More than just Good Luck. How to Explain the Success of Monte Carlo Simulations

Monte Carlo simulation is a powerful method in many natural and social sciences. But what sort of method is it? And where does its power come from? Are Monte Carlo simulations experiments, theories or something else? The aim of this talk is to answer these questions and to explain the power of Monte Carlo simulations. I provide a classification of Monte Carlo techniques and defend the claim that Monte Carlo simulation is a sort of inference.

Saddlepoint approximations to sensitivities of tail probabilities of random sums and comparisons with Monte Carlo estimators

This article proposes computing sensitivities of upper tail probabilities of random sums by the saddlepoint approximation. The considered sensitivity is the derivative of the upper tail probability with respect to the parameter of the summation index distribution. Random sums with Poisson or Geometric distributed summation indices and Gamma or Weibull distributed summands are considered. The score method with importance sampling is considered as an alternative approximation. Numerical studies show that the saddlepoint approximation and the method of score with importance sampling are very accurate. But the saddlepoint approximation is substantially faster than the score method with importance sampling. Thus, the suggested saddlepoint approximation can be conveniently used in various scientific problems.

A critical evaluation of secondary cancer risk models applied to Monte Carlo dose distributions of 2-dimensional, 3-dimensional conformal and hybrid intensity-modulated radiation therapy for breast cancer

The comparison of radiotherapy techniques regarding secondary cancer risk has yielded contradictory results possibly stemming from the many different approaches used to estimate risk. The purpose of this study was to make a comprehensive evaluation of different available risk models applied to detailed whole-body dose distributions computed by Monte Carlo for various breast radiotherapy techniques including conventional open tangents, 3D conformal wedged tangents and hybrid intensity modulated radiation therapy (IMRT). First, organ-specific linear risk models developed by the International Commission on Radiological Protection (ICRP) and the Biological Effects of Ionizing Radiation (BEIR) VII committee were applied to mean doses for remote organs only and all solid organs. Then, different general non-linear risk models were applied to the whole body dose distribution. Finally, organ-specific non-linear risk models for the lung and breast were used to assess the secondary cancer risk for these two specific organs. A total of 32 different calculated absolute risks resulted in a broad range of values (between 0.1% and 48.5%) underlying the large uncertainties in absolute risk calculation. The ratio of risk between two techniques has often been proposed as a more robust assessment of risk than the absolute risk. We found that the ratio of risk between two techniques could also vary substantially considering the different approaches to risk estimation. Sometimes the ratio of risk between two techniques would range between values smaller and larger than one, which then translates into inconsistent results on the potential higher risk of one technique compared to another. We found however that the hybrid IMRT technique resulted in a systematic reduction of risk compared to the other techniques investigated even though the magnitude of this reduction varied substantially with the different approaches investigated. Based on the epidemiological data available, a reasonable approach to risk estimation would be to use organ-specific non-linear risk models applied to the dose distributions of organs within or near the treatment fields (lungs and contralateral breast in the case of breast radiotherapy) as the majority of radiation-induced secondary cancers are found in the beam-bordering regions.

Combining Monte Carlo methods with coherent wave optics for the simulation of phase-sensitive X-ray imaging

Phase-sensitive X-ray imaging shows a high sensitivity towards electron density variations, making it well suited for imaging of soft tissue matter. However, there are still open questions about the details of the image formation process. Here, a framework for numerical simulations of phase-sensitive X-ray imaging is presented, which takes both particle- and wave-like properties of X-rays into consideration. A split approach is presented where we combine a Monte Carlo method (MC) based sample part with a wave optics simulation based propagation part, leading to a framework that takes both particle- and wave-like properties into account. The framework can be adapted to different phase-sensitive imaging methods and has been validated through comparisons with experiments for grating interferometry and propagation-based imaging. The validation of the framework shows that the combination of wave optics and MC has been successfully implemented and yields good agreement between measurements and simulations. This demonstrates that the physical processes relevant for developing a deeper understanding of scattering in the context of phase-sensitive imaging are modelled in a sufficiently accurate manner. The framework can be used for the simulation of phase-sensitive X-ray imaging, for instance for the simulation of grating interferometry or propagation-based imaging.

