Monte Carlo Study Research Articles

Dose equivalent consideration from neutron contamination in modified radiotherapy vault: a Monte Carlo study

Laminated barriers incorporating metal sheets provide effective protection for space-restricted radiotherapy centers. This study aimed to assess photoneutron contamination in smaller vaults protected by different compositions of multilayer barriers during simulated pelvic radiotherapy with 18 MV photon beams. Monte Carlo Simulations of 18 MV LINAC (Varian 2100 C/D) and Medical Internal Radiation Dose (MIRD) phantom were used to assess photoneutron contamination within reconstructed vaults incorporating different combinations of metal sheet and borated polyethylene (BPE) during pelvic radiotherapy. The findings highlight a 3.27 and 2.91 times increase in ambient neutron dose Hn* (10) along the maze of reconstructed vaults that use lead and steel sheets, respectively, compared to concrete. The Hn* (10) outside the treatment room increased after incorporating a metal sheet, but it remained within the permissible limit of 20 μSv/week for uncontrolled areas adjacent to the LINAC bunker, even with a workload of 1000Gy/week. Neutron equivalent doses in the patient’s organs ranged from 0.22 to 0.96 mSv Gy−1. There is no notable distinction in the organ’s neutron equivalent dose, fatal cancer risk, secondary radiation-induced cancer risk, and cancer mortality for various laminated barrier compositions. Furthermore, the use of metal sheets for vault wall reconstruction keeps the variation in cancer risk induced by photoneutrons below 6%, while risks of fatal cancer and cancer mortality vary less than 11%. While the metal portion of the laminated barrier raises the neutron dose, the addition of a BPE plate reduces concerns of increased effective dose and secondary malignancy risk.

Collision energy dependence of source sizes for primary and secondary pions at energies available at the JINR nuclotron-based ion collider facility from Lévy fits

We study the evolution of the two-pion correlation function parameters with collision energy in the context of relativistic heavy-ion collisions within the NICA energy range. To this end, we perform UrQMD simulations in the cascade mode to produce samples of pions from 5×106\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$5\ imes 10^6$$\\end{document} Bi+Bi collisions for each of the studied energies. The effects of the quantum-statistical correlations are introduced using the correlation afterburner code CRAB. We fit the correlation function using Gaussian, exponential and symmetric Lévy shapes and show that for all collision energies the latter provides the best fit. We separate the sample into pions coming from primary processes and pions originating from the decay of long-lived resonances, and show that the source size for the latter is significantly larger than for the former. The source size for the secondaries, is similar but in general larger than the size for the whole pion sample. To further characterize the pion source, we also simulate the effects of a non-ideal detector introducing a momentum smearing parameter, representing the minimum pair momentum and thus a maximum source size that can be resolved. The values of the correlation function intercept parameter are therefore modified from the values they attain for the perfect detector case. Using the core-halo picture of the source, we show that the values of the intercept parameter are influenced by the presence of a significant fraction of core pions coming from the decay of long-lived but slow-moving resonances. These findings serve as a benchmark to compare with future Monte Carlo studies that consider an Equation of State and thus allow for a phase transition within the studied energy domain.

Design and characterisation of a minibeam collimator utilising Monte Carlo simulation and a clinical linear accelerator

