geometry of Venice

2004 ◽  
Vol 1 (1) ◽  
pp. 265-275
Author(s):  
Luigi Calzavara ◽  
Maurizio Brizzi
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Null Hypothesis ◽  
Poisson Model ◽  
Probabilistic Methods ◽  
Simple Index ◽  
Original Group ◽  
Random Location

Having observed that ancient Venice belfries are located in such a way that they generate many Pythagorean triangles, having a great number of vertices in common, it has been decided to test the null hypothesis of random location by statistical and probabilistic methods. A simple index, called Pythagorean Ratio, is proposed, for checking which triangles are to be considered as Pythagorean. Then, a Monte Carlo simulation is performed, generating samples of "random belfries" in the historical kernel of Venice; a Poisson model seems to fit very well the number X of Pythagorean triangles. Combining this number with the number of connections, the null hypothesis is rejected. Adding a further belfry (S.Simeon Grande) to the original group of belfries, the significance becomes even higher.

Stochastic Applications in Crashworthiness

2001 ◽  
Author(s):  
Rama P. Koganti ◽  
Ari G. Caliskan
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Yield Strength ◽  
Extreme Values ◽  
Empirical Relation ◽  
Outer Radius ◽  
Probabilistic Methods ◽  
Stochastic Methods ◽  
Element Analysis ◽  
The Mean

Abstract Due to geometrical, and material property variations, response of any structural member varies from the nominal design value. Typically the geometrical and material variations are the resultant of manufacturing variations. In this paper, the effect of these variations about the nominal values on structural response is studied using stochastic or probabilistic methods. Circular aluminum cross-sections are becoming popular in structural energy management applications. Also, significant research has been done to estimate the mean crush load for a circular section using empirical relations. An empirical relation, which is a function of thickness, outer radius, elastic modulus and yield strength, was used to estimate the mean crush load. Based on the measured thickness, outer radius and yield strength, the mean crush load is calculated using the empirical relation. Also, using the empirical relation, the variation in the mean crush load is estimated using linear statistical approach and Monte-Carlo simulation. In both the stochastic methods, actual mean and standard deviations of thickness, outer radius and yield strength are used. Also, using the extreme variations of these factors, mean crush load is predicted using an implicit Finite Element Analysis (FEA) code. The FEA prediction is in good agreement with the results of the testing. However, the designed mean crush load based on the empirical relation overestimates the crush loads by about 11%. The results of the study showed that the tube thickness and yield strength variations significantly affect the crush loads. Based on the Monte-Carlo simulation and FEA values using the extreme values for the geometrical and mechanical properties, one can design crash structures that take into account the inherent variability of components.

scholarly journals Model Uncertainty in Claims Reserving within Tweedie's Compound Poisson Models

2009 ◽  
Vol 39 (1) ◽  
pp. 1-33 ◽  
Author(s):  
Gareth W. Peters ◽  
Pavel V. Shevchenko ◽  
Mario V. Wüthrich
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Model Uncertainty ◽  
Model Averaging ◽  
Poisson Model ◽  
Compound Poisson ◽  
Poisson Models ◽  
Model Selection Problem

AbstractIn this paper we examine the claims reserving problem using Tweedie's compound Poisson model. We develop the maximum likelihood and Bayesian Markov chain Monte Carlo simulation approaches to fit the model and then compare the estimated models under different scenarios. The key point we demonstrate relates to the comparison of reserving quantities with and without model uncertainty incorporated into the prediction. We consider both the model selection problem and the model averaging solutions for the predicted reserves. As a part of this process we also consider the sub problem of variable selection to obtain a parsimonious representation of the model being fitted.

scholarly journals Detecting Linkage Disequilibrium in Bacterial Populations

Genetics ◽  
1998 ◽  
Vol 150 (4) ◽  
pp. 1341-1348 ◽  
Author(s):  
Bernhard Haubold ◽  
Michael Travisano ◽  
Paul B Rainey ◽  
Richard R Hudson
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Linkage Disequilibrium ◽  
Null Hypothesis ◽  
Critical Value ◽  
Linkage Equilibrium ◽  
Bacterial Populations ◽  
Starting Point ◽  
Pairwise Differences ◽  
New Formula

Abstract The distribution of the number of pairwise differences calculated from comparisons between n haploid genomes has frequently been used as a starting point for testing the hypothesis of linkage equilibrium. For this purpose the variance of the pairwise differences, VD, is used as a test statistic to evaluate the null hypothesis that all loci are in linkage equilibrium. The problem is to determine the critical value of the distribution of VD. This critical value can be estimated either by Monte Carlo simulation or by assuming that VD is distributed normally and calculating a one-tailed 95% critical value for VD, L, L = E(VD) + 1.645 Var(VD), where E(VD) is the expectation of VD, and Var(VD) is the variance of VD. If VD (observed) > L, the null hypothesis of linkage equilibrium is rejected. Using Monte Carlo simulation we show that the formula currently available for Var(VD) is incorrect, especially for genetically highly diverse data. This has implications for hypothesis testing in bacterial populations, which are often genetically highly diverse. For this reason we derive a new, exact formula for Var(VD). The distribution of VD is examined and shown to approach normality as the sample size increases. This makes the new formula a useful tool in the investigation of large data sets, where testing for linkage using Monte Carlo simulation can be very time consuming. Application of the new formula, in conjunction with Monte Carlo simulation, to populations of Bradyrhizobium japonicum, Rhizobium leguminosarum, and Bacillus subtilis reveals linkage disequilibrium where linkage equilibrium has previously been reported.

