Novosibirsk hadronic currents for τ→4π channels of τ decay library TAUOLA

The new parameterization of form factors developed for 4π channels of the τ lepton decay and based on Novosibirsk data on e⁺e⁻→4π has been coded in a form suitable for the TAUOLA Monte Carlo package. Comparison with results from TAUOLA using another parameterization, i.e. the CLEO version of 1998 is also included.     

RacoonWW1.3: A Monte Carlo program for four-fermion production at ee colliders

We present the Monte Carlo generator RacoonWW that computes cross sections to all processes e⁺e⁻→4f and e⁺e⁻→4fγ and calculates the complete electroweak radiative corrections to e⁺e⁻→WW→4f in the electroweak Standard Model in double-pole approximation. The calculation of the tree-level processes e⁺e⁻→4f and e⁺e⁻→4fγ is based on the full matrix elements for massless (polarized) fermions. When calculating radiative corrections to e⁺e⁻→WW→4f, the complete virtual doubly-resonant electroweak corrections are included, i.e. the factorizable and non-factorizable virtual corrections in double-pole approximation, and the real corrections are based on the full matrix elements for e⁺e⁻→4fγ. The matching of soft and collinear singularities between virtual and real corrections is done alternatively in two different ways, namely by using a subtraction method or by applying phase-space slicing. Higher-order initial-state photon radiation and naive QCD corrections are taken into account. RacoonWW also provides anomalous triple gauge-boson couplings for all processes e⁺e⁻→4f and anomalous quartic gauge-boson couplings for all processes e⁺e⁻→4fγ.     

Open-Source Model Checking

We present GMC², a software model checker for GCC, the open-source compiler from the Free Software Foundation (FSF). GMC², which is part of the GMC static-analysis and model-checking tool suite for GCC under development at SUNY Stony Brook, can be seen as an extension of Monte Carlo model checking to the setting of concurrent, procedural programming languages. Monte Carlo model checking is a newly developed technique that utilizes the theory of geometric random variables, statistical hypothesis testing, and random sampling of lassos in Büchi automata to realize a one- sided error, randomized algorithm for LTL model checking. To handle the function call/return mechanisms inherent in procedural languages such as C/C++, the version of Monte Carlo model checking implemented in GMC² is optimized for pushdown-automaton models. Our experimental results demonstrate that this approach yields an efficient and scalable software model checker for GCC.     

eett6f v. 1.0: A program for top quark pair production and decay into 6 fermions at linear colliders

The first version of a computer program eett6f for calculating cross sections of e⁺e⁻→6 fermions processes relevant for a -pair production and decay at centre of mass energies typical for linear colliders is presented. eett6f v. 1.0 allows for calculating both the total and differential cross sections at tree level of the Standard Model (SM). The program can be used as the Monte Carlo generator of unweighted events as well.     

Effects of random system properties on the thermal buckling analysis of laminated composite plates

This paper examines the effect of random system properties on thermal buckling load of laminated composite plates under uniform temperature rise having temperature dependent properties using HSDT. The system properties such as material properties, thermal expansion coefficients and thickness of the laminate are modeled as independent random variables. A C⁰ finite element is used for deriving the eigenvalue problem. A Taylor series based first-order perturbation technique is used to handle the randomness in the system properties. Second-order statistics of the thermal buckling load are obtained. The results are validated with those available in the literature and Monte Carlo simulation.     

Monte Carlo circuits for the abelian permutation group intersection problem

Summary We show that the problem of computing a basis for an abelian transitive permutation group is in N C ^k and also we show that the problem of computing a basis for an abelian permutation group and the problem of computing the intersection of two abelian groups acting on n points, can be solved in depth (log n)^k on a Monte Carlo Boolean circuit of polynomial size. Moreover the latter two problems are shown to be in N C ^k in the restricted case of bounded number of generators.     

Multilevel Monte Carlo method with applications to stochastic partial differential equations

In this work, the approximation of Hilbert-space-valued random variables is combined with the approximation of the expectation by a multilevel Monte Carlo (MLMC) method. The number of samples on the different levels of the multilevel approximation are chosen such that the errors are balanced. The overall work then decreases in the optimal case to O(h ^?2) if h is the error of the approximation. The MLMC method is applied to functions of solutions of parabolic and hyperbolic stochastic partial differential equations as needed, for example, for option pricing. Simulations complete the paper.     

