Monte Carlo Approach Research Articles

Machine learning-based approach for assessing the seismic vulnerability of reinforced concrete frame buildings

Recent artificial intelligence (AI) advancements have significantly impacted the field of structural engineering by offering new solutions to enhance safety, efficiency, and cost-effectiveness in the design, construction, and maintenance of infrastructure and urban areas. This study has investigated a machine learning-based approach to estimate the seismic vulnerability of reinforced concrete (RC) building frames. The study utilized a probabilistic technique to assess the simulation of a 4-story RC building frame in the face of epistemic uncertainty. Data was collected using the Monte-Carlo approach, which created a machine learning (ML) model for predicting structural damage. The problem was formulated as both a regression-based and a classification-based model. An artificial neural network (ANN) feed-forward network architecture model was used to solve the classification problems. The optimal number of neurons in the hidden layer was determined to produce the best estimation model. Three different models were combined for the regression model, including LASSO regression, random forest, and gradient boosting, by implementing the stacking generalization. The investigation results indicate that the stacked predicted model exhibits less variance than other ML models. The classification and regression-based algorithms can forecast damage states with a high degree of accuracy, ranging from 87 to 95 percent. In conclusion, the study has demonstrated the effectiveness of machine learning techniques for predicting the seismic vulnerability of RC building frames. With the continued advancement of AI and big data, these methods will likely play a crucial role in the structural engineering field.

Personalized dosimetry assessment of [177Lu]Lu-PSMA-617 radioligand therapy in the management of metastatic castration-resistant prostate cancer

Introduction Prostate-specific membrane antigen (PSMA)-targeted radioligand therapy (RLT) is revolutionizing the treatment landscape for metastatic castration-resistant prostate cancer (mCRPC) patients. This study aimed to establish patient-specific radiation dosimetry for [177Lu]Lu-PSMA-617 RLT in Iranian patients with mCRPC. Method Twelve biopsy-proven prostate cancer patients (aged 68.73 ± 5.26 yr) underwent 6.62 ± 0.36 GBq [177Lu]Lu-PSMA-617 RLT. Post-therapy whole-body planar scans were acquired approximately at 4, 48, and 72 h post-administration, alongside a single SPECT/CT around 48 h using Siemens Symbia T2 to obtain cumulated activity. An imaging protocol and dosimetry approach were designed to balance between time efficacy and accuracy in post-therapeutic dosimetry. Using accurate activity calibration, S-values were calculated by importing SPECT/CT images as the source/geometry into the Geant4 application for the tomographic emission (GATE) Monte Carlo (MC) toolkit. The Medical Internal Radiation Dose (MIRD) scheme was followed for subsequent absorbed dose (AD) calculations in organs at risk (OAR) and tumoral lesions using the dose actor and accumulated activities for precise dose estimations. Results Using the MC approach, the mean ADs to the liver, spleen, right and left kidneys, and tumor lesions were 0.11 ± 0.04 Gy/GBq, 0.08 ± 0.03 Gy/GBq, 0.34 ± 0.09 Gy/GBq, 0.34 ± 0.10 Gy/GBq, and 0.83 ± 0.54 Gy/GBq, respectively. Notably, tumoral lesions demonstrated significantly higher ADs, indicating enhanced uptake of radiopharmaceuticals by malignant cells. Conclusions This study indicates that the ADs of OARs and tumoral lesions from [177Lu]Lu-PSMA-617 RLT in patients with mCRPC are consistent with existing literature. The dosimetry findings suggest that increasing the administered activity of [177Lu]Lu-PSMA-617 RLT is feasible and does not pose a significant risk of adverse effects on OARs, as supported by our data. However, to validate the safety and efficacy of higher doses, further clinical follow-up studies are recommended.

A Stochastic FRET Study on the Core Dimension of Polystyrene-block-Poly(Polyethylene Glycol Monomethyl Ether Acrylate) Micelles.

