Utilizing the open source symbolic manipulator Sympy, we developed PyDy, a tool for kinematic and dynamic analysis of mechanical systems. PyDy provides a set of tools to analytically formulate, numerically integrate, create 2d/3d plots, and animate the equations of motion, all within the powerful and easy to use Python environment. Some of the useful features of PyDy include: output of symbolically derived expressions as LaTeX code, numerical integration of equations using ODEINT, and the ability to interact with the tool through a web interface.
One of the main features of PyDy is to automate the tedious tasks that are necessary for the kinematical and dynamical description of multibody systems. Expressing vectors in any coordinate system is trivial with PyDy, as well the determination of angular velocity of a frame or velocity of a point with respect to any other frame. Differentiation of vector quantities is also handled automatically.
PyDy formulates the equations of motion using Kane's method, which is particularly well suited to multibody systems and systems with nonholonomic constraints. Constraint-free equations of motion are obtained directly, but if one is interested in the determination of forces and torques of constraint, Kane's method provides for a systematic way for their determination. PyDy combined with Visual Python allows for easy visualization of these forces and/or torques.
The use of PyDy will be demonstrated on three familiar
systems: the simple pendulum, an n-body pendulum, and
the rolling torus. It is our hope that this open source
tool be used for teaching statics and dynamics at the
undergraduate and graduate level, as well for performing
interesting research on multibody dynamical systems.
It was reported that every 70 seconds someone in the U.S. develops Alzheimer's in the "2009 Alzheimer's Disease Facts and Figures" report. There is no known cure, and the best that current medicine can do is slow the rate of decline. In the talk I will describe a method for data mining the world of MR brain images via harmonic analysis techniques. The goal of this work is to provide early detection of Alzheimer's disease and track its development. I will define a new similarity measure between MR images using feature extraction. From this local measure one can define a global structure on the MRI data set. With diffusion maps this structure can be exploited for image analysis, clustering, classification and many other applications.
Tree decompositions and chordal graphs are closely related fields in graph theory where one would like to roughly compare how tree-like a graph is. Applications can be found in engineering, statistics, and mathematics, as well as numerous areas of computer science including computational biology, sparse matrix factorization, databases, machine learning, and networks. I will introduce the main ideas and discuss the role of chordal graphs in the perfect phylogeny problem and Gaussian elimination of sparse symmetric matrices.
Exploring the world of MR brain images via Harmonic Analysis
Blake Hunter
Tree decompositions, chordal graphs, and their applications
Rob Gysel