide the manager with a sufficient knowledge for decisionmaking processes. In general, monitoring networks are characterized by a scarce number of existing wells, irregularly spread over the considered area. This is a typical case of optimization and it may be solved seeking among existing, but unused, wells, all and only those able to make the monitoring network coverage, the most uniform among any arrangement. Using existing wells as new monitoring sites, allows one to drastically reduce the needed budget. In this paper, a four step method, based on simulated annealing, has been implemented with the aim of identifying scarcely monitored zones within the groundwater system boundaries.

With the growth of public environmental awareness and the improvement in national and EU legislation regarding the environment, monitoring assumed great importance in the frame of all managerial activities related to territories. In particular, recently, a number of public environmental agencies have invested great resources in planning and operating improvements on existing monitoring networks within their regions. In this framework, and, at the light of the Water Framework Directive, the optimal monitoring of the qualitative and quantitative state of groundwater becomes a priority, particularly, when severe economic constraints must be imposed and the territory to be monitored is quite wide. There are a lot of reasons justifying the optimal extension of a monitoring network. In fact, a modest coverage of the monitored area often makes impossible to provide the manager with a sufficient knowledge for decisionmaking processes. In general, monitoring networks are characterized by a scarce number of existing wells, irregularly spread over the considered area. This is a typical case of optimization and it may be solved seeking among existing, but unused, wells, all and only those able to make the monitoring network coverage, the most uniform among any arrangement. Using existing wells as new monitoring sites, allows one to drastically reduce the needed budget. In this paper, a four step method, based on simulated annealing, has been implemented with the aim of identifying scarcely monitored zones within the groundwater system boundaries.

With the growth of public environmental awareness and the improvement in national and EU legislation regarding the environment, monitoring assumed great importance in the frame of all managerial activities related to territories. In particular, recently, a number of public environmental agencies have invested great resources in planning and operating improvements on existing monitoring networks within their regions. In this framework, and, at the light of the Water Framework Directive, the optimal monitoring of the qualitative and quantitative state of groundwater becomes a priority, particularly, when severe economic constraints must be imposed and the territory to be monitored is quite wide. There are a lot of reasons justifying the optimal extension of a monitoring network. In fact, a modest coverage of the monitored area often makes impossible to provide the manager with a sufficient knowledge for decisionmaking processes. In general, monitoring networks are characterized by a s...

Actuarial science has traditionally relied on deterministic and stochastic models to quantify insurance risks, calculate premiums, estimate reserves, and evaluate solvency. While probabilistic methods remain indispensable, they often assume that model parameters are known with sufficient precision or can be estimated from stable historical data. In practice, however, many actuarial parameters are not only random but also vague, imprecise, and subject to hesitation due to incomplete information, expert disagreement, structural market changes, or emerging risks. This paper develops a comprehensive framework for dynamic actuarial models with intuitionistic fuzzy parameters in order to address such complexities. The proposed approach integrates intuitionistic fuzzy set theory into dynamic actuarial modeling by representing uncertain parameters through three components: membership degree, non-membership degree, and hesitation degree. This enables a more expressive treatment of epistemic uncertainty than classical fuzzy or purely stochastic methods. The study introduces the theoretical foundations of intuitionistic fuzzy numbers, formalizes their integration into dynamic reserve and pricing models, and discusses their application in premium calculation, claims reserving, ruin theory, life insurance valuation, and solvency capital assessment. Mathematical formulations are provided for intuitionistic fuzzy claim frequency, claim severity, mortality rates, and discount factors. The paper also explores ranking functions, defuzzification mechanisms, and interval-based computational procedures for practical implementation. The results show that dynamic actuarial models with intuitionistic fuzzy parameters offer greater flexibility and realism in settings characterized by limited data, rapidly changing conditions, and expert uncertainty. These models can complement classical actuarial techniques by explicitly quantifying ambiguity and hesitation, thereby improving transparency and supporting robust decision-making. The paper concludes by discussing methodological strengths, computational limitations, and future research opportunities in hybrid stochastic-fuzzy actuarial systems.