Objective. Spatially fractionated radiotherapy is showing promise as a treatment modality. Initial focus was on beams of photons at low energy produced from a synchrotron but more recently research has expanded to include applications in proton therapy. Interest in photon beams remains and this is the focus of this paper Approach. This study presents a 3D printed tungsten minibeam collimator intended to produce peak-to-valley dose ratios (PVDR) of between seven and ten with a 1 MV, bremsstrahlung generated, photon beam. The design of the collimator is motivated by a Monte Carlo study estimating the PVDR for different collimator designs at different energies. This collimator was characterised on a clinical linear accelerator (Elekta VersaHD) as well as an orthovoltage unit. Main results. The performance of the fabricated collimator was measured on Elekta VersaHD running in unflattened mode with a 6 MV beam. On the Elekta VersaHD units the PVDR was measured to be between approximately 1.5 and 2.0 at 3 cm deep. For measurements with the orthovoltage unit PVDRs of greater than 10 were observed at a depth of 4 cm. Significance. The results confirmed that the predictions from simulation could be reproduced on linear accelerators currently in clinical usage, producing PVDRs between 2–2.5. Using the model to predict PVDRs using 1 MV photon beams, the threshold considered to produce enhanced normal tissue dose tolerance ( > 7) was surpassed. This suggests the possibility of using such techniques with versions of existing Linac technology which have been modified to operate at low energy and high beam currents.

Determining ideal offsets of spatially offset Raman spectroscopy for transcutaneous measurements-A Monte Carlo study.

Spatially offset Raman spectroscopy (SORS) is valuable for noninvasive bone assessment but requires a clearer understanding of how offset distances influence detection depth. To address this, our study devised a forward-adjoint Monte Carlo multi-layer (MCML) model to simulate photon paths in SORS, aiming to determine optimal offsets for various tissue types. We examined photon migration at offsets between 0 and 15 mm against layered phantoms of differing thicknesses and compositions to optimize the signal-to-noise ratio for bone layers. The findings highlight that optimal offsets are contingent on tissue characteristics: a metacarpal beneath 2.5 mm of tissue had an ideal offset of 6.7 mm, while a tibia with 5 mm of soft tissue required 10-11 mm. This precise calibration of SORS via MCML modeling promises substantial improvements in bone health diagnostics and potential for expansive medical applications.

Nonnegative GARCH-type models with conditional Gamma distributions and their applications

Most of real data are characterized by positive, asymmetric and skewed distributions of various shapes. Modelling and forecasting of such data are addressed by proposing nonnegative conditional heteroscedastic time series models with Gamma distributions. Three types of time-varying parameters of Gamma distributions are adopted to construct the nonnegative GARCH models. A condition for the existence of a stationary Gamma-GARCH model is given. Parameter estimates are discussed via maximum likelihood estimation (MLE) method. A Monte-Carlo study is conducted to illustrate sample paths of the proposed models and to see finite-sample validity of the MLEs, as well as to evaluate model diagnostics using standardized Pearson residuals. Furthermore, out-of-sample forecasting analysis is performed to compute forecasting accuracy measures. Applications to oil price and Bitcoin data are given, respectively.

Orbital evolution of LIGO/Virgo binaries in stellar clusters driven by cluster tides, stellar encounters, and general relativity

ABSTRACT Origin of LIGO/Virgo gravitational wave events may involve production of binaries with relativistic components in dense stellar systems – globular or nuclear star clusters – and their subsequent evolution towards merger. Orbital parameters of these binaries (the inner orbit) and their motion inside the cluster (the outer orbit) evolve due to both external agents – random encounters with cluster stars and cluster tides due to the smooth cluster potential – and the internal ones – various sources of dissipation and precession within the binary. We present a numerical framework – binary evolution in stellar clusters (besc) – that follows the evolution of the binary inner and outer orbits accounting for all these effects simultaneously, enabling efficient Monte Carlo studies. The secular effect of cluster tides is computed in the singly averaged approximation, without averaging over the outer binary orbit. As to stellar encounters, we include the effects of both close and distant flybys on the inner and outer orbits of the binary, respectively. Also, given our focus on the LIGO/Virgo sources, we include the general relativistic precession (which suppresses cluster tides at high eccentricities) and the gravitational wave emission (shrinking the binary orbit). We use besc to illustrate a number of characteristic binary evolutionary outcomes and discuss relative contributions of different physical processes. In particular, we find that stellar encounters often dominate over the cluster tides in the evolution of compact binaries. besc can also be used to study other objects in clusters, e.g. blue stragglers, hot Jupiters, X-ray binaries, etc.

