Stochastic Modeling Framework Research Articles

Filtered Point Processes Tractably Capture Rhythmic And Broadband Power Spectral Structure in Neural Electrophysiological Recordings.

Neural electrophysiological recordings arise from interacting rhythmic (oscillatory) and broadband (aperiodic) biological subprocesses. Both rhythmic and broadband processes contribute to the neural power spectrum, which decomposes the variance of a neural recording across frequencies. Although an extensive body of literature has successfully studied rhythms in various diseases and brain states, researchers only recently have systematically studied the characteristics of broadband effects in the power spectrum. Broadband effects can generally be categorized as 1) shifts in power across all frequencies, which correlate with changes in local firing rates and 2) changes in the overall shape of the power spectrum, such as the spectral slope or power law exponent. Shape changes are evident in various conditions and brain states, influenced by factors such as excitation to inhibition balance, age, and various diseases. It is increasingly recognized that broadband and rhythmic effects can interact on a sub-second timescale. For example, broadband power is time-locked to the phase of <1 Hz rhythms in propofol induced unconsciousness. Modeling tools that explicitly deal with both rhythmic and broadband contributors to the power spectrum and that capture their interactions are essential to help improve the interpretability of power spectral effects. Here, we introduce a tractable stochastic forward modeling framework designed to capture both narrowband and broadband spectral effects when prior knowledge or theory about the primary biophysical processes involved is available. Population-level neural recordings are modeled as the sum of filtered point processes (FPPs), each representing the contribution of a different biophysical process such as action potentials or postsynaptic potentials of different types. Our approach builds on prior neuroscience FPP work by allowing multiple interacting processes and time-varying firing rates and by deriving theoretical power spectra and cross-spectra. We demonstrate several properties of the models, including that they divide the power spectrum into frequency ranges dominated by rhythmic and broadband effects, and that they can capture spectral effects across multiple timescales, including sub-second cross-frequency coupling. The framework can be used to interpret empirically observed power spectra and cross-frequency coupling effects in biophysical terms, which bridges the gap between theoretical models and experimental results.

The heat modulated infinite dimensional Heston model and its numerical approximation

The HEat modulated Infinite DImensional Heston (HEIDIH) is introduced as a concrete case of the general framework of infinite dimensional Heston stochastic volatility models of (F.E. Benth, I.C. Simonsen '18) for the pricing of forward contracts. It is supported by a comprehensive numerical analysis. The model consists of a one-dimensional stochastic advection equation coupled with a stochastic volatility process. This process is a Cholesky-type decomposition of the tensor product of a Hilbert-space valued Ornstein-Uhlenbeck process, the solution to a stochastic heat equation on the real half-line. The advection and heat equations are driven by independent space-time Gaussian processes which are white in time and coloured in space, with the latter covariance structure expressed by two different kernels. First, a class of weight-stationary kernels are given, under which regularity results for the HEIDIH model in fractional Sobolev spaces are formulated. In particular, the class includes weighted Matérn kernels. Second, numerical approximation of the model is considered. An error decomposition formula, pointwise in space and time, for a finite-difference scheme is proven. For a special case, essentially sharp convergence rates are obtained when this is combined with a fully discrete finite element approximation of the stochastic heat equation. The analysis takes into account a localization error, a pointwise-in-space finite element discretization error and an error stemming from the noise being sampled pointwise in space. The rates obtained in the analysis are higher than what would be obtained using a standard Sobolev embedding technique. Numerical simulations illustrate the results.

