Constance van Eeden Invited Speaker, UBC Statistics Department
Tibshirani will review the lasso method and show an example of its utility in cancer diagnosis via mass spectometry. He will then consider testing the significance of the terms in a fitted regression, fit via the lasso. He will present a novel test statistic for this problem and show that it has a simple asymptotic null distribution. This work builds on the least angle regression approach for fitting the lasso, and the notion of degrees of freedom for adaptive models (Efron 1986) and for the lasso (Efron et. al 2004, Zou et al 2007). He will give examples of this procedure, discuss extensions to generalized linear models and the Cox model, and describe an R language package for its computation.
This work is joint with Richard Lockhart (Simon Fraser University), Jonathan Taylor (Stanford) and Ryan Tibshirani (Carnegie Mellon).
In many physical processes, one is interested in mixing and obstructions to mixing: warm air currents mixing with cold air; pollutant dispersal etc. Analogous questions arise in pure mathematics in dynamical systems and Markov chains. In this talk, I will describe the relationship between obstructions to mixing and eigenvectors of transition operators; in particular I will focus on recent work on the non-stationary case: when the Markov chain or dynamical system is non-homogeneous, or when the physical process is driven by external factors.
I will illustrate my talk with analysis of and data from ocean mixing.
In recent years it has become increasingly clear that stochasticity plays an important role in many biological processes. Examples include bistable genetic switches, noise enhanced robustness of oscillations, and fluctuation enhanced sensitivity or “stochastic focusing". Numerous cellular systems rely on spatial stochastic noise for robust performance. We examine the need for stochastic models, report on the state of the art of algorithms and software for modeling and simulation of stochastic biochemical systems, and identify some computational challenges.
The classification of finite simple groups is of fundamental importance in mathematics. It is also one of the longest and most complicated proofs in mathematics.
We will very briefly discuss the result and a bit of history and then explain how it can and has been used to solve problems in many areas. We will end with mentioning some specific and perhaps surprising consequences in various fields.
The dichotomy between sparse and dense structures is one of the profound, yet fuzzy, features of contemporary mathematics and computer science. We present a framework for this phenomenon, which equivalently defines sparsity and density of structures in many different yet equivalent forms, including effective decomposition properties. This has several applications to model theory, algorithm design and, more recently, to structural limits.
The second PRIMA congress took place at the Jiao Tong University in Shanghai from June 23rd till June 28th of 2013. A separate congress website is available with up-to-date information on the conference program and schedule.