Calibration and performance evaluation of an N-type HPGe detector for a collimated and focused PGNAA system by experimental and Monte Carlo methods

The MCNP code was utilized to assess the operational status of an N-type high-purity germanium (HPGe) detector and to evaluate its potential for a collimated and focused Prompt Gamma Neutron Activation Analysis (PGNAA) detection system. In order to calibrate the detector, a narrow beam γ collimator was designed to scan the detector in both axial and radial directions. The curvature of the crystal front edge and the non-uniform description of the detector dead layer (DL) were taken into account when adjusting the effective crystal size. A collimated 137Cs γ source was used to assess the detection efficiency in the scanning experiments. Monte Carlo studies were performed using 0.662 MeV γ rays, and separately, a uniform γ-ray energy distribution from 0 to 1.6 MeV. Lastly, the effects of a collimation aperture with different sizes and different incident directions were considered to discuss the relationship between the spatial resolution and suitable measurement scenarios. Therefore, a detailed calibration method for non-uniform dead layers was introduced through a comparison between experiments and Monte Carlo simulations. This work reevaluates the performance of HPGe detectors and provides valuable data support for a detailed system design and γ spectroscopy analysis in future.

Enhancing Polymer Blend Compatibility with Linear and Complex Star Copolymer Architectures: A Monte Carlo Simulation Study with the Bond Fluctuation Model.

A Monte Carlo study of the compatibilization of A/B polymer blends has been performed using the bond fluctuation model. The considered compatibilizers are copolymer molecules composed of A and B blocks. Different types of copolymer structures have been included, namely, linear diblock and 4-block alternating copolymers, star block copolymers, miktoarm stars, and zipper stars. Zipper stars are composed of two arms of diblock copolymers arranged in alternate order (AB and BA) from the central unit, along with two homogeneous arms of A and B units. The compatibilization performance has been characterized by analyzing the equilibration of repulsion energy, the simulated scattering intensity obtained with opposite refractive indices for A and B, the profiles along a coordinate axis, the radial distribution functions, and the compatibilizer aggregation numbers. According to the results, linear alternate block copolymers, star block copolymers, and zipper stars exhibit significantly better compatibilization, with zipper stars showing slightly but consistently better performance.

Common and idiosyncratic conditional volatility: Theory and empirical evidence from electricity prices

. We propose and develop a robust score-driven multiplicative dynamic factor model for the conditional volatility of electricity prices. This model allows us to identify both common and idiosyncratic conditional volatility factors in the spot price of electricity across key Nord Pool European markets. Both factors are extracted using a single observation-driven filter that is simple and parsimonious. The common factor is robust by construction as it averages information over the cross-section of the high-dimensional vector of electricity price changes. The idiosyncratic factors are designed to capture the erratic shocks in prices and therefore rely on a robust updating equation which allows for outliers and fat-tailed innovations. Our model is suitable for high-dimensional applications and does not necessarily suffer from the curse of dimensionality. The parsimonious nature of the observation-driven filter leads to simple computations for the estimation of parameters and the signal extraction of factors. We derive the stochastic properties of the filter and its underlying factor model, including bounded moments, stationarity, ergodicity, and filter invertibility. We further establish the consistency and asymptotic normality of the maximum likelihood estimator. The finite sample properties of the estimator and the filter are explored in a Monte Carlo study. Finally, we apply our model and filter to the Nord Pool spot price data and find evidence that net-import and net-export electricity markets exhibit substantially different common and idiosyncratic volatilities. In particular, we confirm that net-import markets are considerably more exposed to cross-market volatility spillovers, and we quantify the relevant degree of exposition.

