An Efficient Modified "Walk On Spheres" Algorithm for the Linearized Poisson-Boltzmann Equation

A discrete random walk method on grids was proposed and used to solve the linearized Poisson-Boltzmann equation (LPBE) \cite{Rammile}. Here, we present a new and efficient grid-free random walk method. Based on a modified `` Walk On Spheres" (WOS) algorithm \cite{Elepov-Mihailov1973} for the LPBE, this Monte Carlo algorithm uses a survival probability distribution function for the random walker in a continuous and free diffusion region. The new simulation method is illustrated by computing four analytically solvable problems. In all cases, excellent agreement is observed.Comment: 12 pages, 5 figure

Improved Combinatorial Group Testing Algorithms for Real-World Problem Sizes

We study practically efficient methods for performing combinatorial group testing. We present efficient non-adaptive and two-stage combinatorial group testing algorithms, which identify the at most d items out of a given set of n items that are defective, using fewer tests for all practical set sizes. For example, our two-stage algorithm matches the information theoretic lower bound for the number of tests in a combinatorial group testing regimen.Comment: 18 pages; an abbreviated version of this paper is to appear at the 9th Worksh. Algorithms and Data Structure

A constraint on the formation timescale of the young open cluster NGC 2264: Lithium abundance of pre-main sequence stars

The timescale of cluster formation is an essential parameter in order to understand the formation process of star clusters. Pre-main sequence (PMS) stars in nearby young open clusters reveal a large spread in brightness. If the spread were considered as a result of a real spread in age, the corresponding cluster formation timescale would be about 5 -- 20 Myr. Hence it could be interpreted that star formation in an open cluster is prolonged for up to a few tens of Myr. However, difficulties in reddening correction, observational errors, and systematic uncertainties introduced by imperfect evolutionary models for PMS stars, can result in an artificial age spread. Alternatively, we can utilize Li abundance as a relative age indicator of PMS star to determine the cluster formation timescale. The optical spectra of 134 PMS stars in NGC 2264 have been obtained with MMT/Hectochelle. The equivalent widths have been measured for 86 PMS stars with a detectable Li line (3500 < T_eff [K] <= 6500). Li abundance under the condition of local thermodynamic equilibrium (LTE) was derived using the conventional curve of growth method. After correction for non-LTE effects, we find that the initial Li abundance of NGC 2264 is A(Li) = 3.2 +/- 0.2. From the distribution of the Li abundances, the underlying age spread of the visible PMS stars is estimated to be about 3 -- 4 Myr and this, together with the presence of embedded populations in NGC 2264, suggests that the cluster formed on a timescale shorter than 5 Myr.Comment: 53 pages, 12 figures, 4 tables, Accepted for publication in the Astrophysical Journa

Forecasting Value-at-Risk Using Nonlinear Regression Quantiles and the Intra-day Range

Value-at-Risk (VaR) is commonly used for financial risk measurement. It has recently become even more important, especially during the 2008-09 global financial crisis. We propose some novel nonlinear threshold conditional autoregressive VaR (CAViaR) models that incorporate intra-day price ranges. Model estimation and inference are performed using the Bayesian approach via the link with the Skewed-Laplace distribution. We examine how a range of risk models perform during the 2008-09 financial crisis, and evaluate how the crisis affects the performance of risk models via forecasting VaR. Empirical analysis is conducted on five Asia-Pacific Economic Cooperation stock market indices as well as two exchange rate series. We examine violation rates, back-testing criteria, market risk charges and quantile loss function values to measure and assess the forecasting performance of a variety of risk models. The proposed threshold CAViaR model, incorporating range information, is shown to forecast VaR more efficiently than other models, across the series considered, which should be useful for financial practitioners.Value-at-Risk; CAViaR model; Skewed-Laplace distribution; intra-day range; backtesting; Markov chain Monte Carlo

Forecasting Value-at-Risk Using Nonlinear Regression Quantiles and the Intra-day Range

Value-at-Risk (VaR) is commonly used for financial risk measurement. It has recently become even more important, especially during the 2008-09 global financial crisis. We pro- pose some novel nonlinear threshold conditional autoregressive VaR (CAViaR) models that incorporate intra-day price ranges. Model estimation and inference are performed using the Bayesian approach via the link with the Skewed-Laplace distribution. We examine how a range of risk models perform during the 2008-09 financial crisis, and evaluate how the crisis aects the performance of risk models via forecasting VaR. Empirical analysis is conducted on five Asia-Pacific Economic Cooperation stock market indices as well as two exchange rate series. We examine violation rates, back-testing criteria, market risk charges and quantile loss function values to measure and assess the forecasting performance of a variety of risk models. The proposed threshold CAViaR model, incorporating range information, is shown to forecast VaR more eficiently than other models, across the series considered, which should be useful for financial practitioners.Value-at-Risk; CAViaR model; Skewed-Laplace distribution; intra-day range; backtesting, Markov chain Monte Carlo.

