Generalized Cell Mapping Method with Deep Learning for Global Analysis and Response Prediction of Dynamical Systems

A novel method that combines generalized cell mapping and deep learning is developed to analyze the global properties and predict the responses of dynamical systems. The proposed method only requires some prior knowledge of the system governing equations and obtains dynamical properties of the system from observed data. By combining the theoretical demonstration and empirical inference results, appropriate network structure and training hyperparameters are computed. Then a robust and efficient neural network approximation with the estimated mapping parameters is obtained. By using the approximate dynamical system model, we construct the one-step transition probability matrix and introduce the digraph analysis method to analyze the global properties. System responses at any time can be obtained with the trained model on the basis of the property of Markov chain. Several examples with periodic or chaotic attractors are presented to validate the proposed method. The influence of the number of hidden layers and the size of training data on calculated results is discussed, and an admissible architecture of the neural network is found. Numerical results indicate that the proposed method is quite effective for both global analysis and response prediction.

Characterization of the Zebrafish Cell Landscape at Single-Cell Resolution

Zebrafish have been found to be a premier model organism in biological and regeneration research. However, the comprehensive cell compositions and molecular dynamics during tissue regeneration in zebrafish remain poorly understood. Here, we utilized Microwell-seq to analyze more than 250,000 single cells covering major zebrafish cell types and constructed a systematic zebrafish cell landscape. We revealed single-cell compositions for 18 zebrafish tissue types covering both embryo and adult stages. Single-cell mapping of caudal fin regeneration revealed a unique characteristic of blastema population and key genetic regulation involved in zebrafish tissue repair. Overall, our single-cell datasets demonstrate the utility of zebrafish cell landscape resources in various fields of biological research.

On the Dynamics of a Biomimetic Model of a Sympodial Tree: From Bifurcations Diagrams and 6D Basins of Attraction to Dynamical Integrity and Robustness

This work is concerned with a mechanical model of a sympodial tree with first-level branches, which has been shown to exhibit certain properties potentially suitable for biomimetic applications. To investigate these potential benefits further from the viewpoint of the system nonlinear behaviour under external periodic excitation, modern numerical tools related to the concept of dynamical integrity are either adjusted or newly developed for this system for the first time. First, multistable regions of interest are isolated from bifurcation diagrams and the effect of damping is investigated. Then, in order to obtain the corresponding basins of attraction of this highly dimensional model, an original computational procedure is developed that includes cell mapping with 406 cells, where each cell represents an initial condition required to construct the map. Full 6D basins are computed, and they are reported for various values of the damping parameter and the excitation frequency. Those basins are then used to calculate the dynamic integrity factors so that the dominant steady state can be determined. Finally, the integrity profiles are reported to illustrate how the robustness varies by changing the system parameters.

Nonlinear Analysis of a Quasi-Zero Stiffness Air Suspension Based on the Cell-Mapping Method

The quasi-zero stiffness system has the characteristics of low dynamic stiffness and high static stiffness, which can bring a better driving experience and lower road dynamic load at high speed on irregular roads. This paper studies a type of interconnected quasi-zero stiffness air suspension system, which has two states, namely, the non-interconnected quasi-zero stiffness air suspension and the interconnected quasi-zero stiffness air suspension, to meet the performance requirements under different loads and vehicle speed. First, the mathematical model of the nonlinear system is established based on the basic principles of fluid mechanics and thermodynamics. Then, the stability of the equilibrium point is analyzed using the Lyapunov first method, where the quantitative analysis of the attractive region of the system is conducted through the bifurcation diagram and phase diagram. By using the Taylor series expansion, cell-mapping theory and domain map of attraction, the attractive region of the system is quantitatively analyzed to obtain the parametric feasible domain under stable conditions. Finally, the performance of the quasi-zero stiffness suspension system with the selected parameters under the stability constraint is verified by simulation analysis and experiment. The results show that the system represented in this paper provides higher suspension comfort and stability.

Single-Cell Mapping and 3D Tissue Reconstruction using Cryosection-derived Images and Tissue Mapper software

The present protocol describes the process of using the MBF Bioscience Tissue Mapper software to create a 3D reconstructed stack from contouring the block face images of serial cryosections and mark the individual immunolabeled cells onto the contoured images. The stack of aligned, contoured and annotated images can be visualized as a 3D reconstruction that depicts the tissue shape as it was embedded and cryosectioned, relative positions of various tissue features, and locations of individually marked neurons within the tissue, yielding a 3D anatomical map of the distribution of cells of interest with a tissue. This protocol can be used in conjunction with other protocols for sampling spatially-tracked single neurons using laser capture micro-dissection and assessed for molecular profiles using transcriptomics approaches. Such integration extends the present protocol to enable 3D visualization of molecular data in conjunction with the anatomical information for spatial transcriptomic analysis.