Applied Mathematics

Hybrid Krylov Subspace Iterative Methods for Inverse Problems

Speaker: 
James Nagy
Date: 
Fri, May 5, 2017
Location: 
PIMS, University of Manitoba
Conference: 
Mathematical Imaging Science
Abstract: 
Inverse problems arise in many imaging applications, such as image reconstruction (e.g., computed tomography), image deblurring, and digital super-resolution. These inverse problems are very difficult to solve; in addition to being large scale, the underlying mathematical model is often ill-posed, which means that noise and other errors in the measured data can be highly magnified in computed solutions. Regularization methods are often used to overcome this difficulty. In this talk we describe hybrid Krylov subspace based regularization approaches that combine matrix factorization methods with iterative solvers. The methods are very efficient for large scale imaging problems, and can also incorporate methods to automatically estimate regularization parameters. We also show how the approaches can be adapted to enforce sparsity and nonnegative constraints. We will use many imaging examples that arise in medicine and astronomy to illustrate the performance of the methods, and at the same time demonstrate a new MATLAB software package that provides an easy to use interface to their implementations. This is joint work with Silvia Gazzola (University of Bath) and Per Christian Hansen (Technical University of Denmark).

The Case for T-Product Tensor Decompositions: Compression, Analysis and Reconstruction of Image Data

Speaker: 
Misha Kilmer
Date: 
Fri, May 5, 2017
Location: 
PIMS, University of Manitoba
Conference: 
Mathematical Imaging Science
Abstract: 
Most problems in imaging science involve operators or data that are inherently multidimensional in nature, yet traditional approaches to modeling, analysis and compression of (sequences of) images involve matricization of the model or data. In this talk, we discuss ways in which multiway arrays, called tensors, can be leveraged in imaging science for tasks such as forward problem modeling, regularization and reconstruction, video analysis, and compression and recognition of facial image data. The unifying mathematical construct in our approaches to these problems is the t-product (Kilmer and Martin, LAA, 2011) and associated algebraic framework. We will see that the t-product permits the elegant extension of linear algebraic concepts and matrix algorithms to tensors, which in turn gives rise to new, highly parallelizable, algorithms for the imaging tasks noted above.

The Geometry of the Phase Retrieval Problem

Speaker: 
Charles Epstein
Date: 
Fri, May 5, 2017
Location: 
PIMS, University of Manitoba
Conference: 
Mathematical Imaging Science
Abstract: 
Phase retrieval is a problem that arises in a wide range of imaging applications, including x-ray crystallography, x-ray diffraction imaging and ptychography. The data in the phase retrieval problem are samples of the modulus of the Fourier transform of an unknown function. To reconstruct this function one must use auxiliary information to determine the unmeasured Fourier transform phases. There are many algorithms to accomplish task, but none work very well. In this talk we present an analysis of the geometry that underlies these failures and points to new approaches for solving this class of problems.

Managing Patients with Chronic Conditions

Speaker: 
Mariel Lavieri
Date: 
Thu, Feb 23, 2017
Location: 
University of Calgary, Downtown Campus
Conference: 
Lunchbox Lecture Series
Abstract: 
Chronic disease management often involves sequential decisions that have long-term implications. Those decisions are based on high dimensional information, which pose a problem for traditional modeling paradigms. In some key instances, the disease dynamics might not be known, but instead are learned as new information becomes available. As a first step, we will describe some of the ongoing research modeling medical decisions of patients with chronic conditions. Key to the models developed is the incorporation of the individual patient's disease dynamics into the parameterization of the models of the disease state evolution. Model conception and validation is described, as well as the role of multidisciplinary collaborations in ensuring practical impact of this work.

PIMS-SFU 20th Anniversary Celebration: Nataša Pržulj - Data Driven Medicine

Speaker: 
Nataša Pržulj
Date: 
Fri, Nov 25, 2016
Location: 
PIMS, Simon Fraser University
Conference: 
PIMS 20th Anniversary Celebration
Abstract: 

The Pacific Institute for the Mathematical Sciences (PIMS) was founded in 1996, and Simon Fraser University is a founding member. The members of PIMS now include all the major Canadian research universities west of Ontario, as well as universities in Washington and Oregon. Please join us to celebrate 20 years of productive collaboration, with a lecture by SFU alumna and professor at UCL Nataša Pržulj on Data Driven Medicine followed by a reception.

