A novel reliability estimation method of complex network based on Monte Carlo

Aiming at the reliability evaluation method of the complex network, and network reliability is an important index in measuring the reliability of large-sized network. The Monte Carlo method is studied, and the general principle of MC simulation and the reliability evaluation approach based on MC are introduced. Sampling is very important in the Monte Carlo simulation, and random variable is studied, and several kinds of discrete distributions are introduced. A novel reliability evaluation method based on Monte Carlo method is proposed. To evaluate network reliability efficiently, the proposed method generates time-pointer of the arc failure events and constructs the event-table of the complex network, and updates the network states, and sampling is selected by geometric distribution. Precision and unbiased of the reliability evaluating are discussed. Furthermore, a series of numerical experiments are implemented to compare the efficiency of the CMC and the other traditional methods under the same experimental condition.     

Monte carlo studies of plant mating system estimation models: the one-pollen parent and mixed mating models

Estimation of mating system parameters in plant populations typically employs family-structured samples of progeny genotypes. These estimation models postulate a mixture of self-fertilization and random outcrossing. One assumption of such models concerns the distribution of pollen genotypes among eggs within single maternal families. Previous applications of the mixed mating model to mating system estimation have assumed that pollen genotypes are sampled randomly from the total population in forming outcrossed progeny within families. In contrast, the one-pollen parent model assumes that outcrossed progeny within a family share a single-pollen parent genotype. Monte Carlo simulations of family-structured sampling were carried out to examine the consequences of violations of the different assumptions of the two models regarding the distribution of pollen genotypes among eggs. When these assumptions are violated, estimates of mating system parameters may be significantly different from their true values and may exhibit distributions which depart from normality. Monte Carlo methods were also used to examine the utility of the bootstrap resampling algorithm for estimating the variances of mating system parameters. The bootstrap method gives variance estimates that approximate empirically determined values. When applied to data from two plant populations which differ in pollen genotype distributions within families, the two estimation procedures exhibit the same behavior as that seen with the simulated data.     

Inference for an epidemic when susceptibility varies

A stochastic epidemic model featuring fixed-length latent periods, gamma-distributed infectious periods and randomly varying heterogeneity among susceptibles is considered. A Markov chain Monte Carlo algorithm is developed for performing Bayesian inference for the parameters governing the infectious-period length and the hyper-parameters governing the heterogeneity of susceptibility. This method of analysis applies to a wider class of diseases than methods proposed previously. An application to smallpox data confirms results about heterogeneity suggested by an earlier analysis that relied on less realistic assumptions.     

A model-free way of representing hyperthermia cell survival data

We present a method of fitting curves to cell survival data that is free from all model assumptions, requiring only that the fitted curves be decreasing and reasonably smooth, where the degree of smoothness is determined from considerations of experimental error. The fitted curves are then differentiated to yield frequency distributions of cell killing times, which may be of value in defining subpopulations with different sensitivities to the cytotoxic agent under study. In addition, confidence intervals on the fitted curves and frequency distributions are obtained by Monte Carlo simulation. The results allow the objective and model-free assessment of the effects of various experimental interventions on cell survival.     

A global approach for sparse representation of uncertainty in Life Cycle Assessments of waste management systems

Purpose

Identification of key inputs and their effect on results from Life Cycle Assessment (LCA) models is fundamental. Because parameter importance varies greatly between cases due to the interaction of sensitivity and uncertainty, these features should never be defined a priori. However, exhaustive parametrical uncertainty analyses may potentially be complicated and demanding, both with analytical and sampling methods. Therefore, we propose a systematic method for selection of critical parameters based on a simplified analytical formulation that unifies the concepts of sensitivity and uncertainty in a Global Sensitivity Analysis (GSA) framework.

Methods

The proposed analytical method based on the calculation of sensitivity coefficients (SC) is evaluated against Monte Carlo sampling on traditional uncertainty assessment procedures, both for individual parameters and for full parameter sets. Three full-scale waste management scenarios are modelled with the dedicated waste LCA model EASETECH and a full range of ILCD recommended impact categories. Common uncertainty ranges of 10 % are used for all parameters, which we assume to be normally distributed. The applicability of the concepts of additivity of variances and GSA is tested on results from both uncertainty propagation methods. Then, we examine the differences in discernibility analyses results carried out with varying numbers of sampling points and parameters.

