Parallelization of kinetic Monte Carlo algorithm to simulate AL3Sc precipitation

The present paper reports the precipitation process of Al3Sc structures in an aluminum scandium alloy, which has been simulated with a synchronous parallel kinetic Monte Carlo (spkMC) algorithm. The spkMC implementation is based on the vacancy diffusion mechanism. To filter the raw data generated by the spkMC simulations, the density-based clustering with noise (DBSCAN) method has been employed. spkMC and DBSCAN algorithms were implemented in the C language and using MPI library. The simulations were conducted in the SeARCH cluster located at the University of Minho. The Al3Sc precipitation was successfully simulated at the atomistic scale with the spkMC. DBSCAN proved to be a valuable aid to identify the precipitates by performing a cluster analysis of the simulation results. The achieved simulations results are in good agreement with those reported in the literature under sequential kinetic Monte Carlo simulations (kMC). The parallel implementation of kMC has provided a 4x speedup over the sequential version.

Influência das características mamárias na cintilografia miocárdica pelo método Monte Carlo

FUNDAMENTO: Pela redução da especificidade associada à perda de informação, a influência da atenuação das mamas é de fundamental importância em estudos de perfusão do miocárdio. Entretanto, apesar de vários estudos terem sido realizados ao longo dos últimos anos, pouco se tem evoluído para determinar com acurácia a influência das características das mamas sobre a qualidade da cintilografia miocárdica, evitando exposições adicionais de radiação às pacientes. OBJETIVO: O objetivo deste estudo é quantificar a atenuação de fótons pelas mamas, em estudos de perfusão do miocárdio com 99mTc, de acordo com diferentes tamanhos e composições. MÉTODOS: Cada mama foi assumida como sendo um cubo composto de tecido adiposo e fibroglandular. Os dados referentes aos fótons de 99mTc foram analisados em um modelo de Monte Carlo. Variamos a espessura e a composição das mamas e analisamos as interferências na atenuação. Foi empregado o software EGS 4 para as simulações. RESULTADOS: Fixando a espessura de uma mama, a variação da sua composição acarreta um acréscimo máximo de 2,3% no número de fótons atenuados. Em contrapartida, mantendo-se uma composição do tecido mamário fixa, a diferença na atenuação de fótons foi de 45,0%, sendo em média de 6,0% para cada acréscimo de centímetro na espessura da mama. CONCLUSÃO: A simulação por Monte Carlo demonstrou que a influência das espessuras das mamas na atenuação de fótons em cintilografias do miocárdio com 99mTc é muito maior do que a influência das suas composições.

Simulación Monte Carlo de las dosis en tumores de pulmón en tratamientos de radioterapia estereotáxica extracraneal

Estudio elaborado a partir de una estancia en el Karolinska University Hospital, Suecia, entre marzo y junio del 2006. En la radioterapia estereotáxica extracraneal (SBRT) de tumores de pulmón existen principalmente dos problemas en el cálculo de la dosis con los sistemas de planificación disponibles: la precisión limitada de los algoritmos de cálculo en presencia de tejidos con densidades muy diferentes y los movimientos debidos a la respiración del paciente durante el tratamiento. El objetivo de este trabajo ha sido llevar a cabo la simulación con el código Monte Carlo PENELOPE de la distribución de dosis en tumores de pulmón en casos representativos de tratamientos con SBRT teniendo en cuenta los movimientos respiratorios y su comparación con los resultados de varios planificadores. Se han estudiado casos representativos de tratamientos de SBRT en el Karolinska University Hospital. Los haces de radiación se han simulado mediante el código PENELOPE y se han usado para la obtención de los resultados MC de perfiles de dosis. Los resultados obtenidos para el caso estático (sin movimiento respiratorio ) ponen de manifiesto que, en comparación con la MC, la dosis (Gy/MU) calculada por los planificadores en el tumor tiene una precisión del 2-3%. En la zona de interfase entre tumor y tejido pulmonar los planificadores basados en el algoritmo PB sobrestiman la dosis en un 10%, mientras que el algoritmo CC la subestima en un 3-4%. Los resultados de la simulación mediante MC de los movimientos respiratorios indican que los resultados de los planificadores son suficientemente precisos en el tumor, aunque en la interfase hay una mayor subestimación de la dosis en comparación con el caso estático. Estos resultados son compatibles con la experiencia clínica adquirida durante 15 años en el Karolinska University Hospital. Los resultados se han publicado en la revista Acta Oncologica.