Polystyrene-b-poly(polyethylene glycol monomethyl ether acrylate) (PSt-b-PPEGA) copolymers featuring pyrene and perylene as the Förster resonance energy transfer (FRET) donor (denoted as D-BCP) and acceptor (denoted as A-BCP), respectively, were synthesized via the reversible addition and fragmentation chain transfer (RAFT) polymerization. These copolymers were then used to form DA-mixed micelles via a dialysis method. The micelles consisted of D-BCP (mole fraction fD = 0.04), A-BCP (fA = 0.04), and label-free PSt-b-PPEGA (fN = 0.92). The decrease in fluorescence intensity of pyrene in the micelles confirmed the occurrence of FRET, with an observed efficiency of 0.32. A Monte Carlo approach was employed to estimate the expected FRET efficiency, assuming the random fractional distribution of D-BCP and A-BCP, along with the random spatial distribution of pyrene and perylene within the micellar core. The observed FRET efficiency suggested a core radius (Rc) of 0.95R0, where R0 was the Förster critical distance. With R0 calculated to be 3.2 nm based on Förster theory, Rc was determined to be approximately 3.0 nm, aligning closely with the dried-out core radius estimated from aggregation number and polystyrene density. This stochastic FRET methodology was further applied to investigate the swelling behavior of the polymer micelles in a mixture of N,N-dimethylformamide (DMF) and water. Dynamic light scattering analysis revealed minimal change in core dimension below 60 vol % DMF content. However, FRET analysis provided a deeper insight, showing an increase in core radius with DMF content up to 20 vol %, followed by saturation up to 50 vol %, offering a more comprehensive understanding of the micelle swelling behavior.

Simultaneous Confidence Intervals for Signal Detection and Ascertaining Precision of Adverse Event Rates in Clinical Trials

The marketing authorization of a medicinal product is contingent upon demonstration of safety and efficacy in support of the product’s labeled conditions of use. To demonstrate safety, one group of adverse events that requires detailed consideration is common adverse reactions (ARs). ARs and their frequency are reported in prescription drug labeling in the US and EU. The determination of these adverse reactions generally takes a simple approach—usually, inclusion is through the frequency of reporting and whether the adverse event (AE) rate for the drug exceeds the placebo rate. This standard method does not account for confounders or multiplicity. To overcome these limitations, we propose a Monte Carlo approach to detect drug safety signals in clinical trials. We fit regression models incorporating covariates to assess the drug effect on the rate of AEs. Adjustment for multiplicity is carried out through the construction of simultaneous confidence intervals accounting for arbitrary correlations. A computationally efficient multiplier bootstrap approach using the Rademacher sequences is developed to generate random samples from the joint distribution of the estimators for all the AE rates. Compared to Bonferroni-based methods, the proposed method leads to narrower simultaneous confidence intervals and is more powerful in detecting potential safety signals.

Tensor-network-based variational Monte Carlo approach to the non-equilibrium steady state of open quantum systems

We introduce a novel method of efficiently simulating the non-equilibrium steady state of large many-body open quantum systems with highly non-local interactions, based on a variational Monte Carlo optimization of a matrix product operator ansatz. Our approach outperforms and offers several advantages over comparable algorithms, such as an improved scaling of the computational cost with respect to the bond dimension for periodic systems. We showcase the versatility of our approach by studying the phase diagrams and correlation functions of the dissipative quantum Ising model with collective dephasing and long-ranged power law interactions for spin chains of up to N=100 spins.

Investigation of the incremental benefits of eccentric collisions in kinetic deflection of potentially hazardous asteroids

In asteroid momentum deflection missions, the presence of ejecta leads to a phenomenon where the system’s momentum appears “amplified” after the impact. This paper makes use of this phenomenon and demonstrates through computational simulations that targeting a point off the geometric center of an asteroid can further enhance the collisional benefit after impact. Due to uncertainties in the attitude of the asteroid and the momentum transfer coefficient (β,γ), this study employs a Monte Carlo approach to address these uncertainties. The results indicate that the strategy proposed in this paper can increase the post-collision deflection distance of the asteroid relative to Earth by an average of 81.05%, while also reducing the standard deviation by an order of magnitude, significantly lowering the uncertainty of the deflection mission. Furthermore, the results show that for certain asteroids particularly sensitive to changes in velocity Δv, blindly targeting their geometric center could result in a 48% probability of reducing the minimum distance to Earth. However, the striking strategy developed in this study can avoid this negative outcome. Finally, based on the computational results, a statistical formula is derived to predict the relative gain of the two strategies, concluding that for asteroids with smaller semi-major axes a, and the interception angle α at impact is greater, the benefits of employing the approach discussed in this paper are greater.