Stochastic optimization of a hybrid photovoltaic/fuel cell/parking lot system incorporating cloud model

The interaction and optimization of electric parking lots (EPLs) with hybrid renewable energy to exchange power and improve the system load reliability has been welcomed systems in energy industry, but it is accompanied by challenges such as uncertain parameters, and also implementing the optimal energy management. This paper proposes a novel stochastic optimization framework for a hybrid energy system including photovoltaic resources, hydrogen storage based-fuel cell integrated with an EPL (PV/FC/EPL) aiming for minimization of the total net present cost (TNPC) while ensuring the maximum probability of power shortage (PPSHmax) to meet a commercial load in Tianjin, China using the real meteorological data. A new improved kepler optimization algorithm (IKOA) utilizing the golden sine strategy is applied to optimize system component sizes and EPL charge/discharge. In a deterministic scenario, the optimal system configuration ensures cost-efficiency and reliability for load supply. Also, a new stochastic modeling framework is proposed using the Cloud Model (CM) to evaluate the effect of uncertainties in irradiance, temperature, and system demand on TNPC and PPSH. Deterministic findings reveal enhanced reliability and reduced TNPC through FC and EPL overlap during power shortages, compared to systems lacking EPL. Specifically, TNPC and PPSH are $8,632,643 and 1.45 %, respectively, for PPSHmax = 2 % over 20 years of operation. However, stochastic optimization demonstrates a 10.82 % increase in TNPC and an 8.67 % decrease in PPSH compared to the deterministic model under PPSHmax = 2 %, indicating heightened cost and reduced reliability when uncertainties are considered. This underscores the efficacy of the cloud model-based stochastic approach in addressing uncertainty in hybrid system optimization. Also, it reveals fluctuations in optimal cost and reliability values with changes in cloud droplet distribution around the expected value, emphasizing the significance of stochastic modeling for robust decision-making in hybrid energy systems. Moreover, evaluating the incorporating the penalty for the system's inability to supply the load, changing the storage investment cost, and interest rate variations on the system optimization cleared considerable effect of the system cost and reliability.

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.

A volume‐averaging and stochastic turbulence modeling framework for homogeneous roughness‐induced drag in turbulent flows

AbstractThe goal of this work is the formulation of a model for the parameterization of homogeneous roughness‐induced drag in turbulent flow simulations. We characterize rough surfaces using their surface‐area moments of roughness‐peaks. Additionally, we consider a probabilistic self‐similar power law distribution for the roughness heights, in such a way that an assumed set of discrete roughness elements can behave as a probabilistic fractal set. Upon these assumptions, the surface characterization is complete and yields wall‐normal profiles of porosity, average roughness element diameter, and equivalent pore diameter of the roughness affected porous flow. The profiles are supplied to a (pore‐based) Reynolds number and porosity‐based drag parameterization for staggered cylinder arrays available in the literature, as well as a one‐dimensional map‐based turbulence model, the one‐dimensional turbulence (ODT) model. The purpose of the latter is a way to provide the missing effects of the equivalent dispersion tensor in the porous flow close to the rough surface, as well as that of the nonlinear turbulent transport away from the wall. Simulations are then carried out in order to evaluate the effects of two different rough surfaces on a turbulent channel flow, comparing results with existing direct numerical simulation (DNS) data. Overall, reasonable agreement is obtained, which suggests that, by using the proposed model, it is possible to model the effects of rough surfaces on wall‐bounded turbulent flows, without the explicit need of the full topological representation of the surface on the numerical domain. To that extent, one clear flow control application for the suggested approach would be that of drag‐based surface optimization.

A Multi-Scale Stochastic Modeling Framework for Predicting the Onset and Progression of Alzheimer's Disease

A Multi-Scale Stochastic Modeling Framework for Predicting the Onset and Progression of Alzheimer's Disease

Particle Swarm Optimization for a redundant repairable machining system with working vacations and impatience in a multi-phase random environment

With the increasing reliance on cloud computing as the foundational manufacturing systems with intricate dynamics, featuring multiple service areas, varying job arrival rates, diverse service requirements, and the interplay of failures and impatience, significant analytical challenges arise. Queueing networks offer a powerful stochastic modeling framework to capture such complex dynamics. This paper develops a novel, exhaustive queueing model for a finite-capacity redundant multi-server system operating in a multi-phase random environment. The proposed model uniquely integrates real-world factors, including server breakdowns and repairs, waiting servers, synchronous working vacations, and state dependent balking and reneging, into a single queueing model, representing a significant advancement in the field. Using the matrix-analytic method, we establish the steady-state solution and derive key performance metrics. Numerical experiments and sensitivity analyses elucidate the impact of system parameters on performance measures. Additionally, a cost model is formulated, enabling cost optimization analysis using direct search method and Particle Swarm Optimization (PSO) to identify efficient operating configurations.

