Stochastic Modeling Framework Research Articles

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.

Channel-Adaptive Transmission Protocols for Smart Grid IoT Communication

This article presents a new paradigm for channel dynamics adaptive transmission of intermittent data in smart grid IoT communication networks, wherein novel channel prediction frameworks using stochastic modeling as well as data-driven learning of channel variability are proposed. A probing-based transmission is also proposed as a benchmark. These prediction frameworks are complemented with an adaptive channel coding scheme to increase the transmission reliability of time-critical grid monitoring data over a wireless channel. Through analyzing the prediction and packet loss performance at varying SNR and fading conditions, it is noted that the stochastic modeling framework is efficient when the fading correlation in the channel is high while the learning-based approach is more adaptive to channel dynamics as the correlation reduces. The proposed frameworks are easily implementable on low-cost end nodes, owing to the optimal selection of parameters for low runtime complexity. When compared to probing-based data transmission for a given fading in the channel, the packet loss probability of the learning-based transmission closely matches while with stochastic model loss probability is found to be 12.3% higher. However, their respective signaling overheads are 38% and 98% lower with respect to the probing-based approach, which is a significant gain at the cost of marginally additional computation complexity.

On the nature of the microwave field emerging from a composite pupil

Further experimental investigations in the microwave field emerging from a composite pupil are reported in order to determine the nature of the wave propagation. The experiments consisted of delay-time measurements as a function of the distance of the detector from the pupil under test, as well as of the phase variation of a radio-frequency signal at 35 MHz that modulated the same microwave carrier at 9.33 GHz. In addition, measurements employing an admittance comparator were made in order to determine the character of the propagation impedance. All results obtained confirmed superluminal behavior in the near field, up to a distance of about 40 cm. These results were then interpreted within the framework of a stochastic model.

Stochastic modeling of chlorophyll-a for probabilistic assessment and monitoring of algae blooms in the Lower Nakdong River, South Korea

Eutrophication is one of the critical water quality issues in the world nowadays. Various studies have been conducted to explore the contributing factors related to eutrophication symptoms. However, in the field of eutrophication modeling, the stochastic nature associated with the eutrophication process has not been sufficiently explored, especially in a multivariate stochastic modeling framework. In this study, a multivariate hidden Markov model (MHMM) that can consider the spatio-temporal dependence in chlorophyll-a concentration over the Nakdong River of South Korea was proposed. The MHMM can effectively cluster the intra-seasonal and inter-annual variability of chlorophyll-a, thereby enabling us to understand the spatio-temporal evolutions of algal blooms. The relationships between hydro-climatic conditions (e.g., temperature and river flow) and chlorophyll-a concentrations were evident, whereas a relatively weak relationship with water quality parameters was observed. The MHMM enables us to effectively infer the conditional probability of the eutrophication state for the following month. The self-transition likelihood of staying in the current state is substantially higher than the likelihood of moving to other states. Moreover, the proposed modeling approach can effectively offer a probabilistic decision-support framework for constructing an alert classification of the eutrophication. The potential use of the proposed modeling framework was also provided.

Correction to: Towards a stochastic programming modeling framework for districting

Correction to: Towards a stochastic programming modeling framework for districting

An Ensemble Stochastic Forecasting Framework for Variable Distributed Demand Loads

Accurate forecasting of demand load is momentous for the efficient economic dispatch of generating units with enormous economic and reliability implications. However, with the high integration levels of grid-tie generations, the precariousness in demand load forecasts is unreliable. This paper proposes a data-driven stochastic ensemble model framework for short-term and long-term demand load forecasts. Our proposed framework reduces uncertainties in the load forecast by fusing homogenous models that capture the dynamics in load state characteristics and exploit model diversities for accurate prediction. The ensemble model caters for factors such as meteorological and exogenous variables that affect load prediction accuracy with adaptable, scalable algorithms that consider weather conditions, load features, and state characteristics of the load. We defined a heuristic trained combiner model and an error correction model to estimate the contributions and compensate for forecast errors of each prediction model, respectively. Acquired data from the Korean Electric Power Company (KEPCO), and building data from the Korea Research Institute, together with testbed datasets, were used to evaluate the developed framework. The results obtained prove the efficacy of the proposed model for demand load forecasting.

