Using the Asymmetric Gaussian Method to Interpret the Electronic Spectroscopy of the Olivine Family

This paper discusses the mathematical aspects of band fitting and introduces the Asymmetric Gaussian curve and its tangent space for the first time. First, we derive an equation for an Asymmetric Gaussian shape. We then derive a rule for the resolution of two Gaussian shaped bands. We then use the Asymmetrical Gaussian equation to derive a Master Equation to fit two overlapping bands. We identify regions of the fitting space where the Asymmetric Gaussian fit is optimal, sub optimal and not optimal. We then demonstrate the use of the Asymmetric Gaussian curve to fit four overlapping Gaussian bands, and show how this is relevant to the olivine family spectral complex at 1 μm. We develop a modified model of the olivine family spectral complex based on previous work by Runciman and Burns. The limitations of the asymmetric band fitting method and a critical assessment of three commonly used numerical minimization methods are also provided.

A.2 Clinical application of T1-w/T2-w ratio images for in vivo comparisons of myelin content in patients with trigeminal neuralgia

Background: Novel magnetic resonance (MR) imaging techniques prompted the emergence of T1-w/T2-w images or “myelin-sensitive maps (MMs)” to measure myelin in vivo. However, acquisition-related variations in MR intensities prevent meaningful quantitative comparisons between MMs. We propose an improved pipeline to standardize MMs that is applied to patients with classic trigeminal neuralgia (CTN) and trigeminal neuralgia secondary to multiple sclerosis (MSTN). Methods: 3T scanner was used to obtain T1-w and T2-w images for 17 CTN and 17 MSTN patients. Template images were obtained from ICBM152 database. MS plaques and normal-appearing white matter (NAWM) were labelled. A Gaussian curve-fit was applied to the histogram of the intensity distribution of each patient image, and transformed to match the Gaussian curve-fit of the template image. Results: MM intensities were decreased within MS plaques, compared to NAWM in MSTN patients (p<0.001) and its corresponding regions in CTN patients (p<0.001). Qualitatively, the standardized patient image and its histogram better resembled the ICBM152 template. Conclusions: MM analysis revealed reduced myelin content in MS plaques compared to corresponding regions in CTN patients and surrounding NAWM in MSTN patients. The standardized MM serves as a non-invasive, clinical tool for quantitative analyses of myelin content between different brain regions and different patients in vivo.

Forecasting American COVID-19 Cases and Deaths through Machine Learning (Preprint)

UNSTRUCTURED COVID-19 has become a great national security problem for the United States and many other countries, where public policy and healthcare decisions are based on the several models for the prediction of the future deaths and cases of COVID-19. While the most commonly used models for COVID-19 include epidemiological models and Gaussian curve-fitting models, recent literature has indicated that these models could be improved by incorporating machine learning. However, within this research on potential machine learning models for COVID-19 forecasting, there has been a large emphasis on providing an array of different types of machine learning models rather than optimizing a single one. In this research, we suggest and optimize a linear machine learning model with a gradient-based optimizer for the prediction of future COVID-19 cases and deaths in the United States. We also suggest that a hybrid of a machine learning model for shorter range predictions and a Gaussian curve-fitting model or an epidemiological model for longer range predictions could greatly increase the accuracy of COVID-19 forecasting. INTERNATIONAL REGISTERED REPORT RR2-https://doi.org/10.1101/2020.08.13.20174631

Forecasting American COVID-19 Cases and Deaths through Machine Learning

COVID-19 has become a great national security problem for the United States and many other countries, where public policy and healthcare decisions are based on the several models for the prediction of the future deaths and cases of COVID-19. While the most commonly used models for COVID-19 include epidemiological models and Gaussian curve-fitting models, recent literature has indicated that these models could be improved by incorporating machine learning. However, within this research on potential machine learning models for COVID-19 forecasting, there has been a large emphasis on providing an array of different types of machine learning models rather than optimizing a single one. In this research, we suggest and optimize a linear machine learning model with a gradient-based optimizer for the prediction of future COVID-19 cases and deaths in the United States. We also suggest that a hybrid of a machine learning model for shorter range predictions and a Gaussian curve-fitting model or an epidemiological model for longer range predictions could greatly increase the accuracy of COVID-19 forecasting.

Ultrafast fiber laser delivering conservative, dispersion-managed, and dissipative solitons

A thulium-doped fiber laser, delivering the temporal solitons, has been proposed with a carbon nanotubes saturable absorber. By adjusting the dispersion design in the laser cavity, the proposed laser can generate three types of solitons, which are conservative soliton (CS), dispersion-managed soliton (DMS), and dissipative soliton (DS), respectively. The experimental results show that, for the first time to the best of our knowledge, the autocorrelation traces of CS, DMS, and DS are in good agreement with hyperbolic secant curve, Gaussian curve, and super-Gaussian curve, respectively. DS with the broad spectral bandwidth of 45.3 nm is emitted from the cavity while the dispersion is adjusted to 0.005 ps2.