In this paper, we will present some recent progress in both global controllability and global asymptotical controllability of affine nonlinear systems. Our method is based on some basic facts in planar topology and in the geometric theory of ordinary differential equations. We will first present a necessary and sufficient condition for global controllability of general planar affine nonlinear s...

1. We’ll follow the notation of [3]. Assume that n seats have already been assigned, and that each elector of type k is represented in the amount rk. We consider allocating a new seat to candidate (or party) i and distributing it between the electors that approved i. Let xk be the amount of this new seat that is given to each elector of type k (we are omitting the reference to i). The xk are su...

In this work we obtain a new criterion to establish ergodicity and non-uniform hyperbolicity of smooth measures of diffeomorphisms. This method allows us to give a more accurate description of certain ergodic components. The use of this criterion in combination with topological devices such as blenders lets us obtain global ergodicity and abundance of non-zero Lyapunov exponents in some context...

In this paper time-delay effects on the master–slave synchronization scheme are investigated. Sufficient conditions for master–slave synchronization of Lur’e systems are presented for a known time-delay in the master and slave systems. A delay-dependent synchronization criterion is given based upon a new Lyapunov–Krasovskii function. The derived criterion is a sufficient condition for global as...

Based on a geometrical method, the internal relationships between locally parameterized curves and the local parameterized surfaces are analyzed. A necessary and sufficient condition is derived for the local convexity of parameterized surfaces and functional surfaces. A criterion for local convexity (concavity) of parameterized surfaces is found, also, the criterion condition of binary function...

In this paper, the problemof robust exponential stability analysis of uncertain discrete-time recurrent neural networks withMarkovian jumping and time-varying delays is studied. By employing the Lyapunov functional and linear matrix inequality (LMI) approach, a new sufficient criterion is proposed for the global robust exponential stability of discrete-time recurrent neural networks which conta...

In this paper, we model the salient object detection problem under a probabilistic framework encoding the boundary connectivity saliency cue and smoothness constraints in an optimization problem. We show that this problem has a closed form global optimum which estimates the salient object. We further show that along with the probabilistic framework, the proposed method also enjoys a wide range ...

This paper puts forward a comprehensive study of the design of global stopping criteria for multi-objective optimization. In this study we propose a global stopping criterion, which is terms as MGBM after the authors surnames. MGBM combines a novel progress indicator, called mutual domination rate (MDR) indicator, with a simplified Kalman filter, which is used for evidence-gathering purposes. T...

In this work we propose a new framework for extracting deformable clothing items from images by using a three stage global-local fitting procedure. First, a set of initial segmentation templates are generated from a handcrafted database. Then, each template initiates an object extraction process by a global alignment of the model, followed by a local search minimizing a measure of the misfit wi...

Phylogenetic trees are important in biology since their applications range from determining protein function to understanding the evolution of species. Maximum Likelihood (ML) is a popular optimization criterion in phylogenetics. However, inference of phylogenies with ML is NP-hard. Recursive-Iterative-DCM3 (Rec-I-DCM3) is a divideand-conquer framework that divides a dataset into smaller subset...