The Impact of Retinal Configuration on the Protein–Chromophore Interactions in Bistable Jumping Spider Rhodopsin-1

Bistable rhodopsins have two stable forms that can be interconverted by light. Due to their ability to act as photoswitches, these proteins are considered as ideal candidates for applications such as optogenetics. In this work, we analyze a recently crystalized bistable rhodopsin, namely the jumping spider rhodopsin-1 (JSR1). This rhodopsin exhibits identical absorption maxima for the parent and the photoproduct form, which impedes its broad application. We performed hybrid QM/MM simulations to study three isomers of the retinal chromophore: the 9-cis, 11-cis and all-trans configurations. The main aim was to gain insight into the specific interactions of each isomer and their impact on the absorption maximum in JSR1. The absorption spectra were computed using sampled snapshots from QM/MM molecular dynamics trajectories and compared to their experimental counterparts. The chromophore–protein interactions were analyzed by visualizing the electrostatic potential of the protein and projecting it onto the chromophore. It was found that the distance between a nearby tyrosine (Y126) residue plays a larger role in the predicted absorption maximum than the primary counterion (E194). Geometric differences between the isomers were also noted, including a structural change in the polyene chain of the chromophore, as well as changes in the nearby hydrogen bonding network.     

A note on the first passage time of diffusions with holding and jumping boundary

In this note we are concerned with the first passage time (FPT) of diffusions with holding and jumping boundary (DHJ) in one dimensional case. We first show that the Laplace transform of FPT of DHJ can be represented explicitly by the behavior of the killed process for one holding and jumping point. The results are then extended to the Laplace transform of FPT of DHJ with two end points. Finally, we demonstrate how the results are applied to a Wiener-type neuronal model in the presence of exponential refractoriness.     

Secondary Buckling Analysis of Thin Rectangular Plates Based on the Wavelet Galerkin Method北大核心CSCD

Application of the wavelet Galerkin method (WGM) to numerical solution of nonlinear buckling problems was studied with classical elastic thin rectangular plates. First, the discretized scheme of the von Kármán equation were introduced, then a simple calculation approach to the Jacobian and Hessian matrices based on the WGM was proposed, and the wavelet discretized scheme-based eigenvalue equation method, the extended equation method and the pseudo arc-length method for nonlinear buckling analysis were discussed. Second, the secondary post-buckling equilibrium paths of elastic thin rectangular plates and the effects of aspect ratios, boundary conditions and bi-directional compression on the mode jumping behaviors, were discussed in detail. Numerical results show that, the WGM possesses good convergence for solving buckling loads on rectangular plates, and the obtained equilibrium paths are in good agreement with those from the stability experiments, the 2-step perturbation method and the nonlinear finite element method. Given the feasibility of combination with different bifurcation computation methods, the WGM makes an efficient spatial discretization method for complex nonlinear stability problems of typical plates and shells. © 2023 Editorial Office of Applied Mathematics and Mechanics. All rights reserved.     

Exponential synchronization of Markovian jumping chaotic neural networks with sampled-data and saturating actuators

This paper deals with the problem of exponential synchronization of Markovian jumping chaotic neural networks with saturating actuators using a sampled-data controller. By constructing a proper Lyapunov–Krasovskii functional (LKF) with triple integral terms, and employing Jensen’s inequality, some new sufficient conditions for the exponential synchronization of considered chaotic neural networks are derived in terms of linear matrix inequalities (LMIs). The obtained LMIs can be easily solved by any of the available software. Finally, the numerical examples are provided to demonstrate the effectiveness of our theoretical results.     