Impact of resource reconfiguration on the dairy supply chain resilience

Investment in food supply chain resilience, as a critical infrastructure, has become necessary for all governments. Disruption of food supply chains can lead to significant economic challenges. Building a resilient supply chain requires resources; however, it is difficult for firms to allocate resources to various resilience strategies. This study allocates the budget to resilient capacity, that is, absorptive, adaptive, and restorative capacity, to minimize supply chain costs and maximize service levels. We developed a novel multi-objective mixed-integer nonlinear programming method for problem formulation. The developed model was converted into an equivalent linear model. We used the Monte Carlo approach to generate the scenarios and the average sample approximation to determine the required scenarios. Finally, the Lexicographic max-min approach solves the model using actual data from a dairy supply chain. The analysis revealed that allocating 50% of the budget to restorative capacity and the remaining to adaptive and absorptive capacity optimizes supply chain performance. This study provides insights for managers to make better decisions with a knowledge-based background, allocate resources to various resilient strategies, and build a more resilient and efficient supply chain.

Modeling hadronic interactions in ultra-high-energy cosmic rays within astrophysical environments: A parametric approach

Interactions of ultra-high energy cosmic-rays (UHECRs) accelerated in astrophysical environments have been shown to shape the energy production rate of nuclei escaping from the confinement zone. To address the influence of hadronic interactions, Hadronic Interaction Models (HIMs) come into play. In this context, we present a parameterization capable of capturing the outcomes of two distinct HIMs, namely EPOS-LHC and Sibyll2.3d, in terms of secondary fluxes, including escaping nuclei, nucleons, neutrinos, photons, and electrons. Our parameterization is systematically evaluated against the source codes, both at fixed energy and mass, as well as in a physical case scenario. The comparison demonstrates that our parameterization aligns well with the source codes, establishing its reliability as a viable alternative for analytical or fast Monte Carlo approaches dedicated to the study of UHECR propagation within source environments. This suggests the potential for utilizing our parameterization as a practical substitute in studies focused on the intricate dynamics of ultra-high energy cosmic rays.

Evaluating the damage tolerant behavior of cold spray repaired aluminum alloys

Cold spray presents a promising solution for repair of damaged material within high-value components. However, before employing cold spray for component repair, it is crucial to assess its damage tolerance and durability. This study focuses on evaluating the fatigue behavior of helium-sprayed AA6061 applied to an A356-T6 cast substrate compared to the same specimen geometry made entirely of the A356-T6 material. Fatigue testing was conducted using a marker band schedule to analyze fatigue crack growth rates in the cold spray and substrate materials. To complement the fatigue testing, experimental uncertainties and variabilities were incorporated into a crack growth model using a Monte Carlo approach to probabilistically assess reliability. The results indicate that the AA6061 cold spray material exhibited faster crack growth, resulting in a ∼25% lower life compared to the baseline A356-T6 material. Given the cost effectiveness of the cold spray repair process, it appears to be a viable approach, with the caveats that the residual life is expected to be less than the pristine substrate material and the cold spray interface is prone to delamination during crack impingement.

Late time cosmic acceleration through parametrization of Hubble parameter in [formula omitted] gravity

This paper explores the rapid expansion of the Universe during its later stages within the context of f(R,Lm) gravity theory. We present a novel parametrization of the Hubble parameter in a manner independent of any specific model and employ it to analyze the Friedmann equations within the FLRW Universe framework. Using a Markov Chain Monte Carlo (MCMC) approach, we derive the model parameters by analyzing a composite dataset comprising 31 Cosmic Chronometers (CC) data points, 26 independent Baryonic Acoustic Oscillations (BAO) measurements, and 1701 data points from Pantheon+SH0ES dataset. The trajectory of the deceleration parameter highlights the shift from deceleration to acceleration in the evolution of the Universe. Additionally, we delve into the dynamics of fundamental cosmological variables for two nonlinear f(R,Lm) models, including energy density, pressure, equation of state (EoS) parameter, and energy conditions.