Towards a stochastic programming modeling framework for districting

In this paper a stochastic districting problem is investigated. Demand is assumed to be represented by a random vector with a given joint probability distribution function. A two-stage mixed-integer stochastic programming model is proposed. The first stage comprises the decision about the initial territory design: the districts are defined and all the territory units assigned to one and exactly one of them. In the second stage, i.e., after demand becomes known, balancing requirements are to be met. This is ensured by means of two recourse actions: outsourcing and reassignment of territory units. The objective function accounts for the total expected cost that includes the cost for the first-stage territory design plus the expected cost incurred at the second stage by outsourcing and reassignment. The (re)assignment costs are associated with the distances between territory units, i.e., the focus is put on the compactness of the solution. The model is then extended in different ways to account for aspects of practical relevance such as a maximum desirable dispersion, reallocation constraints, or similarity of the second-stage solution w.r.t. the first-stage one. The new modeling framework proposed is tested computationally using instances built using real geographical data.

Assessing external sulfate attack on thin-shell artificial reef structures under uncertainty

Thin-shell artificial reef (AR) structures with spatial internal volumes have demonstrated superior stock recruitment ability and material efficiency than many gravity-based reef blocks, and cementitious materials, given the easy-to-tailor nature, remains the most popular in reef constructions to date. However, under constant seawater immersion, external sulfate attack (ESA) introduces a major and uncertain reliability concern to this type of AR system, due to the inherent material randomness. This study is concerned with developing a novel stochastic modelling framework for assessing the ESA under material uncertainty. In this paper, the main difficulty associated with the stochastic ESA modelling is identified for the first time, and a novel machine learning aided chemophysical modelling approach is proposed. The performance of the developed framework is carefully examined through the analyses on two types of cementitious materials under ESA.

Primary Drying Optimization in Pharmaceutical Freeze-Drying: A Multivial Stochastic Modeling Framework

Primary drying is the most time-consuming and energy-intensive step in pharmaceutical freeze-drying. Minimizing the duration of this stage is of paramount importance to speed up process development...

Modeling Tumor Evolutionary Dynamics to Predict Clinical Outcomes for Patients with Metastatic Colorectal Cancer: A Retrospective Analysis.

Over 50% of colorectal cancer patients develop resistance after a transient response to therapy. Understanding tumor resistance from an evolutionary perspective leads to better predictions of treatment outcomes. The objectives of this study were to develop a computational framework to analyze tumor longitudinal measurements and recapitulate the individual evolutionary dynamics in metastatic colorectal cancer (mCRC) patients. A stochastic modeling framework was developed to depict the whole spectrum of tumor evolution prior to diagnosis and during and after therapy. The evolutionary model was optimized using a nonlinear mixed effect (NLME) method based on the longitudinal measurements of liver metastatic lesions from 599 mCRC patients. The deterministic limits in the NLME model were applied to optimize the stochastic model for each patient. Cox proportional hazards models coupled with the least absolute shrinkage and selection operator (LASSO) algorithm were applied to predict patients' progression-free survival (PFS) and overall survival (OS). The stochastic evolutionary model well described the longitudinal profiles of tumor sizes. The evolutionary parameters optimized for each patient indicated substantial interpatient variability. The number of resistant subclones at diagnosis was found to be a significant predictor to survival, and the hazard ratios with 95% CI were 1.09 (0.79-1.49) and 1.54 (1.01-2.34) for patients with three or more resistant subclones. Coupled with several patient characteristics, evolutionary parameters strongly predict patients' PFS and OS. A stochastic computational framework was successfully developed to recapitulate individual patient evolutionary dynamics, which could predict clinical survival outcomes in mCRC patients. SIGNIFICANCE: A data analysis framework depicts the individual evolutionary dynamics of mCRC patients and can be generalized to project patient survival outcomes.