Results and discussion

The proposed analytical method complies with the Monte Carlo results for all scenarios and impact categories, but offers substantially simpler mathematical formulation and shorter computation times. The coefficients of variation obtained with the analytical method and Monte Carlo differ only by 1 %, indicating that the analytical method provides a reliable representation of uncertainties and allows determination of whether a discernibility analysis is required. The additivity of variances and the GSA approach show that the uncertainty in results is determined by a limited set of important parameters. The results of the discernibility analysis based on these critical parameters vary only by 1 % from discernibility analyses based on the full set, but require significantly fewer Monte Carlo runs.

Conclusions

The proposed method and GSA framework provide a fast and valuable approximation for uncertainty quantification. Uncertainty can be represented sparsely by contextually identifying important parameters in a systematic manner. The proposed method integrates with existing step-wise approaches for uncertainty analysis by introducing a global importance analysis before uncertainty propagation.

     

The permeability and the effect of acyl-chain length for phospholipid bilayers containing cholesterol: theory and experiment.

The model of Cruzeiro-Hansson et al. (Biochim. Biophys. Acta (1989) 979, 166-1176) for lipid-cholesterol bilayers at low cholesterol concentrations is used to predict the thermodynamic properties and the passive ion permeability of lipid bilayers as a function of acyl-chain length and cholesterol concentration. Numerical simulations based on the Monte Carlo method are used to determine the equilibrium state of the system near the main gel-fluid phase transition. The permeability is calculated using an ansatz which relates the passive permeability to the amount of interfaces formed in the bilayer when cholesterol is present. The model predicts at low cholesterol contents an increase in the membrane permeability in the transition region both for increasing cholesterol concentration and for decreasing chain length at a given value of the reduced temperature. This is in contrast to the case of lipid bilayers containing high cholesterol concentrations where the cholesterol strongly suppresses the permeability. Experimental results for the Na+ permeability of C15PC and DPPC (C16PC) bilayers containing cholesterol are presented which confirm the theoretical predictions at low cholesterol concentrations.     

Suitability of Pharmacokinetic Models for Dynamic Contrast-Enhanced MRI of Abdominal Aortic Aneurysm Vessel Wall: A Comparison

Purpose

Increased microvascularization of the abdominal aortic aneurysm (AAA) vessel wall has been related to AAA progression and rupture. The aim of this study was to compare the suitability of three pharmacokinetic models to describe AAA vessel wall enhancement using dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI).

Materials and Methods

Patients with AAA underwent DCE-MRI at 1.5 Tesla. The volume transfer constant (K^trans), which reflects microvascular flow, permeability and surface area, was calculated by fitting the blood and aneurysm vessel wall gadolinium concentration curves. The relative fit errors, parameter uncertainties and parameter reproducibilities for the Patlak, Tofts and Extended Tofts model were compared to find the most suitable model. Scan-rescan reproducibility was assessed using the interclass correlation coefficient and coefficient of variation (CV). Further, the relationship between K^trans and AAA size was investigated.

Results

DCE-MRI examinations from thirty-nine patients (mean age±SD: 72±6 years; M/F: 35/4) with an mean AAA maximal diameter of 49±6 mm could be included for pharmacokinetic analysis. Relative fit uncertainties for K^trans based on the Patlak model (17%) were significantly lower compared to the Tofts (37%) and Extended Tofts model (42%) (p<0.001). K^trans scan-rescan reproducibility for the Patlak model (ICC = 0.61 and CV = 22%) was comparable with the Tofts (ICC = 0.61, CV = 23%) and Extended Tofts model (ICC = 0.76, CV = 22%). K^trans was positively correlated with maximal AAA diameter (Spearman’s ρ = 0.38, p = 0.02) using the Patlak model.

Conclusion

Using the presented imaging protocol, the Patlak model is most suited to describe DCE-MRI data of the AAA vessel wall with good K^trans scan-rescan reproducibility.     

