Critical Periods of Perturbations of Reversible Rigidly Isochronous Centers

We study the problem of bifurcation of critical periods of a time-reversible polynomial system of degree n. We first present a new method to find the number of zeros of the period function. Then applying our results, we study the number of critical periods for some polynomial systems and obtain new results

Critiquing Recommenders for Public Taste Products

Critiquing-based recommenders do not require users to state all of their preferences upfront or rate a set of previously experienced products. Compared to other types of recommenders, they require relatively little user effort, especially initially, despite potential accuracy problems. On the other hand, they rely on a set of critiques to elicit users feedback in order to improve accuracy. Thus the better the critiques are, the more accurately and efficiently the system becomes in generating its recommendations. This method has been successfully applied to high-involvement products. However, it was never tested on public taste products such as music, films, perfumes, fashion goods or wine. Indeed our initial trial adapting traditional critiquing methods to this new domain led to unsatisfactory results. This has motivated us to develop a novel approach named "editorial picked critiques" (EPC) that accounts for users’ needs for popularity information, editorial suggestions, as well as their needs for personalization and diversity. Through an empirical study, we demonstrate that EPC presents a viable recommender approach and is superior on several dimensions to critiques generated by data mining methods

Multiple Focus and Hopf Bifurcations in a Predator-Prey System with Nonmonotonic Functional Response

In this paper, we develop a criterion to calculate the multiplicity of a multiple focus for general predator prey systems. As applications of this criterion, we calculate the most multiplicity of a multiple focus in a predator prey system with nonmonotonic functional response p(x) = x/(ax^2+bx+1) studied by Zhu, Campbell and Wolkowicz [26] and prove that the degenerate Hopf bifurcation is of codimension two. Furthermore, we show that there exist parameter values for which this system has a unique positive hyperbolic stable equilibrium and exactly two limit cycles, the inner one is unstable and outer one is stable. Numerical simulations for the existence of the two limit cycles bifurcated from the multiple focus were also given in support of the criterion

A Visual Navigation Algorithm for UAV Based on Visual-Geography Optimization

The estimation of Unmanned Aerial Vehicle (UAV) poses using visual information is essential in Global Navigation Satellite System (GNSS)-denied environments. In this paper, we propose a UAV visual navigation algorithm based on visual-geography Bundle Adjustment (BA) to address the challenge of missing geolocation information in monocular visual navigation. This algorithm presents an effective approach to UAV navigation and positioning. Initially, Visual Odometry (VO) was employed for tracking the UAV’s motion and extracting keyframes. Subsequently, a geolocation method based on heterogeneous image matching was utilized to calculate the geographic pose of the UAV. Additionally, we introduce a tightly coupled information fusion method based on visual-geography optimization, which provides a geographic initializer and enables real-time estimation of the UAV’s geographical pose. Finally, the algorithm dynamically adjusts the weight of geographic information to improve optimization accuracy. The proposed method is extensively evaluated in both simulated and real-world environments, and the results demonstrate that our proposed approach can accurately and in real-time estimate the geographic pose of the UAV in a GNSS-denied environment. Specifically, our proposed approach achieves a root-mean-square error (RMSE) and mean positioning accuracy of less than 13 m