An Application of the Moving Frame Method to Integral Geometry in the Heisenberg Group

We show the fundamental theorems of curves and surfaces in the 3-dimensional Heisenberg group and find a complete set of invariants for curves and surfaces respectively. The proofs are based on Cartan's method of moving frames and Lie group theory. As an application of the main theorems, a Crofton-type formula is proved in terms of p-area which naturally arises from the variation of volume. The application makes a connection between CR geometry and integral geometry

A Study on the Management Effectiveness and Problems of Tribal Colleges in Taiwan

The main purpose of this study is to analyze the development background and objectives of indigenous tribal colleges, and to understand the effectiveness and problems of its management in Taiwan. After SWOT analysis, the main findings are as follows: 1. Advantages: the unique culture of indigenous people is an opportunity for economic development. In addition, the protection of laws and regulations is the main advantage of tribal college. 2. Weakness: under the current economic system, the indigenous people are limited in land use, inconvenient transportation, inadequate agricultural technology, and unsmooth sales channels, which limit their economic development. 3. Threats: because the population flows to the city, the tribal people do not understand what kind of institution the tribal university is, and some of the funds have to be paid by the learners themselves, resulting in the low participation of the tribal people. Moreover, the units that handle tribal college are almost different every year, which affects the preservation of data. 4. Opportunities: the existence of tribal college also provides an opportunity for the inheritance and reconstruction of indigenous culture. Based on the above analysis, this study puts forward relevant suggestions for the management of tribal colleg

Shallow Triple Stream Three-dimensional CNN (STSTNet) for Micro-expression Recognition

In the recent year, state-of-the-art for facial micro-expression recognition have been significantly advanced by deep neural networks. The robustness of deep learning has yielded promising performance beyond that of traditional handcrafted approaches. Most works in literature emphasized on increasing the depth of networks and employing highly complex objective functions to learn more features. In this paper, we design a Shallow Triple Stream Three-dimensional CNN (STSTNet) that is computationally light whilst capable of extracting discriminative high level features and details of micro-expressions. The network learns from three optical flow features (i.e., optical strain, horizontal and vertical optical flow fields) computed based on the onset and apex frames of each video. Our experimental results demonstrate the effectiveness of the proposed STSTNet, which obtained an unweighted average recall rate of 0.7605 and unweighted F1-score of 0.7353 on the composite database consisting of 442 samples from the SMIC, CASME II and SAMM databases.Comment: 5 pages, 1 figure, Accepted and published in IEEE FG 201