Cod (Gadus morhua) and American plaice (Hippoglossoides platessoides) on the Grand Bank of Newfoundland supported substantial commercial fisheries for extensive periods in the past. Both stocks declined and have been under fisheries moratoria since 1994, but continue to be harvested as by-catch in other directed fisheries on the Grand Bank. For each stock, a precautionary spawning stock biomass limit reference point (B lim ) has been established by the Scientific Council of the Northwest Atlantic Fisheries Organization. In this study, stochastic simulations were used to evaluate the probability distributions of the time horizons required to rebuild each of the two stocks to above B lim . A range of by-catch mortality levels, recruitment models, and body growth and maturation rates were applied in the simulations. Uncertainty in the estimates of the numbers at age in the last assessed year and uncertainty in future recruitment were also incorporated within the simulations. If by-catches are not substantially reduced, the modelling results indicate there is virtually zero probability of attaining B lim by 2020 for either the cod or American plaice stocks on the Grand Bank.

Cod (Gadus morhua) and American plaice (Hippoglossoides platessoides) on the Grand Bank of Newfoundland supported substantial commercial fisheries for extensive periods in the past. Both stocks declined and have been under fisheries moratoria since 1994, but continue to be harvested as by-catch in other directed fisheries on the Grand Bank. For each stock, a precautionary spawning stock biomass limit reference point (B lim ) has been established by the Scientific Council of the Northwest Atlantic Fisheries Organization. In this study, stochastic simulations were used to evaluate the probability distributions of the time horizons required to rebuild each of the two stocks to above B lim . A range of by-catch mortality levels, recruitment models, and body growth and maturation rates were applied in the simulations. Uncertainty in the estimates of the numbers at age in the last assessed year and uncertainty in future recruitment were also incorporated within the simulations. If by-catches are not substantially reduced, the modelling results indicate there is virtually zero probability of attaining B lim by 2020 for either the cod or American plaice stocks on the Grand Bank.

This chapter provides a brief introduction to the theory and practice of spatial stochastic simulations. It begins with an overview of different methods available for biochemical simulations highlighting their strengths and limitations. Spatial stochastic modeling approaches are indicated when diffusion is relatively slow and spatial inhomogeneities involve relatively small numbers of particles. The popular software package MCell allows particle-based stochastic simulations of biochemical systems in complex three dimensional (3D) geometries, which are important for many cell biology applications. Here, we provide an overview of the simulation algorithms used

Re-engineered fourth-generation management (R4thGM) emerged in 2022 as an innovative systems approach to make production systems more contemporary (e.g., more sustainable and open to diverse stakeholders), while complex system governance (CSG), as a systems approach, enables the control, coordination, communication, and integration of smart energy systems. However, there remains a lack of literature: (i) discussing how R4thGM, integrated energy system (IES) governance (as CSG), artificial intelligence (AI), advanced simulation, robust optimization methods, and stakeholders should be taken into account in the task of enhancing IES's resilience and sustainability, particularly against extreme natural events; (ii) discussing the role of IES governance in enhancing control, coordination, integration, and communication of IES infrastructures; (iii) emphasizing the role of R4thGM for enhancing the resilience and sustainability of an IES; (iv) presenting an integrated energy meta-system (IEM) resulting from IES governance and relying on three technical enablers, i.e., (resilience) robust optimization, AI, and advanced simulation methods. This study aims to propose a novel integrative systems approach based on R4thGM and IES governance, using AI, advanced simulation, and optimization methods to enhance the resilience and sustainability of IES infrastructures in the design and operational phases. To achieve this goal, we have reviewed 85 Scopus-and Web of Science-indexed papers published in 2017-2025. The novelty of this study lies in presenting an integrative systems approach best suited to resilient and sustainable IES infrastructures against extreme natural hazards. Moreover, propositions are formulated to reflect on the suggested framework. Finally, research implications and future directions are provided.