Second-order mean-field approximation for calculating dynamics in Au-nanoparticle networks.

Exploiting physical processes for fast and energy-efficient computation bears great potential in the advancement of modern hardware components. This paper explores nonlinear charge tunneling in nanoparticle networks, controlled by external voltages. The dynamics are described by a master equation, which expresses the time-evolution of a distribution function over the set of charge occupation numbers. The driving force behind this evolution is charge tunneling events among nanoparticles and their associated rates. We introduce two mean-field approximations to this master equation. By parametrization of the distribution function using its first- and second-order statistical moments, and a subsequent projection of the dynamics onto the resulting moment manifold, one can deterministically calculate expected charges and currents. Unlike a kinetic Monte Carlo approach, which extracts samples from the distribution function, this mean-field approach avoids any random elements. A comparison of results between the mean-field approximation and an already available kinetic Monte Carlo simulation demonstrates great accuracy. Our analysis also reveals that transitioning from a first-order to a second-order approximation significantly enhances the accuracy. Furthermore, we demonstrate the applicability of our approach to time-dependent simulations, using Eulerian time-integration schemes.

Dissolution Mechanisms and Surface Charge of Clay Mineral Nanoparticles: Insights from Kinetic Monte Carlo Simulations

The widespread use of clay minerals and clays in environmental engineering, industry, medicine, and cosmetics largely stems from their adsorption properties and surface charge, as well as their ability to react with water. The dissolution and growth of minerals as a function of pH are closely related to acid–base reactions at their surface sites and their surface charge. The vivid tapestry of different types of surface sites across different types of clay minerals generates difficulties in experimental studies of structure–property relationships. The aim of this paper is to demonstrate how a mesoscale stochastic kinetic Monte Carlo (kMC) approach altogether with atomistic acid-base models and empirical data can be used for understanding the mechanisms of dissolution and surface charge behavior of clay minerals. The surface charge is modeled based on equilibrium equations for de/protonated site populations, which are defined by the pH and site-specific acidity constants (pKas). Lowered activation energy barriers for these sites in de/protonated states introduce pH-dependent effects into the dissolution kinetics. The V-shaped curve observed in laboratory experiments is reproduced with the new kMC model. A generic rate law for clay mineral dissolution as a function of pH is derived from this study. Thus, the kMC approach can be used as a hypothesis-testing tool for the verification of acid–base models for clay and other minerals and their influence on the kinetics of mineral dissolution and growth.

Deep learning-aided active subspace exploration of free-stream effects for fan-shaped film cooling

Film cooling plays a critical role in protecting engine components from high temperatures that can influence safety and performance of gas turbines. However, the process is fraught with uncertainties due to complex inflow conditions and geometrical configurations. These uncertainties significantly impact cooling effectiveness, underscoring the importance of identifying the dominant factors in a quantified manner. Traditional methods, such as the Monte Carlo approach, encounter the “curse of dimensionality,” making them computationally intensive as the number of variable increases. This study tackles these challenges by employing a deep learning strategy with a convolutional neural network (CNN) model to predict film cooling effectiveness efficiently, reducing computational loads compared to traditional computational fluid dynamics (CFD) simulations. It enables the CNN model to act as a surrogate for the CFD simulation and provides gradient information for subsequent analyses. Additionally, this study employs active subspace (AS) analysis for dimensionality reduction, identifying dominant parameters based on the trained CNN model. This approach not only enhances the speed of simulations but also provides an effective way to analyze dominant parameters and carry out optimizations. Results demonstrate a strong correlation between the CNN predictions and detailed CFD simulations, with all the mean absolute errors below 0.08, validating the model's efficacy in capturing complex cooling dynamics. The dominant analysis based on the AS method gives the blowing ratio as the most important factors, and the subsequent parameter dimension reduction and suggested optimization region are also explored by applying the low-dimensional active variable. The tested optimal factors yield higher spatially averaged cooling effectiveness above 0.35 and show reasonable pattern changes compared to the maximum and minimum results in the sample.

