Y. S. Hung | Searcharxiv

arXiv2023

K-Essence Induced by Derivative Couplings of the Inflaton

We consider two models which couple derivatives of the inflaton to ordinary matter, both to fermions and to scalars. Such couplings induce changes to the inflaton kinetic energy, analogous to the cosmological Coleman-Weinberg potentials which come from nonderivative couplings. Our purpose is to investigate whether these quantum-induced K-Essence models can provide efficient reheating without affecting the observational constraints on primordial inflation. Our numerical studies show that it is difficult to preserve both properties.

gr-qc↗

arXiv2010

Comparison of Spearman's rho and Kendall's tau in Normal and Contaminated Normal Models

This paper analyzes the performances of the Spearman's rho (SR) and Kendall's tau (KT) with respect to samples drawn from bivariate normal and bivariate contaminated normal populations. The exact analytical formulae of the variance of SR and the covariance between SR and KT are obtained based on the Childs's reduction formula for the quadrivariate normal positive orthant probabilities. Close form expressions with respect to the expectations of SR and KT are established under the bivariate contaminated normal models. The bias, mean square error (MSE) and asymptotic relative efficiency (ARE) of the three estimators based on SR and KT to the Pearson's product moment correlation coefficient (PPMCC) are investigated in both the normal and contaminated normal models. Theoretical and simulation results suggest that, contrary to the opinion of equivalence between SR and KT in some literature, the behaviors of SR and KT are strikingly different in the aspects of bias effect, variance, mean square error, and asymptotic relative efficiency. The new findings revealed in this work provide not only deeper insights into the two most widely used rank based correlation coefficients, but also a guidance for choosing which one to use under the circumstances where the PPMCC fails to apply.

cs.IT↗