Monotone Iterative Technique for Partial Dynamic Equations of First Order on Time Scales

This work is concerned with the monotone iterative technique for partial dynamic equations of first order on time scales and for this purpose, the existence, uniqueness, and comparison results are also established

Quasilinearization method for first-order impulsive integro-differential equations

In this article we study first-order impulsive integro-differential equations with integral boundary conditions, employing the method of quasilinearization with reversed ordering upper and lower solutions. We obtain two monotone sequences of iterates converging uniformly and quadratically to the unique solution of the problem. Two examples are given to illustrate the applications of the established results

Practical Stability and Integral Stability for Singular Differential Systems with Maxima

In this paper, we introduce various definitions of practical stability and integral stability for nonlinear singular differential systems with maxima and give criteria of stability for such systems via the Lyapunov method and comparison principle

On Novel Nonhomogeneous Multivariable Grey Forecasting Model NHMGM

A novel nonhomogeneous multivariable grey forecasting model termed NHMGM(1,m,kp,c) is proposed in this paper for use in nonhomogeneous multivariable exponential data sequences. The NHMGM(1,m,kp,c) model is able to reflect the nonlinear relation of the data sequences in the system, and it is proved that many classic grey forecasting models can be derived from NHMGM(1,m,kp,c) model. Parameters of the novel model are obtained by using least square method, and the time response function is given. A numerical example is presented to show the effectiveness of the proposed model, six different grey forecasting models are built for modeling, and two popular accuracy criteria (ARPE and MAPE) are adopted to test the reliability of the novel model. The example demonstrates that NHMGM-2 model provides favorable performance compared with the other five grey models. Additionally, the multiplication transformation properties of NHMGM(1,m,kp,c) are systematically analysed, which establish a theoretical foundation for further applications of the model

Comprehensive Ocean Information-Enabled AUV Motion Planning Based on Reinforcement Learning

Motion planning based on the reinforcement learning algorithms of the autonomous underwater vehicle (AUV) has shown great potential. Motion planning algorithms are primarily utilized for path planning and trajectory-tracking. However, prior studies have been confronted with some limitations. The time-varying ocean current affects algorithmic sampling and AUV motion and then leads to an overestimation error during path planning. In addition, the ocean current makes it easy to fall into local optima during trajectory planning. To address these problems, this paper presents a reinforcement learning-based motion planning algorithm with comprehensive ocean information (RLBMPA-COI). First, we introduce real ocean data to construct a time-varying ocean current motion model. Then, comprehensive ocean information and AUV motion position are introduced, and the objective function is optimized in the state-action value network to reduce overestimation errors. Finally, state transfer and reward functions are designed based on real ocean current data to achieve multi-objective path planning and adaptive event triggering in trajectorytracking to improve robustness and adaptability. The numerical simulation results show that the proposed algorithm has a better path planning ability and a more robust trajectory-tracking effect than those of traditional reinforcement learning algorithms

On almost periodicity of solutions of second-order differential equations involving reflection of the argument

Abstract We study almost periodic solutions for a class of nonlinear second-order differential equations involving reflection of the argument. We establish existence results of almost periodic solutions as critical points by a variational approach. We also prove structure results on the set of strong almost periodic solutions, existence results of weak almost periodic solutions, and a density result on the almost periodic forcing term for which the equation possesses usual almost periodic solutions

High Value of Information Guided Data Enhancement for Heterogeneous Underwater Wireless Sensor Networks

Ensuring the freshness of high Value of Information (VoI) data has a significant practice meaning for marine observations and emergencies. The traditional forward method with an auv-aid is used to ensure the freshness of high VoI data. However, the methods suffer from two issues: an insufficient high VoI data throughput and random forwarding for cluster heads (CHs). The AUV (Autonomous Underwater Vehicle) with limited energy cannot meet the demand for the random generation of high VoI data. Low VoI data packets compete with high VoI data packets for channels, resulting in an insufficient high VoI data throughput and a low freshness. To address the above issues, we propose the Data Access Channel Scheme based on High Value of Information (DACS-HVOI), which is suitable for prioritizing the transmission packets with a high VoI. First, according to the level of VoI, the packets are divided into K classes, and the packets that are collected and forwarded by the AUV are defined as the highest K+1 class. Second, based on prior knowledge in the network, a Markov chain algorithm-based method is employed to predict which nodes should preferentially use the channel, to avoid conflict between a low and high VoI. Third, based on the stochastic fluid theory, a multilevel queueing system for CHs are constructed to avoid random forwarding. Last, compared with state-of-art protocols, experimental simulation shows that the proposed scheme has a low latency and high network throughput, while improving the throughput of high-VoI packets and ensuring the priority transmission of high-VoI packets

Quantitative Analysis of Intracellular Motility Based on Optical Flow Model

Analysis of cell mobility is a key issue for abnormality identification and classification in cell biology research. However, since cell deformation induced by various biological processes is random and cell protrusion is irregular, it is difficult to measure cell morphology and motility in microscopic images. To address this dilemma, we propose an improved variation optical flow model for quantitative analysis of intracellular motility, which not only extracts intracellular motion fields effectively but also deals with optical flow computation problem at the border by taking advantages of the formulation based on L1 and L2 norm, respectively. In the energy functional of our proposed optical flow model, the data term is in the form of L2 norm; the smoothness of the data changes with regional features through an adaptive parameter, using L1 norm near the edge of the cell and L2 norm away from the edge. We further extract histograms of oriented optical flow (HOOF) after optical flow field of intracellular motion is computed. Then distances of different HOOFs are calculated as the intracellular motion features to grade the intracellular motion. Experimental results show that the features extracted from HOOFs provide new insights into the relationship between the cell motility and the special pathological conditions