Searches for multi-Z boson productions and anomalous gauge boson couplings at a muon collider* *Supported in part by the National Natural Science Foundation of China (12150005, 12075004, 12061141002) and MOST (2018YFA0403900)

Multi-boson productions can be exploited as novel probes either for standard model precision tests or new physics searches, and have become a popular research topic in ongoing LHC experiments and future collider studies, including those for electron–positron and muon–muon colliders. In this study, we focus on two examples, i.e., direct productions through annihilation at a muon collider, and productions through vector boson scattering (VBS) at a muon collider, with an integrated luminosity of . Various channels are considered, including and +2jets. The expected significance on these multi-Z boson production processes is reported based on a detailed Monte Carlo study and signal background analysis. Sensitivities on anomalous gauge boson couplings are also presented.

Three-dimensional Heisenberg model with Dzyaloshinskii-Moriya interaction: A Monte Carlo study.

The three-dimensional classical Heisenberg model on a simple cubic lattice with Dzyaloshinskii-Moriya (DM) interactions between nearest-neighbors in all directions has been studied using Monte Carlo simulations. The Metropolis algorithm, combined with single histogram reweighting techniques and finite-size scaling analyses, has been used to obtain the thermodynamic behavior of the system in the thermodynamic limit. Simulations were performed with the same set of interaction parameters for both shifted boundary conditions (SBC) and fluctuating boundary conditions (FBC). Because of an incommensurability caused by the DM interaction, the SBC incorporated a fixed shift angle at the boundary which varies as a function of the DM interaction and lattice size. This SBC method decreases the simulation time significantly, but the distribution of states is somewhat different than that obtained with FBC. The ground state for nonzero DM interaction is a spiral configuration where the spins are restricted to lie in planes perpendicular to the DM vector. We found that this spiral configuration undergoes a conventional second-order phase transition into a disordered, paramagnetic state with the transition temperature being a function of the magnitude of the DM interaction. The limiting case with only DM interaction in the model has also been considered. The critical exponent ν, the critical exponent ratios α/ν, β/ν, γ/ν, as well as the critical temperature T_{c} and fourth-order cumulant of the order parameter U_{4}^{*} at T_{c} have been estimated for different magnitudes of DM interaction. The critical exponents and cumulants at the transition are different from those for the three-dimensional Heisenberg model, but the ratios α/ν, β/ν, γ/ν, U_{4}^{*}/ν are the same, implying that weak universality is valid for all values of DM interaction. Structure factor calculations for particular cases have been performed considering SBC and FBC in the simulations with different lattice sizes at the critical temperatures.

On Modi-Exponential Distribution under Conventional Type-I and Type-II Censoring

In this article, a new Modi-Exponential distribution is considered under Type-I and Type-II censoring. Some statistical and reliability characteristics of the distribution are specified. Statistical inferences of the Modi-Exponential parameters based on Type-I and Type-II censored data are discussed. The maximum likelihood estimation method is used for estimation of unknown parameters along with reliability characteristics. Asymptotic confidence intervals are also obtained for interval estimation. Monte-Carlo Simulation study is performed to study the performances of estimators. Further, two real data sets are provided to illustrate the results.. KEYWORDS :Censoring, Maximum likelihood estimation, Confidence bounds, Simulation.

Can cross-lagged panel modeling be relied on to establish cross-lagged effects? The case of contemporaneous and reciprocal effects.

This article considers identification, estimation, and model fit issues for models with contemporaneous and reciprocal effects. It explores how well the models work in practice using Monte Carlo studies as well as real-data examples. Furthermore, by using models that allow contemporaneous and reciprocal effects, the paper raises a fundamental question about current practice for cross-lagged panel modeling using models such as cross-lagged panel model (CLPM) or random intercept cross-lagged panel model (RI-CLPM): Can cross-lagged panel modeling be relied on to establish cross-lagged effects? The article concludes that the answer is no, a finding that has important ramifications for current practice. It is suggested that analysts should use additional models to probe the temporalities of the CLPM and RI-CLPM effects to see if these could be considered contemporaneous rather than lagged. (PsycInfo Database Record (c) 2024 APA, all rights reserved).