A Monte Carlo model for the internal dosimetry of choroid plexuses in nuclear medicine procedures

Choroid plexuses are vascular structures located in the brain ventricles, showing specific uptake of some diagnostic and therapeutic radiopharmaceuticals currently under clinical investigation, such as integrin-binding arginine-glycine-aspartic acid (RGD) peptides. No specific geometry for choroid plexuses has been implemented in commercially available software for internal dosimetry.The aims of the present study were to assess the dependence of absorbed dose to the choroid plexuses on the organ geometry implemented in Monte Carlo simulations, and to propose an analytical model for the internal dosimetry of these structures for ¹⁸F, ⁶⁴Cu, ⁶⁷Cu, ⁶⁸Ga, ⁹⁰Y, ¹³¹I and ¹⁷⁷Lu nuclides. A GAMOS Monte Carlo simulation based on direct organ segmentation was taken as the gold standard to validate a second simulation based on a simplified geometrical model of the choroid plexuses. Both simulations were compared with the OLINDA/EXM sphere model.The gold standard and the simplified geometrical model gave similar dosimetry results (dose difference < 3.5%), indicating that the latter can be considered as a satisfactory approximation of the real geometry. In contrast, the sphere model systematically overestimated the absorbed dose compared to both Monte Carlo models (range: 4–50% dose difference), depending on the isotope energy and organ mass. Therefore, the simplified geometric model was adopted to introduce an analytical approach for choroid plexuses dosimetry in the mass range 2–16 g. The proposed model enables the estimation of the choroid plexuses dose by a simple bi-parametric function, once the organ mass and the residence time of the radiopharmaceutical under investigation are provided.     

Niche overlap and invasion of competitors in random environments I. Models without demographic stochasticity

The relationship between persistent, small to moderate levels of random environmental fluctuations and limits to the similarity of competing species is studied. The analytical theory hinges on deriving conditions under which a rare invading species will tend to increase when faced with an array of resident competitors in a fluctuating environment. A general approximation scheme predicts that the effects of low levels of stochasticity will typically be small. The technique is applied explicitly to a class of symmetric, discrete-time stochastic analogs of the Lotka-Volterra equations that incorporate cross-correlation but no autocorrelation. The random environment limits to similarity are always very close to the corresponding constant environment limits. However, stochasticity can either facilitate or hinder invasion. The exact limits to similarity are extremely model-dependent. In addition to the symmetric models, an analytically tractable class of models is presented that incorporates both auto- and cross-correlation and no symmetry assumptions. For all of the models investigated, the analytical theory predicts that small-scale stochasticity does little, if anything, to limit similarity. Extensive Monte Carlo results are presented that confirm the analytical results whenever the dynamics of the discretetime models are biologically reasonable in the sense that trajectories do not exhibit unrealistic crashes. Interestingly, the class of stochastic models that is well behaved in this sense includes models whose deterministic analogs are chaotic. The qualitative conclusion, supported by both the analytical and simulation results, is that for competitive guilds adequately modeled by Lotka-Volterra equations including small to moderate levels of random fluctuations, practical limits to similarity can be obtained by ignoring the stochastic terms and performing a deterministic analysis. The mathematical and biological robustness of this conclusion is discussed.     

Analytical Propagation of Uncertainty in Life Cycle Assessment Using Matrix Formulation

Inventory data and characterization factors in life cycle assessment (LCA) contain considerable uncertainty. The most common method of parameter uncertainty propagation to the impact scores is Monte Carlo simulation, which remains a resource‐intensive option—probably one of the reasons why uncertainty assessment is not a regular step in LCA. An analytical approach based on Taylor series expansion constitutes an effective means to overcome the drawbacks of the Monte Carlo method. This project aimed to test the approach on a real case study, and the resulting analytical uncertainty was compared with Monte Carlo results. The sensitivity and contribution of input parameters to output uncertainty were also analytically calculated. This article outlines an uncertainty analysis of the comparison between two case study scenarios. We conclude that the analytical method provides a good approximation of the output uncertainty. Moreover, the sensitivity analysis reveals that the uncertainty of the most sensitive input parameters was not initially considered in the case study. The uncertainty analysis of the comparison of two scenarios is a useful means of highlighting the effects of correlation on uncertainty calculation. This article shows the importance of the analytical method in uncertainty calculation, which could lead to a more complete uncertainty analysis in LCA practice.     