Forward treatment planning for modulated electron radiotherapy (MERT) employing Monte Carlo methods

PURPOSE This paper describes the development of a forward planning process for modulated electron radiotherapy (MERT). The approach is based on a previously developed electron beam model used to calculate dose distributions of electron beams shaped by a photon multi leaf collimator (pMLC). METHODS As the electron beam model has already been implemented into the Swiss Monte Carlo Plan environment, the Eclipse treatment planning system (Varian Medical Systems, Palo Alto, CA) can be included in the planning process for MERT. In a first step, CT data are imported into Eclipse and a pMLC shaped electron beam is set up. This initial electron beam is then divided into segments, with the electron energy in each segment chosen according to the distal depth of the planning target volume (PTV) in beam direction. In order to improve the homogeneity of the dose distribution in the PTV, a feathering process (Gaussian edge feathering) is launched, which results in a number of feathered segments. For each of these segments a dose calculation is performed employing the in-house developed electron beam model along with the macro Monte Carlo dose calculation algorithm. Finally, an automated weight optimization of all segments is carried out and the total dose distribution is read back into Eclipse for display and evaluation. One academic and two clinical situations are investigated for possible benefits of MERT treatment compared to standard treatments performed in our clinics and treatment with a bolus electron conformal (BolusECT) method. RESULTS The MERT treatment plan of the academic case was superior to the standard single segment electron treatment plan in terms of organs at risk (OAR) sparing. Further, a comparison between an unfeathered and a feathered MERT plan showed better PTV coverage and homogeneity for the feathered plan, with V95% increased from 90% to 96% and V107% decreased from 8% to nearly 0%. For a clinical breast boost irradiation, the MERT plan led to a similar homogeneity in the PTV compared to the standard treatment plan while the mean body dose was lower for the MERT plan. Regarding the second clinical case, a whole breast treatment, MERT resulted in a reduction of the lung volume receiving more than 45% of the prescribed dose when compared to the standard plan. On the other hand, the MERT plan leads to a larger low-dose lung volume and a degraded dose homogeneity in the PTV. For the clinical cases evaluated in this work, treatment plans using the BolusECT technique resulted in a more homogenous PTV and CTV coverage but higher doses to the OARs than the MERT plans. CONCLUSIONS MERT treatments were successfully planned for phantom and clinical cases, applying a newly developed intuitive and efficient forward planning strategy that employs a MC based electron beam model for pMLC shaped electron beams. It is shown that MERT can lead to a dose reduction in OARs compared to other methods. The process of feathering MERT segments results in an improvement of the dose homogeneity in the PTV.

Monte Carlo modeling of polarized light propagation: Stokes vs Jones - Part I

This bipartite comparative study aims at inspecting the similarities and differences between the Jones and Stokes–Mueller formalisms when modeling polarized light propagation with numerical simulations of the Monte Carlo type. In this first part, we review the theoretical concepts that concern light propagation and detection with both pure and partially/totally unpolarized states. The latter case involving fluctuations, or “depolarizing effects,” is of special interest here: Jones and Stokes–Mueller are equally apt to model such effects and are expected to yield identical results. In a second, ensuing paper, empirical evidence is provided by means of numerical experiments, using both formalisms.

Monte Carlo modeling of polarized light propagation: Stokes vs Jones - Part II

In this second part of our comparative study inspecting the (dis)similarities between “Stokes” and “Jones,” we present simulation results yielded by two independent Monte Carlo programs: (i) one developed in Bern with the Jones formalism and (ii) the other implemented in Ulm with the Stokes notation. The simulated polarimetric experiments involve suspensions of polystyrene spheres with varying size. Reflection and refraction at the sample/air interfaces are also considered. Both programs yield identical results when propagating pure polarization states, yet, with unpolarized illumination, second order statistical differences appear, thereby highlighting the pre-averaged nature of the Stokes parameters. This study serves as a validation for both programs and clarifies the misleading belief according to which “Jones cannot treat depolarizing effects.”

The Utilization of Classical Spin Monte Carlo Methods to Simulate the Magnetic Behavior of Extended Three-Dimensional Cubic Networks Incorporating M(II) Ions with an S = 5/2 Ground State Spin

The numerical simulations of the magnetic properties of extended three-dimensional networks containing M(II) ions with an S = 5/2 ground-state spin have been carried out within the framework of the isotropic Heisenberg model. Analytical expressions fitting the numerical simulations for the primitive cubic, diamond, together with (10−3) cubic networks have all been derived. With these empirical formulas in hands, we can now extract the interaction between the magnetic ions from the experimental data for these networks. In the case of the primitive cubic network, these expressions are directly compared with those from the high-temperature expansions of the partition function. A fit of the experimental data for three complexes, namely [(N(CH3)4][Mn(N3)] 1, [Mn(CN4)]n 2, and [FeII(bipy)3][MnII2(ox)3] 3, has been carried out. The best fits were those obtained using the following parameters, J = −3.5 cm-1, g = 2.01 (1); J = −8.3 cm-1, g = 1.95 (2); and J = −2.0 cm-1, g = 1.95 (3).

