We prove the exact controllability of the systems with the optimal number of controls and propose an algorithm recovering the unknown densities of the strings, lengths of the edges, attached masses, and the topology of the graph.

The proofs are based on the boundary control and leaf peeling methods de-
veloped in our previous papers. The boundary control method is a powerful method in inverse theory which uses deep connections between controllability and identifiability of distributed parameter systems and lends itself to straight-forward algorithmic implementations.

Course Description: If you ever worry about the validity of the common variance or other parametric distribution assumptions for your data analysis, quantile regression might be a relief for you because quantile regression is a distribution-agnostic methodology. Whereas generalized linear regression models the conditional means via link functions, quantile regression enables you to more fully explore your data by modeling conditional quantiles, tail distributions, or the entire conditional distributions. Quantile regression is particularly useful when your data are heterogeneous and when you cannot assume a parametric distribution for the response. This tutorial provides an overview and a set of intuitive examples of the quantile regression methodology.  From the basic concepts and comparison to linear regression to more advanced applications and research topics, this tutorial demonstrates the benefits and potentials of using quantile regression methods and introduces computing tools for quantile model fitting, quantile predictions, conditional distribution estimation, conditional percentage estimation, and other inferences and hypothesis testing.  The attendees are assumed to be familiar with basic probability distributions, linear algebra, and linear regression.

The first lecture covers:

1. Benefits and basics
2. a) Motivation
3. b) Comparison to linear regression
4. Single-level quantile regression
5. a) Computation software
6. b) Parameter estimates and quantile predictions
7. c) Interpretation, inferences, and hypothesis testing
8. Quantile process regression
9. a) Functional parameter estimates
10. b) Conditional distribution estimation
11. c) Conditional percentages versus unconditional percentages

The second lecture covers:

4. Model selection
5. a) Selection methods
6. b) Model fitness criteria
7. c) Model selection for quantile process regression
8. Extended applications
9. a) Trimmed mean regression
10. b) Censored data analysis
11. c) Counterfactual analysis
12. d) Quantile factorization machine for recommendation system
13. e) Values at risk
14. f) Extreme value analysis
15. g) More research area
16. Summary

ComputingSoftware:  Neither personal computer nor pre-installed software are required in classroom. This short course will present SAS outputs for relevant example programs.  You are welcome to try the programs on SAS 9.22 or later release including the free SAS University Edition.

Short Biography:   Dr. Yonggang Yao is a principal research statistician at SAS Institute Inc. He joined SAS in 2008 after obtaining his PhD in statistics from The Ohio State University. Dr. Yao has developed several SAS quantile-regression procedures for standard and distributed computing environments including PROC QUANTSELECT and PROC HPQUANTSELECT. He is also the key supporting developer for two other SAS procedures: PROC QUANTREG for quantile regression and PROC ROBUSTREG for robust regression. Dr. Yao has taught tutorials on quantile regression at SAS Global Forums, the Joint Statistical Meetings, and for the ASA traveling courses.

Parking:         Visitor parking is available inEast Deck 1.

Abstract: The difficulties of detecting association, measuring correlation, and establishing cause and effect have fascinated mankind since time immemorial. Democritus, the Greek philosopher, underscored well the importance and the difficulty of proving causality when he wrote, “I would rather discover one cause than gain the kingdom of Persia.’’

To address the difficulties of relating cause and effect, statisticians have developed many inferential techniques. Perhaps the most well-known method stems from Karl Pearson’s coefficient of correlation, introduced in the late 19th century.

I will introduce in this lecture the recently-devised distance correlation coefficient and describe its advantages over the Pearson and other classical measures of correlation. We will review an application of the distance correlation coefficient to data drawn from large astrophysical databases, where it is desired to classify galaxies according to various types. Further, the lecture will analyze data arising in the on-going national discussion of the relationship between state-by-state homicide rates and the stringency of state laws governing firearm ownership.

The lecture will also describe a remarkable singular integral which lies at the core of the theory of the distance correlation coefficient. We will describe generalizations of this singular integral to truncated Maclaurin expansions of the cosine function and to the theory of spherical functions on symmetric cones.