Large joints in graphs

We show that if G is a graph of sufficiently large order n containing as many r-cliques as the r-partite Turan graph of order n; then for some C>0 G has more than Cn^(r-1) (r+1)-cliques sharing a common edge unless G is isomorphic to the the r-partite Turan graph of order n. This structural result generalizes a previous result that has been useful in extremal graph theory.Comment: 9 page

Modeling Stiffness and Damping in Rotational Degrees of Freedom Using Multibond Graphs

A contribution is proposed for the modeling of mechanical systems using multibond graphs. When modeling a physical system, it may be needed to catch the dynamic behavior contribution of the joints between bodies of the system and therefore to characterize the stiffness and damping of the links between them. The visibility of where dissipative or capacitive elements need to be implemented to represent stiffness and damping in multibond graphs is not obvious and will be explained. A multibond graph architecture is then proposed to add stiffness and damping in hree rotational degrees of freedom. The resulting joint combines the spherical joint multibond graph relaxed causal constraints while physically representing three concatenated revolute joints. The mathematical foundations are presented, and then illustrated through the modeling and simulation of an inertial navigation system; in which stiffness and damping between the gimbals are taken into account. This method is particularly useful when modeling and simulating multibody systems using Newton-Euler formalism in multibond graphs. Future work will show how this method can be extended to more complex systems such as rotorcraft blades' connections with its rotor hub.Fondation Airbus Grou

Skeleton-based Action Recognition of People Handling Objects

In visual surveillance systems, it is necessary to recognize the behavior of people handling objects such as a phone, a cup, or a plastic bag. In this paper, to address this problem, we propose a new framework for recognizing object-related human actions by graph convolutional networks using human and object poses. In this framework, we construct skeletal graphs of reliable human poses by selectively sampling the informative frames in a video, which include human joints with high confidence scores obtained in pose estimation. The skeletal graphs generated from the sampled frames represent human poses related to the object position in both the spatial and temporal domains, and these graphs are used as inputs to the graph convolutional networks. Through experiments over an open benchmark and our own data sets, we verify the validity of our framework in that our method outperforms the state-of-the-art method for skeleton-based action recognition.Comment: Accepted in WACV 201

Combinatorial models of rigidity and renormalization

We first introduce the percolation problems associated with the graph theoretical concepts of $(k,l)$-sparsity, and make contact with the physical concepts of ordinary and rigidity percolation. We then devise a renormalization transformation for $(k,l)$-percolation problems, and investigate its domain of validity. In particular, we show that it allows an exact solution of $(k,l)$-percolation problems on hierarchical graphs, for $k\leq l<2k$. We introduce and solve by renormalization such a model, which has the interesting feature of showing both ordinary percolation and rigidity percolation phase transitions, depending on the values of the parameters.Comment: 22 pages, 6 figure