A stochastic modelling framework for predicting flexural properties of ultra-thin randomly oriented strands

A stochastic modelling framework is developed to predict the flexural properties of high-strength sheet moulding compounds made of randomly oriented ultra-thin carbon fibre-reinforced thermoplastic prepreg tapes. The model enables reliable designs using ultra-thin randomly oriented strands with less testing, leading to potential applications in automotive primary structures. The stochastic model is based on a Monte Carlo simulation. The flexural modulus is predicted using classical laminate theory, while the flexural strength is predicted by following a Weibull distribution. Fibre discontinuities are considered through stress concentrations introduced by tape overlaps. The results are validated against new 3-point bending and previously reported 4-point bending experimental results. A scaling effect on strength and scatter is predicted, and its implications for structural applications are also discussed.

Stochastic model for migration and breakage of detrital and authigenic fines

Mobilisation of attached particles during flow in rocks occurs in geo-energy processes. Particle mobilisation, their migration through rocks and pore plugging yield significant decline in permeability and well injectivity and productivity. While much is currently known about the underlying mechanisms governing the detachment of detrital particles against attracting electrostatic forces, a critical gap exists in the theoretical understanding of detachment by breakage of widely spread authigenic particles, which naturally grow on rock grains during geological times. Previous works derived micro-scale mechanical equilibrium equations for both detrital and authigenic particles, and the upscaling procedure from particle to pore and core scales for detrital fines. In this paper, for the first time we derive a stochastic model for migration and breakage of authigenic fines and authigenic–detrital mixtures. This allows for core-scale transport modelling based on the particle-scale torque balance. We introduce a novel framework for predictive stochastic detachment modelling by particle–rock bond breakage that integrates the beam theory of elastic particle deformation, strength failure criteria and viscous flow around the attached particle. The analytical expressions for stress maxima and stress diagrams for a single particle allow determining the critical failure stresses, breakage points of the beam and breakage flow velocity. The mathematical model describing lab coreflood includes the maximum retention function for both authigenic and detrital fines. The matching laboratory coreflood data under increasing velocity at micro- and core-scales achieved high matching of the experimental data by the model. High matching validates the upscaling and downscaling procedures derived.

Modeling spillover dynamics: understanding emerging pathogens of public health concern

The emergence of infectious diseases with pandemic potential is a major public health threat worldwide. The World Health Organization reports that about 60% of emerging infectious diseases are zoonoses, originating from spillover events. Although the mechanisms behind spillover events remain unclear, mathematical modeling offers a way to understand the intricate interactions among pathogens, wildlife, humans, and their shared environment. Aiming at gaining insights into the dynamics of spillover events and the outcome of an eventual disease outbreak in a population, we propose a continuous time stochastic modeling framework. This framework links the dynamics of animal reservoirs and human hosts to simulate cross-species disease transmission. We conduct a thorough analysis of the model followed by numerical experiments that explore various spillover scenarios. The results suggest that although most epidemic outbreaks caused by novel zoonotic pathogens do not persist in the human population, the rising number of spillover events can avoid long-lasting extinction and lead to unexpected large outbreaks. Hence, global efforts to reduce the impacts of emerging diseases should not only address post-emergence outbreak control but also need to prevent pandemics before they are established.

Community detection in the human connectome: Method types, differences and their impact on inference.

