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.

Computational and experimental methodology for site-matched investigations of the influence of mineral mass fraction and collagen orientation on the axial indentation modulus of lamellar bone

Relationships between mineralization, collagen orientation and indentation modulus were investigated in bone structural units from the mid-shaft of human femora using a site-matched design. Mineral mass fraction, collagen fibril angle and indentation moduli were measured in registered anatomical sites using backscattered electron imaging, polarized light microscopy and nano-indentation, respectively. Theoretical indentation moduli were calculated with a homogenization model from the quantified mineral densities and mean collagen fibril orientations. The average indentation moduli predicted based on local mineralization and collagen fibers arrangement were not significantly different from the average measured experimentally with nanoindentation (p=0.9). Surprisingly, no substantial correlation of the measured indentation moduli with tissue mineralization and/or collagen fiber arrangement was found. Nano-porosity, micro-damage, collagen cross-links, non-collagenous proteins or other parameters affect the indentation measurements. Additional testing/simulation methods need to be considered to properly understand the variability of indentation moduli, beyond the mineralization and collagen arrangement in bone structural units.

Computer simulation of glioma growth and morphology.

Despite major advances in the study of glioma, the quantitative links between intra-tumor molecular/cellular properties, clinically observable properties such as morphology, and critical tumor behaviors such as growth and invasiveness remain unclear, hampering more effective coupling of tumor physical characteristics with implications for prognosis and therapy. Although molecular biology, histopathology, and radiological imaging are employed in this endeavor, studies are severely challenged by the multitude of different physical scales involved in tumor growth, i.e., from molecular nanoscale to cell microscale and finally to tissue centimeter scale. Consequently, it is often difficult to determine the underlying dynamics across dimensions. New techniques are needed to tackle these issues. Here, we address this multi-scalar problem by employing a novel predictive three-dimensional mathematical and computational model based on first-principle equations (conservation laws of physics) that describe mathematically the diffusion of cell substrates and other processes determining tumor mass growth and invasion. The model uses conserved variables to represent known determinants of glioma behavior, e.g., cell density and oxygen concentration, as well as biological functional relationships and parameters linking phenomena at different scales whose specific forms and values are hypothesized and calculated based on in vitro and in vivo experiments and from histopathology of tissue specimens from human gliomas. This model enables correlation of glioma morphology to tumor growth by quantifying interdependence of tumor mass on the microenvironment (e.g., hypoxia, tissue disruption) and on the cellular phenotypes (e.g., mitosis and apoptosis rates, cell adhesion strength). Once functional relationships between variables and associated parameter values have been informed, e.g., from histopathology or intra-operative analysis, this model can be used for disease diagnosis/prognosis, hypothesis testing, and to guide surgery and therapy. In particular, this tool identifies and quantifies the effects of vascularization and other cell-scale glioma morphological characteristics as predictors of tumor-scale growth and invasion.

Computer simulation of glioma growth and morphology.

Despite major advances in the study of glioma, the quantitative links between intra-tumor molecular/cellular properties, clinically observable properties such as morphology, and critical tumor behaviors such as growth and invasiveness remain unclear, hampering more effective coupling of tumor physical characteristics with implications for prognosis and therapy. Although molecular biology, histopathology, and radiological imaging are employed in this endeavor, studies are severely challenged by the multitude of different physical scales involved in tumor growth, i.e., from molecular nanoscale to cell microscale and finally to tissue centimeter scale. Consequently, it is often difficult to determine the underlying dynamics across dimensions. New techniques are needed to tackle these issues. Here, we address this multi-scalar problem by employing a novel predictive three-dimensional mathematical and computational model based on first-principle equations (conservation laws of physics) that describe mathematically the diffusion of cell substrates and other processes determining tumor mass growth and invasion. The model uses conserved variables to represent known determinants of glioma behavior, e.g., cell density and oxygen concentration, as well as biological functional relationships and parameters linking phenomena at different scales whose specific forms and values are hypothesized and calculated based on in vitro and in vivo experiments and from histopathology of tissue specimens from human gliomas. This model enables correlation of glioma morphology to tumor growth by quantifying interdependence of tumor mass on the microenvironment (e.g., hypoxia, tissue disruption) and on the cellular phenotypes (e.g., mitosis and apoptosis rates, cell adhesion strength). Once functional relationships between variables and associated parameter values have been informed, e.g., from histopathology or intra-operative analysis, this model can be used for disease diagnosis/prognosis, hypothesis testing, and to guide surgery and therapy. In particular, this tool identifies and quantifies the effects of vascularization and other cell-scale glioma morphological characteristics as predictors of tumor-scale growth and invasion.