Resolving Cytosolic Diffusive States in Bacteria by Single-Molecule Tracking

The trajectory of a single protein in the cytosol of a living cell contains information about its molecular interactions in its native environment. However, it has remained challenging to accurately resolve and characterize the diffusive states that can manifest in the cytosol using analytical approaches based on simplifying assumptions. Here, we show that multiple intracellular diffusive states can be successfully resolved if sufficient single-molecule trajectory information is available to generate well-sampled distributions of experimental measurements and if experimental biases are taken into account during data analysis. To address the inherent experimental biases in camera-based and MINFLUX-based single-molecule tracking, we use an empirical data analysis framework based on Monte Carlo simulations of confined Brownian motion. This framework is general and adaptable to arbitrary cell geometries and data acquisition parameters employed in two-dimensional or three-dimensional single-molecule tracking. We show that, in addition to determining the diffusion coefficients and populations of prevalent diffusive states, the timescales of diffusive state switching can be determined by stepwise increasing the time window of averaging over subsequent single-molecule displacements. Time-averaged diffusion analysis of single-molecule tracking data may thus provide quantitative insights into binding and unbinding reactions among rapidly diffusing molecules that are integral for cellular functions.     

Calculation of the shock Hugoniot of deuterium at pressures above 1 Mbar by the path-integral Monte Carlo method

Plasma Physics Reports - The shock Hugoniot of deuterium at pressures above 1 Mbar is calculated by the path-integral Monte Carlo method without introducing additional physical assumptions and...     

基于动态光热作用模型的激光诱导肿瘤间质热疗中的参数选择

建立了描述温控加热方式下激光诱导肿瘤间质热疗过程中动态光热作用的二维圆柱坐标下的数学模型,采用基于网格的蒙特卡罗方法数值模拟热疗过程中激光能量在非均质生物组织内的传输过程,基于Pennes生物传热方程和Arrhen ius方程数值求解组织内的温度场和热损伤体积的变化。通过数值模拟的方法分析了激光波长、激光功率、温控范围等因素对激光诱导肿瘤间质热疗中热损伤体积的影响。数值模拟的结果表明,通过选择合适的治疗参数,可以得到各种不同大小的热疗区域。本文的结果和结论对于临床治疗方案的制定具有一定的理论指导意义。     

Simulation methods for protein structure fluctuations

Three numerical techniques for generating thermally accessible configurations of globular proteins are considered; these techniques are the molecular dynamics method, the Metropolis Monte Carlo method, and a modified Monte Carlo method which takes account of the forces acting on the protein atoms. The molecular dynamics method is shown to be more efficient than either of the Monte Carlo methods. Because it may be necessary to use Monte Carlo methods in certain important types of sampling problems, the behavior of these methods is examined in some detail. It is found that an acceptance ratio close to 1/6 yields optimum efficiency for the Metropolis method, in contrast to what is often assumed. This result, together with the overall inefficiency of the Monte Carlo methods, appears to arise from the anisotropic forces acting on the protein atoms due to their covalent bonding. Possible ways of improving the Monte Carlo methods are suggested.     

A mixture theory model of fluid and solute transport in the microvasculature of normal and malignant tissues. I. Theory

In order to better understand the mechanisms governing transport of drugs, nanoparticle-based treatments, and therapeutic biomolecules, and the role of the various physiological parameters, a number of mathematical models have previously been proposed. The limitations of the existing transport models indicate the need for a comprehensive model that includes transport in the vessel lumen, the vessel wall, and the interstitial space and considers the effects of the solute concentration on fluid flow. In this study, a general model to describe the transient distribution of fluid and multiple solutes at the microvascular level was developed using mixture theory. The model captures the experimentally observed dependence of the hydraulic permeability coefficient of the capillary wall on the concentration of solutes present in the capillary wall and the surrounding tissue. Additionally, the model demonstrates that transport phenomena across the capillary wall and in the interstitium are related to the solute concentration as well as the hydrostatic pressure. The model is used in a companion paper to examine fluid and solute transport for the simplified case of an axisymmetric geometry with no solid deformation or interconversion of mass.     

