Stochastic Computational Model Research Articles

A Statistical Comparison of the Simultaneous Attack/ Persistent Pursuit Theory Against Current Methods in Counterterrorism Using a Stochastic Model

Though current strategies in counterterrorism are somewhat effective, various counterinsurgency theorists have raised doubts about the true efficacy of current methods. Established current strategies are fundamentally flawed, with an overemphasis on eliminating leaders and highly connected agents. Colonel Derek Jones, a counterinsurgency theorist, proposed the Simultaneous Attack/Persistent Pursuit (SAPP) Theory as a superior alternative to current methods. In this strategy, attacks are conducted equally across all fronts of a clandestine intelligence network, from which connections are pursued with further attacks. To determine whether current methods are more or less effective in counterterrorism than the method proposed by the SAPP Theory, a stochastic computational model was developed to represent a traditional eastern clandestine network for an isolated sub-cell of a terrorist organization. Attacks were modeled through the loss of agents within specific components of the network. After an analysis of relevant literature discussing the efficacy of current methods in counterterrorism, we hypothesized that the SAPP model would lead to a greater reduction in the number of terrorist attacks than other methods. We simulated five attack strategies, with each strategy being simulated for thirty trials, and the resulting final number of attacks of the terrorist network was recorded. Through four two-sample t-tests comparing each of the four non SAPP strategies to the SAPP model, we concluded that the SAPP model was significantly more effective in reducing the final number of terrorist attacks. This demonstrates the comparative advantage of utilizing the SAPP model, which may prove to be critical in future efforts in counterterrorism.

Sequential Model-Based Optimization for Continuous Inputs with Finite Decision Space

Optimization using stochastic computer experiments is commonplace in engineering and industry. This article addresses the problem of optimization, in which the input space of stochastic computer model is continuous, whereas the decision space in the real problem is restricted to be finite. We propose a sequential model-based optimization method to tackle this problem. The knowledge gradient based on this restricted decision space is used as the criterion to choose new design points, and the fixed rank kriging or Gaussian process is used as the surrogate. This combination takes advantage of the continuous search space to decrease the uncertainty over the finite decision space. We demonstrate the benefit of our proposed methodology compared with existing sequential model-based optimization methods.

An efficient algorithm for a class of stochastic forward and inverse Maxwell models in [formula omitted

We describe an efficient algorithm for reconstruction of the electromagnetic parameters of an unbounded dielectric medium from noisy cross section data induced by a point source in R3. The efficiency of our Bayesian inverse algorithm for the parameters is based on developing an offline high order forward stochastic model and also an associated deterministic dielectric media Maxwell solver. Underlying the inverse/offline approach is our high order fully discrete Galerkin algorithm for solving an equivalent surface integral equation reformulation that is stable for all frequencies. The efficient algorithm includes approximating the likelihood distribution in the Bayesian model by a decomposed fast generalized polynomial chaos (gPC) model as a surrogate for the forward model. Offline construction of the gPC model facilitates fast online evaluation of the posterior distribution of the dielectric medium parameters. Parallel computational experiments demonstrate the efficiency of our deterministic, forward stochastic, and inverse dielectric computer models.

Data-Driven Identification of Stochastic Model Parameters and State Variables: Application to the Study of Cardiac Beat-to-Beat Variability

Enhanced spatiotemporal ventricular repolarization variability has been associated with ventricular arrhythmias and sudden cardiac death, but the involved mechanisms remain elusive. In this paper, a methodology for estimation of parameters and state variables of stochastic human ventricular cell models from input voltage data is proposed for investigation of repolarization variability. The proposed methodology formulates state-space representations based on developed stochastic cell models and uses the unscented Kalman filter to perform joint parameter and state estimation. Evaluation over synthetic and experimental data is presented. Results on synthetically generated data show the ability of the methodology to: first, filter out measurement noise from action potential (AP) traces; second, identify model parameters and state variables from each of those individual AP traces, thus allowing robust characterization of cell-to-cell variability; and, third, replicate statistical population's distributions of input AP-based markers, including dynamic markers quantifying beat-to-beat variability. Application onto experimental data demonstrates the ability of the methodology to match input AP traces while concomitantly inferring the characteristics of underlying stochastic cell models. A novel methodology is presented for estimation of parameters and hidden variables of stochastic cardiac computational models, with the advantage of providing a one-to-one match between each individual AP trace and a corresponding set of model characteristics. The proposed methodology can greatly help in the characterization of temporal (beat-to-beat) and spatial (cell-to-cell) variability in human ventricular repolarization and in ascertaining the corresponding underlying mechanisms, particularly in scenarios with limited available experimental data.