Computational selection of inhibitors of Abeta aggregation and neuronal toxicity.

Alzheimer's disease (AD) is characterized by the cerebral accumulation of misfolded and aggregated amyloid-beta protein (Abeta). Disease symptoms can be alleviated, in vitro and in vivo, by 'beta-sheet breaker' pentapeptides that reduce plaque load. However the peptide nature of these compounds, made them biologically unstable and unable to penetrate membranes with high efficiency. The main goal of this study was to use computational methods to identify small molecule mimetics with better drug-like properties. For this purpose, the docked conformations of the active peptides were used to identify compounds with similar activities. A series of related beta-sheet breaker peptides were docked to solid state NMR structures of a fibrillar form of Abeta. The lowest energy conformations of the active peptides were used to design three dimensional (3D)-pharmacophores, suitable for screening the NCI database with Unity. Small molecular weight compounds with physicochemical features and a conformation similar to the active peptides were selected, ranked by docking and biochemical parameters. Of 16 diverse compounds selected for experimental screening, 2 prevented and reversed Abeta aggregation at 2-3microM concentration, as measured by Thioflavin T (ThT) fluorescence and ELISA assays. They also prevented the toxic effects of aggregated Abeta on neuroblastoma cells. Their low molecular weight and aqueous solubility makes them promising lead compounds for treating AD.

Benchmarking the simulation of Cr isotope fractionation

A benchmark problem set consisting of four problem levels was developed for the simulation of Cr isotope fractionation in 1D and 2D domains. The benchmark is based on a recent field study where Cr(VI) reduction and accompanying Cr isotope fractionation occurs abiotically by an aqueous reaction with dissolved Fe 2+ (Wanner et al., 2012., Appl. Geochem., 27, 644–662). The problem set includes simulation of the major processes affecting the Cr isotopic composition such as the dissolution of various Cr(VI) bearing minerals, fractionation during abiotic aqueous Cr(VI) reduction, and non-fractionating precipitation of Cr(III) as sparingly soluble Cr-hydroxide. Accuracy of the presented solutions was ensured by running the problems with four well-established reactive transport modeling codes: TOUGHREACT, MIN3P, CRUNCHFLOW, and FLOTRAN. Results were also compared with an analytical Rayleigh-type fractionation model. An additional constraint on the correctness of the results was obtained by comparing output from the problem levels simulating Cr isotope fractionation with the corresponding ones only simulating bulk concentrations. For all problem levels, model to model comparisons showed excellent agreement, suggesting that for the tested geochemical processes any code is capable of accurately simulating the fate of individual Cr isotopes.

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.

Computational fluid dynamics modelling in cardiovascular medicine.

This paper reviews the methods, benefits and challenges associated with the adoption and translation of computational fluid dynamics (CFD) modelling within cardiovascular medicine. CFD, a specialist area of mathematics and a branch of fluid mechanics, is used routinely in a diverse range of safety-critical engineering systems, which increasingly is being applied to the cardiovascular system. By facilitating rapid, economical, low-risk prototyping, CFD modelling has already revolutionised research and development of devices such as stents, valve prostheses, and ventricular assist devices. Combined with cardiovascular imaging, CFD simulation enables detailed characterisation of complex physiological pressure and flow fields and the computation of metrics which cannot be directly measured, for example, wall shear stress. CFD models are now being translated into clinical tools for physicians to use across the spectrum of coronary, valvular, congenital, myocardial and peripheral vascular diseases. CFD modelling is apposite for minimally-invasive patient assessment. Patient-specific (incorporating data unique to the individual) and multi-scale (combining models of different length- and time-scales) modelling enables individualised risk prediction and virtual treatment planning. This represents a significant departure from traditional dependence upon registry-based, population-averaged data. Model integration is progressively moving towards 'digital patient' or 'virtual physiological human' representations. When combined with population-scale numerical models, these models have the potential to reduce the cost, time and risk associated with clinical trials. The adoption of CFD modelling signals a new era in cardiovascular medicine. While potentially highly beneficial, a number of academic and commercial groups are addressing the associated methodological, regulatory, education- and service-related challenges.

