Initialisation from lattice Boltzmann to multi-step Finite Difference methods: modified equations and discrete observability

Latitude on the choice of initialisation is a shared feature between one-step extended state-space and multi-step methods. The paper focuses on lattice Boltzmann schemes, which can be interpreted as examples of both previous categories of numerical schemes. We propose a modified equation analysis of the initialisation schemes for lattice Boltzmann methods, determined by the choice of initial data. These modified equations provide guidelines to devise and analyze the initialisation in terms of order of consistency with respect to the target Cauchy problem and time smoothness of the numericalsolution. In detail, the larger the number of matched terms between modified equations for initialisation and bulk methods, the smoother the obtained numerical solution. This is particularly manifest for numerical dissipation. Starting from the constraints to achieve time smoothness, which can quickly become prohibitive, we explain how the distinct lack of observability for certain lattice Boltzmann schemes -- seen as dynamical systems on a commutative ring -- can yield rather simple conditions and be easily studied as far as their initialisation is concerned. This comes from the reduced numberof initialisation schemes at the fully discrete level. These theoretical results are successfully assessed on several lattice Boltzmann methods

Semi-analytic approximations for production of atmospheric muons and neutrinos

Simple approximations for fluxes of atmospheric muons and muon neutrinos are developed which display explicitly how the fluxes depend on primary cosmic ray energy and on features of pion production. For energies of approximately 10 GeV and above the results are sufficiently accurate to calculate response functions and to use for estimates of systematic uncertainties.Comment: 15 pages with 8 figure

Support Vector Machines for Credit Scoring and discovery of significant features

The assessment of risk of default on credit is important for financial institutions. Logistic regression and discriminant analysis are techniques traditionally used in credit scoring for determining likelihood to default based on consumer application and credit reference agency data. We test support vector machines against these traditional methods on a large credit card database. We find that they are competitive and can be used as the basis of a feature selection method to discover those features that are most significant in determining risk of default. 1

Variations on KamLAND: likelihood analysis and frequentist confidence regions

In this letter the robustness of the first results from the KamLAND reactor neutrino experiment with respect to variations in the statistical analysis is considered. It is shown that an event-by-event based likelhood analysis provides a more powerful tool to extract information from the currently available data sample than a least-squares method based on energy binned data. Furthermore, a frequentist analysis of KamLAND data is performed. Confidence regions with correct coverage in the plane of the oscillation parameters are calculated by means of a Monte Carlo simulation. I find that the results of the usually adopted $\chi^2$-cut approximation are in reasonable agreement with the exact confidence regions, however, quantitative differences are detected. Finally, although the current data is consistent with an energy independent flux suppression, a $\sim 2\sigma$ indication in favour of oscillations can be stated, implying quantum mechanical interference over distances of the order of 200 km.Comment: New figure added and discussion of results extended, version to appear in Phys. Lett. B, 14 pages, 5 figure

A Compilation of High Energy Atmospheric Muon Data at Sea Level

We collect and combine all published data on the vertical atmospheric muon flux and the muon charge ratio for muon momenta above 10 GeV. At sea level the world average of the momentum spectra agrees with the flux calculated by E.V. Bugaev et al. within 15%. The observed shape of the differential flux versus momentum is slightly flatter than predicted in this calculation. The experimental accuracy varies from 7% at 10 GeV to 17% at 1 TeV. The ratio of fluxes of positive to negative muons is found to be constant, at a value of 1.268, with relative uncertainties increasing from approximately 1% at low momenta to about 6% at 300 GeV

An Experimentalist's View of Neutrino Oscillations

Neutrinos, and primarily neutrino oscillations, have undoubtedly been one of the most exciting topics in the field of high-energy physics over the past few years. The existence of neutrino oscillations would require an extension of the currently accepted description of sub-nuclear phenomena beyond the Standard Model. Compelling evidence of new physics, which seems to be pointing towards neutrino oscillations, is coming from the solar neutrino deficit and from the atmospheric neutrino anomaly. More controversial effects have been observed with artificially produced neutrinos. The present experimental status of neutrino oscillations is reviewed, as well as the planned future experimental programme, which, it is hoped, will solve most of the outstanding puzzles.Comment: 64 pages, 29 figures, to be published in Intern. J. Mod. Phys. A (2001

Consumer Credit-Risk Models Via Machine-Learning Algorithms

We apply machine-learning techniques to construct nonlinear nonparametric forecasting models of consumer credit risk. By combining customer transactions and credit bureau data from January 2005 to April 2009 for a sample of a major commercial bank’s customers, we are able to construct out-of-sample forecasts that significantly improve the classification rates of credit-card-holder delinquencies and defaults, with linear regression R2’s of forecasted/realized delinquencies of 85%. Using conservative assumptions for the costs and benefits of cutting credit lines based on machine-learning forecasts, we estimate the cost savings to range from 6% to 25% of total losses. Moreover, the time-series patterns of estimated delinquency rates from this model over the course of the recent financial crisis suggest that aggregated consumer credit-risk analytics may have important applications in forecasting systemic risk.Massachusetts Institute of Technology. Laboratory for Financial EngineeringMassachusetts Institute of Technology. Center for Future Bankin