Density-driven free convection in heterogeneous aquifers with connectivity features

Free convection usually happens in variable-density groundwater flow systems, and it favors contaminant transport by enlarging length scales and shortening timescales compared to advection and diffusion/dispersion alone. Previous studies have demonstrated that heterogeneity with multi-variate Gaussian distribution for logarithmic permeabilities (log10k) plays an important role in the onset, growth, and/or decay of instability during the density-driven convective process. Nevertheless, the connectivity features (i.e., connected structures of extremely high/low-k values), which are common in natural aquifers, have received little attention. In this study, the classical problem of transient free convection has been modified and numerically simulated by Monte Carlo approach to investigate the effects of connectivity features in heterogeneity on the unstable convective processes. Results show that free convection is promoted by the connected high-k structures and retarded by the connected low-k structures during mainly the early-stage mass loading. The impacts of connectivity features tend to be amplified by higher variation in log10k distributions, and can be secondarily influenced by correlation lengths and anisotropy. Under the multi-variate Gaussian assumption, the existence of connected high-k structures leads to underestimation of density-driven instability, in which the risk differs based on the statistics of permeability fields, metrics of interest and timeframe. This study highlights the importance of understanding connectivity features in heterogeneous geological media when assessing density-dependent solute transport in groundwater systems.

Enhancing machine learning thermobarometry for clinopyroxene-bearing magmas

In this study, we proposed a general workflow that aims to enhance the ML-based geothermobarometer modelling. Our workflow focuses on three key areas. Firstly, we developed a robust pre-processing pipeline that addresses data imbalance, feature engineering, and data augmentation. Secondly, we assessed modelling errors using a Monte Carlo approach to quantify the impact of analytical uncertainties on the final pressure and temperature estimates. Thirdly, we implemented a robust strategy to validate and test the ML models to avoid over- and under-fitting issues while correcting biases associated with the application of specific ML models (i.e., tree-based ensembles).To facilitate the use of our workflow, we have developed a web app (https://bit.ly/ml-pt-web) and a Python module (https://bit.ly/ml-pt-py). The robustness of this strategy has been tested on two calibrations: clinopyroxene (cpx) and clinopyroxene-liquid (cpx-liq). Our results show a significant reduction in errors compared to the baseline model, as well as good generalization ability on an independent external dataset. The Root Mean Squared Errors are 57 °C and 2.5 kbar for the cpx calibration, and 36 °C and 2.1 kbar for the cpx-liq calibration. Finally, our models show improved outcomes on the external dataset compared to existing ML and classical cpx and cpx-liq thermobarometers.

Assignment of a Physical Energy Scale for the Dimensionless Interaction Energies within the PRIME20 Peptide Model.

We present a calibration scheme to determine the conversion factors from a coarse-grained stochastic approximation Monte Carlo approach using the PRIME20 peptide interaction model into atomistic force-field interaction energies at full explicit aqueous solvation. The conversion from coarse-grained to atomistic structures was done according to our previously established inverse coarse-graining protocol. We provide a physical energy scale for both the backbone hydrogen bonding interactions and the sidechain interactions by correlating the dimensionless energy descriptors of the PRIME20 model with the energies averaged over molecular dynamics simulations. The conversion factor for these interactions turns out to be around 2kJ/mol for the backbone interactions, and zero for the sidechain interactions. We discuss these surprisingly small values in terms of their molecular interpretation.

A Two-Step Longstaff Schwartz Monte Carlo Approach to Game Option Pricing

We proposed a two-step Longstaff Schwartz Monte Carlo (LSMC) method with two regression models fitted at each time step to price game options. Although the original LSMC can be used to price game options with an enlarged range of path in regression and a modified cashflow updating rule, we identified a drawback of such approach, which motivated us to propose our approach. We implemented numerical examples with benchmarks using binomial tree and numerical PDE, and it showed that our method produces more reliable results comparing to the original LSMC.