Shower approach in the simulation of ion scattering from solids

An efficient approach for the simulation of ion scattering from solids is proposed. For every encountered atom, we take multiple samples of its thermal displacements among those which result in scattering with high probability to finally reach the detector. As a result, the detector is illuminated by intensive “showers,” where each event of detection must be weighted according to the actual probability of the atom displacement. The computational cost of such simulation is orders of magnitude lower than in the direct approach, and a comprehensive analysis of multiple and plural scattering effects becomes possible. We use this method for two purposes. First, the accuracy of the approximate approaches, developed mainly for ion-beam structural analysis, is verified. Second, the possibility to reproduce a wide class of experimental conditions is used to analyze some basic features of ion-solid collisions: the role of double violent collisions in low-energy ion scattering; the origin of the “surface peak” in scattering from amorphous samples; the low-energy tail in the energy spectra of scattered medium-energy ions due to plural scattering; and the degradation of blocking patterns in two-dimensional angular distributions with increasing depth of scattering. As an example of simulation for ions of MeV energies, we verify the time reversibility for channeling and blocking of 1-MeV protons in a W crystal. The possibilities of analysis that our approach offers may be very useful for various applications, in particular, for structural analysis with atomic resolution.

An approach to automatic learning assessment based on the computational theory of perceptions

E-learning systems output a huge quantity of data on a learning process. However, it takes a lot of specialist human resources to manually process these data and generate an assessment report. Additionally, for formative assessment, the report should state the attainment level of the learning goals defined by the instructor. This paper describes the use of the granular linguistic model of a phenomenon (GLMP) to model the assessment of the learning process and implement the automated generation of an assessment report. GLMP is based on fuzzy logic and the computational theory of perceptions. This technique is useful for implementing complex assessment criteria using inference systems based on linguistic rules. Apart from the grade, the model also generates a detailed natural language progress report on the achieved proficiency level, based exclusively on the objective data gathered from correct and incorrect responses. This is illustrated by applying the model to the assessment of Dijkstra’s algorithm learning using a visual simulation-based graph algorithm learning environment, called GRAPHs

Computational Fluid Dynamics Expert System using Artificial Neural Networks

The design of a modern aircraft is based on three pillars: theoretical results, experimental test and computational simulations. As a results of this, Computational Fluid Dynamic (CFD) solvers are widely used in the aeronautical field. These solvers require the correct selection of many parameters in order to obtain successful results. Besides, the computational time spent in the simulation depends on the proper choice of these parameters. In this paper we create an expert system capable of making an accurate prediction of the number of iterations and time required for the convergence of a computational fluid dynamic (CFD) solver. Artificial neural network (ANN) has been used to design the expert system. It is shown that the developed expert system is capable of making an accurate prediction the number of iterations and time required for the convergence of a CFD solver.