Is the Compact Source at the Center of Cas A Pulsed?

A 50 ksec observation of the Supernova Remnant Cas A was taken using the Chandra X-Ray Observatory High Resolution Camera (HRC) to search for periodic signals from the compact source located near the center. Using the HRC-S in imaging mode, problems with correctly assigning times to events were overcome, allowing the period search to be extended to higher frequencies than possible with previous observations. In an extensive analysis of the HRC data, several possible candidate signals are found using various algorithms, including advanced techniques developed by Ransom to search for low significance periodic signals. Of the candidate periods, none is at a high enough confidence level to be particularly favored over the rest. When combined with other information, however (e.g., spectra, total energetics, and the historical age of the remnant), a 12 ms candidate period seems to be more physically plausible than the others, and we use it for illustrative purposes in discussing the possible properties of a putative neutron star in the remnant. We emphasize that this is not necessarily the true period, and that a follow-up observation, scheduled for the fall of 2001, is required. A 50 ksec Advanced CCD Imaging Spectrometer (ACIS) observation was taken, and analysis of these data for the central object shows that the spectrum is consistent with several forms, and that the emitted X-ray luminosity in the 0.1 -10 keV band is 10^{33}-10^{35}erg cm^{-2}sec^{-1} depending on the spectral model and the interstellar absorption along the line of sight to the source.Comment: 14 pages, 3 figures Submitted to ApJ 2001 June 2

Effect of time-varying flow-shear on the nonlinear stability of the boundary of magnetized toroidal plasmas

We propose a phenomenological yet general model in a form of extended complex Ginzburg-Landau equation to understand edge-localized modes (ELMs), a class of quasi-periodic fluid instabilities in the boundary of toroidal magnetized high-temperature plasmas. The model reproduces key dynamical features of the ELMs (except the final explosive relaxation stage) observed in the high-confinement state plasmas on the Korea Superconducting Tokamak Advanced Research: quasi-steady states characterized by field-aligned filamentary eigenmodes, transitions between different quasi-steady eigenmodes, and rapid transition to non-modal filamentary structure prior to the relaxation. It is found that the inclusion of time-varying perpendicular sheared flow is crucial for reproducing all of the observed dynamical features

Quantum Dot Potentials: Symanzik Scaling, Resurgent Expansions and Quantum Dynamics

This article is concerned with a special class of the ``double-well-like'' potentials that occur naturally in the analysis of finite quantum systems. Special attention is paid, in particular, to the so-called Fokker-Planck potential, which has a particular property: the perturbation series for the ground-state energy vanishes to all orders in the coupling parameter, but the actual ground-state energy is positive and dominated by instanton configurations of the form exp(-a/g), where a is the instanton action. The instanton effects are most naturally taken into account within the modified Bohr-Sommerfeld quantization conditions whose expansion leads to the generalized perturbative expansions (so-called resurgent expansions) for the energy values of the Fokker-Planck potential. Until now, these resurgent expansions have been mainly applied for small values of coupling parameter g, while much less attention has been paid to the strong-coupling regime. In this contribution, we compare the energy values, obtained by directly resumming generalized Bohr-Sommerfeld quantization conditions, to the strong-coupling expansion, for which we determine the first few expansion coefficients in powers of g^(-2/3). Detailed calculations are performed for a wide range of coupling parameters g and indicate a considerable overlap between the regions of validity of the weak-coupling resurgent series and of the strong-coupling expansion. Apart from the analysis of the energy spectrum of the Fokker-Planck Hamiltonian, we also briefly discuss the computation of its eigenfunctions. These eigenfunctions may be utilized for the numerical integration of the (single-particle) time-dependent Schroedinger equation and, hence, for studying the dynamical evolution of the wavepackets in the double-well-like potentials.Comment: 13 pages; RevTe