Metamodel-based optimization of stochastic computer models for engineering design under uncertain objective function

Stochastic computer models are prevailingly used to help the design engineer to understand and optimize analytically intractable systems. A frequently encountered, but often ignored problem is that the objective function representing system performance may contain some uncertain parameters. Due to lack of computationally efficient tools, rational procedures for dealing with the problem such as finding multiple Pareto-optimal solutions or conducting sensitivity analysis on the uncertain parameters require the stochastic computer model to be optimized many times, which would incur extensive computational burden. In this work, we provide a computationally efficient metamodel-based solution to capture this uncertainty. This solution first constructs a Cartesian product design over the space of both design variables and uncertain parameters. Thereafter, a radial basis function metamodel is used to provide a smooth prediction surface of the objective value over the space of both design variables and uncertain parameters. Based on the Cartesian product design structure, a fast fitting algorithm is also derived for fitting the metamodel. To illustrate the effectiveness of the developed tools in solving practical problems, they are applied to seek a robust optimal solution to a drug delivery system with uncertain desirability function parameters based on a criterion that we propose.

Predicting Effects of Tropomyosin Stiffness on Cardiac Muscle Contraction Using Coarse-Grained Stochastic Modeling

During the cardiac thin filament activation process, Tropomyosin (Tm) oscillates over the surface of actin filament in the azimuthal direction to regulate the access of Myosin heads to actin binding sites. These dynamical modes of oscillation and the resultant cooperative activation effects depend critically on the stiffness characteristics and the mobility of Tm molecules. In this study, we developed a stochastic coarse-grained computational model to describe the Tm motions over the surface of actin filament using Langevin-Brownian dynamics. The model represents the structural arrangement of Tm molecules as a flexible chain with variable torsional stiffness using a crystal elastic network approach. The model accounts for the spatial interactions among nearest-neighbor regulatory units (RUs), which are thought to appear from the structural coupling of adjacent Tropomyosins. This elastic coupling between RUs is accomplished by assigning a multi-well potential energy for each RU. The model is then used to study the effects of Tm torsional stiffness variations on the cooperative activation of the thin filament. The results suggest that small perturbations in Tm torsional stiffness can lead to a significant effect on force-Ca2+ sensitivity, the rate of tension redevelopment, relaxation rate, and other contraction characteristics. The present stochastic computational model draws for the first time a more detailed molecular connection between Tm torsional stiffness, Tm modes of oscillations over actin surface, cooperativity among RUs, and dynamic muscle twitches. Thus, this coarse-graining approach may be useful in explaining many cardiomyopathies induced by structural remodeling and stiffening in Tm molecules as a result of point mutations in the human gene TPM1.

