scholarly journals Wavelength of a Turing-type mechanism regulates the morphogenesis of meshwork patterns

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Shan Guo ◽  
Ming-zhu Sun ◽  
Xin Zhao
Keyword(s):  
Pattern Formation ◽  
Functional Relationship ◽  
Turing Instability ◽  
Biological Tissues ◽  
Model Parameters ◽  
Spot Pattern ◽  
Variable Model ◽  
Type Pattern ◽  
Simulation Results ◽  
Rho A

AbstractThe meshwork pattern is a significant pattern in the development of biological tissues and organs. It is necessary to explore the mathematical mechanism of meshwork pattern formation. In this paper, we found that the meshwork pattern is formed by four kinds of stalk behaviours: stalk extension, tip bifurcation, side branching and tip fusion. The Turing-type pattern underlying the meshwork pattern is a Turing spot pattern, which indicates that the Turing instability of the spot pattern promotes activator peak formation and then guides the formation of meshwork patterns. Then, we found that the Turing wavelength decreased in turn from tip bifurcation to side branching to tip fusion via statistical evaluation. Through the functional relationship between the Turing wavelength and model parameters ($$\upvarepsilon ,{ \rho }_{A}$$ ε , ρ A and $${\rho }_{H}$$ ρ H ), we found that parameters $$\upvarepsilon $$ ε and $${\rho }_{H}$$ ρ H had monotonic effects on the Turing wavelength and that parameter $${\rho }_{A}$$ ρ A had nonmonotonic effects. Furthermore, we performed simulations of local meshwork pattern formation under variable model parameter values. The simulation results verified the corresponding relationship between the Turing wavelength and stalk behaviours and the functional relationship between the Turing wavelength and model parameters. The simulation results showed that the Turing wavelength regulated the meshwork pattern and that the small Turing wavelength facilitated dense meshwork pattern formation. Our work provides novel insight into and understanding of the formation of meshwork patterns. We believe that studies associated with network morphogenesis can benefit from our work.

scholarly journals A Separated Calibration Method for Inertial Measurement Units Mounted on Three-Axis Turntables

Sensors ◽  
2018 ◽  
Vol 18 (9) ◽  
pp. 2846 ◽  
Author(s):  
Chun-mei Dong ◽  
Shun-qing Ren ◽  
Xi-jun Chen ◽  
Zhen-huan Wang
Keyword(s):  
Inertial Measurement Unit ◽  
Functional Relationship ◽  
Calibration Method ◽  
Measurement Unit ◽  
Model Parameters ◽  
Inertial Measurement ◽  
Measurement Units ◽  
Suboptimal Design ◽  
Calibration Accuracy ◽  
Simulation Results

Inertial Measurement Unit (IMU) calibration accuracy is easily affected by turntable errors, so the primary aim of this study is to reduce the dependence on the turntable’s precision during the calibration process. Firstly, the indicated-output of the IMU considering turntable errors is constructed and with the introduction of turntable errors, the functional relationship between turntable errors and the indicated-output was derived. Then, based on a D-suboptimal design, a calibration method for simultaneously identifying the IMU error model parameters and the turntable errors was proposed. Simulation results showed that some turntable errors could thus be effectively calibrated and automatically compensated. Finally, the theoretical validity was verified through experiments. Compared with the traditional method, the method proposed in this paper can significantly reduce the influence of the turntable errors on the IMU calibration accuracy.

scholarly journals Glassy dynamics in three-dimensional embryonic tissues

2013 ◽  
Vol 10 (89) ◽  
pp. 20130726 ◽  
Author(s):  
Eva-Maria Schötz ◽  
Marcos Lanio ◽  
Jared A. Talbot ◽  
M. Lisa Manning
Keyword(s):  
Pattern Formation ◽  
Mechanical Response ◽  
Three Dimensional ◽  
Biological Tissues ◽  
Model Parameters ◽  
Elastic Solids ◽  
Cell Dynamics ◽  
Cell Parameters ◽  
Embryonic Tissues ◽  
Long Timescales