As more and more data about mining complex operations are collected and stored, it becomes increasingly important for computer systems to help human operators make better, more informed decisions. This can be done indirectly, through improved visualization or prediction, or directly by suggesting decisions that respond to new information. This paper contributes to the direct approach by showing how state-of-the-art data-driven decision making can be used for optimizing material flows in a large mining complex. To this end, a combination of neural networks and policy gradient reinforcement learning is used for computing material destination decisions that automatically respond to new information. Results using a computational model of a large copper mining complex show that the proposed method significantly outperforms an optimized cut-off grade policy similar to the one currently used at the mine.

The optimization of mine complexes and related value chains is a challenging problem due to the simultaneous presence of a highly-dimensional decision space, integer decision variables, non-linear constraints and recovery functions, as well as geological and market uncertainty. In addition, if the uncertainty is revealed progressively then decisions need to continuously adapt to new information, which poses additional challenges. Stochastic dynamic programming is a well-known class of methods for addressing problems where a decision-maker reacts to new information. While simplistic applications of dynamic programming using exact representations would be intractable for any realistic mine planning problem, new dynamic programming methods using approximate value function representations have been successfully implemented in the past to address problems of similar complexity. This work formulates the problem of mine complex optimization as an approximate dynamic program, and presents a...

This paper presents a stochastic traffic generator in which (i) the driving manner is assumed to be stochastic, (ii) random unexpected stops are considered and (iii) the stop time in the stations is also supposed to be stochastic. This simulation tool provides a large number of different driving scenarios to be used for a Monte Carlo load flow analysis. Traffic simulations algorithms are described in detail. Reference to a section of the Madrid–Barcelona high-speed line illustrates the potential of such a tool.

In many clinical situations the evaluation of renal function is required, particularly common in antibiotic therapy. The direct metric is glomerular filtration rate (GFR) but its measurement is complicated, so a variety of formulae and nomograms have been derived to obtain a surrogate of GFR, the creatinine clearance (CrCL). CrCL is then calculated based on empirical functions of varying complexity that include serum creatinine concentration and patient demographics. The MDRD (Modification of Diet in Renal Disease) method of CrCL calculation is increasingly used but the appropriateness of its use has not been demonstrated for all applications.1

The United States faces a critical national security vulnerability stemming from its near-total dependence on foreign sources, predominantly China, for heavy rare earth elements (HREEs) essential to advanced defense systems and emerging clean energy technologies. Despite the strategic importance of HREEs such as dysprosium and terbium—critical inputs for precision-guided munitions, advanced fighter aircraft, satellite systems, and permanent magnets—the current National Defense Stockpile provides only approximately 30 days of supply coverage, far below the levels maintained by allied nations and recommended by international best practices. This quantitative study developed and validated a comprehensive stochastic optimization framework to determine optimal HREE stockpile levels that balance acquisition costs, holding costs, and shortage costs under conditions of supply uncertainty. Employing a two-stage stochastic programming model integrated with Monte Carlo simulation (n = 10,000 iterations), the research analyzed four supply disruption scenarios ranging from baseline conditions to severe disruption events. Data were compiled from authoritative sources including the U.S. Geological Survey, International Energy Agency, and United Nations Comtrade database spanning a 15-year historical period (2010–2024). The optimization model identified optimal stockpile levels of 500 metric tons of dysprosium and 150 metric tons of terbium, requiring an initial acquisition investment of approximately $370 million. These levels would provide 608–730 days of supply coverage compared to the current 30-day threshold, achieving a 96% defense continuity rate and 75.5% probability of zero shortage events across the 10-year planning horizon. Sensitivity analysis revealed the shortage cost multiplier as the most influential parameter, while Pareto frontier analysis illuminated the cost-security trade-off frontier for policy decision-making. The findings demonstrate a 22-fold gap between optimal and current stockpile levels, providing quantitative justification for immediate policy intervention to enhance U.S. critical mineral security.

