Pacific Institute for the Mathematical Sciences - PIMS

Absolutely continuous spectrum for random Schrödinger operators on tree-strips of finite cone-type.

Joslin Goh
Title: Prediction and Calibration Using Outputs From Multiple Simulators
Abstract: Deterministic simulators are widely used to describe physical processes in lieu of physical observations. In some cases, more than one computer simulator can be used to explore the physical system. Through the combination of field observations and simulated outputs, predictive models are developed for the real physical system. The resulting model can be used to perform sensitivity analysis for the system, solve inverse problems and make predictions. The proposed approach is Bayesian and will be illustrated through applications in predictive science at the Centre for Radiative Shock Hydrodynamics at the University of Michigan.

Seong-Hwan Jun
Title: Entangled Monte Carlo
Abstract: We propose a novel method for scalable parallelization of SMC algorithms, Entangled Monte Carlo simulation (EMC). EMC avoids the transmission of particles between nodes, and instead reconstructs them from the particle genealogy. In particular, we show that we can reduce the communication to the particle weights for each machine while efficiently maintaining implicit global coherence of the parallel simulation. We explain methods to efficiently maintain a genealogy of particles from which any particle can be reconstructed. We demonstrate using examples from Bayesian phylogenetic that the computational gain from parallelization using EMC significantly outweighs the cost of particle reconstruction. The timing experiments show that reconstruction of particles is indeed much more efficient as compared to transmission of particles.

Zheng Sun
Title: EDF Tests for Ordered Categorical Data
Abstract: In this talk, we consider a general class of EDF (Empirical Distribution Function) tests for ordered categorical data (ordered contingency tables), that is when the cells have a natural ordering, for example, letter grades on exams. Asymptotic distributions are found under the null hypothesis
H_0: each row follows the same distribution.
Asymptotic distributions under some contiguous alternatives are also found and asymptotic power of these tests can be calculated.  A theorem is proved connecting the cases when parameters are known with those when parameters must be estimated.
Components of these test statistics are examined and the first 4 components can be interpreted as tests that are aimed at specific alternatives: location, scale, skewness and kurtosis.
We compare powers of the EDF tests with many competing tests including tests derived from the Neyman Pearson Lemma. EDF tests compare favourably.
A example data set is analyzed.

Dr. Ruben Zamar
Title: Robustness and Other Things
Abstract: Data quality is typically affected by the presence of outliers and other forms of data contamination. It may also be affected by missing data, data duplication, etc. From a broad perspective I am interested in the study of the detrimental effect of poor data quality on statistical inference, and in developing appropriate alternative methods to address these problems. The purpose of this talk is to give students a broad picture of my research interests and some current research projects. "Other things"  in the title refers to other related topics I am interested in, such as cluster analysis, model selection, bootstrap and data mining.

Dr. Joan Hu
Title: Statistical Analysis for Forest Fire Control
Abstract: This talk discusses statistical issues arising from forest fire control. We start with brief background information to motivate the statistical problems. Models and inference procedures are then proposed. A set of Canadian forest fire data is used throughout the talk for illustration.
This is an on-going project jointly with W. John Braun.


Jabed Hossain Tomal
Title: Ensembling Descriptor Sets using Phalanxes of Variables to Rank Activity of Compounds in QSAR Studies
Abstract: In QSAR studies, molecular descriptors are used to model biological activity of compounds. The statistical model aims to rank rare actives early in a list of compounds. The classifier “random forest” has been found highly accurate in QSAR studies. To enhance its performance in terms of predictive ranking, we propose an ensemble method by grouping variables together. The variables in a group (we call phalanx) are good to put together, whereas the variables in different groups (phalanxes) are good to ensemble. Finally, our method aggregates the phalanxes. There exist several molecular descriptor sets in QSAR studies, and a particular set might do well in ranking activity of compounds for some assays, and fail to do well for other assays. We have considered four assays and five descriptor sets for each. We apply the ensemble of phalanxes to each descriptor set and further ensemble across the five descriptor sets we generated. The performance of our ensemble is compared with random forest. Specifically, random forest was applied to each of the five descriptor sets and to the pool of descriptor sets. We found our method superior to any of the random forests using two rigorous evaluation procedures.

