Related Experiment Video
Updated: Aug 2, 2025

ExCYT: A Graphical User Interface for Streamlining Analysis of High-Dimensional Cytometry Data
Published on: January 16, 2019
Tug of War games and PDEs on graphs with applications in image and high dimensional data processing
Hamza Ennaji1, Yvain Quéau2, Abderrahim Elmoataz2
1UNICAEN, ENSICAEN, CNRS, GREYC, Normandie Univ, 14000, Caen, France. hamza.ennaji@unicaen.fr.
Abstract:
The aim of this note is to revisit the connections between some stochastic games, namely Tug-of-War games, and a class of nonlocal PDEs on graphs. We consider a general formulation of Tug-of-War games which is shown to be related to many classical PDEs in the continuous setting. We transcribe these equations on graphs using ad hoc differential operators and we show that it covers several nonlocal PDEs on graphs such as [Formula: see text]-Laplacian, game p-Laplacian and the eikonal equation. This unifying mathematical framework allows us to easily design simple algorithms to solve several inverse problems in imaging and data science, with a particular focus on cultural heritage and medical imaging.
Related Concept Videos
Manipulation and Analysis
Vector Algebra: Graphical Method
We use the laws of geometry to construct resultant vectors, followed by trigonometry to find vector magnitudes and directions. For a geometric construction of the sum of two vectors in a plane, we follow the parallelogram rule. Suppose two vectors are at arbitrary positions. Translate either one of...
Convolution: Math, Graphics, and Discrete Signals
To simplify the convolution integral, it is assumed that both the input signal and impulse response are zero for negative time values. The graphical convolution process...
Three-Dimensional Analysis of Strain
Collisions in Multiple Dimensions: Problem Solving
A small car of mass 1,200 kg traveling east at 60 km/h collides at an intersection with a truck of mass 3,000 kg traveling due north at 40 km/h. The two vehicles are locked together. What is the...
Two-Dimensional Force System: Problem Solving
The first step to solving a two-dimensional force system problem is to draw a free-body diagram of the object under consideration. This diagram helps identify all the external forces acting on the object, including their...