Magnetic and electronic properties of double perovskite Sr2CrMoO6 for spintronic applications: Insights from first-principles and Monte Carlo approaches

Abstract In this work, we studied the electronic and magnetic properties of the double perovskite Sr2CrMoO6 using ab initio calculations with Generalized Gradient Approximation (GGA) and Monte Carlo (MC) simulations. The compound has two magnetic sublattices: one occupied by Mo5+ with spin (S = 1/2) and the other by Cr3+ with spin (σ = 3/2). The results showed half-metallic behavior with a total magnetic moment of 2.0 μB. Using Monte Carlo simulations, we investigated the phase transitions and observed interesting phenomena such as a critical endpoint and both second-order and first-order phase transitions. Additionally, the results revealed compensation points for specific values of the crystal field.

Decomposing Imaginary-Time Feynman Diagrams Using Separable Basis Functions: Anderson Impurity Model Strong-Coupling Expansion

We present a deterministic algorithm for the efficient evaluation of imaginary-time diagrams based on the recently introduced discrete Lehmann representation (DLR) of imaginary-time Green’s functions. In addition to the efficient discretization of diagrammatic integrals afforded by its approximation properties, the DLR basis is separable in imaginary-time, allowing us to decompose diagrams into linear combinations of nested sequences of one-dimensional products and convolutions. Focusing on the strong-coupling bold-line expansion of generalized Anderson impurity models, we show that our strategy reduces the computational complexity of evaluating an Mth-order diagram at inverse temperature β and spectral width ωmax from O((βωmax)2M−1) for a direct quadrature to O(M(log(βωmax))M+1), with controllable high-order accuracy. We benchmark our algorithm using third-order expansions for multiband impurity problems with off-diagonal hybridization and spin-orbit coupling, presenting comparisons with exact diagonalization and quantum Monte Carlo approaches. In particular, we perform a self-consistent dynamical mean-field theory calculation for a three-band Hubbard model with strong spin-orbit coupling representing a minimal model of Ca2RuO4, demonstrating the promise of the method for modeling realistic strongly correlated multiband materials. For both strong and weak coupling expansions of low and intermediate order, in which diagrams can be enumerated, our method provides an efficient, straightforward, and robust blackbox evaluation procedure. In this sense, it fills a gap between diagrammatic approximations of the lowest order, which are simple and inexpensive but inaccurate, and those based on Monte Carlo sampling of high-order diagrams. Published by the American Physical Society 2024

Effects of Statistical Practices for Longitudinal Group Comparison of the Penetration-Aspiration Scale on Power and Effect Size Estimation: A Monte Carlo Simulation Study.

Multiple bolus trials are administered during clinical and research swallowing assessments to comprehensively capture an individual's swallowing function. Despite valuable information obtained from these boluses, it remains common practice to use a single bolus (e.g., the worst score) to describe the degree of dysfunction. Researchers also often collapse continuous or ordinal swallowing measures into categories, potentially exacerbating information loss. These practices may adversely affect statistical power to detect and estimate smaller, yet potentially meaningful, treatment effects. This study sought to examine the impact of aggregating and categorizing penetration-aspiration scale (PAS) scores on statistical power and effect size estimates. We used a Monte Carlo approach to simulate three hypothetical within-subject treatment studies in Parkinson's disease and head and neck cancer across a range of data characteristics (e.g., sample size, number of bolus trials, variability). Different statistical models (aggregated or multilevel) as well as various PAS reduction approaches (i.e., types of categorizations) were performed to examine their impact on power and the accuracy of effect size estimates. Across all scenarios, multilevel models demonstrated higher statistical power to detect group-level longitudinal change and more accurate estimates compared to aggregated (worst score) models. Categorizing PAS scores also reduced power and biased effect size estimates compared to an ordinal approach, though this depended on the type of categorization and baseline PAS distribution. Multilevel models should be considered as a more robust approach for the statistical analysis of multiple boluses administered in standardized swallowing protocols due to its high sensitivity and accuracy to compare group-level changes in swallowing function. Importantly, this finding appears to be consistent across patient populations with distinct pathophysiology (i.e., PD and HNC) and patterns of airway invasion. The decision to categorize a continuous or ordinal outcome should be grounded in the clinical or research question with recognition that scale reduction may negatively affect the quality of statistical inferences in certain scenarios.