Shirin Golchi
Title: Monotone Interpolation: Sampling from a Constrained Gaussian Posterior
Abstract: Gaussian process (GP) models are popular tools for non-parametric modelling and function estimation. They are commonly used in the area of computer experiments where a finite number of function evaluations are available from a simulator and the underlying functin is to be estimated using a statistical model while interpolating the given points. However, in the case that extra information such as monotonicity of the underlying function is available, it is not straight- forward to incorporate the constraints in a GP model. I will talk about the constrained posterior distribution together with a recipe to sample from it.

Vincenzo Coia
Title: A New Sieve Model for Extreme Values
Abstract: Although rare, extreme events leave a lasting impact on our lives and the world in general. It is therefore important to determine the potential magnitude and frequency of such events, especially when these extremes are dangerous. We focus on the case when these extreme values are heavy tailed. Extreme Value Theory provides a theoretical

basis for extrapolating and making inference into these heavy tails; however, there is room for improvement in the extrapolation methods. One modification to the heavy tail is to add an upper truncation; we propose a modification which "progressively truncates" the tail with permeable filters like a sieve. The techniques are then applied to the largest Atlantic hurricanes and the largest black sea bass in Buzzard's Bay. We find that, in most cases, the sieve model provides the best fit, followed by the truncated model.
 
 

Combinatorial structures arising as discrete mathematical models of physical phenomena are increasingly found lurking at the interface of mathematics and other sciences. Such models, while apparently simple, are sufficiently rich to play a key role in our understanding of the underlying phenomena being studied.

Computational Geometry

The PIMS YRC is a unique and important opportunity for young graduate students in mathematics and statistics from PIMS universities to meet their peers and discover the wide range of research currently undertaken in Western Canada and the Pacific Northwest. Participants will have opportunities to build and strengthen personal and professional relationships, develop and improve communication skills, and gain valuable experience in the environment of a scientific conference.

This conference has grown from the collaboration between the universities of Alberta and Calgary into a truly inter-PIMS universities project.  The PIMS YRC 2012 will offer:    An overview of current mathematical research at PIMS universities, an opportunity to present a short talk in a professional context, a panel discussion on employability in both industry and academia, a chance for graduate students to start building their scientific network, and plenary talks by leading mathematical experts in their fields.Since its inception in 2004 by graduate students at the University of Alberta, the PIMS YRC has been held alternately at the University of Alberta, the University of Calgary, and last year in 2011, the PIMS YRC was hosted for the first time outside of Alberta at the University of British Columbia. The conference has become a well-recognized and popular event; in 2007 the CYRC boasted over 90 participants from 11 different universities and in 2008 welcomed participants from six different provinces from across Canada. The PIMS YRC will continue to gain momentum, respect, and popularity among young researchers in mathematics and statistics.

The stability of coherent structure and patterns.

Stability plays an essential role in many branches of science and engineering, including several aspects of fluid mechanics, high-speed transmission of information, and feasibility of MHD fusion devices. The objective of the workshop is to give an overview of current state-of-the-art methods for examining stability, as well as to present some widely applicable new techniques. The format will consist of three invited speakers giving a series of lectures at a level aimed at graduate students but useful for researchers from a variety of disciplines, such as mathematics, engineering, biology, etc. 

There will be two main courses, given by Omer Angel and Gregory Miermont. There will be a number of invited talks. Participants will have an option of giving a presentation as well.

Omer Angel - Interacting particle systems

Particles attempt to follow a simple dynamic (random walk, constant flow, etc) in some space (interval, line, cycle, arbitrary graph). Add a simple interaction between particles, and the behaviour can change completely. The resulting dynamical systems are far more complex than the ingredients suggest. These processes (interchange process, TASEP, sorting networks, etc) have diverse to many topics: growth processes, queuing theory, representation theory, algebraic combinatorics. I will discuss recent progress on and open problems arising from several models of interacting particle systems.

Gregory Miermont - Planar Maps

The study of maps, that is of graphs embedded in surfaces, is a popular subject that has implications in many branches of mathematics, the most famous aspects being purely graph-theoretical, such as the four-color theorem. The study of random maps has met an increasing interest in the recent years. This is motivated in particular by problems in theoretical physics, in which random maps serve as discrete models of random continuum surfaces. The probabilistic interpretation of bijective counting methods for maps happen to be particularly fruitful, and relates random maps to other important combinatorial random structures like the continuum random tree and the Brownian snake. This course will survey these aspects and present recent developments in this area.

This is a satellite event to the 2012 Summer Meeting of the Canadian Mathematical Society that will take place from June 2 to 4, and it will continue into that meeting as a Special Session on the same topic.

This workshop will introduce participants to current research topics in the intersection of Algebra and Geometry