 

We are faced with a flood of molecular and clinical data. Various biomolecules interact in a cell to perform biological function, forming large, complex systems. Large amounts of patient-specific datasets are available, providing complementary information on the same disease type. The challenge is how to model and mine these complex data systems to answer fundamental questions, gain new insight into diseases and improve therapeutics. Just as computational approaches for analyzing genetic sequence data have revolutionized biological and medical understanding, the expectation is that analyses of networked “omics” and clinical data will have similar ground-breaking impacts. However, dealing with these data is nontrivial, since many questions we ask about them fall into the category of computationally intractable problems, necessitating the development of heuristic methods for finding approximate solutions.

We develop methods for extracting new biomedical knowledge from the wiring patterns of large networked biomedical data, linking network wiring patterns with function and translating the information hidden in the wiring patterns into everyday language. We introduce a versatile data fusion (integration) framework that can effectively integrate somatic mutation data, molecular interactions and drug chemical data to address three key challenges in cancer research: stratification of patients into groups having different clinical outcomes, prediction of driver genes whose mutations trigger the onset and development of cancers, and re-purposing of drugs for treating particular cancer patient groups. Our new methods stem from network science approaches coupled with graph-regularised non-negative matrix tri-factorization, a machine learning technique for co-clustering heterogeneous datasets.

About Irreversibility in Rarefied Gas Dynamics

Speaker: 
Laure Saint-Raymond
Date: 
Fri, Oct 7, 2016
Location: 
PIMS, University of British Columbia
Conference: 
PIMS/UBC Distinguished Colloquium
Abstract: 
About Irreversibility in Rarefied Gas Dynamics

A glamorous Hollywood star, a renegade composer, and the mathematical development of spread spectrum communications.

Speaker: 
Mark Goresky
Date: 
Mon, May 30, 2016
Location: 
PIMS, University of British Columbia
Conference: 
2016 Niven Lecture
Abstract: 
During World War II Hedy Lamarr, a striking Hollywood actress, together with George Antheil, a radical composer, invented and patented a secret signaling system for the remote control of torpedoes. The ideas in this patent have since developed into one of the ingredients in modern digital wireless communications. The unlikely biography of these two characters, along with some of the more modern developments in wireless communications will be described.

Bayesian study design for nonlinear systems: an animal disease transmission experiment case study

Speaker: 
Rob Deardon
Date: 
Tue, May 3, 2016
Location: 
PIMS, University of Calgary
Conference: 
Lunchbox Lecture Series
Abstract: 
Experimental design is a branch of statistics focused upon designing experimental studies in a way that maximizes the amount of salient information produced by the experiment. It is a topic which has been well studied in the context of linear systems. However, many physical, biological, economic, financial and engineering systems of interest are inherently non-linear in nature. Experimental design for non-linear models is complicated by the fact that the optimal design depends upon the parameters that we are using the experiment to estimate. A Bayesian, often simulation-based, framework is a natural setting for such design problems. We will illustrate the use of such a framework by considering the design of an animal disease transmission experiment where the underlying goal is to identify some characteristics of the disease dynamics (e.g. a vaccine effect, or the infectious period).

Optimal Strategic Sizing of Energy Storage Facilities in Restructured Electricity Markets

Author: 
Hamidreza Zareipour
Date: 
Wed, Apr 6, 2016
Location: 
PIMS, University of Calgary
Conference: 
Lunchbox Lecture Series
Abstract: 
In this seminar we will discuss a new model for strategic investment model for a merchant energy storage facility. The facility's actions impact market-clearing outcomes, and thus it is a price-maker facility. We consider the uncertainties associated with other generation units offering strategies and future load levels in the proposed model. Thestrategic investment decisions include the sizes of charging device,discharging device, and energy reservoir. The proposed model is astochastic bi-level optimization problem where planning and operation decisions of the energy storage facility are made in the upper level, and market clearing is modeled in the lower level under different operating conditions. To make the proposed model computationally tractable, an iterative solution technique based on Benders¹ decomposition is implemented. This provides a master problem and a set of subproblems for each scenario. Each subproblem is recast as a Mathematical Programs with Equilibrium Constraints (MPEC). Numerical results based on real-lifemarket data from Alberta's electricity market will be provided.
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