Many biological tissues are viscoelastic, behaving as elastic solids on short timescales and fluids on long timescales. This collective mechanical behaviour enables and helps to guide pattern formation and tissue layering. Here, we investigate the mechanical properties of three-dimensional tissue explants from zebrafish embryos by analysing individual cell tracks and macroscopic mechanical response. We find that the cell dynamics inside the tissue exhibit features of supercooled fluids, including subdiffusive trajectories and signatures of caging behaviour. We develop a minimal, three-parameter mechanical model for these dynamics, which we calibrate using only information about cell tracks. This model generates predictions about the macroscopic bulk response of the tissue (with no fit parameters) that are verified experimentally, providing a strong validation of the model. The best-fit model parameters indicate that although the tissue is fluid-like, it is close to a glass transition, suggesting that small changes to single-cell parameters could generate a significant change in the viscoelastic properties of the tissue. These results provide a robust framework for quantifying and modelling mechanically driven pattern formation in tissues.

scholarly journals Modeling of German Low Voltage Cables with Ground Return Path

Energies ◽  
2021 ◽  
Vol 14 (5) ◽  
pp. 1265 ◽  
Author(s):  
Johanna Geis-Schroer ◽  
Sebastian Hubschneider ◽  
Lukas Held ◽  
Frederik Gielnik ◽  
Michael Armbruster ◽  
...  
Keyword(s):  
Low Voltage ◽  
Measurement Data ◽  
Analytical Calculation ◽  
Laboratory Measurement ◽  
Model Parameters ◽  
Calculation Methods ◽  
Modeling Approach ◽  
Measurement Results ◽  
Simulation Results ◽  
Return Path

In this contribution, measurement data of phase, neutral, and ground currents from real low voltage (LV) feeders in Germany is presented and analyzed. The data obtained is used to review and evaluate common modeling approaches for LV systems. An alternative modeling approach for detailed cable and ground modeling, which allows for the consideration of typical German LV earthing conditions and asymmetrical cable design, is proposed. Further, analytical calculation methods for model parameters are described and compared to laboratory measurement results of real LV cables. The models are then evaluated in terms of parameter sensitivity and parameter relevance, focusing on the influence of conventionally performed simplifications, such as neglecting house junction cables, shunt admittances, or temperature dependencies. By comparing measurement data from a real LV feeder to simulation results, the proposed modeling approach is validated.

scholarly journals Gaussian Processes Proxy Model with Latent Variable Models and Variogram-Based Sensitivity Analysis for Assisted History Matching

Energies ◽  
2020 ◽  
Vol 13 (17) ◽  
pp. 4290
Author(s):  
Dongmei Zhang ◽  
Yuyang Zhang ◽  
Bohou Jiang ◽  
Xinwei Jiang ◽  
Zhijiang Kang
Keyword(s):  
Sensitivity Analysis ◽  
Gaussian Processes ◽  
Latent Variable ◽  
History Matching ◽  
Latent Variable Models ◽  
High Dimensional ◽  
Model Parameters ◽  
Variable Model ◽  
Assisted History Matching ◽  
Proxy Models

