Theoretical problem statement
Lift the Shannon/Parry Markov chain of a strongly connected
finite graph to the timed automata settings.
(aka MME of an irreducible SFT)
Practical problem statement
Generate quickly and as uniformly as possible runs of a timed
◮ quickly: Step by step simulation as with a finite state Markov
Chain → Stochastic Process Over Runs (SPOR)
◮ ≈ uniformly → SPOR of maximal entropy + asymptotic
• A model for verification of real-time systems
• Invented by Alur and Dill in early 1990s
• Precursors: time Petri nets (Bethomieu)
• Now: an efficient model for verification, supported by
• A popular researh topic (¿8000 citation for papers by Alur
• modeling and verification
• decidability and algorithmics
• automata and language theory
• very recent: dynamics
• Inspired by TA: hybrid automata, data automata,
automata on nominal sets
International Workshop on the Perspectives on High Dimensional Data Analysis III
Folded concave penalization methods have been shown to enjoy the strong oracle property for high-dimensional sparse estimation. However, a folded concave penalization problem usually has multiple local solutions and the oracle property is established only for one of the unknown local solutions. A challenging fundamental issue still remains that it is not clear whether the local optimal solution computed by a given optimization algorithm possesses those nice theoretical properties. To close this important theoretical gap in over a decade, we provide a unified theory to show explicitly how to obtain the oracle solution using the local linear approximation algorithm. For a folded concave penalized estimation problem, we show that as long as the problem is localizable and the oracle estimator is well behaved, we can obtain the oracle estimator by using the one-step local linear approximation. In addition, once the oracle estimator is obtained, the local linear approximation algorithm converges, namely produces the same estimator in the next iteration. We show that the LASSO is a good initial estimator, which produces the oracle estimator using the one-step LLA algorithm for folded concave penalization methods. This is demonstrated by using three classical sparse estimation problems, namely, the sparse linear regression, the sparse logistic regression and the sparse precision matrix estimation, and illustrates the power of combining the LASSO and SCAD to solve sparse inartistical estimation problem. (joint work with Lingzhou Xue and Hui Zou)
In 1757, Euler presented to the Berlin Academy of Sciences the basic equations of fluid mechanics. As pointed out by V.I. Arnold in 1966, the Euler equations for incompressible fluids have a very simple geometric interpretation that combines the concept of geodesics and the concept of volume preserving maps. The later concept is very simple and nothing but a continuous version of the discrete and more elementary concept of permutation. Conversely, the Euler equations have a natural discrete counterpart in terms of permutation and combinatorial optimization, which establishes a direct link with the mathematical theory of "optimal transport". This theory, that goes back to Monge 1781 and has been renewed by Kantorovich since 1942, is nowadays a flourishing field with many applications, in natural sciences, economics, differential geometry and analysis.
This tutorial will introduce you to the theory and practice of ggplot2. I'll introduce you to the rich theory that underlies ggplot2, and then we'll get our hands dirty making graphics to help understand data. I'll also point you towards resources where you can learn more, and highlight some of the other packages that work hand in hand with ggplot2 to make data analysis easy.
You will have the opportunity to practice what you learn, so please bring along your laptop, with the latest version of R installed. Make sure that your version of ggplot2 is up-to-date by running install.packages("ggplot2").
To get the most out of the course, I'd recommend that you're already comfortable with R: you know how to get your data into R, you've done some graphics (base or lattice) in the past, and you've written an R function.
This five week summer camp is for students currently attending grades 9 to 12. The main purpose of this camp is to help students with their academics and for them to get work experience at the university. Students take 90 minutes of math and English every day and three days a week they will be working with a faculty member in the area of their choice. Students will get $100 a week for 7.5 hours of work experience. The summer camp takes place at UBC, and students will take classes at PIMS and the Long House. Last year we had students working with the nuclear accelerator, and working at labs in the physics and chemistry departments, among other opportunities.
For more information on the program see Emerging Aboriginal Scholars Program.