Simulation of wind farms in flat and complex terrain using CFD

Use of computational fluid dynamic (CFD) methods to predict the power production from wind entire wind farms in flat and complex terrain is presented in this paper. Two full 3D Navier–Stokes solvers for incompressible flow are employed that incorporate the k–ε and k–ω turbulence models respectively. The wind turbines (W/Ts) are modelled as momentum absorbers by means of their thrust coefficient using the actuator disk approach. The WT thrust is estimated using the wind speed one diameter upstream of the rotor at hub height. An alternative method that employs an induction-factor based concept is also tested. This method features the advantage of not utilizing the wind speed at a specific distance from the rotor disk, which is a doubtful approximation when a W/T is located in the wake of another and/or the terrain is complex. To account for the underestimation of the near wake deficit, a correction is introduced to the turbulence model. The turbulence time scale is bounded using the general “realizability” constraint for the turbulent velocities. Application is made on two wind farms, a five-machine one located in flat terrain and another 43-machine one located in complex terrain. In the flat terrain case, the combination of the induction factor method along with the turbulence correction provides satisfactory results. In the complex terrain case, there are some significant discrepancies with the measurements, which are discussed. In this case, the induction factor method does not provide satisfactory results.

A stochastic model updating method for parameter variability quantification based on response surface models and Monte Carlo simulation

Stochastic model updating must be considered for quantifying uncertainties inherently existing in real-world engineering structures. By this means the statistical properties,instead of deterministic values, of structural parameters can be sought indicating the parameter variability. However, the implementation of stochastic model updating is much more complicated than that of deterministic methods particularly in the aspects of theoretical complexity and low computational efficiency. This study attempts to propose a simple and cost-efficient method by decomposing a stochastic updating process into a series of deterministic ones with the aid of response surface models and Monte Carlo simulation. The response surface models are used as surrogates for original FE models in the interest of programming simplification, fast response computation and easy inverse optimization. Monte Carlo simulation is adopted for generating samples from the assumed or measured probability distributions of responses. Each sample corresponds to an individual deterministic inverse process predicting the deterministic values of parameters. Then the parameter means and variances can be statistically estimated based on all the parameter predictions by running all the samples. Meanwhile, the analysis of variance approach is employed for the evaluation of parameter variability significance. The proposed method has been demonstrated firstly on a numerical beam and then a set of nominally identical steel plates tested in the laboratory. It is found that compared with the existing stochastic model updating methods, the proposed method presents similar accuracy while its primary merits consist in its simple implementation and cost efficiency in response computation and inverse optimization.

Simulation of impulse response for indoor visible light communications using 3D CAD models

n this article, a tool for simulating the channel impulse response for indoor visible light communications using 3D computer-aided design (CAD) models is presented. The simulation tool is based on a previous Monte Carlo ray-tracing algorithm for indoor infrared channel estimation, but including wavelength response evaluation. The 3D scene, or the simulation environment, can be defined using any CAD software in which the user specifies, in addition to the setting geometry, the reflection characteristics of the surface materials as well as the structures of the emitters and receivers involved in the simulation. Also, in an effort to improve the computational efficiency, two optimizations are proposed. The first one consists of dividing the setting into cubic regions of equal size, which offers a calculation improvement of approximately 50% compared to not dividing the 3D scene into sub-regions. The second one involves the parallelization of the simulation algorithm, which provides a computational speed-up proportional to the number of processors used.

Computational Study of the Fe(CN)(2)CO Cofactor and Its Binding to HypC Protein.

In the intricate maturation process of [NiFe]-hydrogenases, the Fe(CN)2CO cofactor is first assembled in a HypCD complex with iron coordinated by cysteines from both proteins and CO is added after ligation of cyanides. The small accessory protein HypC is known to play a role in delivering the cofactor needed for assembling the hydrogenase active site. However, the chemical nature of the Fe(CN)2CO moiety and the stability of the cofactor–HypC complex are open questions. In this work, we address geometries, properties, and the nature of bonding of all chemical species involved in formation and binding of the cofactor by means of quantum calculations. We also study the influence of environmental effects and binding to cysteines on vibrational frequencies of stretching modes of CO and CN used to detect the presence of Fe(CN)2CO. Carbon monoxide is found to be much more sensitive to sulfur binding and the polarity of the medium than cyanides. The stability of the HypC–cofactor complex is analyzed by means of molecular dynamics simulation of cofactor-free and cofactor-bound forms of HypC. The results show that HypC is stable enough to carry the cofactor, but since its binding cysteine is located at the N-terminal unstructured tail, it presents large motions in solution, which suggests the need for a guiding interaction to achieve delivery of the cofactor.