Community structure is a fundamental topological characteristic of optimally organized brain networks. Currently, there is no clear standard or systematic approach for selecting the most appropriate community detection method. Furthermore, the impact of method choice on the accuracy and robustness of estimated communities (and network modularity), as well as method-dependent relationships between network communities and cognitive and other individual measures, are not well understood. This study analyzed large datasets of real brain networks (estimated from resting-state fMRI from = 5251 pre/early adolescents in the adolescent brain cognitive development [ABCD] study), and = 5338 synthetic networks with heterogeneous, data-inspired topologies, with the goal to investigate and compare three classes of community detection methods: (i) modularity maximization-based (Newman and Louvain), (ii) probabilistic (Bayesian inference within the framework of stochastic block modeling (SBM)), and (iii) geometric (based on graph Ricci flow). Extensive comparisons between methods and their individual accuracy (relative to the ground truth in synthetic networks), and reliability (when applied to multiple fMRI runs from the same brains) suggest that the underlying brain network topology plays a critical role in the accuracy, reliability and agreement of community detection methods. Consistent method (dis)similarities, and their correlations with topological properties, were estimated across fMRI runs. Based on synthetic graphs, most methods performed similarly and had comparable high accuracy only in some topological regimes, specifically those corresponding to developed connectomes with at least quasi-optimal community organization. In contrast, in densely and/or weakly connected networks with difficult to detect communities, the methods yielded highly dissimilar results, with Bayesian inference within SBM having significantly higher accuracy compared to all others. Associations between method-specific modularity and demographic, anthropometric, physiological and cognitive parameters showed mostly method invariance but some method dependence as well. Although method sensitivity to different levels of community structure may in part explain method-dependent associations between modularity estimates and parameters of interest, method dependence also highlights potential issues of reliability and reproducibility. These findings suggest that a probabilistic approach, such as Bayesian inference in the framework of SBM, may provide consistently reliable estimates of community structure across network topologies. In addition, to maximize robustness of biological inferences, identified network communities and their cognitive, behavioral and other correlates should be confirmed with multiple reliable detection methods.

How effective were Australian Quarantine Stations in mitigating transmission aboard ships during the influenza pandemic of 1918-19?

The influenza pandemic of 1918-19 was the most devastating pandemic of the 20th century. It killed an estimated 50-100 million people worldwide. In late 1918, when the severity of the disease was apparent, the Australian Quarantine Service was established. Vessels returning from overseas and inter-state were intercepted, and people were examined for signs of illness and quarantined. Some of these vessels carried the infection throughout their voyage and cases were prevalent by the time the ship arrived at a Quarantine Station. We study four outbreaks that took place on board the Medic, Boonah, Devon, and Manuka in late 1918. These ships had returned from overseas and some of them were carrying troops that served in the First World War. By analysing these outbreaks under a stochastic Bayesian hierarchical modeling framework, we estimate the transmission rates among crew and passengers aboard these ships. Furthermore, we ask whether the removal of infectious, convalescent, and healthy individuals after arriving at a Quarantine Station in Australia was an effective public health response.

A Copula-Based Stochastic Frontier Analysis of Thai Jasmine Rice Production in the Northeast of Thailand

Thai jasmine rice holds immense economic significance both domestically and as a major export, making it a vital contributor to the Thai economy. Traditional and modern agricultural practices, centered around rice cultivation, play a pivotal role in the culture and economy of the Northeast region. However, concerns have arisen regarding rice production efficiency in recent times due to capital and labor availability challenges. Motivated by these concerns, this study employs a copula-based stochastic frontier modeling (copula-SFM) framework to investigate production efficiency empirically. The research is based on a sample of 384 farmers in the Northeast of Thailand. The Akaike Information Criterion (AIC) is utilized to select the most appropriate model. The results indicate that the Gaussian copula-SFM outperforms other copula models. Notably, the study identifies total area, capital, and labor as critical factors significantly contributing to the positive impact on jasmine rice production. Furthermore, the research ranks provinces based on average technical efficiency (TE) scores, revealing Khon Kaen Province, Yasothon Province, and Roi Et Province as the top-performing regions.