Reservoir history matching is a well-known inverse problem for production prediction where enormous uncertain reservoir parameters of a reservoir numerical model are optimized by minimizing the misfit between the simulated and history production data. Gaussian Process (GP) has shown promising performance for assisted history matching due to the efficient nonparametric and nonlinear model with few model parameters to be tuned automatically. Recently introduced Gaussian Processes proxy models and Variogram Analysis of Response Surface-based sensitivity analysis (GP-VARS) uses forward and inverse Gaussian Processes (GP) based proxy models with the VARS-based sensitivity analysis to optimize the high-dimensional reservoir parameters. However, the inverse GP solution (GPIS) in GP-VARS are unsatisfactory especially for enormous reservoir parameters where the mapping from low-dimensional misfits to high-dimensional uncertain reservoir parameters could be poorly modeled by GP. To improve the performance of GP-VARS, in this paper we propose the Gaussian Processes proxy models with Latent Variable Models and VARS-based sensitivity analysis (GPLVM-VARS) where Gaussian Processes Latent Variable Model (GPLVM)-based inverse solution (GPLVMIS) instead of GP-based GPIS is provided with the inputs and outputs of GPIS reversed. The experimental results demonstrate the effectiveness of the proposed GPLVM-VARS in terms of accuracy and complexity. The source code of the proposed GPLVM-VARS is available at https://github.com/XinweiJiang/GPLVM-VARS.

scholarly journals ONLINE PARAMETER IDENTIFICATION OF RICE TRANSPLANTER MODEL BASED ON IPSO-EKF ALGORITHM

2020 ◽  
Vol 61 (2) ◽  
pp. 25-34 ◽  
Author(s):  
Yibo Li ◽  
Hang Li ◽  
Xiaonan Guo
Keyword(s):  
Parameter Identification ◽  
Measured Data ◽  
Model Parameters ◽  
Identification Algorithm ◽  
Output Data ◽  
Swarm Optimization ◽  
Model Based ◽  
Simulation Results ◽  
Filtering Effect ◽  
Ipso Algorithm

In order to improve the accuracy of rice transplanter model parameters, an online parameter identification algorithm for the rice transplanter model based on improved particle swarm optimization (IPSO) algorithm and extended Kalman filter (EKF) algorithm was proposed. The dynamic model of the rice transplanter was established to determine the model parameters of the rice transplanter. Aiming at the problem that the noise matrices in EKF algorithm were difficult to select and affected the best filtering effect, the proposed algorithm used the IPSO algorithm to optimize the noise matrices of the EKF algorithm in offline state. According to the actual vehicle tests, the IPSO-EKF was used to identify the cornering stiffness of the front and rear tires online, and the identified cornering stiffness value was substituted into the model to calculate the output data and was compared with the measured data. The simulation results showed that the accuracy of parameter identification for the rice transplanter model based on the IPSO-EKF algorithm was improved, and established an accurate rice transplanter model.

A Variable Step Size LMS Adaptive Filtering Algorithm and Simulations Based on Computational Verb Theory

2013 ◽  
Vol 756-759 ◽  
pp. 3972-3976 ◽  
Author(s):  
Li Hui Sun ◽  
Bao Yu Zheng
Keyword(s):  
Adaptive Filtering ◽  
Adaptive Algorithm ◽  
Linear Functional ◽  
Functional Relationship ◽  
Lms Algorithm ◽  
Variable Step Size ◽  
Step Size ◽  
Filtering Algorithm ◽  
Variable Step ◽  
Simulation Results

Based on traditional LMS algorithm, variable step LMS algorithm and the analysis for improved algorithm, a new variable step adaptive algorithm based on computational verb theory is put forward. A kind of sectorial linear functional relationship is established between step parameters and the error. The simulation results show that the algorithm has the advantage of slow change which is closely to zero. And overcome the defects of some variable step size LMS algorithm in adaptive steady state value is too large.

Robustness Analysis of a Simple and Augmented Proportional Plus Derivative Controller in Trajectory Following Robots Using the Floquet Theory

2018 ◽  
Vol 13 (7) ◽  
Author(s):  
B. Sandeep Reddy ◽  
Ashitava Ghosal
Keyword(s):  
Numerical Simulation ◽  
Degrees Of Freedom ◽  
Floquet Theory ◽  
Robustness Analysis ◽  
Periodic Trajectory ◽  
Model Parameters ◽  
Asymptotically Stable ◽  
Pd Controller ◽  
Simulation Results ◽  
Trajectory Following

