In this survey paper we discuss some tools and methods which are of use in quasiMonte Carlo (QMC) theory. We group them in chapters on Numerical Analysis, Harmonic Analysis, Algebra and Number Theory, and Probability Theory. We do not provide a comprehensive survey of all tools, but focus on a few of them, including reproducing and covariance kernels, Littlewood-Paley theory, Riesz products, Mi...

This self-contained tutorial surveys the state of the art in quasi-Monte Carlo rendering algorithms as used for image synthesis in the product design and movie industry. Based on the number theoretic constructions of low discrepancy sequences, it explains techniques to generate light transport paths to connect cameras and light sources. Summing up their contributions on the image plane results ...

We consider the problem of improving the efficiency of randomized Fourier feature maps to accelerate training and testing speed of kernel methods on large datasets. These approximate feature maps arise as Monte Carlo approximations to integral representations of shiftinvariant kernel functions (e.g., Gaussian kernel). In this paper, we propose to use QuasiMonte Carlo (QMC) approximations instea...

In this paper we develop a Stochastic Collocation Method (SCM) for flow in randomly heterogeneous porous media. At first, the Karhunen-Loève expansion is taken to decompose the log transformed hydraulic conductivity field, which leads to a stochastic PDE that only depends on a finite number of i.i.d. Gaussian random variables. Based on the eigenvalue decay property and a rough error estimate of...

in this paper, the pricing of a european call option on the underlying asset is performed by using a monte carlo method, one of the powerful simulation methods, where the price development of the asset is simulated and value of the claim is computed in terms of an expected value. the proposed approach, applied in monte carlo simulation, is based on the black-scholes equation which generally def...

one of known methods for measuring, forecasting and managing risk is value at risk, which recently has been used by financial institutions extensively. value at risk (var) is a method for recognizing and evaluating risk and uses standard statistical techniques that have daily using in other contexts. this research is seeking a career for managing investment risk in stock exchange and selection ...

The t-value of a (t,m, s)-net is an important criterion of point sets for quasiMonte Carlo integration, and many point sets are constructed in terms of tvalues, as this leads to small integration error bounds. Recently, Matsumoto, Saito, and Matoba proposed the Walsh figure of merit (WAFOM) as a quickly computable criterion of point sets that ensure higher order convergence for function classes...

background: the monte carlo method is the most accurate method for simulation of radiation therapy equipment. the linear accelerators are currently the most widely used machines in radiation therapy centers. methods: in this work, a monte carlo modelling of the siemens oncor linear accelerator in 6 mv and 18 mv beams was performed. the results of simulation were validated by measurements in wat...

introduction: the key characteristics of positron emission tomography (pet) are its quantitative capability and its sensitivity, which allow the in vivo imaging of biochemical interactions with small amounts of tracer concentrations. therefore, accurate quantification is important. however, it can be sensitive to several physical factors. the aim of this investigation is the assessment of the e...

the determination of gyration radius is a strong research for configuration of a macromolecule. italso reflects molecular compactness shape. in this work, to characterize the behavior of theprotein, we observe quantities such as the radius of gyration and the average energy. we studiedthe changes of these factors as a function of temperature for acetylcholine receptor protein in gasphase with n...