Bayesian nonparametric tests via sliced inverse modeling

We study the problem of independence and conditional independence tests between categorical covariates and a continuous response variable, which has an immediate application in genetics. Instead of estimating the conditional distribution of the response given values of covariates, we model the conditional distribution of covariates given the discretized response (aka "slices"). By assigning a prior probability to each possible discretization scheme, we can compute efficiently a Bayes factor (BF)-statistic for the independence (or conditional independence) test using a dynamic programming algorithm. Asymptotic and finite-sample properties such as power and null distribution of the BF statistic are studied, and a stepwise variable selection method based on the BF statistic is further developed. We compare the BF statistic with some existing classical methods and demonstrate its statistical power through extensive simulation studies. We apply the proposed method to a mouse genetics data set aiming to detect quantitative trait loci (QTLs) and obtain promising results.Comment: 32 pages, 7 figure

Monte-Carlo Simulations of Spin-Crossover Phenomena Based on a Vibronic Ising-like Model with Realistic Parameters

Materials with spin-crossover (SCO) properties hold great potentials in information storage and therefore have received a lot of concerns in the recent decades. The hysteresis phenomena accompanying SCO is attributed to the intermolecular cooperativity whose underlying mechanism may have a vibronic origin. In this work, a new vibronic Ising-like model in which the elastic coupling between SCO centers is included by considering harmonic stretching and bending (SAB) interactions is proposed and solved by Monte Carlo simulations. The key parameters in the new model, $k_1$ and $k_2$, corresponding to the elastic constant of the stretching and bending mode, respectively, can be directly related to the macroscopic bulk and shear modulus of the material in study, which can be readily estimated either based on experimental measurements or first-principles calculations. The convergence issue in the MC simulations of the thermal hysteresis has been carefully checked, and it was found that the stable hysteresis loop can be more readily obtained when using the SAB model compared to that using the Wajnflasz-Pick model. Using realistic parameters estimated based on first-principles calculations of a specific polymeric coordination SCO compound, [Fe(pz)Pt(CN)$_4$]$\cdot$2H$_2$O, temperature-induced hysteresis and pressure effects on SCO phenomena are simulated successfully.Comment: 8 pages, 8 figure

On the nonintegrability of equations for long- and short-wave interactions

We examine the integrability of two models used for the interaction of long and short waves in dispersive media. One is more classical but arguably cannot be derived from the underlying water wave equations, while the other one was recently derived. We use the method of Zakharov and Schulman to attempt to construct conserved quantities for these systems at different orders in the magnitude of the solutions. The coupled KdV-NLS model is shown to be nonintegrable, due to the presence of fourth-order resonances. A coupled real KdV - complex KdV system is shown to suffer the same fate, except for three special choices of the coefficients, where higher-order calculations or a different approach are necessary to conclude integrability or the absence thereof.Comment: 9 pages, presented as a poster at The Tenth IMACS International Conference on Nonlinear Evolution Equations and Wave Phenomena: Computation and Theor