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The paper presents two different approaches to estimating the region of stability of differential equation. Estimation of the region of stability is an essential practice in relation to control of the dynamical system. In this paper the objects of examination are differential equations with quasi-derivation. The equations have features that do not allow the application of classical methods for establishing stability. The goal is to compare the results of an analytic approach using Lyapunov method and computer simulation using a numerical method. The brief description of both methods are introduced and graphical results are presented and compared. [ABSTRACT FROM AUTHOR]

Most man-made environments, such as urban and indoor scenes, consist of a set of parallel and orthogonal planar structures. These structures are approximated by the Manhattan world assumption, in which notion can be represented as a Manhattan frame (MF). Given a set of inputs such as surface normals or vanishing points, we pose an MF estimation problem as a consensus set maximization that maximizes the number of inliers over the rotation search space. Conventionally, this problem can be solved by a branch-and-bound framework, which mathematically guarantees global optimality. However, the computational time of the conventional branch-and-bound algorithms is rather far from real-time. In this paper, we propose a novel bound computation method on an efficient measurement domain for MF estimation, i.e., the extended Gaussian image (EGI). By relaxing the original problem, we can compute the bound with a constant complexity, while preserving global optimality. Furthermore, we quantitatively and qualitatively demonstrate the performance of the proposed method for various synthetic and real-world data. We also show the versatility of our approach through three different applications: extension to multiple MF estimation, 3D rotation based video stabilization, and vanishing point estimation (line clustering). [ABSTRACT FROM AUTHOR]

In this paper, the synchronisation problems of multi-agent systems with asynchronous and synchronous event-triggered control under a novel event-triggered condition are solved. Our event-triggered control protocols only require each agent to send its state information to its neighbouring agents when an event-triggered condition is satisfied. Such control protocols substantially reduce the cost of communication. It is worth mentioning that the proposed protocols also ensure that the synchronisation of the multi-agent system with asynchronous and synchronous event-triggered can be achieved asymptotically without Zeno-behaviour. Meanwhile, an ultimate synchronisation trajectory is given. Moreover, our results are applied to solve the formation control problem. Some numerical simulations are presented to illustrate the effectiveness of our protocols. [ABSTRACT FROM AUTHOR]

Most existing dimensionality reduction algorithms have two disadvantages: their computational cost is high and they cannot estimate the intrinsic dimension of the original dataset by themselves. To deal with these problems, in this paper we propose a fast linear dimensionality reduction method named Orthogonal Component Analysis (OCA). While avoiding solving eigenproblem and matrix inverse problem, OCA successfully achieves high-speed orthogonal component extraction. By proposing an adaptive threshold scheme, OCA is able to estimate the dimension of the feature space automatically. Meanwhile, the algorithm is guaranteed to be numerical stable. In the experiments, OCA is compared with several typical dimensionality reduction algorithms. The experimental results demonstrate that as a universal algorithm, OCA is efficient and effective. [ABSTRACT FROM AUTHOR]