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.

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).

Treatment planning aspects and Monte Carlo methods in proton therapy

Over the last years, the interest in proton radiotherapy is rapidly increasing. Protons provide superior physical properties compared with conventional radiotherapy using photons. These properties result in depth dose curves with a large dose peak at the end of the proton track and the finite proton range allows sparing the distally located healthy tissue. These properties offer an increased flexibility in proton radiotherapy, but also increase the demand in accurate dose estimations. To carry out accurate dose calculations, first an accurate and detailed characterization of the physical proton beam exiting the treatment head is necessary for both currently available delivery techniques: scattered and scanned proton beams. Since Monte Carlo (MC) methods follow the particle track simulating the interactions from first principles, this technique is perfectly suited to accurately model the treatment head. Nevertheless, careful validation of these MC models is necessary. While for the dose estimation pencil beam algorithms provide the advantage of fast computations, they are limited in accuracy. In contrast, MC dose calculation algorithms overcome these limitations and due to recent improvements in efficiency, these algorithms are expected to improve the accuracy of the calculated dose distributions and to be introduced in clinical routine in the near future.

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.

Inverse modelling of the 14C bomb pulse in stalagmites to constrain the dynamics of soil carbon cycling at selected European cave sites

The decomposition of soil organic matter (SOM) is temperature dependent, but its response to a future warmer climate remains equivocal. Enhanced rates of decomposition of SOM under increased global temperatures might cause higher CO2 emissions to the atmosphere, and could therefore constitute a strong positive feedback. The magnitude of this feedback however remains poorly understood, primarily because of the difficulty in quantifying the temperature sensitivity of stored, recalcitrant carbon that comprises the bulk (>90%) of SOM in most soils. In this study we investigated the effects of climatic conditions on soil carbon dynamics using the attenuation of the 14C ‘bomb’ pulse as recorded in selected modern European speleothems. These new data were combined with published results to further examine soil carbon dynamics, and to explore the sensitivity of labile and recalcitrant organic matter decomposition to different climatic conditions. Temporal changes in 14C activity inferred from each speleothem was modelled using a three pool soil carbon inverse model (applying a Monte Carlo method) to constrain soil carbon turnover rates at each site. Speleothems from sites that are characterised by semi-arid conditions, sparse vegetation, thin soil cover and high mean annual air temperatures (MAATs), exhibit weak attenuation of atmospheric 14C ‘bomb’ peak (a low damping effect, D in the range: 55–77%) and low modelled mean respired carbon ages (MRCA), indicating that decomposition is dominated by young, recently fixed soil carbon. By contrast, humid and high MAAT sites that are characterised by a thick soil cover and dense, well developed vegetation, display the highest damping effect (D = c. 90%), and the highest MRCA values (in the range from 350 ± 126 years to 571 ± 128 years). This suggests that carbon incorporated into these stalagmites originates predominantly from decomposition of old, recalcitrant organic matter. SOM turnover rates cannot be ascribed to a single climate variable, e.g. (MAAT) but instead reflect a complex interplay of climate (e.g. MAAT and moisture budget) and vegetation development.

Interfaces, strings, and a soft mode in the square lattice quantum dimer model

The quantum dimer model on the square lattice is a U(1) gauge theory that addresses aspects of the physics of high-Tc superconductors. Using a quantum Monte Carlo method, we show that the theory exists in a confining columnar valence bond solid phase. The interfaces separating distinct columnar phases display plaquette order, which, however, is not realized as a bulk phase. Static “electric” charges are confined by flux tubes that consist of multiple strands, each carrying a fractionalized flux ¼. A soft pseudo-Goldstone mode (which becomes exactly massless at the Rokhsar-Kivelson point) extends deep into the columnar phase, with potential implications for high-Tc physics.

Why does placement of persons with Alzheimer's disease into long-term care improve caregivers' well-being? Examination of psychological mediators.

Caregiving for individuals with Alzheimer's disease is associated with chronic stress and elevated symptoms of depression. Placement of the care receiver (CR) into a long-term care setting may be associated with improved caregiver well-being; however, the psychological mechanisms underlying this relationship are unclear. This study evaluated whether decreases in activity restriction and increases in personal mastery mediated placement-related reductions in caregiver depressive symptoms. In a 5-year longitudinal study of 126 spousal Alzheimer's disease caregivers, we used multilevel models to evaluate placement-related changes in depressive symptoms (short form of the Center for Epidemiologic Studies Depression scale), activity restriction (Activity Restriction Scale), and personal mastery (Pearlin Mastery Scale) in 44 caregivers who placed their spouses into long-term care relative to caregivers who never placed their CRs. The Monte Carlo method for assessing mediation was used to evaluate the significance of the indirect effect of activity restriction and personal mastery on postplacement changes in depressive symptoms. Placement of the CR was associated with significant reductions in depressive symptoms and activity restriction and was also associated with increased personal mastery. Lower activity restriction and higher personal mastery were associated with reduced depressive symptoms. Furthermore, both variables significantly mediated the effect of placement on depressive symptoms. Placement-related reductions in activity restriction and increases in personal mastery are important psychological factors that help explain postplacement reductions in depressive symptoms. The implications for clinical care provided to caregivers are discussed.