W E present our preliminary work that develops a new approach to hybrid packet/analytic network simulations for improved network simulation fidelity, scale, and simulation efficiency. Much work in the literature addresses this topic, including [10] [11] [8] [12] [13] and others. Current approaches rely upon models, which we refer to in this paper as Deterministic Fluid Models [9] [12], to address the analytic modeling aspects of these hybrid simulations. Instead we draw upon an extensive literature on stochastic models of queues and (eventually) networks of queues to implement a hybrid stochastic model/packet network simulation. We will refer to our approach as Stochastic Fluid Models throughout this paper. We outline our approach, present test cases, and present simulation results comparing the measured queue metrics from our approach for hybrid simulation to those of a deterministic fluid model hybrid simulation and a full packet-level simulation. We also discuss plans for future areas of research on this approach.

We demonstrate how the freedom in the definition of the positive-P representation may be used to reduce stochastic sampling errors, using the single-mode anharmonic oscillator as an example. In the modeling of this system, which is well known for being problematic, we achieve an improvement of more than 20 orders of magnitude in the distribution of the trajectories.

Summary The performance of naturally fractured reservoirs is controlled by the orientation, intensity and spatial distribution of open fractures. In this paper we present the results of a recent fracture characterization study based on P-wave azimuthal anisotropy using interval velocities and RMS amplitude maps. A consistent processing sequence was applied to all azimuth sectors in order to preserve the quality of the azimuthal anisotropy information. A proprietary geostatistical decomposition technique was applied to ensure more stable and accurate estimates of the fracture intensity and direction. These results provide detailed maps of the fracture system and show good correlation with sub-seismic scale fracture analysis from FMI/ FMS logs.

In a hydropower system, inflow is an uncertain stochastic process that depends on the meteorology of the reservoir’s location. To properly utilize the stored water in reservoirs, it is necessary to have a good forecast or a historical inflow record. In the absence of these two pieces of information, which is the case in Ethiopia and most African countries, the derivation of the synthetic historical inflow series with the appropriate time resolution will be a solution. This paper presents a method of developing synthetic historical inflow time series and techniques to identify the stochastic process that mimics the behavior of the time series and generates inflow scenarios. The methodology was applied to the Ethiopian power system. The time series were analyzed using statistical methods, and the stochastic process that mimics the inflow patterns in Ethiopia was identified. The Monte Carlo simulation was used to generate sample realizations of random scenarios from the identified stoc...

This research explores the intersection of mathematics and chemistry through the mathematical modeling of chemical reaction kinetics. By employing differential equations and numerical methods, we analyze the rates of chemical reactions and predict the concentration of reactants and products over time. The study focuses on both first-order and second-order reactions, extending to complex reaction mechanisms including reversible and consecutive reactions. Real-world chemical systems, such as enzyme kinetics and industrial catalytic process are used to validate the models. This interdisciplinary approach not only deepens the understanding of chemical behaviour but also showcases the power of mathematical tools in solving problems in the physical sciences. The paper aims to provide a framework for students and researchers to bridge the gap between theoretical mathematics and experimental chemistry.

The content of the publication reflects the authors' views and the Managing Authority cannot be held liable for the information published by the project partners. ISBN 978-952-216-449-0 (printed) ISSN 1457-7925 (printed) Printed by Suomen Yliopistopaino-Juvenes Print Oy, Tampere 2014 ISBN 978-952-216-450-6 (PDF) ISSN 1459-7764 (electronic) Distribution: http://loki.turkuamk.fi

Individuals newly infected with hiv have an increased viral load than at other phases of hiv infection, which is associated with a higher rate of transmission. Combined with ignorance about infection status, individuals in the acute phase not only contribute to the growing epidemic but are believed by some to be the driving force behind new infections. Unfortunately, due to the high costs of testing, individuals are not routinely tested for acute hiv infection. The matrix pooling algorithm we present is more economical than individual testing whilst improving accuracy -reducing the number of false positive and false negative test results. Although matrix pooling may require more tests compared to other pooling algorithms, the significant increase in accuracy and rapidity with which results are obtained makes this method more desirable when identifying acute hiv infections, even in resource poor settings.