Adaptive Continuous time Markov Chain Approximation Model to General Jump-Diusions

We propose a non-equidistant Q rate matrix formula and an adaptive numerical algorithm for a continuous time Markov chain to approximate jump-diffusions with affine or non-affine functional specifications. Our approach also accommodates state-dependent jump intensity and jump distribution, a flexibility that is very hard to achieve with other numerical methods. The Kolmogorov-Smirnov test shows that the proposed Markov chain transition density converges to the one given by the likelihood expansion formula as in Ait-Sahalia (2008). We provide numerical examples for European stock option pricing in Black and Scholes (1973), Merton (1976) and Kou (2002).

Evaluation of organ-specific peripheral doses after 2-dimensional, 3-dimensional and hybrid intensity modulated radiation therapy for breast cancer based on Monte Carlo and convolution/superposition algorithms: implications for secondary cancer risk assessment.

To make a comprehensive evaluation of organ-specific out-of-field doses using Monte Carlo (MC) simulations for different breast cancer irradiation techniques and to compare results with a commercial treatment planning system (TPS). Three breast radiotherapy techniques using 6MV tangential photon beams were compared: (a) 2DRT (open rectangular fields), (b) 3DCRT (conformal wedged fields), and (c) hybrid IMRT (open conformal+modulated fields). Over 35 organs were contoured in a whole-body CT scan and organ-specific dose distributions were determined with MC and the TPS. Large differences in out-of-field doses were observed between MC and TPS calculations, even for organs close to the target volume such as the heart, the lungs and the contralateral breast (up to 70% difference). MC simulations showed that a large fraction of the out-of-field dose comes from the out-of-field head scatter fluence (>40%) which is not adequately modeled by the TPS. Based on MC simulations, the 3DCRT technique using external wedges yielded significantly higher doses (up to a factor 4-5 in the pelvis) than the 2DRT and the hybrid IMRT techniques which yielded similar out-of-field doses. In sharp contrast to popular belief, the IMRT technique investigated here does not increase the out-of-field dose compared to conventional techniques and may offer the most optimal plan. The 3DCRT technique with external wedges yields the largest out-of-field doses. For accurate out-of-field dose assessment, a commercial TPS should not be used, even for organs near the target volume (contralateral breast, lungs, heart).

Monte Carlo simulations of metasomatic enrichment in the lithosphere and implications for the source of alkaline basalts