On the Stress-Strength Reliability of Transmuted GEV Random Variables with Applications to Financial Assets Selection.

In reliability contexts, probabilities of the type R=P(X<Y), where X and Y are random variables, have shown to be useful tools to compare the performance of these stochastic entities. By considering that both X and Y follow a transmuted generalized extreme-value (TGEV) distribution, new analytical relationships were derived for R in terms of special functions. The results hereby obtained are more flexible when compared to similar results found in the literature. To highlight the applicability and correctness of our results, we conducted a Monte-Carlo simulation study and investigated the use of the reliability measure P(X<Y) to select among financial assets whose returns were characterized by the random variables X and Y. Our results highlight that R is an interesting alternative to modern portfolio theory, which usually relies on the contrast of involved random variables by a simple comparison of their means and standard deviations.

HETEROSKEDASTICITY ROBUST SPECIFICATION TESTING IN SPATIAL AUTOREGRESSION

Spatial autoregressive (SAR) and related models offer flexible yet parsimonious ways to model spatial and network interactions. SAR specifications typically rely on a particular parametric functional form and an exogenous choice of the so-called spatial weight matrix with only limited guidance from theory in making these specifications. Also, the choice of a SAR model over other alternatives, such as spatial Durbin (SD) or spatial lagged X (SLX) models, is often arbitrary, raising issues of potential specification error. To address such issues, this paper develops a new specification test within the SAR framework that can detect general forms of misspecification including that of the spatial weight matrix, the functional form and the model itself. The test is robust to the presence of heteroskedasticity of unknown form in the disturbances and the approach relates to the conditional moment test framework of Bierens ([1982, Journal of Econometrics 20, 105–134], [1990, Econometrica 58, 1443–1458]). The Bierens test is shown to be inconsistent in general against spatial alternatives and the new test introduces modifications to achieve test consistency in the spatial setting. A central element is the infinite-dimensional endogeneity induced by spatial linkages. This complexity is addressed by introducing a new component to the omnibus test that captures the effects of potential spatial matrix misspecification. With this modification, the approach leads to a simple pivotal test procedure with standard critical values that is the first test in the literature to have power against misspecifications in the spatial linkages. We derive the asymptotic distribution of the test under the null hypothesis of correct SAR specification and prove consistency. A Monte Carlo study is conducted to study its finite sample performance. An empirical illustration on the performance of the test in modeling tax competition in Finland is included.

Upgrading event driven Monte Carlo simulations for molecule‐based morphological control for battery and sensor applications

AbstractMultiphase polymeric materials and applications play a prominent role in our society. One of the key challenges is the design and modification of their macromolecules so that the composition and structuring of the phases as well as the interactions between them can be controlled from the molecular scale onwards. In the present contribution, it is highlighted that more recently developed event driven (kinetic) Monte Carlo models provide an interesting framework to grasp molecular variations over various length scales. The strength lies in the tracking of individual molecules per phase of interest so that interphase transfer events can be sampled based on the distributed nature of the (macro)molecules present. Hence, the micro‐scale of local concentrations and temperatures can be connected to the meso‐scale defining interphase transport and morphological variations, with an additional connection to the macro‐ or application scale within reach by adding macro‐scale transfer events to the overall sampling scheme. Starting from a benchmark coupled matrix based Monte Carlo (CMMC) study on the multiphase formation of engineering composites which explicitly acknowledges the type of (macro)molecules present in each phase, it is showcased that the CMMC framework can support the general field of energy and electronics applications. This is highlighted through (i) a case study devoted to the design of polymer electrolytes for batteries, and (ii) a case study on blend design for the regulated stretching of piezoresistive sensors.

Markov models for clinical decision-making in radiation oncology: A systematic review.