scholarly journals A Monte Carlo simulation to validate the EAR cut-point method for assessing the prevalence of nutrient inadequacy at the population level

2004 ◽  
Vol 7 (7) ◽  
pp. 893-900 ◽  
Author(s):  
B de Lauzon ◽  
JL Volatier ◽  
A Martin
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Population Level ◽  
Point Method ◽  
Probabilistic Methods ◽  
Recommended Dietary Allowance ◽  
The Real ◽  
Cut Point ◽  
Probability Approach ◽  
Dietary Allowance

AbstractObjective:The aim of this study was to validate the EAR cut-point method for assessing the prevalence of nutrient inadequacy at the population level.Design and subjects:Different methods for estimating the prevalence of inadequate intake were compared: the cut-off point method, with cut-off points at the Recommended Dietary Allowance (RDA), 0.66 RDA, 0.50 RDA and the Estimated Average Requirement (EAR); the probability approach; and a Monte Carlo simulation. In total, 591 men and 674 women, aged 20–55 years, were included in the analyses.Results:The prevalence of inadequate intake as estimated by the EAR cut-point method was similar to the prevalence of inadequacy estimated by both probabilistic methods. The cut-point method with RDA, 0.66 RDA and 0.50 RDA as cut-off limits induced an over- or an underestimation of the real prevalence of inadequacy.Conclusions:Probabilistic methods consider both the intake variability and the requirement variability, and, as a result, their estimation should be closer to the real prevalence of inadequacy. The use of the EAR cut-point method yields a good estimation of the prevalence of inadequate intake, comparable to the probability approach, and limits over- and underestimation of the prevalence induced by other cut-off points.

A Monte Carlo Approach to Estimating the Significance of Segregation

1984 ◽  
Vol 16 (2) ◽  
pp. 225-231 ◽  
Author(s):  
A Findlay ◽  
Anne Findlay
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Case Studies ◽  
Spatial Statistics ◽  
Null Hypothesis ◽  
Dissimilarity Index ◽  
Monte Carlo Approach ◽  
Simulation Methodology ◽  
Simulation Techniques ◽  
Social Segregation

Simulation techniques are not new to geography, but they have focused traditionally on attempts to replicate observed patterns rather than on seeking to assist in the formulation of a null hypothesis. The benefits and problems of a Monte Carlo simulation methodology are examined with reference to the latter objective. The flexibility of the approach in the evaluation of spatial statistics is shown to be considerable. Specific case studies are pursued which exemplify its potential in the investigation of social segregation using familiar measures such as the dissimilarity index and the P* index.

Electron Scattering in Solids

1990 ◽  
Vol 48 (2) ◽  
pp. 4-5
Author(s):  
Ryuichi Shimizu ◽  
Ze-Jun Ding
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Angular Distribution ◽  
Elastic Scattering ◽  
Electron Scattering ◽  
Cross Sections ◽  
Expansion Method ◽  
Electron Excitation ◽  
Partial Wave Expansion ◽  
Backscattered Electrons

Monte Carlo simulation has been becoming most powerful tool to describe the electron scattering in solids, leading to more comprehensive understanding of the complicated mechanism of generation of various types of signals for microbeam analysis.The present paper proposes a practical model for the Monte Carlo simulation of scattering processes of a penetrating electron and the generation of the slow secondaries in solids. The model is based on the combined use of Gryzinski’s inner-shell electron excitation function and the dielectric function for taking into account the valence electron contribution in inelastic scattering processes, while the cross-sections derived by partial wave expansion method are used for describing elastic scattering processes. An improvement of the use of this elastic scattering cross-section can be seen in the success to describe the anisotropy of angular distribution of elastically backscattered electrons from Au in low energy region, shown in Fig.l. Fig.l(a) shows the elastic cross-sections of 600 eV electron for single Au-atom, clearly indicating that the angular distribution is no more smooth as expected from Rutherford scattering formula, but has the socalled lobes appearing at the large scattering angle.

Determination of Stoichiometry of GaAs Component in (Gaas)Ge Epitaxially Grown Thin Films by Electron Microprobe X-Ray Analysis

1990 ◽  
Vol 48 (2) ◽  
pp. 264-265
Author(s):  
D. R. Liu ◽  
S. S. Shinozaki ◽  
R. J. Baird
Keyword(s):  
Thin Film ◽  
Thin Films ◽  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Compound Semiconductors ◽  
Energy Dispersive Analysis ◽  
X Ray ◽  
Metastable Alloys ◽  
Lower Voltage

The epitaxially grown (GaAs)Ge thin film has been arousing much interest because it is one of metastable alloys of III-V compound semiconductors with germanium and a possible candidate in optoelectronic applications. It is important to be able to accurately determine the composition of the film, particularly whether or not the GaAs component is in stoichiometry, but x-ray energy dispersive analysis (EDS) cannot meet this need. The thickness of the film is usually about 0.5-1.5 μm. If Kα peaks are used for quantification, the accelerating voltage must be more than 10 kV in order for these peaks to be excited. Under this voltage, the generation depth of x-ray photons approaches 1 μm, as evidenced by a Monte Carlo simulation and actual x-ray intensity measurement as discussed below. If a lower voltage is used to reduce the generation depth, their L peaks have to be used. But these L peaks actually are merged as one big hump simply because the atomic numbers of these three elements are relatively small and close together, and the EDS energy resolution is limited.

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