Stochastic Weather Modeling-Based Protection Scheme for Hybrid PV–Wind System With Immunity Against Solar Irradiance and Wind Speed

The intermittency in weather complicates the task of determining the optimal setting of protective relays in hybrid photovoltaic (PV)-wind-based microgrids. Classical overcurrent relays quite often maloperate during fluctuations in wind speed and solar irradiance. Motivated by the significance of reducing the sensitivity of microgrid protection against weather intermittency, this article proposes a protection scheme based on the combined framework of stochastic modeling of weather intermittency using probability distribution function and ensemble-based classifier. Considering the possible similar weather scenario to which both the distributed energy resources are subjected to, the covariability has been considered to develop the joint probabilistic model of variation in wind speed and solar irradiance. The model derived using the historical data allows incorporating the weather intermittency in the formulation of the protection algorithm. The data generated under intermittency are processed using a wavelet transform to derive discriminatory attributes. Using the derived attributes, a rotation forest-based classifier has been developed to perform fault detection/classification and faulty section identification. The scheme has been validated for a wide range of weather and fault scenarios. The comparison of the proposed scheme with other reported techniques reflects its significance in providing resilient and robust protection to the microgrid against weather intermittency.

Common‐factor stochastic volatility modelling with observable proxy

AbstractMulti‐asset modelling is of fundamental importance to financial applications such as risk management and portfolio selection. In this article, we propose a multivariate stochastic volatility modelling framework with a parsimonious and interpretable correlation structure. Building on well‐established evidence of common volatility factors among individual assets, we consider a multivariate diffusion process with a common‐factor structure in the volatility innovations. Upon substituting an observable market proxy for the common volatility factor, we markedly improve the estimation of several model parameters and latent volatilities. The model is applied to a portfolio of several important constituents of the S&P500 in the financial sector, with the VIX index as the common‐factor proxy. We find that the prediction intervals for asset forecasts are comparable to those of more complex dependence models, but that option‐pricing uncertainty can be greatly reduced by adopting a common‐volatility structure. The Canadian Journal of Statistics 48: 36–61; 2020 © 2020 Statistical Society of Canada

Convergence Analysis for Continuous-Time Markov Chain Approximation of Stochastic Local Volatility Models: Option Pricing and Greeks

This paper establishes the precise second order convergence rates of the continuous-time Markov chain (CTMC) approximation method for pricing options and calculating its Greeks under the general framework of stochastic local volatility models, which include the Heston and SABR models as special cases. Numerical examples confirm the theoretical findings.

Stochastic Hierarchical Multimodal Hub Location Problem for Cargo Delivery Systems: Formulation and Algorithm

This study aims at developing a stochastic hierarchical multimodal hub location modeling framework for cargo delivery systems to capture uncertainty in hub construction cost and travel time at the strategic level. From a ring-star-star type network design perspective, a stochastic model is established to formulate this problem formally via the expected value and chance-constrained programming techniques. In particular, three types of chance constraints are proposed to ensure that the on-time delivery with pre-specified confidence levels in their respective layer networks. For normal distributions, the original stochastic model can be reformulated as a crisp equivalent mixed-integer linear programming (MILP) model by invoking the central limit theorem. Since the number of constraints and variables increases drastically with the size of cargo delivery distribution network, a memetic algorithm (MA) is designed. This algorithm incorporates genetic search and local intensification to obtain optimal/near-optimal solutions for realistic instance size within a reasonable time limit. For general distributions, it is difficult to convert the stochastic model into its deterministic counterpart. Hence, a hybrid methodology is further designed by combining the MA and Monte Carlo (MC) simulation to solve the proposed stochastic model. To demonstrate the properties of the proposed model and the performance of the designed algorithm, a series of numerical experiments are set up based on the Civil Aeronautics Board (CAB) and Turkish network data sets. Computational results indicate as the confidence level increases, the airport hubs are located further apart in the cargo delivery distribution network for gaining a greater time advantage. In addition, comparative results demonstrate that the MA algorithm proposed herein performs better than the genetic algorithm (GA) in terms of computing speed and quality of the solution.