Representing model uncertainties in brittle fracture simulations

This work focuses on the representation of model-form uncertainties in phase-field models of brittle fracture. Such uncertainties can arise from the choice of the degradation function for instance, and their consideration has been unaddressed to date. The stochastic modeling framework leverages recent developments related to the analysis of nonlinear dynamical systems and relies on the construction of a stochastic reduced-order model. In the latter, a POD-based reduced-order basis is randomized using Riemannian projection and retraction operators, as well as an information-theoretic formulation enabling proper concentration in the convex hull defined by a set of model proposals. The model thus obtained is mathematically admissible in the almost sure sense and involves a low-dimensional hyperparameter, the calibration of which is facilitated through the formulation of a quadratic programming problem. The relevance of the modeling approach is further assessed on one- and two-dimensional applications. It is shown that model uncertainties can be efficiently captured and propagated to macroscopic quantities of interest. An extension based on localized randomization is also proposed to handle the case where the forward simulation is highly sensitive to sample localization. This work constitutes a methodological development allowing phase-field predictions to be endowed with statistical measures of confidence, accounting for the variability induced by modeling choices.

Stochastic Model Updating with Uncertainty Quantification: An Overview and Tutorial

This paper presents an overview of the theoretic framework of stochastic model updating, including critical aspects of model parameterisation, sensitivity analysis, surrogate modelling, test-analysis correlation, parameter calibration, etc. Special attention is paid to uncertainty analysis, which extends model updating from the deterministic domain to the stochastic domain. This extension is significantly promoted by uncertainty quantification metrics, no longer describing the model parameters as unknown-but-fixed constants but random variables with uncertain distributions, i.e. imprecise probabilities. As a result, the stochastic model updating no longer aims at a single model prediction with maximum fidelity to a single experiment, but rather a reduced uncertainty space of the simulation enveloping the complete scatter of multiple experiment data. Quantification of such an imprecise probability requires a dedicated uncertainty propagation process to investigate how the uncertainty space of the input is propagated via the model to the uncertainty space of the output. The two key aspects, forward uncertainty propagation and inverse parameter calibration, along with key techniques such as P-box propagation, statistical distance-based metrics, Markov chain Monte Carlo sampling, and Bayesian updating, are elaborated in this tutorial. The overall technical framework is demonstrated by solving the NASA Multidisciplinary UQ Challenge 2014, with the purpose of encouraging the readers to reproduce the result following this tutorial. The second practical demonstration is performed on a newly designed benchmark testbed, where a series of lab-scale aeroplane models are manufactured with varying geometry sizes, following pre-defined probabilistic distributions, and tested in terms of their natural frequencies and model shapes. Such a measurement database contains naturally not only measurement errors but also, more importantly, controllable uncertainties from the pre-defined distributions of the structure geometry. Finally, open questions are discussed to fulfil the motivation of this tutorial in providing researchers, especially beginners, with further directions on stochastic model updating with uncertainty treatment perspectives.

GPS tracking analyses reveal finely-tuned shorebird space use and movement patterns throughout the non-breeding season in high-latitude austral intertidal areas

BackgroundLong-distance migratory birds spend most of their annual cycle in non-breeding areas. During this period birds must meet their daily nutritional needs and acquire additional energy intake to deal with future events of the annual cycle. Therefore, patterns of space use and movement may emerge as an efficient strategy to maintain a trade-off between acquisition and conservation of energy during the non-breeding season. However, there is still a paucity of research addressing this issue, especially in trans-hemispheric migratory birds.MethodsUsing GPS-tracking data and a recently developed continuous-time stochastic process modeling framework, we analyzed fine-scale movements in a non-breeding population of Hudsonian godwits (Limosa haemastica), a gregarious long-distance migratory shorebird. Specifically, we evaluated if these extreme migrants exhibit restricted, shared, and periodic patterns of space use on one of their main non-breeding grounds in southern South America. Finally, via a generalized additive model, we tested if the observed patterns were consistent within a circadian cycle.ResultsOverall, godwits showed finely-tuned range-residence and periodic movements (each 24–72 h), being similar between day and night. Remarkably, range-resident individuals segregated spatially into three groups. In contrast, a smaller fraction of godwits displayed unpredictable and irregular movements, adding functional connectivity within the population.ConclusionsIn coastal non-breeding areas where resource availability is highly predictable due to tidal cycles, range-resident strategies during both the day and night are the common pattern in a long-distance shorebird population. Alternative patterns exhibited by a fraction of non-resident godwits provide functional connectivity and suggest that the exploratory tendency may be essential for information acquisition and associated with individual traits. The methodological approach we have used contributes to elucidate how the composition of movement phases operates during the non-breeding season in migratory species and can be replicated in non-migratory species as well. Finally, our results highlight the importance of considering movement as a continuum within the annual cycle.