This paper deals with the issue of robustness in control of robots using the proportional plus derivative (PD) controller and the augmented PD controller. In the literature, a variety of PD and model-based controllers for multilink serial manipulator have been claimed to be asymptotically stable for trajectory tracking, in the sense of Lyapunov, as long as the controller gains are positive. In this paper, we first establish that for simple PD controllers, the criteria of positive controller gains are insufficient to establish asymptotic stability, and second that for the augmented PD controller the criteria of positive controller gains are valid only when there is no uncertainty in the model parameters. We show both these results for a simple planar two-degrees-of-freedom (2DOFs) robot with two rotary (R) joints, following a desired periodic trajectory, using the Floquet theory. We provide numerical simulation results which conclusively demonstrate the same.

Trade-offs among transcription elongation rate, number, and duration of ubiquitous pauses on highly transcribed bacterial genes

2021 ◽  
pp. 2150020
Author(s):  
Tomáš Gedeon ◽  
Lisa Davis ◽  
Katelyn Weber ◽  
Jennifer Thorenson
Keyword(s):  
Functional Relationship ◽  
Surrounding Medium ◽  
Elongation Rate ◽  
Model Parameters ◽  
Transcription Rate ◽  
Initiation Rate ◽  
Protein Coding ◽  
Protein Coding Genes ◽  
Trade Offs ◽  
Elongation Process

In this paper, we study the limitations imposed on the transcription process by the presence of short ubiquitous pauses and crowding. These effects are especially pronounced in highly transcribed genes such as ribosomal genes (rrn) in fast growing bacteria. Our model indicates that the quantity and duration of pauses reported for protein-coding genes is incompatible with the average elongation rate observed in rrn genes. When maximal elongation rate is high, pause-induced traffic jams occur, increasing promoter occlusion, thereby lowering the initiation rate. This lowers average transcription rate and increases average transcription time. Increasing maximal elongation rate in the model is insufficient to match the experimentally observed average elongation rate in rrn genes. This suggests that there may be rrn-specific modifications to RNAP, which then experience fewer pauses, or pauses of shorter duration than those in protein-coding genes. We identify model parameter triples (maximal elongation rate, mean pause duration time, number of pauses) which are compatible with experimentally observed elongation rates. Average transcription time and average transcription rate are the model outputs investigated as proxies for cell fitness. These fitness functions are optimized for different parameter choices, opening up a possibility of differential control of these aspects of the elongation process, with potential evolutionary consequences. As an example, a gene’s average transcription time may be crucial to fitness when the surrounding medium is prone to abrupt changes. This paper demonstrates that a functional relationship among the model parameters can be estimated using a standard statistical analysis, and this functional relationship describes the various trade-offs that must be made in order for the gene to control the elongation process and achieve a desired average transcription time. It also demonstrates the robustness of the system when a range of maximal elongation rates can be balanced with transcriptional pause data in order to maintain a desired fitness.

Mathematical modeling of biological tissues electrical conductivity based on the ion electrodiffusion equations

2021 ◽  
Author(s):  
N.V. Kovalenko ◽  
K.V. Sovin ◽  
O.A. Ryabushkin
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Electrical Properties ◽  
Biological Tissue ◽  
Physiological State ◽  
Biological Tissues ◽  
Radiation Heating ◽  
Tissue Degradation ◽  
Simulation Results ◽  
Electrical Properties Of Tissues

Problem formulating. The vital processes of biological tissues are closely related to their electrical properties. An important task is to create a physical and mathematical model that will link the electrical properties of tissues to their physiological state. Goal. Construction of a model of biological tissue electrical properties based on the equations of ion electrodiffusion. Result. The paper presents the model of biological tissue electrical properties based on the ion electrodiffusion equations, and compares the simulation results with the experimental results presented in the literature. Practical meaning. The presented model can be used to describe processes occurring in tissue at the level of concentration and conductivity of ions in individual cells and cell membranes. In particular, the process of tissue degradation during laser radiation heating can be described.

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