Ring closure probabilities for DNA fragments by Monte Carlo simulation

The rate of ligation of DNA molecules into circular forms depends on the ring closure probability, commonly called the j-factor, which is a sensitive measure of the extent to which thermal fluctuations contribute to bending and twisting of DNA molecules in solution. We present a theoretical treatment of the cyclization equilibria of DNA that employs a special Monte Carlo method for generating large ensembles of model DNA chains. Using this method, the chain length dependence of the j-factor was calculated for molecules. in the size range 250 to 2000 base-pairs. The Monte Carlo results are compared with recent analytical theory and experimental data. We show that a value of 475 A for the persistence length of DNA, close to values measured by a number of other methods, is in excellent agreement with the cyclization results. Preliminary applications of the Monte Carlo method to the problem of systematically bent DNA molecules are presented. The calculated j-factor is shown to be very sensitive to the amount of bending in these fragments. This fact suggests that ligase closure measurements of systematically bent DNA molecules should be a useful method for studying sequence-directed bending in DNA.     

A Simulation Tool for Dynamic Contrast Enhanced MRI

The quantification of bolus-tracking MRI techniques remains challenging. The acquisition usually relies on one contrast and the analysis on a simplified model of the various phenomena that arise within a voxel, leading to inaccurate perfusion estimates. To evaluate how simplifications in the interstitial model impact perfusion estimates, we propose a numerical tool to simulate the MR signal provided by a dynamic contrast enhanced (DCE) MRI experiment. Our model encompasses the intrinsic and relaxations, the magnetic field perturbations induced by susceptibility interfaces (vessels and cells), the diffusion of the water protons, the blood flow, the permeability of the vessel wall to the the contrast agent (CA) and the constrained diffusion of the CA within the voxel. The blood compartment is modeled as a uniform compartment. The different blocks of the simulation are validated and compared to classical models. The impact of the CA diffusivity on the permeability and blood volume estimates is evaluated. Simulations demonstrate that the CA diffusivity slightly impacts the permeability estimates ( for classical blood flow and CA diffusion). The effect of long echo times is investigated. Simulations show that DCE-MRI performed with an echo time may already lead to significant underestimation of the blood volume (up to 30% lower for brain tumor permeability values). The potential and the versatility of the proposed implementation are evaluated by running the simulation with realistic vascular geometry obtained from two photons microscopy and with impermeable cells in the extravascular environment. In conclusion, the proposed simulation tool describes DCE-MRI experiments and may be used to evaluate and optimize acquisition and processing strategies.     

Modeling Multivalent Ligand-Receptor Interactions with Steric Constraints on Configurations of Cell-Surface Receptor Aggregates

We use flow cytometry to characterize equilibrium binding of a fluorophore-labeled trivalent model antigen to bivalent IgE-FcεRI complexes on RBL cells. We find that flow cytometric measurements are consistent with an equilibrium model for ligand-receptor binding in which binding sites are assumed to be equivalent and ligand-induced receptor aggregates are assumed to be acyclic. However, this model predicts extensive receptor aggregation at antigen concentrations that yield strong cellular secretory responses, which is inconsistent with the expectation that large receptor aggregates should inhibit such responses. To investigate possible explanations for this discrepancy, we evaluate four rule-based models for interaction of a trivalent ligand with a bivalent cell-surface receptor that relax simplifying assumptions of the equilibrium model. These models are simulated using a rule-based kinetic Monte Carlo approach to investigate the kinetics of ligand-induced receptor aggregation and to study how the kinetics and equilibria of ligand-receptor interaction are affected by steric constraints on receptor aggregate configurations and by the formation of cyclic receptor aggregates. The results suggest that formation of linear chains of cyclic receptor dimers may be important for generating secretory signals. Steric effects that limit receptor aggregation and transient formation of small receptor aggregates may also be important.     

Development of PARMA: PHITS-based analytical radiation model in the atmosphere

Estimation of cosmic-ray spectra in the atmosphere has been essential for the evaluation of aviation doses. We therefore calculated these spectra by performing Monte Carlo simulation of cosmic-ray propagation in the atmosphere using the PHITS code. The accuracy of the simulation was well verified by experimental data taken under various conditions, even near sea level. Based on a comprehensive analysis of the simulation results, we proposed an analytical model for estimating the cosmic-ray spectra of neutrons, protons, helium ions, muons, electrons, positrons and photons applicable to any location in the atmosphere at altitudes below 20 km. Our model, named PARMA, enables us to calculate the cosmic radiation doses rapidly with a precision equivalent to that of the Monte Carlo simulation, which requires much more computational time. With these properties, PARMA is capable of improving the accuracy and efficiency of the cosmic-ray exposure dose estimations not only for aircrews but also for the public on the ground.