高温分离式Hopkinson压杆技术及其应用

本文介绍了在分离式Hopkinson压杆装置上通过使用一种气动同步机构,实现对试样进行高温高应变率加载的技术。利用此技术仅对试样加高温度而保持入射杆和透射杆与试样脱离且处在较低温度,到预定温度时,借助气动同步机构使入射杆、透射杆与试样接触并同时实现对试样加载。利用波形抑制技术,仅对试样实现一次加载,入射杆中的后续二次加载波通过反作用质量块吸收。通过这些技术的结合,1)可以进行材料在高温高应变率下应力应变测试;2)可以测试材料在高应变率不同温度下的等温曲线;3)可以间接对材料的塑性功热转换系数进行测试;4)可以进行不同温度高应变率下的中断跳跃试验等。在文中给出了一些典型的试验曲线和结果,并对测试方法和结果进行了分析讨论。     

Optical measurements of self-induced oscillations

High speed digital holographic interferometry is used to measure the self-induced mechanical oscillations produced by frequency signals near the first natural resonance mode of a rectangular polyester membrane. The external excitation produces very low mechanical amplitude levels in the membrane. This non-invasive optical technique has high temporal and spatial resolution allowing large data acquisition and hence allowing the processing of thousands of recorded images acquired in a CMOS camera set at 5000 frames per second (fps).     

Dynamic analysis of Markovian jumping impulsive stochastic Cohen–Grossberg neural networks with discrete interval and distributed time-varying delays

In this paper, the dynamic analysis problem is considered for a new class of Markovian jumping impulsive stochastic Cohen–Grossberg neural networks (CGNNs) with discrete interval and distributed delays. The parameter uncertainties are assumed to be norm bounded and the discrete delay is assumed to be time-varying and belonging to a given interval, which means that the lower and upper bounds of interval time-varying delays are available. Based on the Lyapunov–Krasovskii functional and stochastic stability theory, delay-interval dependent stability criteria are obtained in terms of linear matrix inequalities. Some asymptotic stability criteria are formulated by means of the feasibility of a linear matrix inequality (LMI), which can be easily calculated by LMI Toolbox in Matlab. A numerical example is provided to show that the proposed results significantly improve the allowable upper bounds of delays over some existing results in the literature.     

Delay Range-Dependent Stability Analysis for Markovian Jumping Stochastic Systems with Nonlinear Perturbations

This article addresses the problem of delay-dependent stability for Markovian jumping stochastic systems with interval time-varying delays and nonlinear perturbations. The delay is assumed to be time-varying and belongs to a given interval. By resorting to Lyapunov–Krasovskii functionals and stochastic stability theory, a new delay interval-dependent stability criterion for the system is obtained. It is shown that the addressed problem can be solved if a set of linear matrix inequalities (LMIs) are feasible. Finally, a numerical example is employed to illustrate the effectiveness and less conservativeness of the developed techniques.     

Stochastic asymptotical synchronization of chaotic Markovian jumping fuzzy cellular neural networks with mixed delays and the Wiener process based on sampled-data control

We investigate the stochastic asymptotical synchronization of chaotic Markovian jumping fuzzy cellular neural networks (MJFCNNs) with discrete, unbounded distributed delays, and the Wiener process based on sampled-data control using the linear matrix inequality (LMI) approach. The Lyapunov-Krasovskii functional combined with the input delay approach as well as the free-weighting matrix approach is employed to derive several sufficient criteria in terms of LMIs to ensure that the delayed MJFCNNs with the Wiener process is stochastic asymptotical synchronous. Restrictions (e.g., time derivative is smaller than one) are removed to obtain a proposed sampled-data controller. Finally, a numerical example is provided to demonstrate the reliability of the derived results.     

FINITE-TIME H_∞ CONTROL FOR A CLASS OF MARKOVIAN JUMPING NEURAL NETWORKS WITH DISTRIBUTED TIME VARYING DELAYS-LMI APPROACH

In this article, we investigates finite-time H_∞ control problem of Markovian jumping neural networks of neutral type with distributed time varying delays. The mathematical model of the Markovian jumping neural networks with distributed delays is established in which a set of neural networks are used as individual subsystems. Finite time stability analysis for such neural networks is addressed based on the linear matrix inequality approach.Numerical examples are given to illustrate the usefulness of our proposed method. The results obtained are compared with the results in the literature to show the conservativeness.