Scattering and Bound States of a Deformed Quantum Mechanics

We construct the exact position representation of a deformed quantum mechanics which exhibits an intrinsic maximum momentum and use it to study problems such as a particle in a box and scattering from a step potential, among others. In particular, we show that unlike usual quantum mechanics, the present deformed case delays the formation of bound states in a finite potential well. In the process we also highlight some limitations and pit-falls of low-momentum or perturbative treatments and thus resolve two puzzles occurring in the literature

Generalized Relativistic Wave Equations with Intrinsic Maximum Momentum

We examine the nonperturbative effect of maximum momentum on the relativistic wave equations. In momentum representation, we obtain the exact eigen-energies and wavefunctions of one-dimensional Klein-Gordon and Dirac equation with linear confining potentials, and the Dirac oscillator. Bound state solutions are only possible when the strength of scalar potential are stronger than vector potential. The energy spectrum of the systems studied are bounded from above, whereby classical characteristics are observed in the uncertainties of position and momentum operators. Also, there is a truncation in the maximum number of bound states that is allowed. Some of these quantum-gravitational features may have future applications.Comment: 20 pages, 4 figure

The Constraints and Spectra of a Deformed Quantum Mechanics

We examine a deformed quantum mechanics in which the commutator between coordinates and momenta is a function of momenta. The Jacobi identity constraint on a two-parameter class of such modified commutation relations (MCR's) shows that they encode an intrinsic maximum momentum; a sub-class of which also imply a minimum position uncertainty. Maximum momentum causes the bound state spectrum of the one-dimensional harmonic oscillator to terminate at finite energy, whereby classical characteristics are observed for the studied cases. We then use a semi-classical analysis to discuss general concave potentials in one dimension and isotropic power-law potentials in higher dimensions. Among other conclusions, we find that in a subset of the studied MCR's, the leading order energy shifts of bound states are of opposite sign compared to those obtained using string-theory motivated MCR's, and thus these two cases are more easily distinguishable in potential experiments.Comment: 30 pages inclusive of 7 figure

Detection of Gravitational Wave - An Application of Relativistic Quantum Information Theory

We show that a passing gravitational wave may influence the spin entropy and spin negativity of a system of $N$ massive spin-1/2 particles, in a way that is characteristic of the radiation. We establish the specific conditions under which this effect may be nonzero. The change in spin entropy and negativity, however, is extremely small. Here, we propose and show that this effect may be amplified through entanglement swapping. Relativistic quantum information theory may have a contribution towards the detection of gravitational wave.Comment: 9 page

Real-world experience of first-line afatinib in patients with EGFR-mutant advanced NSCLC: a multicenter observational study

Background: This study aimed to evaluate the efficacy, side-effects and resistance mechanisms of first-line afatinib in a real-world setting. Methods: This is a multicenter observational study of first-line afatinib in Malaysian patients with epidermal growth factor receptor (EGFR)-mutant advanced non-small cell lung cancer (NSCLC). Patients’ demographic, clinical and treatment data, as well as resistance mechanisms to afatinib were retrospectively captured. The statistical methods included Chi-squared test and independent t-test for variables, Kaplan-Meier curve and log-rank test for survival, and Cox regression model for multivariate analysis. Results: Eighty-five patients on first-line afatinib from 1st October 2014 to 30th April 2018 were eligible for the study. EGFR mutations detected in tumors included exon 19 deletion in 80.0%, exon 21 L858R point mutation in 12.9%, and rare or complex EGFR mutations in 7.1% of patients. Among these patients, 18.8% had Eastern Cooperative Oncology Group performance status of 2–4, 29.4% had symptomatic brain metastases and 17.6% had abnormal organ function. Afatinib 40 mg or 30 mg once daily were the most common starting and maintenance doses. Only one-tenth of patients experienced severe side-effects with none having grade 4 toxicities. The objective response rate was 76.5% while the disease control rate was 95.3%. At the time of analysis, 56 (65.9%) patients had progression of disease (PD) with a median progression-free survival (mPFS) of 14.2 months (95% CI, 11.85–16.55 months). Only 12.5% of the progressed patients developed new symptomatic brain metastases. The overall survival (OS) data was not mature. Thirty-three (38.8%) patients had died with a median OS of 28.9 months (95% CI, 19.82–37.99 months). The median follow-up period for the survivors was 20.0 months (95% CI, 17.49–22.51 months). Of patients with PD while on afatinib, 55.3% were investigated for resistance mechanisms with exon 20 T790M mutation detected in 42.0% of them. Conclusions: Afatinib is an effective first-line treatment for patients with EGFR-mutant advanced NSCLC with a good response rate and long survival, even in patients with unfavorable clinical characteristics. The side-effects of afatinib were manageable and T790 M mutation was the most common resistance mechanism causing treatment failure

Rate of brain aging associates with future executive function in Asian children and older adults

Brain age has emerged as a powerful tool to understand neuroanatomical aging and its link to health outcomes like cognition. However, there remains a lack of studies investigating the rate of brain aging and its relationship to cognition. Furthermore, most brain age models are trained and tested on cross-sectional data from primarily Caucasian, adult participants. It is thus unclear how well these models generalize to non-Caucasian participants, especially children. Here, we tested a previously published deep learning model on Singaporean elderly participants (55−88 years old) and children (4−11 years old). We found that the model directly generalized to the elderly participants, but model finetuning was necessary for children. After finetuning, we found that the rate of change in brain age gap was associated with future executive function performance in both elderly participants and children. We further found that lateral ventricles and frontal areas contributed to brain age prediction in elderly participants, while white matter and posterior brain regions were more important in predicting brain age of children. Taken together, our results suggest that there is potential for generalizing brain age models to diverse populations. Moreover, the longitudinal change in brain age gap reflects developing and aging processes in the brain, relating to future cognitive function