Binding Kinetics between Membrane-Bound Kinesin Motors and Microtubules

Despite the vital role that kinesin plays in transporting membraneous organelles in eukaryotic cells, there is a knowledge gap between our understanding of the chemomechanical cycle of single motors and the dynamics of multi-motor-driven vesicle transport in vivo. One of the fundamental mechanisms that remain obscure is how a lipid bilayer affects the binding kinetics between kinesin and microtubules. We set up a 2D system in which kinesin-1 motors were attached to a supported lipid bilayer to monitor the ensemble kinetics of motor binding to microtubules under total internal reflection fluorescence (TIRF) microscope. Freely diffusing kinesin-1 motors rapidly accumulated onto the microtubule upon its landing and the accumulation process reached steady-state within seconds. The observed accumulation rate was found to scale linearly with motor density. Using a simple model of binding kinetics between diffusing kinesin motors and the bound microtubule, we calculated a bi-molecular on-rate constant of 1.2 x 10−4 (motors/μm2)−1s−1. When 30% cholesterol was incorporated into the lipid membrane, which lead to a 4-fold drop in diffusion coefficient, the on-rate constant of kinesin was not altered, meaning that the binding of motors to microtubules was not limited by membrane diffusion. We developed a stochastic computational model in which kinesin-1 motors freely diffused on a lipid bilayer and bound to the microtubule with a first-order on-rate constant when they were within the binding zone where microtubule was accessible. The computational simulation recapitulated the experimental data and the theoretical model well.

Reliability and Variability of Hepatic Venous Pressure Gradient as a Surrogate of Portal Pressure Gradient: Insights from a Computational Model-Based Study

Hepatic venous pressure gradient (HVPG) measurement has been increasingly accepted as a useful means for indirectly measuring portal venous pressure in patients with portal hypertension (PHT) caused by chronic liver diseases. Despite the existence of numerous studies addressing the clinical utility of HVPG measurement, it is as yet unclear how the accuracy of measured HVPG as a surrogate of portal pressure gradient (PPG) is influenced by the pathological status of the hepatic circulation that not only changes with the progression of liver disease but also differs considerably among patients. In addition, it remains unclear whether HVPGs measured in different hepatic veins (HVs) are exchangeable, and if not, what factors determine inter-HV HVPG differences? In this context, we developed a stochastic computational model of the hepatic circulation, and performed a series of model-based numerical experiments to quantitatively investigate the respective/combined effects of various hepatic vascular properties on the accuracy of HVPG measurement. Major findings were: 1) a variation in presinusoidal portal vascular resistance significantly altered the difference between HVPG and PPG, whereas, an enhancement in portosystemic collateral flow (caused by growth of portosystemic collateral vessels or shunt intervention) tended to improve the accuracy of HVPG measurement; and 2) misdiagnosis of clinically significant PHT with HVPG was more likely to occur in the presence of high splanchnic vascular resistance combined with low presinusoidal and postsinusoidal portal vascular resistances. Stochastic numerical simulations of HVPG measurement in multiple HVs revealed that HVPGs measured in the right and middle HVs were basically exchangeable, whereas HVPGs measured in the left HV were relatively lower. The difference in measured HVPG between the middle/left and right HVs correlated positively with the proportion of blood flow rate through the middle/left HV, implying that the lower reading of left-HV HVPG measurement is due primarily to the lower blood flow rate through the HV. These findings may contribute as useful theoretical references for guiding data interpretation or choosing a proper HV for implementing catheterization in the clinical application of HVPG measurement.

Pattems and models of flowering of some Gampanulaceae Juss. species

The present work is devoted to the phenology of individual flowering and the construction of structure-dynamic models of this process on its basis. The results of the study of the flowering phenology of Campanula bononiensis, C. sarmatica and Platycodon grandiflorus are presented. The data obtained characterize both the phenological (time and duration of flowering, lifespan of individual flowers) and structural features (degree of branching of the inflorescence, length of floral axes, number of flowers, order of their blooming) that describe the flowering of a monocarpic shoot. Inflorescences of the species are elongated and multiflorous, of the compound type inherent for Campanulaceae, and characterized by a high variability of all structural features. Observation data were processed by standard statistical methods and used to construct stochastic computer models of flowering shoots, while omissions in data were restored by using the maximum likelihood method. Flowering patterns of the species, due to differences in phenological and structural features, have been revealed. It has been shown that flowering curves depend on the synchrony in the flowers blooming on the main (first-order) axis and lateral (second-order) axes. C. bononiensis has one asymmetrical peak with a broadening on the left, achieved with the simultaneous blooming of flowers in the upper and lower parts of the main axis and on lateral axes in the middle part of the inflorescence, where the first-order flowers have already finished blooming (they provided the broadening). Flowering curves for C. sarmatica and P grandiflorus are bimodal, with the first peak being due to the flowers blooming on the main axis and the second one on lateral axes. The constructed models reproduce the patterns of individual flowering well, with natural variability, and can be used to simulate the flowering of a group of individuals (population), for example, in landscape design. In combination with visualization tools, they can be used for augmenting plant phenotyping datasets with rendered images of synthetic plants for the purpose of training neural networks in this field.