Predicer: abstract stochastic optimisation model framework for multi-market operation

An open-source modelling framework Predicer, standing for Predictive Decider, for multi-market day-ahead market operation purposes is described in this paper. The Predicer model uses scenario-based stochastic optimisation to obtain decision variables and bid matrixes for energy and reserve markets by maximising the risk-adjusted expected value of the profit during the model time frame. The modelled energy system structure is abstract, that is, based on basic elements such as nodes representing different energy types and processes representing flows between nodes. The abstract model structure enables user to construct arbitrary energy systems and define links between assets, commodities, energy markets and reserve markets. Predicer model can include properties such as unit ramp rates, online units, dynamic energy storages, market realisation and market bidding requirements. The aggregation of unit-based energy and reserve opportunities into a virtual power plant allows the asset owner to make optimized portfolio-level bids for different market products. The model scenarios consist of user defined forecasts for market prices, renewable energy supply, energy demand and other system related time series. Predicer is implemented in Julia programming language and uses the JuMP optimisation package.

Multiscale stochastic modeling of microporous layers and bi-layer gas diffusion media for polymer electrolyte fuel cells

The microporous layer (MPL) is placed between the catalyst layer and gas diffusion layer (GDL) substrate to enhance mass transport, performance, and durability of fuel cells. Considering the significant experimental challenges in the prototyping and characterization of MPLs, the objective of the present work is to develop a multiscale stochastic modeling framework for MPLs and complete MPL-coated bi-layer GDLs. A comprehensive range of MPLs is considered, including carbon nanoparticle and graphite particle-based materials. Following experimental validation, the modeling framework is applied to simulate the effects of MPL morphology and composition on the salient transport properties of MPLs and full GDLs. The MPL morphology is shown to have a major, controlling influence on the overall GDL properties and can therefore be used as a design strategy for enhanced transport within the membrane electrode assembly of the fuel cell. Additionally, the validated multiscale modeling approach is reliable and flexible enough to be applied as a virtual design tool for MPL and GDL prototyping assignments to reduce the cost and time of the design cycle.

Selecting a significance level in sequential testing procedures for community detection

While there have been numerous sequential algorithms developed to estimate community structure in networks, there is little available guidance and study of what significance level or stopping parameter to use in these sequential testing procedures. Most algorithms rely on prespecifiying the number of communities or use an arbitrary stopping rule. We provide a principled approach to selecting a nominal significance level for sequential community detection procedures by controlling the tolerance ratio, defined as the ratio of underfitting and overfitting probability of estimating the number of clusters in fitting a network. We introduce an algorithm for specifying this significance level from a user-specified tolerance ratio, and demonstrate its utility with a sequential modularity maximization approach in a stochastic block model framework. We evaluate the performance of the proposed algorithm through extensive simulations and demonstrate its utility in controlling the tolerance ratio in single-cell RNA sequencing clustering by cell type and by clustering a congressional voting network.

APPROXIMATE PRICING OF DERIVATIVES UNDER FRACTIONAL STOCHASTIC VOLATILITY MODEL

AbstractThis paper examines the issue of derivative pricing within the framework of a fractional stochastic volatility model. We present a deterministic partial differential equation system to derive an approximate expression for the derivative price. The proposed approach allows for the stochastic volatility to be expressed as a composition of deterministic functions of time and a fractional Ornstein–Uhlenbeck process. We apply this method to the European option pricing under the fractional Stein–Stein volatility model, demonstrating its feasibility and reliability through numerical simulations. Our numerical simulations also illustrate the impact of the parameters in the fractional stochastic volatility model on the option price.