Time Series Simulation with Quasi Monte Carlo Methods

This paper compares quasi Monte Carlo methods, in particularso-called (t, m, s)-nets, with classical Monte Carlo approaches forsimulating econometric time-series models. Quasi Monte Carlomethods have found successful application in many fields, such asphysics, image processing, and the evaluation of financederivatives. However, they are rarely used in econometrics. Here,we apply both traditional and quasi Monte Carlo simulation methodsto time-series models that typically arise in macroeconometrics.The numerical experiments demonstrate that quasi Monte Carlomethods outperform traditional ones for all models we investigate.     

Quasirandom Number Generators for Parallel Monte Carlo Algorithms

A method for generating sequences of quasirandom numbers allows conventional serial Monte Carlo algorithms to be parallelized using a leapfrog scheme. Specifically, a Sobol' sequence can be broken up into interleaved subsets; with each processing node calculating a unique subset of the full sequence, all of the computational advantages of quasirandom Monte Carlo methods over pseudorandom algorithms or grid-based techniques are retained. Tests with several parallel supercomputers demonstrate that as many as 10⁶integration points (up to 6 dimensions) can be generated per second per node in the optimal case where the number of nodes is a power of 2. The speed of communication-free parallel Sobol' sequence generators and the rapid convergence properties of quasirandom Monte Carlo schemes indicate that the method described here may be gainfully applied to a wide range of problems.     

Fault detection and isolation in non-linear stochastic systems—A combined adaptive Monte Carlo filtering and likelihood ratio approach

This paper presents the development of a new method for solving fault detection and isolation (FDI) problem in general non-linear stochastic systems. In this paper, the faults are modelled as unknown changes in system parameters and adaptive Monte Carlo filtering approach is used in deriving an FDI scheme. Essentially, a set of adaptive Monte Carlo filters are designed based on the augmented system models along with a nominal Monte Carlo filter designed based on the nominal system model. The likelihood functions of the observations are then evaluated using the particles from these (adaptive) Monte Carlo filters and FDI is eventually achieved via the likelihood ratio test. The simulation results on a highly non-linear system are provided which demonstrates the effectiveness of the proposed method.     

Computation of global illumination in a participating medium by monte carlo simulation

This paper discusses techniques for the computation of global illumination in environments with a participating medium using a Monte Carlo simulation of the particle model of light. Efficient algorithms and data structures for tracking the particles inside the volume have been developed. The necessary equation for computing the illumination along any given direction has been derived for rendering a scene with a participating medium. A major issue in any Monte Carlo simulation is the uncertainty in the final simulation results. Various steps of the algorithm have been analysed to identify major sources of uncertainty. To reduce the uncertainty, suitable modifications to the simulation algorithm have been suggested using variance reduction methods of forced collision, absorption suppression and particle divergence. Some sample scenes showing the results of applying these methods are also included.     

A bootstrap goodness of fit test for the generalized Pareto distribution

This paper proposes a bootstrap goodness of fit test for the Generalized Pareto distribution (GPd) with shape parameter γ. The proposed test is an intersection–union test which tests separately the cases of γ≥0 and γ<0 and rejects if both cases are rejected. If the test does not reject, then it is known whether the shape parameter γ is either positive or negative. A Monte Carlo simulation experiment was conducted to assess the power of performance of the intersection–union test. The GPd hypothesis was tested on a data set containing Mexico City’s ozone levels. ¹     

Condition for relaxed Monte Carlo method of solving systems of linear equations

In this paper, we point out the limitation of the paper entitled “Solving Systems of Linear Equations with Relaxed Monte Carlo Method” published in this journal (Tan in J. Supercomput. 22:113–123, 2002). We argue that the relaxed Monte Carlo method presented in Sect. 7 of the paper is only correct under the condition that the coefficient matrix A must be diagonal dominate. However, for nondiagonal dominate case; the corresponding Neumann series may diverge, which would lead to infinite loop when simulating the iterative Monte Carlo algorithm. In this paper, we first prove that only for the diagonal dominate matrix, the corresponding von Neumann series can converge, and the Monte Carlo algorithm can be relaxed. Therefore, it is not true for nondiagonal dominate matrix, no matter the relaxed parameter γ is a single value or a set of values. We then present and analyze the numerical experiment results to verify our arguments.     

A Quantum Monte Carlo method at fixed energy

In this paper we explore ways to study the zero temperature limit of quantum statistical mechanics using Quantum Monte Carlo simulations. We develop a Quantum Monte Carlo method in which one fixes the ground state energy as a parameter. The Hamiltonians we consider are of the form H=H₀+λV with ground state energy E. For fixed H₀ and V, one can view E as a function of λ whereas we view λ as a function of E. We fix E and define a path integral Quantum Monte Carlo method in which a path makes no reference to the times (discrete or continuous) at which transitions occur between states. For fixed E we can determine λ(E) and other ground state properties of H.     

