An improved maximal inequality for 2D fractional order Schr\"{o}dinger operators

The local maximal inequality for the Schr\"{o}dinger operators of order \a>1 is shown to be bounded from $H^s(\R^2)$ to $L^2$ for any $s>\frac38$. This improves the previous result of Sj\"{o}lin on the regularity of solutions to fractional order Schr\"{o}dinger equations. Our method is inspired by Bourgain's argument in case of \a=2. The extension from \a=2 to general \a>1 confronts three essential obstacles: the lack of Lee's reduction lemma, the absence of the algebraic structure of the symbol and the inapplicable Galilean transformation in the deduction of the main theorem. We get around these difficulties by establishing a new reduction lemma at our disposal and analyzing all the possibilities in using the separateness of the segments to obtain the analogous bilinear $L^2-$estimates. To compensate the absence of Galilean invariance, we resort to Taylor's expansion for the phase function. The Bourgain-Guth inequality in \cite{ref Bourgain Guth} is also rebuilt to dominate the solution of fractional order Schr\"{o}dinger equations.Comment: Pages47, 3figures. To appear in Studia Mathematic

Systematic Review on Fabrication, Properties, and Applications of Advanced Materials in Wearable Photoplethysmography Sensors

Photoplethysmography (PPG) technology enables the measurement of multiple physiological and psychological parameters with low‐cost wearable sensors and is reshaping modern healthcare. Advanced materials play a vital role in improving reliability and accuracy of PPG sensors. Recently, various advanced materials have been explored to optimize PPG sensor design, while some challenges exist toward large‐scale validation and mass production. This paper focuses on advanced materials applied in the photodetectors, light sources, and circuits of PPG sensors. The materials are categorized into four groups: inorganic, organic, nanomaterials, and hybrid materials. The properties and fabrication processes are summarized. Other technical details including the mode of operation, measurement sites, testing, and validation are discussed. The merits and limitations of the state of the art are highlighted to provide some suggestions for the future development of PPG sensors based on advanced materials

Assessing the Reidentification Risks Posed by Deep Learning Algorithms Applied to ECG Data

ECG (Electrocardiogram) data analysis is one of the most widely used and important tools in cardiology diagnostics. In recent years the development of advanced deep learning techniques and GPU hardware have made it possible to train neural network models that attain exceptionally high levels of accuracy in complex tasks such as heart disease diagnoses and treatments. We investigate the use of ECGs as biometrics in human identification systems by implementing state-of-the-art deep learning models. We train convolutional neural network models on approximately 81k patients from the US, Germany and China. Currently, this is the largest research project on ECG identification. Our models achieved an overall accuracy of 95.69%. Furthermore, we assessed the accuracy of our ECG identification model for distinct groups of patients with particular heart conditions and combinations of such conditions. For example, we observed that the identification accuracy was the highest (99.7%) for patients with both ST changes and supraventricular tachycardia. We also found that the identification rate was the lowest for patients diagnosed with both atrial fibrillation and complete right bundle branch block (49%). We discuss the implications of these findings regarding the reidentification risks of patients based on ECG data and how seemingly anonymized ECG datasets can cause privacy concerns for the patients