scholarly journals A skeleton model to enumerate standard puzzle sequences

2021 ◽  
Vol 30 (1) ◽  
pp. 179-203
Author(s):  
Shishuo Fu ◽  
◽  
Jiaxi Lu ◽  
Yuanzhe Ding ◽  
Keyword(s):  
Catalan Numbers ◽  
Skeleton Model ◽  
Combinatorial Object ◽  
Enumeration Problem ◽  
Secant Numbers

<abstract><p>Guo-Niu Han [Sémin. Lothar. Comb. 85 (2021) B85c (electronic)] has introduced a new combinatorial object named standard puzzle. We use digraphs to show the relations between numbers in standard puzzles and propose a skeleton model. By this model, we solve the enumeration problem of over fifty thousand standard puzzle sequences. Most of them can be represented by classical numbers, such as Catalan numbers, double factorials, secant numbers and so on. Also, we prove several identities for standard puzzle sequences.</p></abstract>

Generating the Mapping Class Group

2017 ◽  
Author(s):  
Benson Farb ◽  
Dan Margalit
Keyword(s):  
Exact Sequence ◽  
Simplicial Complex ◽  
Mapping Class Group ◽  
Class Group ◽  
Mapping Class ◽  
Detailed Structure ◽  
Inductive Step ◽  
Closed Curves ◽  
Combinatorial Object ◽  
Generating Sets

This chapter considers the Dehn–Lickorish theorem, which states that when g is greater than or equal to 0, the mapping class group Mod(Sɡ) is generated by finitely many Dehn twists about nonseparating simple closed curves. The theorem is proved by induction on genus, and the Birman exact sequence is introduced as the key step for the induction. The key to the inductive step is to prove that the complex of curves C(Sɡ) is connected when g is greater than or equal to 2. The simplicial complex C(Sɡ) is a useful combinatorial object that encodes intersection patterns of simple closed curves in Sɡ. More detailed structure of C(Sɡ) is then used to find various explicit generating sets for Mod(Sɡ), including those due to Lickorish and to Humphries.

Based on spatio-temporal graph convolution networks with residual connection for intelligence behavior recognition

2021 ◽  
pp. 002072092199660
Author(s):  
Yinong Zhang ◽  
Shanshan Guan ◽  
Cheng Xu ◽  
Hongzhe Liu
Keyword(s):  
Human Behavior ◽  
Behavior Recognition ◽  
Convolutional Network ◽  
Skeleton Model ◽  
Basic Technology ◽  
Temporal Model ◽  
Temporal Graph ◽  
Spatio Temporal ◽  
Human Behavior Recognition ◽  
Behavior Characteristics

In the era of intelligent education, human behavior recognition based on computer vision is an important branch of pattern recognition. Human behavior recognition is a basic technology in the fields of intelligent monitoring and human-computer interaction in education. The dynamic changes of human skeleton provide important information for the recognition of educational behavior. Traditional methods usually use manual information to label or traverse rules only, resulting in limited representation capabilities and poor generalization performance of the model. In this paper, a kind of dynamic skeleton model with residual is adopted—a spatio-temporal graph convolutional network based on residual connections, which not only overcomes the limitations of previous methods, but also can learn the spatio-temporal model from the skeleton data. In the big bone NTU-RGB + D dataset, the network model not only improved the representation ability of human behavior characteristics, but also improved the generalization ability, and achieved better recognition effect than the existing model. In addition, this paper also compares the results of behavior recognition on subsets of different joint points, and finds that spatial structure division have better effects.

scholarly journals ON DIVISIBILITY OF BINOMIAL COEFFICIENTS

2012 ◽  
Vol 93 (1-2) ◽  
pp. 189-201 ◽  
Author(s):  
ZHI-WEI SUN
Keyword(s):  
Higher Order ◽  
Catalan Numbers ◽  
Binomial Coefficients

AbstractIn this paper, motivated by Catalan numbers and higher-order Catalan numbers, we study factors of products of at most two binomial coefficients.

3D hand skeleton model estimation from a depth image

2015 ◽  
Author(s):  
Chin-Yun Fan ◽  
Meng-Hsuan Lin ◽  
Te-Feng Su ◽  
Shang-Hong Lai ◽  
Chih-Hsiang Yu
Keyword(s):  
Depth Image ◽  
Model Estimation ◽  
Skeleton Model

Video-Based Human Motion Analysis

2011 ◽  
Vol 403-408 ◽  
pp. 2593-2597
Author(s):  
Hong Bao ◽  
Zhi Min Liu
Keyword(s):  
Motion Analysis ◽  
Human Body ◽  
Body Shape ◽  
Human Motion ◽  
Random Motion ◽  
Human Motion Analysis ◽  
Mass Center ◽  
Shape Features ◽  
Skeleton Model ◽  
Regular Motion

In the analysis of human motion, movement was divided into regular motion (such as walking and running) and random motion (such as falling down).Human skeleton model is used in this paper to do the video-based analysis. Key joints on human body were chosen to be traced instead of tracking the entire human body. Shape features like mass center trajectory were used to describe the movement, and to classify human motion. desired results achieved.

Sign in / Sign up

Export Citation Format

Share Document