Computer Science

Reconfiguration of Triangulations of a Planar Point Set

Speaker: 
Anna Lubiw
Date: 
Thu, Feb 15, 2018
Location: 
PIMS, University of Manitoba
Conference: 
PIMS-UManitoba Distinguished Lecture
Abstract: 
In a reconfiguration problem, the goal is to change an initial configuration of some structure to a final configuration using some limited set of moves. Examples include: sorting a list by swapping pairs of adjacent elements; finding the edit distance between two strings; or solving a Rubik’s cube in a minimum number of moves. Central questions are: Is reconfiguration possible? How many moves are required? In this talk I will survey some reconfiguration problems, and then discuss the case of triangulations of a point set in the plane. A move in this case is a flip that replaces one edge by the opposite edge of its surrounding quadrilateral when that quadrilateral is convex. In joint work with Zuzana Masárová and Uli Wagner we characterize when one edge-labelled triangulation can be reconfigured to another via flips. The proof involves combinatorics, geometry, and topology. Anna Lubiw is a professor in the Cheriton School of Computer Science, University of Waterloo. She has a PhD from the University of Toronto (1986) and a Master of Mathematics degree from the University of Waterloo (1983). Her research is in the areas of Computational Geometry, Graph Drawing and Graph Algorithms. She was named the Ross and Muriel Cheriton Faculty Fellow in 2014, received the University of Waterloo outstanding performance award in 2012 and was named a Distinguished Scientist by the Association for Computing Machinery in 2009. She serves on the editorial boards of the Journal of Computational Geometry and the Journal of Graph Algorithms and Applications.

Using physical metaphors to understand networks

Speaker: 
Daniel A. Spielman
Date: 
Mon, May 29, 2017
Location: 
PIMS, University of British Columbia
Conference: 
2017 Niven Lecture
Abstract: 
Networks describe how things are connected, and are ubiquitous in science and society. Networks can be very concrete, like road networks connecting cities or networks of wires connecting computers. They can represent more abstract connections such as friendship on Facebook. Networks are widely used to model connections between things that have no real connections. For example, Biologists try to understand how cells work by studying networks connecting proteins that interact with each other, and Economists try to understand markets by studying networks connecting institutions that trade with each other. Questions we ask about a network include "which components of the network are the most important?", "how well do things like information, cars, or disease spread through the network?", and "does the network have a governing structure?". Professor Spielman will explain how mathematicians address these questions by modeling networks as physical objects, imagining that the connections are springs, electrical resistors, or pipes that carry fluid, and analyzing the resulting systems.

Using physical metaphors to understand networks

Speaker: 
Daniel A. Spielman
Date: 
Mon, May 29, 2017
Location: 
PIMS, University of British Columbia
Conference: 
2017 Niven Lecture
Abstract: 
Networks describe how things are connected, and are ubiquitous in science and society. Networks can be very concrete, like road networks connecting cities or networks of wires connecting computers. They can represent more abstract connections such as friendship on Facebook. Networks are widely used to model connections between things that have no real connections. For example, Biologists try to understand how cells work by studying networks connecting proteins that interact with each other, and Economists try to understand markets by studying networks connecting institutions that trade with each other. Questions we ask about a network include "which components of the network are the most important?", "how well do things like information, cars, or disease spread through the network?", and "does the network have a governing structure?". Professor Spielman will explain how mathematicians address these questions by modeling networks as physical objects, imagining that the connections are springs, electrical resistors, or pipes that carry fluid, and analyzing the resulting systems.

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.

Sparsity, Complexity and Practicality in Symbolic Computation

Speaker: 
Mark Giesbrecht
Date: 
Thu, Mar 17, 2016
Location: 
PIMS, University of Manitoba
Conference: 
PIMS-UManitoba Distinguished Lecture
Abstract: 

Modern symbolic computation systems provide an expressive language for describing mathematical objects. For example, we can easily enter equations such as

$$f=x^{2^{100}}y^2 + 2x^{2^{99}+1}y^{2^{99}+1}+2x^{2^{99}}y+y^{2^{100}}x^{2}+2y^{2^{99}}x+1$$

into a computer algebra system. However, to determine the factorization

$$f -> (x^{2^{99}}y+y^{2^{99}}x+1)^2$$

with traditional methods would incur huge expression swell and high complexity. Indeed, many problems related to this one are provably intractable under various reasonable assumptions, or are suspected to be so. Nonetheless, recent work has yielded exciting new algorithms for computing with sparse mathematical expressions. In this talk, we will attempt to navigate this hazardous computational terrain of sparse algebraic computation. We will discuss new algorithms for sparse polynomial root finding and functional decomposition. We will also look at the "inverse" problem of interpolating or reconstructing sparse mathematical functions from a small number of sample points. Computations over both traditional" exact and symbolic domains, such as the integers and finite fields, as well as approximate (floating point) data, will be considered.

The Mathematics of Lattice-based Cryptography

Speaker: 
Jill Pipher
Date: 
Fri, Mar 13, 2015
Location: 
PIMS, University of British Columbia
Abstract: 

TBA

High dimensional expanders and Ramanujan complexes

Speaker: 
Alexander Lubotzky
Date: 
Fri, Sep 19, 2014
Location: 
PIMS, University of British Columbia
Conference: 
PIMS/UBC Distinguished Colloquium
Abstract: 

Expander graphs have played, in the last few decades, an important role in computer science, and  in the last decade, also in pure mathematics.  In recent years a theory of "high-dimensional expanders" is starting to emerge - i.e., simplical complexes which generalize various properties of expander graphs. This has some geometric motivations (led by Gromov) and combinatorial ones (started by Linial and Meshulam).  The talk will survey the various directions of research and their applications, as well as potential applications in math and CS.  Some of these lead to questions about buildings and representation theory of p-adic groups.

 

We will survey the work of a number of people. The works of the speaker in this direction are with various subsets of  { S. Evra, K. Golubev,  T. Kaufman,  D. Kazhdan , R. Meshulam, S. Mozes }

High Dimensional Expanders and Ramanujan Complexes

Speaker: 
Alexander Lubotzky
Date: 
Fri, Sep 19, 2014
Location: 
PIMS, University of British Columbia
Conference: 
PIMS/UBC Distinguished Colloquium
Abstract: 

Expander graphs have played, in the last few decades, an important role in computer science, and  in the last decade, also in pure mathematics.  In recent years a theory of "high-dimensional expanders" is starting to emerge - i.e., simplical complexes which generalize various properties of expander graphs. This has some geometric motivations (led by Gromov) and combinatorial ones (started by Linial and Meshulam).  The talk will survey the various directions of research and their applications, as well as potential applications in math and CS.  Some of these lead to questions about buildings and representation theory of p-adic groups.

 

We will survey the work of a number of people. The works of the speaker in this direction are with various subsets of  { S. Evra, K. Golubev,  T. Kaufman,  D. Kazhdan , R. Meshulam, S. Mozes }

Sparse - Dense Phenomena

Speaker: 
Jaroslav Nesetril
Date: 
Fri, Feb 28, 2014
Location: 
PIMS, University of British Columbia
Conference: 
PIMS/UBC Distinguished Colloquium
Abstract: 

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.

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