Probabilistic Verification of Structural Stability Design Procedures

Introduction: This contribution presents a comparison of three methods of the statistical computation of the design load-carrying capacity of a steel plane frame. Two approaches of the European Standard Eurocode 3 and one stochastic approach are applied. The stochastic approach takes into account the random influence of all imperfections and can be applied to the reliability verification of design according to Eurocode 3. Methods: The columns and beams in the steel frame are modelled with beam elements using the stability solution with buckling length and the geometrically nonlinear solution. The stochastic computational model is based on the geometrically nonlinear solution and on the random influence of initial imperfections, whose random samplings are simulated using the Monte Carlo method. Results and Conclusion: The design load-carrying capacity of the steel plane frame computed using the stability solution with buckling length is in good agreement with the stochastic solution in which the design value is calculated as 0.1 percentile. On the contrary, the geometrically nonlinear solution according to Eurocode 3 gives the lowest (safest) values of design load-carrying capacity.

Fitness variation in isogenic populations leads to a novel evolutionary mechanism for crossing fitness valleys

Individuals in a population often have different fitnesses even when they have identical genotypes, but the effect of this variation on the evolution of a population through complicated fitness landscapes is unknown. Here, we investigate how populations with non-genetic fitness variation cross fitness valleys, common barriers to adaptation in rugged fitness landscapes in which a population must pass through a deleterious intermediate to arrive at a final advantageous stage. We develop a stochastic computational model describing the dynamics of an asexually reproducing population crossing a fitness valley, in which individuals of the same evolutionary stage can have variable fitnesses. We find that fitness variation that persists over multiple generations increases the rate of valley crossing through a novel evolutionary mechanism different from previously characterized mechanisms such as stochastic tunneling. By reducing the strength of selection against deleterious intermediates, persistent fitness variation allows for faster adaptation through rugged fitness landscapes.

3D stochastic computational homogenization model for carbon fiber reinforced CNT/epoxy composites with spatially random properties

In this paper, a 3D stochastic computational homogenization model for carbon fiber-reinforced (CFR) CNT/epoxy matrix composites was presented. Stochastic waviness, agglomeration and orientation of CNT fillers cause random spatial variations of the elasticity tensor of the CNT/epoxy matrix within a microscale RVE, resulting in probabilistic variations of the effective homogenized stiffness of the RVE. The present computational homogenization model is based on two-scale asymptotic homogenization theory. An ensemble average of the multiple homogenized effective stiffnesses was obtained for structural analysis of the macroscale CFR CNT/epoxy composite materials. From the proposed model, we could observe significant effects of the CNT alignment orientations, agglomeration and waviness on the effective stiffnesses. Effective stiffness changes of a microscale RVE caused by the nanoscale uncertainties were investigated. The proposed multiscale modeling method and approach will be a basis for hierarchical multiscale material design of nanocomposite materials.

Microstructure evolution under isothermal and continuous cooling conditions via a combined multiphase field and nucleation approach

We demonstrate the microstructure evolution involving the nucleation and grain growth of a binary alloy during the continuous cooling process via a combined multiphase field model and stochastic nucleation computational model. The nuclei are initiated by adding into the total free energy a term of the nucleation energy related to the variables that represents grains of different orientation. Moelans’ interpolation functions are implemented to construct the chemical bulk free energy from coexisting phases/grains for increased stability of multiphase/grain junctions. It was found that the temperature dependent nucleation rate and interface mobility are the main materials properties controlling the features of the resultant microstructures. More even-sized and fine grains can be formed under a high cooling rate given the specified temperature dependent nucleation rate. Solute trapping is the most prominent and solute segregation is the slightest at the highest cooling rate. Equipped with a grain-tracking method, this computational framework provides a viable and computationally efficiently pathway to investigate the large-scale microstructure evolution under various temperature histories that could occur in manufacturing processes.