One hypothesis for the origin of alkaline lavas erupted on oceanic islands and in intracontinental settings is that they represent the melts of amphibole-rich veins in the lithosphere (or melts of their dehydrated equivalents if metasomatized lithosphere is recycled into the convecting mantle). Amphibole-rich veins are interpreted as cumulates produced by crystallization of low-degree melts of the underlying asthenosphere as they ascend through the lithosphere. We present the results of trace-element modelling of the formation and melting of veins formed in this way with the goal of testing this hypothesis and for predicting how variability in the formation and subsequent melting of such cumulates (and adjacent cryptically and modally metasomatized lithospheric peridotite) would be manifested in magmas generated by such a process. Because the high-pressure phase equilibria of hydrous near-solidus melts of garnet lherzolite are poorly constrained and given the likely high variability of the hypothesized accumulation and remelting processes, we used Monte Carlo techniques to estimate how uncertainties in the model parameters (e.g. the compositions of the asthenospheric sources, their trace-element contents, and their degree of melting; the modal proportions of crystallizing phases, including accessory phases, as the asthenospheric partial melts ascend and crystallize in the lithosphere; the amount of metasomatism of the peridotitic country rock; the degree of melting of the cumulates and the amount of melt derived from the metasomatized country rock) propagate through the process and manifest themselves as variability in the trace-element contents and radiogenic isotopic ratios of model vein compositions and erupted alkaline magma compositions. We then compare the results of the models with amphibole observed in lithospheric veins and with oceanic and continental alkaline magmas. While the trace-element patterns of the near-solidus peridotite melts, the initial anhydrous cumulate assemblage (clinopyroxene +/- garnet +/- olivine +/- orthopyroxene), and the modelled coexisting liquids do not match the patterns observed in alkaline lavas, our calculations show that with further crystallization and the appearance of amphibole (and accessory minerals such as rutile, ilmenite, apatite, etc.) the calculated cumulate assemblages have trace-element patterns that closely match those observed in the veins and lavas. These calculated hydrous cumulate assemblages are highly enriched in incompatible trace elements and share many similarities with the trace-element patterns of alkaline basalts observed in oceanic or continental setting such as positive Nb/La, negative Ce/Pb, and similiar slopes of the rare earth elements. By varying the proportions of trapped liquid and thus simulating the cryptic and modal metasomatism observed in peridotite that surrounds these veins, we can model the variations in Ba/Nb, Ce/Pb, and Nb/U ratios that are observed in alkaline basalts. If the isotopic compositions of the initial low-degree peridotite melts are similar to the range observed in mid-ocean ridge basalt, our model calculations produce cumulates that would have isotopic compositions similar to those observed in most alkaline ocean island basalt (OIB) and continental magmas after similar to 0 center dot 15 Gyr. However, to produce alkaline basalts with HIMU isotopic compositions requires much longer residence times (i.e. 1-2 Gyr), consistent with subduction and recycling of metasomatized lithosphere through the mantle. such as a heterogeneous asthenosphere. These modelling results support the interpretation proposed by various researchers that amphibole-bearing veins represent cumulates formed during the differentiation of a volatile-bearing low-degree peridotite melt and that these cumulates are significant components of the sources of alkaline OIB and continental magmas. The results of the forward models provide the potential for detailed tests of this class of hypotheses for the origin of alkaline magmas worldwide and for interpreting major and minor aspects of the geochemical variability of these magmas.

Estimation of the probability of congestion using Monte Carlo method in OPS networks

In networks with small buffers, such as optical packet switching based networks, the convolution approach is presented as one of the most accurate method used for the connection admission control. Admission control and resource management have been addressed in other works oriented to bursty traffic and ATM. This paper focuses on heterogeneous traffic in OPS based networks. Using heterogeneous traffic and bufferless networks the enhanced convolution approach is a good solution. However, both methods (CA and ECA) present a high computational cost for high number of connections. Two new mechanisms (UMCA and ISCA) based on Monte Carlo method are proposed to overcome this drawback. Simulation results show that our proposals achieve lower computational cost compared to enhanced convolution approach with an small stochastic error in the probability estimation

A Monte Carlo-Based Fiber Tracking Algorithm using Diffusion Tensor MRI

Diffusion tensor magnetic resonance imaging, which measures directional information of water diffusion in the brain, has emerged as a powerful tool for human brain studies. In this paper, we introduce a new Monte Carlo-based fiber tracking approach to estimate brain connectivity. One of the main characteristics of this approach is that all parameters of the algorithm are automatically determined at each point using the entropy of the eigenvalues of the diffusion tensor. Experimental results show the good performance of the proposed approach

Error and complexity of random walk Monte Carlo radiosity

The author studies the error and complexity of the discrete random walk Monte Carlo technique for radiosity, using both the shooting and gathering methods. The author shows that the shooting method exhibits a lower complexity than the gathering one, and under some constraints, it has a linear complexity. This is an improvement over a previous result that pointed to an O(n log n) complexity. The author gives and compares three unbiased estimators for each method, and obtains closed forms and bounds for their variances. The author also bounds the expected value of the mean square error (MSE). Some of the results obtained are also shown

Markov chain montecarlo method applied to rounding zeros of compositional data: first approach