Recent Advances in Adaptive Sampling and Reconstruction for Monte Carlo Rendering

Monte Carlo integration is firmly established as the basis for most practical realistic image synthesis algorithms because of its flexibility and generality. However, the visual quality of rendered images often suffers from estimator variance, which appears as visually distracting noise. Adaptive sampling and reconstruction algorithms reduce variance by controlling the sampling density and aggregating samples in a reconstruction step, possibly over large image regions. In this paper we survey recent advances in this area. We distinguish between “a priori” methods that analyze the light transport equations and derive sampling rates and reconstruction filters from this analysis, and “a posteriori” methods that apply statistical techniques to sets of samples to drive the adaptive sampling and reconstruction process. They typically estimate the errors of several reconstruction filters, and select the best filter locally to minimize error. We discuss advantages and disadvantages of recent state-of-the-art techniques, and provide visual and quantitative comparisons. Some of these techniques are proving useful in real-world applications, and we aim to provide an overview for practitioners and researchers to assess these approaches. In addition, we discuss directions for potential further improvements.

Denoising Your Monte Carlo Renders: Recent Advances in Image Space-Adaptive Sampling and Reconstruction

With the ongoing shift in the computer graphics industry toward Monte Carlo rendering, there is a need for effective, practical noise-reduction techniques that are applicable to a wide range of rendering effects and easily integrated into existing production pipelines. This course surveys recent advances in image-space adaptive sampling and reconstruction algorithms for noise reduction, which have proven very effective at reducing the computational cost of Monte Carlo techniques in practice. These approaches leverage advanced image-filtering techniques with statistical methods for error estimation. They are attractive because they can be integrated easily into conventional Monte Carlo rendering frameworks, they are applicable to most rendering effects, and their computational overhead is modest.

Monte-Carlo simulation of Callisto's exosphere

We model Callisto's exosphere based on its ice as well as non-ice surface via the use of a Monte-Carlo exosphere model. For the ice component we implement two putative compositions that have been computed from two possible extreme formation scenarios of the satellite. One composition represents the oxidizing state and is based on the assumption that the building blocks of Callisto were formed in the protosolar nebula and the other represents the reducing state of the gas, based on the assumption that the satellite accreted from solids condensed in the jovian sub-nebula. For the non-ice component we implemented the compositions of typical CI as well as L type chondrites. Both chondrite types have been suggested to represent Callisto's non-ice composition best. As release processes we consider surface sublimation, ion sputtering and photon-stimulated desorption. Particles are followed on their individual trajectories until they either escape Callisto's gravitational attraction, return to the surface, are ionized, or are fragmented. Our density profiles show that whereas the sublimated species dominate close to the surface on the sun-lit side, their density profiles (with the exception of H and H-2) decrease much more rapidly than the sputtered particles. The Neutral gas and Ion Mass (NIM) spectrometer, which is part of the Particle Environment Package (PEP), will investigate Callisto's exosphere during the JUICE mission. Our simulations show that NIM will be able to detect sublimated and sputtered particles from both the ice and non-ice surface. NIM's measured chemical composition will allow us to distinguish between different formation scenarios. (C) 2015 Elsevier Inc. All rights reserved.

3D Direct Simulation Monte Carlo Modelling of the Inner Gas Coma of Comet 67P/Churyumov-Gerasimenko: A Parameter Study

Direct Simulation Monte Carlo (DSMC) is a powerful numerical method to study rarefied gas flows such as cometary comae and has been used by several authors over the past decade to study cometary outflow. However, the investigation of the parameter space in simulations can be time consuming since 3D DSMC is computationally highly intensive. For the target of ESA's Rosetta mission, comet 67P/Churyumov-Gerasimenko, we have identified to what extent modification of several parameters influence the 3D flow and gas temperature fields and have attempted to establish the reliability of inferences about the initial conditions from in situ and remote sensing measurements. A large number of DSMC runs have been completed with varying input parameters. In this work, we present the simulation results and conclude on the sensitivity of solutions to certain inputs. It is found that among cases of water outgassing, the surface production rate distribution is the most influential variable to the flow field.

A first look at maximally twisted mass lattice QCD calculations at the physical point

In this contribution, a first look at simulations using maximally twisted mass Wilson fermions at the physical point is presented. A lattice action including clover and twisted mass terms is presented and the Monte Carlo histories of one run with two mass-degenerate flavours at a single lattice spacing are shown. Measurements from the light and heavy-light pseudoscalar sectors are compared to previous Nf = 2 results and their phenomenological values. Finally, the strategy for extending simulations to Nf = 2+1+1 is outlined.

Conformational preferences of natural and C3-modified epothilones in aqueous solution

The conformational properties of the microtubule-stabilizing agent epothilone A ( 1a) and its 3-deoxy and 3-deoxy-2,3-didehydro derivatives 2 and 3 have been investigated in aqueous solution by a combination of NMR spectroscopic methods, Monte Carlo conformational searches, and NAMFIS calculations. The tubulin-bound conformation of epothilone A ( 1a), as previously proposed on the basis of solution NMR data, was found to represent a significant fraction of the ensemble of conformations present for the free ligands in aqueous solution.