A novel computer simulation method for simulating the multiscale transduction dynamics of signal proteins

Signal proteins are able to adapt their response to a change in the environment, governing in this way a broad variety of important cellular processes in living systems. While conventional molecular-dynamics (MD) techniques can be used to explore the early signaling pathway of these protein systems at atomistic resolution, the high computational costs limit their usefulness for the elucidation of the multiscale transduction dynamics of most signaling processes, occurring on experimental timescales. To cope with the problem, we present in this paper a novel multiscale-modeling method, based on a combination of the kinetic Monte-Carlo- and MD-technique, and demonstrate its suitability for investigating the signaling behavior of the photoswitch light-oxygen-voltage-2-Jα domain from Avena Sativa (AsLOV2-Jα) and an AsLOV2-Jα-regulated photoactivable Rac1-GTPase (PA-Rac1), recently employed to control the motility of cancer cells through light stimulus. More specifically, we show that their signaling pathways begin with a residual re-arrangement and subsequent H-bond formation of amino acids near to the flavin-mononucleotide chromophore, causing a coupling between β-strands and subsequent detachment of a peripheral α-helix from the AsLOV2-domain. In the case of the PA-Rac1 system we find that this latter process induces the release of the AsLOV2-inhibitor from the switchII-activation site of the GTPase, enabling signal activation through effector-protein binding. These applications demonstrate that our approach reliably reproduces the signaling pathways of complex signal proteins, ranging from nanoseconds up to seconds at affordable computational costs.

An efficient simulation algorithm for the generalized von Mises distribution of order two

In this article we propose an exact efficient simulation algorithm for the generalized von Mises circular distribution of order two. It is an acceptance-rejection algorithm with a piecewise linear envelope based on the local extrema and the inflexion points of the generalized von Mises density of order two. We show that these points can be obtained from the roots of polynomials and degrees four and eight, which can be easily obtained by the methods of Ferrari and Weierstrass. A comparative study with the von Neumann acceptance-rejection, with the ratio-of-uniforms and with a Markov chain Monte Carlo algorithms shows that this new method is generally the most efficient.

Regional Radiation Pneumonitis After SIRT of a Subcapsular Liver Metastasis: What is the Effect of Direct Beta Irradiation?

We herein present a patient undergoing selective internal radiation therapy with an almost normal lung shunt fraction of 11.5 %, developing histologically proven radiation pneumonitis. Due to a predominance of pulmonary consolidations in the right lower lung and its proximity to a large liver metastases located in the dome of the right liver lobe a Monte Carlo simulation was performed to estimate the effect of direct irradiation of the lung parenchyma. According to our calculations direct irradiation seems negligible and RP is almost exclusively due to ectopic draining of radioactive spheres.

Conceptual design and simulation of a water Cherenkov muon veto for the XENON1T experiment

XENON is a dark matter direct detection project, consisting of a time projection chamber (TPC) filled with liquid xenon as detection medium. The construction of the next generation detector, XENON1T, is presently taking place at the Laboratori Nazionali del Gran Sasso (LNGS) in Italy. It aims at a sensitivity to spin-independent cross sections of 2 10-47 c 2 for WIMP masses around 50 GeV2, which requires a background reduction by two orders of magnitude compared to XENON100, the current generation detector. An active system that is able to tag muons and muon-induced backgrounds is critical for this goal. A water Cherenkov detector of ~ 10 m height and diameter has been therefore developed, equipped with 8 inch photomultipliers and cladded by a reflective foil. We present the design and optimization study for this detector, which has been carried out with a series of Monte Carlo simulations. The muon veto will reach very high detection efficiencies for muons (>99.5%) and showers of secondary particles from muon interactions in the rock (>70%). Similar efficiencies will be obtained for XENONnT, the upgrade of XENON1T, which will later improve the WIMP sensitivity by another order of magnitude. With the Cherenkov water shield studied here, the background from muon-induced neutrons in XENON1T is negligible.

Fast Update of Conditional Simulation Ensembles

Gaussian random field (GRF) conditional simulation is a key ingredient in many spatial statistics problems for computing Monte-Carlo estimators and quantifying uncertainties on non-linear functionals of GRFs conditional on data. Conditional simulations are known to often be computer intensive, especially when appealing to matrix decomposition approaches with a large number of simulation points. This work studies settings where conditioning observations are assimilated batch sequentially, with one point or a batch of points at each stage. Assuming that conditional simulations have been performed at a previous stage, the goal is to take advantage of already available sample paths and by-products to produce updated conditional simulations at mini- mal cost. Explicit formulae are provided, which allow updating an ensemble of sample paths conditioned on n ≥ 0 observations to an ensemble conditioned on n + q observations, for arbitrary q ≥ 1. Compared to direct approaches, the proposed formulae proveto substantially reduce computational complexity. Moreover, these formulae explicitly exhibit how the q new observations are updating the old sample paths. Detailed complexity calculations highlighting the benefits of this approach with respect to state-of-the-art algorithms are provided and are complemented by numerical experiments.

Clues on the frequency of giant planets in wide orbits

The available results of deep imaging searches for planetary companions around nearby stars provide us useful constraints on the frequencies of giant planets in very wide orbits. Here we present some preliminary results of the Monte Carlo simulation which compare the published detection limits with the generated planetary masses and orbital parameters. This allow us to consider the impications of the null detection, which comes from the direct imaging techniques, on the distributions of mass and semimajor axis derived from the results of the other search techniques and also to check the agreement of the observations with the available planetary formation models.