Efficient estimation of distance‐dependent metrics in edge‐failing networks

This article introduces a method for estimating performability metrics built upon non‐binary network states, determined by the hop distances between distinguished nodes. The estimation is performed by a Monte Carlo simulation where the sampling space is reduced using edge sets known as d‐pathsets and d‐cutsets. Numerical experiments over two mesh‐like networks are presented. They show significant efficiency improvements relative to the crude Monte Carlo method, in particular as link failures become rarer events, which is usually the case in most real communication networks.     

Quantum Monte Carlo simulations of antiferromagnetism in ultracold fermions on optical lattices within real-space dynamical mean-field theory

We present a massively parallel quantum Monte Carlo based implementation of real-space dynamical mean-field theory for general inhomogeneous correlated fermionic lattice systems. As a first application, we study magnetic order in a binary mixture of repulsively interacting fermionic atoms harmonically trapped in an optical lattice. We explore temperature effects and establish signatures of the Néel transition in observables directly accessible in cold-atom experiments; entropy estimates are also provided. We demonstrate that the local density approximation (LDA) fails for ordered phases. In contrast, a “slab” approximation allows us to reach experimental system sizes with O(¹⁰⁵) atoms without significant loss of accuracy.     

WTO — a deterministic approach to 4-fermion physics

The program WTO, which is designed for computing cross sections and other relevant observables in the e⁺e⁻ annihilation into four fermions, is described. The various quantities are computed over both a completely inclusive experimental set-up and a realistic one, i.e. with cuts on the final state energies, final state angles, scattering angles and final state invariant masses. Initial state QED corrections are included by means of the structure function approach while final state QCD corrections are applicable in their naive formulation. A gauge restoring mechanism is included according to the Fermion-Loop scheme. The program structure is highly modular and particular care has been devoted to computing efficiency and speed.     

Regression analysis between environmental factors and earthquake-damaged trace: a case study in Wenchuan County,China

This article discusses the integration of remote sensing (RS), geographic information system (GIS), GPS and ground survey technologies to establish the accuracy of supervised classification. N _e, the proportion of earthquake-damaged trace in a specific region, as a relative value expresses the influence of the characteristics of an area on the distribution of earthquake-damaged trace; it reflects the earthquake-damaged trace's distribution characteristics better. Four factors – distance to central fault, slope, elevation and distance to river – were selected to quantify the association between environmental factors and N _e by regression analysis. The results show the following. (1) The association between N _e and distance to river (R ²?=?0.99) and between N _e and distance to central fault (R ²?=?1.00) is better modelled by an inverse second-order line. N _e is largest within 0.5 km of the river and within 5 km of the central fault. When the distance is more than 2.0 km from the river and more than 30 km from the central fault, N _e dramatically decreases. (2) The association between N _e and elevation (R ²?=?0.94) is better modelled by the exponential decay line. With an increasing elevation, N _e decreases with the weakening of human activities. (3) The association between N _e and slope (R ²?=?0.93) is better modelled by exponential growth. With an increasing slope, N _e first decreases and then increases. (4) A possible mechanism is that the earthquake energy first acts on the area near the central fault. The erosion of the river leads to a steep slope; the unstable geologic structure is easily destroyed by the effect of seismic waves. Consequently, earthquake-damaged trace and N _e are greater in regions near the central fault and river bank than in other regions.     

Improving Markov Chain Monte Carlo Model Search for Data Mining

The motivation of this paper is the application of MCMC model scoring procedures to data mining problems, involving a large number of competing models and other relevant model choice aspects.To achieve this aim we analyze one of the most popular Markov Chain Monte Carlo methods for structural learning in graphical models, namely, the MC ³ algorithm proposed by D. Madigan and J. York (International Statistical Review, 63, 215–232, 1995). Our aim is to improve their algorithm to make it an effective and reliable tool in the field of data mining. In such context, typically highly dimensional in the number of variables, little can be known a priori and, therefore, a good model search algorithm is crucial.We present and describe in detail our implementation of the MC ³ algorithm, which provides an efficient general framework for computations with both Directed Acyclic Graphical (DAG) models and Undirected Decomposable Models (UDG). We believe that the possibility of commuting easily between the two classes of models constitutes an important asset in data mining, where an a priori knowledge of causal effects is usually difficult to establish.Furthermore, in order to improve the MC ³ method we propose provide several graphical monitors which can help extracting results and assessing the goodness of the Markov chain Monte Carlo approximation to the posterior distribution of interest.We apply our proposed methodology first to the well-known coronary heart disease dataset (D. Edwards &; T. Havránek, Biometrika, 72:2, 339–351, 1985). We then introduce a novel data mining application which concerns market basket analysis.