As stated in Aitchison (1986), a proper study of relative variation in a compositional data set should be based on logratios, and dealing with logratios excludes dealing with zeros. Nevertheless, it is clear that zero observations might be present in real data sets, either because the corresponding part is completelyabsent –essential zeros– or because it is below detection limit –rounded zeros. Because the second kind of zeros is usually understood as “a trace too small to measure”, it seems reasonable to replace them by a suitable small value, and this has been the traditional approach. As stated, e.g. by Tauber (1999) and byMartín-Fernández, Barceló-Vidal, and Pawlowsky-Glahn (2000), the principal problem in compositional data analysis is related to rounded zeros. One should be careful to use a replacement strategy that does not seriously distort the general structure of the data. In particular, the covariance structure of the involvedparts –and thus the metric properties– should be preserved, as otherwise further analysis on subpopulations could be misleading. Following this point of view, a non-parametric imputation method isintroduced in Martín-Fernández, Barceló-Vidal, and Pawlowsky-Glahn (2000). This method is analyzed in depth by Martín-Fernández, Barceló-Vidal, and Pawlowsky-Glahn (2003) where it is shown that thetheoretical drawbacks of the additive zero replacement method proposed in Aitchison (1986) can be overcome using a new multiplicative approach on the non-zero parts of a composition. The new approachhas reasonable properties from a compositional point of view. In particular, it is “natural” in the sense thatit recovers the “true” composition if replacement values are identical to the missing values, and it is coherent with the basic operations on the simplex. This coherence implies that the covariance structure of subcompositions with no zeros is preserved. As a generalization of the multiplicative replacement, in thesame paper a substitution method for missing values on compositional data sets is introduced

A Monte Carlo method for accelerating the computation of animated radiosity sequences

Realistic rendering animation is known to be an expensive processing task when physically-based global illumination methods are used in order to improve illumination details. This paper presents an acceleration technique to compute animations in radiosity environments. The technique is based on an interpolated approach that exploits temporal coherence in radiosity. A fast global Monte Carlo pre-processing step is introduced to the whole computation of the animated sequence to select important frames. These are fully computed and used as a base for the interpolation of all the sequence. The approach is completely view-independent. Once the illumination is computed, it can be visualized by any animated camera. Results present significant high speed-ups showing that the technique could be an interesting alternative to deterministic methods for computing non-interactive radiosity animations for moderately complex scenarios

Biblioteca de l'heurística constructiva Clarke and Wright combinada amb simulació Monte Carlo per resoldre el problema d'adreçament de vehicles

En aquesta recerca es presenta una biblioteca de programari lliure basada en l'heurística constructiva de Clarke & Wright combinada amb simulació Monte Carlo que permet, de manera simple, generar solucions al problema d'adreçament de vehicles. Aquesta metodologia construeix solucions competents en poc temps i sense necessitat d'ajustar o configurar paràmetres previs. La biblioteca pot integrar-se fàcilment en projectes que resolguin variants del VRP amb canvis mínims sobre el codi. Aquest es troba ben documentat i accessible de manera lliure a través de la xarxa. Els resultats computacionals indiquen que es resolen instàncies VRP en temps i costos significativament inferiors a altres propostes de la mateixa família.

Analysis and Monte Carlo simulations of a model for the spread of infectious diseases in heterogeneous metapopulations

We present a study of the continuous-time equations governing the dynamics of a susceptible infected-susceptible model on heterogeneous metapopulations. These equations have been recently proposed as an alternative formulation for the spread of infectious diseases in metapopulations in a continuous-time framework. Individual-based Monte Carlo simulations of epidemic spread in uncorrelated networks are also performed revealing a good agreement with analytical predictions under the assumption of simultaneous transmission or recovery and migration processes

Main results of the Monte Carlo studies carried out for nuclear medicine practices within the ORAMED project

The aim of ORAMED work package 4 was the optimization of the medical practices in nuclear medicine during the preparation of radiopharmaceuticals and their administration to the patient. During the project a wide campaign of measurements was performed in the nuclear medicine departments of the collaborating hospitals. Such data were intrinsically characterized by a large variability that depended on the procedure, the employed techniques and the operator's habits. That variability could easily hide some important parameter, for example, the effectiveness of the adopted shielding (for syringe and vial) or the effect of the distances from the source. This information is necessary for a valuable optimization purpose of radiation protection. To this end a sensitivity analysis was carried out through Monte Carlo simulations employing voxel models, representing operator's hand during the considered practices. Such analysis allowed understanding at what extent the range of personal dose equivalent evaluated during measurements can be considered intrinsically related to the procedures. Furthermore, with the Monte Carlo simulations it was possible to study the appropriateness of the shielding usually utilized in these practices.