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 Events
Univeristy of Michigan
Fri 31 Oct 2014, 3:00pm
Department Colloquium
ESB 2012 (PIMS)
Imaging with waves in complex environments (PIMS-IAM-UBC distinguished colloquium)
ESB 2012 (PIMS)
Fri 31 Oct 2014, 3:00pm-4:00pm

Abstract

The talk is concerned with the application of sensor array imaging in complex environments. The goal of imaging is to estimate the support of remote sources or strong reflectors using time resolved measurements of waves at a collection of sensors (the array). This is a challenging problem when the imaging environment is complex, due to numerous small scale inhomogeneities and/or rough boundaries that scatter the waves. Mathematically we model such complexity (which is necessarily uncertain in applications) using random processes, and thus study imaging in random media. I will focus attention on the application of imaging in random waveguides, which exhibits all the challenges of imaging in random media. I will present a quantitative study of cumulative scattering effects in such waveguides and then explain how we can use such a study to design high fidelity imaging methods.

Note for Attendees

Coffee, tea and cookies served at 2:30pm in the PIMS Lounge, ESB 4133.
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Mathematics, Guelph
Mon 3 Nov 2014, 3:00pm SPECIAL
Institute of Applied Mathematics
LSK 460
The Good, the Bad, and the Ugly: From Biofilms to Mathematics and Back Again
LSK 460
Mon 3 Nov 2014, 3:00pm-4:00pm

Abstract

Bacterial biofilms are microbial depositions that form on immersed surfaces wherever environmental conditions sustain bacterial growth. They have been called the most successful life form on Earth and cities of microbes. Biofilms have important applications in environmental engineering, but are detrimental in a medical or industrial context. They have been characterised as both, spatially structured microbial populations, and as mechanical objects. Life in biofilm communities significantly differs from life in planktonic cultures. This is reflected in the complexity of mathematical models of biofilms that are essentially more involved than models of suspended microbial communities. In this talk I will focus on a class of highly degenerate diffusion-reaction biofilm models. In its simplest form this includes simultaneously two nonlinear diffusion effects: (i) a porous medium equation like degeneracy when the dependent variable biomass density vanishes, and (ii) a super-diffusion singularity when it attains its {\it a priori} known upper bound. I will summarize some analytical (well-posedness) results, and discuss applications of the model to answer questions about biofilms by numerical simulations. I will hereby focus on the contribution of mathematical models (this and others) to understand the formation of cluster-and-channel biofilm architectures, and I will illustrate how our model framework, extended by a model of bacterial communication by quorum sensing, can be used to shed light on the transition from an initial mode of biofilm colonization to a protected mode of biofilm growth.
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UBC
Mon 3 Nov 2014, 3:00pm
Harmonic Analysis Seminar
Math 204
Restriction theory and quadratic equations in dense variables
Math 204
Mon 3 Nov 2014, 3:00pm-4:00pm

Abstract

We are interested in the problem of solving a translation-invariant linear equation in a dense subset of the squares. We focus on the quality of density bounds, and we explain how the efficient energy increment method developed by Heath-Brown and Szemeredi for Roth's theorem can be adapted to this problem. A key tool in the process is a restriction estimate of Bourgain for lattice sets, and we discuss its role in our density increment strategy.
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Kyoto University
Tue 4 Nov 2014, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB 2012
TBA
ESB 2012
Tue 4 Nov 2014, 3:30pm-4:30pm

Abstract

 
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Justin Chan
SFU
Tue 4 Nov 2014, 4:00pm
Discrete Math Seminar
ESB 4127
An infinite family of inv-Wilf-equivalent permutation pairs
ESB 4127
Tue 4 Nov 2014, 4:00pm-5:00pm

Abstract

Wilf-equivalence is one of the central concepts of pattern-avoiding permutations, and has been studied for more than thirty years. The two known infi nite families of Wilf-equivalent permutation pairs, due to Stankova-West and Backelin-West-Xin, both satisfy the stronger condition of shape-Wilf-equivalence. Dokos et al. recently studied a di fferent strengthening of Wilf-equivalence called inv-Wilf-equivalence, which takes account of the inversion number of a permutation. They conjectured that all inv-Wilf-equivalent permutation pairs arise from trivial symmetries. We disprove this conjecture by constructing an infi nite family of counterexamples derived from the permutation pair (231) and (312). The key to this construction is to generalize simultaneously the concepts of shape-Wilf-equivalence and inv-Wilf-equivalence. A further consequence is a proof of the recent Baxter-Jaggard conjecture on even-shape-Wilf-equivalent permutation pairs.
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Bonn
Wed 5 Nov 2014, 3:00pm
CRG Geometry and Physics Seminar
ESB 4127 (host: UAlberta)
TBA
ESB 4127 (host: UAlberta)
Wed 5 Nov 2014, 3:00pm-4:00pm