Stochastic Computer Model of the Kinetics of Multicomponent Intercrystalline Adsorption in Solid Solutions

The basic principles of constructing a stochastic computer model of intergranular adsorption kinetics controlled by interatomic pair interactions and the volume diffusion mobility of the components of a solid solution are developed, allowing for the bulk structure of crystals and the equilibrium atomic configuration of intergranular boundaries. The results are presented from computer simulations of the grain boundary segregation of S and P in α-Fe-based alloys.

Stochastic simulations of nanoparticle internalization through transferrin receptor dependent clathrin-mediated endocytosis

BackgroundReceptor dependent clathrin-mediated endocytosis (CME) is one of the most important endocytic pathways for the internalization of bioparticles into cells. During CME, the ligand-receptor interactions, development of clathrin-coated pit (CCP) and membrane evolution all act together to drive the internalization of bioparticles. In this work, we develop a stochastic computational model to investigate the CME based on the Metropolis Monte Carlo simulations. MethodsThe model is based on the combination of a stochastic particle binding model with a membrane model. The energetic costs of membrane bending, CCP formation and ligand-receptor interactions are systematically linked together. ResultsWe implement our model to investigate the effects of particle size, ligand density and membrane stiffness on the overall process of CME from the drug delivery perspectives. Consistent with some experiments, our results show that the intermediate particle size and ligand density favor the particle internalization. Moreover, our results show that it is easier for a particle to enter a cell with softer membrane. ConclusionsThe model presented here is able to provide mechanistic insights into CME and can be readily modified to include other important factors, such as actins. The predictions from the model will aid in the therapeutic design of intracellular/transcellular drug delivery and antiviral interventions.

Global sensitivity analysis of hepatic venous pressure gradient (HVPG) measurement with a stochastic computational model of the hepatic circulation

Hepatic venous pressure gradient (HVPG) is a widely employed surrogate of portal pressure gradient (PPG) in the diagnosis of portal hypertension (PHT). However, little is known about how HVPG measurement is affected by the complex vascular changes associated with PHT. In this study, we employed a computational method to quantitatively evaluate the sensitivity of HVPG measurement to various vascular factors involved in the development of sinusoidal PHT, aiming to provide a theoretical reference to guide the clinical application of HVPG measurement. The method consisted of developing a lumped-parameter model of the hepatic circulation to simulate HVPG measurement, stochastic parameter sampling used to represent a wide range of pathological conditions, and global sensitivity analysis performed to identify factors that dominate the accuracy of HVPG measurement. The major findings included 1) presinusoidal portal vascular resistance (Rpxs) and splanchnic vascular resistance (Rspl) were the major factors determining the relative difference (EHVPG) between HVPG and PPG; 2) hepatic arteriolar resistance and portosystemic collateral resistance had little influence on EHVPG although they relate closely to the severity of PHT; and 3) postsinusoidal vascular resistance (Rpts) only mildly affected EHVPG, despite its marked influence on HVPG and PPG. Moreover, stochastic simulations calibrated to HVPG/PPG data measured in a patient cohort revealed that misdiagnosis of clinically significant PHT with HVPG was more likely to occur in the presence of high Rspl combined with low Rpxs and Rpts. These findings suggest that understanding patient-specific vascular conditions can help to improve the application or interpretation of HVPG measurement.