The intrinsic stochasticity of patients' response to treatment is a major consideration for clinical decision-making in radiation therapy. Markov models are powerful tools to capture this stochasticity and render effective treatment decisions. This paper provides an overview of the Markov models for clinical decision analysis in radiation oncology. A comprehensive literature search was conducted within MEDLINE using PubMed, following the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) guidelines. Only studies published from 2000 to 2023 were considered. Selected publications were summarized in two categories: (i) studies that compare two (or more) fixed treatment policies using Monte Carlo simulation and (ii) studies that seek an optimal treatment policy through Markov Decision Processes (MDPs). Relevant to the scope of this study, 61 publications were selected for detailed review. The majority of these publications (n = 56) focused on comparative analysis of two or more fixed treatment policies using Monte Carlo simulation. Classifications based on cancer site, utility measures and the type of sensitivity analysis are presented. Five publications considered MDPs with the aim of computing an optimal treatment policy; a detailed statement of the analysis and results is provided for each work. As an extension of Markov model-based simulation analysis, MDP offers a flexible framework to identify an optimal treatment policy among a possibly large set of treatment policies. However, the applications of MDPs to oncological decision-making have been understudied, and the full capacity of this framework to render complex optimal treatment decisions warrants further consideration.

Fractional gaussian noise: Spectral density and estimation methods

The fractional Brownian motion (fBm) process, governed by a fractional parameter , is a continuous‐time Gaussian process with its increment being the fractional Gaussian noise (fGn). This article first provides a computationally feasible expression for the spectral density of fGn. This expression enables us to assess the accuracy of a range of approximation methods, including the truncation method, Paxson's approximation, and the Taylor series expansion at the near‐zero frequency. Next, we conduct an extensive Monte Carlo study comparing the finite sample performance and computational cost of alternative estimation methods for under the fGn specification. These methods include two semi‐parametric methods (based on the Taylor series expansion), two versions of the Whittle method (utilising either the computationally feasible expression or Paxson's approximation of the spectral density), a time‐domain maximum likelihood (ML) method (employing a recursive approach for its likelihood calculation), and a change‐of‐frequency method. Special attention is paid to highly anti‐persistent processes with close to zero, which are of empirical relevance to financial volatility modelling. Considering the trade‐off between statistical and computational efficiency, we recommend using either the Whittle ML method based on Paxson's approximation or the time‐domain ML method. We model the log realized volatility dynamics of 40 financial assets in the US market from 2012 to 2019 with fBm. Although all estimation methods suggest rough volatility, the implied degree of roughness varies substantially with the estimation methods, highlighting the importance of understanding the finite sample performance of various estimation methods.

Monte Carlo study of magnetic properties of the fullerene C24 structure

ABSTRACT The fullerene C24 is one of the most active types of nanostructures and has been used as an active component in important applications. In this study, we investigated the magnetic characteristics of the mixed spins 5/2 and 3/2 of the Fullerene C24 system using Monte Carlo simulations. We start by offering a theoretical analysis of ground state phase diagrams. In fact, out of all potential configurations, we only present and analyze the stable configurations. Secondly, calculations are done to determine how the magnetic characteristics of this compound change as various physical parameters are changed. Additionally, we offer the examined magnetic behavior of the system with reduced temperature, reduced crystal field, reduced exchange-coupling interactions, and reduced external magnetic field. Finally, we looked into and talked about the critical reduced temperature of Fullerene C24. We showed and examined the hysteresis loops for various physical parameter values to end our work.

Goodness–of–fit tests based on the min–characteristic function

Tests of fit for classes of distributions that include the Weibull, the Pareto and the Fréchet families are proposed. The new tests employ the novel tool of the min–characteristic function and are based on an L2–type weighted distance between this function and its empirical counterpart applied on suitably standardized data. If data–standardization is performed using the MLE of the distributional parameters then the method reduces to testing for the standard member of the family, with parameter values known and set equal to one. Asymptotic properties of the tests are investigated. A Monte Carlo study is presented that includes the new procedure as well as competitors for the purpose of specification testing with three extreme value distributions. The new tests are also applied on a few real–data sets.