FULLY EXPONENTIAL LAPLACE APPROXIMATION EM ALGORITHM FOR NONLINEAR MIXED EFFECTS MODELS

Nonlinear mixed effects models provide a flexible and powerful platform for the analysis of clustered data that arise in numerous fields, such as pharmacology, biology, agriculture, forestry, and economics. This dissertation focuses on fitting parametric nonlinear mixed effects models with single- and multi-level random effects. A new, efficient, and accurate method that gives an error of order O(1/n2), fully exponential Laplace approximation EM algorithm (FELA-EM), for obtaining restricted maximum likelihood (REML) estimates in nonlinear mixed effects models is developed. Sample codes for implementing FELA-EM algorithm in R are given. Simulation studies have been conducted to evaluate the accuracy of the new approach and compare it with the Laplace approximation as well as four different linearization methods for fitting nonlinear mixed effects models with single-level and two-crossed-level random effects. Of all approximations considered in the thesis, FELA-EM algorithm is the only one that gives unbiased or close-to-unbiased (%Bias \u3c 1%) estimates for both the fixed effects and variance-covariance parameters. Finally, FELA-EM algorithm is applied to a real dataset to model feeding pigs’ body temperature and a unified strategy for building crossed and nested nonlinear mixed effects models with treatments and covariates is provided

Frame dependence of transition form factors in light-front dynamics

We study the radiative transitions between vector and pseudoscalar quarkonia in the light-front Hamiltonian approach, and investigate the effects of using different current component and different reference frames. In practical calculations with truncated Fock spaces, transition form factors may acquire current component dependence and frame dependence, and such dependences could serve as a measure for the Lorentz symmetry violation. We suggest using the transverse current with $m_j=0$ state of the vector meson, since this procedure employs the dominant spin components of the light-front wavefunctions and is more robust in practical calculations. We calculate the transition form factor between vector and pseudoscalar quarkonia and investigate the frame dependence with light-front wavefunctions calculated from the valence Fock sector. We suggest using frames with minimal longitudinal momentum transfer for calculations in the valence Fock sector, namely the Drell-Yan frame for the space-like region and a specific longitudinal frame for the timelike region; at $q^2=0$ these two frames give the same result

Mesons on the light front

This lecture note is written for 'Courses on Light-Cone Techniques applied to QCD', Nov 21-25, 2022, IGFAE. It is intended to provide basic knowledge and selective perspectives on the application of light-front Hamiltonian approach to mesons in two 1.5-hour lectures

Assessing QT prolongation and electrocardiography restitution using a beat-to-beat method

Historically, the heart rate corrected QT (QTc) interval has been the standard method to assess for impaired ventricular repolarization, particularly for drug development. However, QTc does not reflect changes in autonomic state or QT-RR hysteresis which can also affect the interpretation of arrhythmogenic risk. With the advent of more accurate algorithms to automatically measure the QT interval from continuously collected digital ECG data, usage of heart rate corrected functions is no longer necessary. The dynamic beat-to-beat QT interval method compares the QT interval to individual cardiac cycles from all normal autonomic states at similar RR intervals, thus eliminating the need for correction functions. The upper 97.5% reference boundary of these beat-to-beat QT interval values is defined across the entire 24-hour RR interval range. Beats with QT intervals exceeding this limit are flagged as outlier beats for further arrhythmia vulnerability assessment. The same beat-to-beat technique can also be used to assess the QT-TQ interval relationship known as ECG restitution. This analysis potentially provides an additional means to quantify cardiac stress or arrhythmia vulnerability as the heart works more in relationship to each rest cycle. (Cardiol J 2010; 17, 3: 230-243

Anisotropic flow and the valence quark skeleton of hadrons

We study transverse momentum anisotropies, in particular, the elliptic flow $v_2$ due to the interference effect sourced by valence quarks in high-energy hadron-hadron collisions. Our main formula is derived as the high-energy (eikonal) limit of the impact-parameter dependent cross section in quantum field theory, which agrees with that in terms of the impact parameter in the classical picture. As a quantitative assessment of the interference effect, we calculate $v_2$ in the azimuthal distribution of gluons at a comprehensive coverage of the impact parameter and the transverse momentum in high-energy pion-pion collisions. In a broad range of the impact parameter, a sizable amount of $v_2$, comparable with that produced due to saturated dense gluons or final-state interactions, is found to develop. In our calculations, the valence sector of the pion wave function is obtained numerically from the Basis Light-Front Quantization, a non-perturbative light-front Hamiltonian approach. And our formalism is generic and can be applied to other small collision systems like proton-proton collisions

Two-photon transitions of charmonia on the light front

We investigate the two-photon transitions H-c (C) over bar -> gamma*gamma of the charmonium system in light-front dynamics. The light-front wave functions were obtained from solving the effective Hamiltonian based on light-front holography and one-gluon exchange interaction within the basis light-front quantization approach. We compute the two-photon transition form factors as well as the two-photon decay widths for S- and P-wave charmonia, eta(c) and chi(cJ) and their excitations. Without introducing any free parameters, our predictions are in good agreement with the recent experimental measurements by BABAR and Belle, shedding light on the relativistic nature of charmonium.Peer reviewe