Coordination of electricity transmission and generation investments

For over twenty years, electricity market liberalization has advanced short-term market efficiency in wholesale markets, but little progress has been made on coordinated transmission and generation investments. With fast penetration of renewables, widespread of distributed energy resources and emergence of smart-grid and energy storage technologies, the stake is growing significantly higher for the long-term efficiency of liberalized wholesale markets with an aging transmission infrastructure.This paper presents a methodology based on a general framework of two-stage stochastic optimization model for analyzing interactions between transmission and generation investments. The methodology features economic effects of prices, incentives and welfare impacts under alternative coordination approaches and cost recovery mechanisms. Application to scenarios under efficient coordination, merchant transmission, and sequential coordination are illustrated using a simple radial transmission network. Interestingly, a Boiteux-Ramsey cost sharing rule produces energy prices and social welfare impacts that appear essentially indistinguishable from those obtained under efficient coordination.

3D stochastic modeling framework for Quaternary sediments using multiple-point statistics: A case study in Minjiang Estuary area, southeast China

Multiple-point statistics (MPS) has shown promise in representing complicated subsurface structures, such as the sedimentary system. The Quaternary sedimentary system possesses prominent anisotropy characteristics. For a practical three-dimensional (3D) application, therefore, the critical challenges come not only from the difficulty of obtaining credible 3D training images, but also from the serious non-stationarity. Moreover, MPS-based simulations are usually performed on a regular Cartesian grid so that they cannot realistically reflect the actual shape and distribution of geological structures. In our work, an integrated MPS-based 3D modeling framework is presented by incorporating the characteristics of Quaternary sediments and the datasets obtained from geological exploration. The framework is embedded into a 3D modeling grid to achieve more precise visualization for the subsurface structures. Following the proposed workflow, we perform the 3D modeling practices for Quaternary sedimentary facies and Quaternary stratigraphic structures by using the datasets from a Quaternary geological survey project at a southeast coastal city in China. The multiple-scale models are constructed by performing the MPS simulations which take into account the constraints of structural conditions. The application verifies the rationality and applicability of the presented workflow where the various structural features are integrated into a unified 3D model to achieve a more realistic characterization.

Consistent community detection in multi-layer network data

Summary We consider multi-layer network data where the relationships between pairs of elements are reflected in multiple modalities, and may be described by multivariate or even high-dimensional vectors. Under the multi-layer stochastic block model framework we derive consistency results for a least squares estimation of memberships. Our theorems show that, as compared to single-layer community detection, a multi-layer network provides much richer information that allows for consistent community detection from a much sparser network, with required edge density reduced by a factor of the square root of the number of layers. Moreover, the multi-layer framework can detect cohesive community structure across layers, which might be hard to detect by any single-layer or simple aggregation. Simulations and a data example are provided to support the theoretical results.

The Effect of Minimum Wage on Iran's Macroeconomic Variables in The Framework of a Dynamic Stochastic General Equilibrium Model

The Effect of Minimum Wage on Iran's Macroeconomic Variables in The Framework of a Dynamic Stochastic General Equilibrium Model

Free-energy-based framework for early forecasting of stem cell differentiation.

Commitment of stem cells to different lineages is inherently stochastic but regulated by a range of environmental bio/chemo/mechanical cues. Here, we develop an integrated stochastic modelling framework for predicting the differentiation of hMSCs in response to a range of environmental cues, including sizes of adhesive islands, stiffness of substrates and treatment with ROCK inhibitors in both growth and mixed media. The statistical framework analyses the fluctuations of cell morphologies over approximately a 24 h period after seeding the cells in the specific environment and uses the cytoskeletal free-energy distribution to forecast the lineage the hMSCs will commit to. The cytoskeletal free energy which succinctly parametrizes the biochemical state of the cell is shown to capture hMSC commitment over a range of environments while simple morphological factors such as cell shape, tractions on their own are unable to correlate with lineages hMSCs adopt.