A stochastic multiple mapping conditioning computational model in OpenFOAM for turbulent combustion

Computational models for combustion must account for complex and inherently interconnected physical processes including dispersion, mixing, chemical reactions, particulate nucleation and growth and, critically, the interactions of these with turbulence. The development of affordable and accurate models that are widely applicable is a work in progress. Stochastic multiple mapping conditioning (MMC) is a fast-emerging approach that has been successfully applied to non-premixed, premixed and partially premixed flames as well to the modelling of liquid and solid particulate synthesis. The method solves the conventional PDF transport equation but incorporates an additional constraint in that the mixing is localised in a reference space. This paper describes the numerical implementation of stochastic MMC in an OpenFOAM compatible code called mmcFoam. The model concepts and equations along with alternative submodels, code structure and numerical schemes are explained. A focus is placed on validation of the computational methods in particular demonstrating numerical convergence and mass consistency of the hybrid Eulerian/Lagrangian schemes. Four validation cases are selected including a combustion direct numerical simulation (DNS) case, two combustion experimental jet flame cases and a non-combusting particulate synthesis case. The results show that the total mass and mass distribution of Eulerian and Lagrangian schemes are consistent and confirm that the solutions numerically converge with increasing number of stochastic computational particles and sections for describing particulate size distribution.

Multifidelity Analysis for Predicting Rare Events in Stochastic Computational Models of Complex Biological Systems.

Rare events such as genetic mutations or cell-cell interactions are important contributors to dynamics in complex biological systems, eg, in drug-resistant infections. Computational approaches can help analyze rare events that are difficult to study experimentally. However, analyzing the frequency and dynamics of rare events in computational models can also be challenging due to high computational resource demands, especially for high-fidelity stochastic computational models. To facilitate analysis of rare events in complex biological systems, we present a multifidelity analysis approach that uses medium-fidelity analysis (Monte Carlo simulations) and/or low-fidelity analysis (Markov chain models) to analyze high-fidelity stochastic model results. Medium-fidelity analysis can produce large numbers of possible rare event trajectories for a single high-fidelity model simulation. This allows prediction of both rare event dynamics and probability distributions at much lower frequencies than high-fidelity models. Low-fidelity analysis can calculate probability distributions for rare events over time for any frequency by updating the probabilities of the rare event state space after each discrete event of the high-fidelity model. To validate the approach, we apply multifidelity analysis to a high-fidelity model of tuberculosis disease. We validate the method against high-fidelity model results and illustrate the application of multifidelity analysis in predicting rare event trajectories, performing sensitivity analyses and extrapolating predictions to very low frequencies in complex systems. We believe that our approach will complement ongoing efforts to enable accurate prediction of rare event dynamics in high-fidelity computational models.

Stochastic Analysis of Multiplex Boolean Networks for Understanding Epidemic Propagation

Many large systems are not isolated but rather an integration of several parallel systems, referred to as multiplex networks. Aiming to improve the evaluation efficiency of a simulation-based approach, stochastic computational models are proposed for multiplex Boolean networks with non-Bernoulli sequences encoding signal probabilities. Then, the epidemic spreading process consisting of awareness diffusion on the virtual contact layer and epidemic spreading via physical contacts, is further considered. Given the impacts of nodes in the virtual contact layer, several benchmarks are used to test the average infection probability. The computational results indicate that a node with a larger spreading degree is likely to be an effective target for affecting the average infection probability, which extends the scope of existing observations, although the network topology also plays an important role in determining the infection effect.

Pathwise Error Bounds in Multiscale Variable Splitting Methods for Spatial Stochastic Kinetics

Stochastic computational models in the form of pure jump processes occur frequently in the description of chemical reactive processes, of ion channel dynamics, and of the spread of infections in populations. For spatially extended models, the computational complexity can be rather high such that approximate multiscale models are attractive alternatives. Within this framework some variables are described stochastically, while others are approximated with a macroscopic point value. We devise theoretical tools for analyzing the pathwise multiscale convergence of this type of variable splitting methods, aiming specifically at spatially extended models. Notably, the conditions we develop guarantee well-posedness of the approximations without requiring explicit assumptions of a priori bounded solutions. We are also able to quantify the effect of the different sources of errors, namely, the multiscale error and the splitting error, respectively, by developing suitable error bounds. Computational experiments on selected problems serve to illustrate our findings.