Constructing minimal telescopers for rational functions in three discrete variables

We present a new algorithm for constructing minimal telescopers for rational functions in three discrete variables. This is the first discrete reduction-based algorithm that goes beyond the bivariate case. The termination of the algorithm is guaranteed by a known existence criterion of telescopers. Our approach has the important feature that it avoids the potentially costly computation of certificates. Computational experiments are also provided so as to illustrate the efficiency of our approach

MULTI-OBJECTIVE OPTIMIZATION RESEARCH ON VR TASK SCENARIO DESIGN BASED ON COGNITIVE LOAD

In order to improve the efficiency of information acquisition and task selection in Virtual Reality (VR) systems, enhance the interactive experience, and reduce cognitive load for users, it is crucial to effectively organize and leverage user cognitive psychology and design elements during the VR scene design phase. This paper focuses on analyzing the low cognitive load requirements of users and the need for a satisfactory user perceptual experience based on the cognitive resource theory. We propose a method for optimizing the design of VR system scenario tasks under low cognitive load requirements. By utilizing human-computer hybrid intelligent assistance for predicting user cognitive load and incorporating intelligent optimization genetic algorithms into the optimization of VR system design elements, we aim to minimize cognitive load as the objective function based on the principle of low cognitive load. Important knowledge granularity nodes are used as fitness functions in the optimization process of VR system design resource elements. An application study is conducted, combining the multi-channel cognition in a smart city VR system task information interface, to optimize the system resource features. The study validates and compares the solutions obtained through traditional design processes and the solutions optimized by the method proposed in this paper, using virtual reality eye-tracking experiments for the same design task requirements in VR systems. The results demonstrate that users experience lower cognitive load and better task operation experience when interacting with the optimized solutions proposed in this paper. Therefore, the optimization method studied in this paper can serve as a reference for the construction of virtual reality systems

Photoplethysmographic imaging and analysis of pulsatile pressure wave in palmar artery at 10 wavelengths

CC BY: © The Authors. Published by SPIE under a Creative Commons Attribution 4.0 International License. Distribution or reproduction of this work in whole or in part requires full attribution of the original publication, including its DOI.Significance As a noncontact method, imaging photoplethysmography (iPPG) may provide a powerful tool to measure pulsatile pressure wave (PPW) in superficial arteries and extract biomarkers for monitoring of artery wall stiffness. Aim We intend to develop a approach for extraction of the very weak cardiac component from iPPG data by identifying locations of strong PPW signals with optimized illumination wavelength and determining pulse wave velocity (PWV). Approach Monochromatic in vivo iPPG datasets have been acquired from left hands to investigate various algorithms for retrieval of PPW signals, distribution maps and waveforms, and their dependence on arterial location and wavelength. Results A robust algorithm of pixelated independent component analysis (pICA) has been developed and combined with spatiotemporal filtering to retrieve PPW signals. Spatial distributions of PPW signals have been mapped in 10 wavelength bands from 445 to 940 nm and waveforms were analyzed at multiple locations near the palmar artery tree. At the wavelength of 850 nm selected for timing analysis, we determined PWV values from 12 healthy volunteers in a range of 0.5 to 5.8 m/s across the hand region from wrist to midpalm and fingertip.ECU Open Access Publishing Support Fun