Modeling of constrained motion

This paper presents an investigation of modeling and solving of differential equations in the study of mechanical systems with holonomic constraints. The 2D and 3D mathematical models of constrained motion are made. The structure of the models consists of nonlinear first or second order differential equations. Cases of free movement and movement with resistance are investigated. Solutions of the Cauchy problem of obtained differential equations were obtained by Runge–Kutta method.

Real-Time Messenger RNA Dynamics in Bacillus subtilis

Messenger RNA molecules have been localized to different positions in cells and have been followed by time-lapse microscopy. We have used MS2-mVenus–labeled mRNA and single-particle tracking to obtain information on the dynamics of single-mRNA molecules in real time. Using single-molecule tracking, we show that several mRNA molecules visualized via two MS2-binding sites and MS2-mVenus expressed in Bacillus subtilis cells show free diffusion through the entire cell and constrained motion predominantly close to the cell membrane and at the polar regions of the cells. Because constrained motion of mRNAs likely reflects molecules complexed with ribosomes, our data support the idea that translation occurs at sites surrounding the nucleoids. Squared displacement analyses show the existence of at least two distinct populations of molecules with different diffusion constants or possibly of three populations, for example, freely mobile mRNAs, mRNAs in transition complexes, or in complex with polysomes. Diffusion constants between differently sized mRNAs did not differ dramatically and were much lower than that of cytosolic proteins. These data agree with the large size of mRNA molecules and suggest that, within the viscous cytoplasm, size variations do not translate into mobility differences. However, at observed diffusion constants, mRNA molecules would be able to reach all positions within cells in a frame of seconds. We did not observe strong differences in the location of confined motion for mRNAs encoding mostly soluble or membrane proteins, indicating that there is no strong bias for localization of membrane protein-encoding transcripts for the cell membrane.

Motion and Illumination Resistant Facial Video based Heart Rate Estimation Method using Levenberg-Marquardt Algorithm Optimized Undercomplete Independent Component Analysis

<div>Heart Rate (HR) estimation is of utmost need due to its applicability in diverse fields. Conventional methods for HR estimation require skin contact and are not suitable for scenarios such as sensitive skin or prolonged unobtrusive HR monitoring. Therefore remote photoplethysmography (rPPG) methods have been an active area of research. These methods utilize the facial videos acquired using a camera followed by extracting the Blood Volume Pulse (BVP) signal for heart rate calculation. The existing rPPG methods either used a single color channel or weighted color differences, which has limitations dealing with motion and illumination artifacts. This study considers BVP extraction as an undercomplete problem and proposed a method U-LMA. First, a non-linear Cumulative Density Function (CDF) approximated by a hyperbolic tangent (tanh) was used to deal with the non-linearity associated with rigid and non-rigid motions and illumination variations. Then, the entropy of the proposed non-linear CDF was optimized using a customized LMA for BVP signal extraction, followed by maximum peak estimation for HR calculation. The performance of the proposed method was tested under three scenarios: constrained, motion, and illumination variations scenarios. High Pearson correlation coefficient values and smaller lower-upper statistical limits of bland-altman plots , justified the good performance of the U-LMA. Comparative analysis of U-LMA with undercomplete ICA with negentropy (U-neg) and other state-of-the-art methods demonstrated its best performance of U-LMA by achieving the lowest error and highest correlation values (0.01 significance level) . Additionally, higher accuracy satisfying the clinically accepted error differences also justified its clinical relevance.</div>

Motion and Illumination Resistant Facial Video based Heart Rate Estimation Method using Levenberg-Marquardt Algorithm Optimized Undercomplete Independent Component Analysis

<div>Heart Rate (HR) estimation is of utmost need due to its applicability in diverse fields. Conventional methods for HR estimation require skin contact and are not suitable for scenarios such as sensitive skin or prolonged unobtrusive HR monitoring. Therefore remote photoplethysmography (rPPG) methods have been an active area of research. These methods utilize the facial videos acquired using a camera followed by extracting the Blood Volume Pulse (BVP) signal for heart rate calculation. The existing rPPG methods either used a single color channel or weighted color differences, which has limitations dealing with motion and illumination artifacts. This study considers BVP extraction as an undercomplete problem and proposed a method U-LMA. First, a non-linear Cumulative Density Function (CDF) approximated by a hyperbolic tangent (tanh) was used to deal with the non-linearity associated with rigid and non-rigid motions and illumination variations. Then, the entropy of the proposed non-linear CDF was optimized using a customized LMA for BVP signal extraction, followed by maximum peak estimation for HR calculation. The performance of the proposed method was tested under three scenarios: constrained, motion, and illumination variations scenarios. High Pearson correlation coefficient values and smaller lower-upper statistical limits of bland-altman plots , justified the good performance of the U-LMA. Comparative analysis of U-LMA with undercomplete ICA with negentropy (U-neg) and other state-of-the-art methods demonstrated its best performance of U-LMA by achieving the lowest error and highest correlation values (0.01 significance level) . Additionally, higher accuracy satisfying the clinically accepted error differences also justified its clinical relevance.</div>