Abstract

 TBA
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MIT
Wed 5 Nov 2014, 3:00pm SPECIAL
Discrete Math Seminar / Harmonic Analysis Seminar
MATX1118
On geometric incidences
MATX1118
Wed 5 Nov 2014, 3:00pm-4:00pm

Abstract

 
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York University
Wed 5 Nov 2014, 3:10pm
Probability Seminar
ESB 2012
Random walk in non-elliptic random environments
ESB 2012
Wed 5 Nov 2014, 3:10pm-4:10pm

Abstract

Much of the literature on random walk in random environment assumes uniformly ellipticity, i.e., that nearest neighbour steps have probabilities bounded away from zero. I’ll describe some work with Mark Holmes (Univ. of Auckland) in which we relax this assumption, and allow some such steps to be forbidden. This leads naturally to percolation models, using which one can in some cases prove ballisticity of the random walks (existence of non-zero asymptotic speeds).
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Mike Wakin
Colorado School of Mines
Thu 6 Nov 2014, 12:00pm
Mathematics of Information and Applications Seminar
4133 ESB (PIMS lounge)
The Sketched SVD and Applications in Structural Health Monitoring
4133 ESB (PIMS lounge)
Thu 6 Nov 2014, 12:00pm-1:00pm

Abstract

We present a simple technique for estimating parts of the Singular Value Decomposition (SVD) of a data matrix from a small randomly compressed "sketch" of that matrix. In sensor network settings--where each column of the data matrix comes from a separate sensor--the sketch can be assembled using operations local to each sensor. As an application of this work, we consider the problem of Structural Health Monitoring (SHM). SHM systems are critical for monitoring aging infrastructure (such as buildings or bridges) in a cost-effective manner. Such systems typically involve collections of battery-operated wireless sensors that sample vibration data over time. After the data is transmitted to a central node, modal analysis can be used to detect damage in the structure. We propose and study three frameworks for Compressive Sensing (CS) in SHM systems; these methods are intended to minimize power consumption by allowing the data to be sampled and/or transmitted more efficiently. At the central node, all of these frameworks involve a very simple technique for estimating the structure's mode shapes without requiring a traditional CS reconstruction of the vibration signals; all that is needed is to compute a simple SVD. We support our proposed techniques theoretically and using simulations based on synthetic and real data. This project is joint work with Anna Gilbert and Jae Young Park.
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UBC
Thu 6 Nov 2014, 12:30pm
Graduate Student Seminar
Math 225
Supersymmetric integration
Math 225
Thu 6 Nov 2014, 12:30pm-1:45pm

Abstract

We begin by defining the Grassmann integral of a function of both commuting ("bosonic") and anti-commuting ("fermionic") variables. An important example is the mixed bosonic-fermionic ("supersymmetric") Gaussian integral, which exhibits a surprising self-normalization property. Time permitting, we will mention applications of the Grassmann integral to the representation of self-avoiding walk as a supersymmetric quantum field theory.
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Yariv Mizrahi
Thu 6 Nov 2014, 12:30pm SPECIAL
One Time Event
Room 200 of the Graduate Student Centre
Doctoral Exams
Room 200 of the Graduate Student Centre
Thu 6 Nov 2014, 12:30pm-2:30pm

Details

ABSTRACT We introduce a new class of parallel parameter learning algorithms for Markov random fields (MRFs) with untied parameters, which are efficient for a large class of practical models. The algorithms parallelize naturally over cliques and, for graphs of bounded degree, have complexity that is linear in the number of cliques. We refer to these algorithms with the acronym LAP, which stands for Linear And Parallel. Unlike their competitors, the marginal versions of the proposed algorithms are fully parallel and for log-linear models they are also data efficient, requiring only the local sufficient statistics of the data to estimate parameters. LAP algorithms are ideal for parameter learning in big graphs and big data applications. The correctness of the newly proposed algorithms relies heavily on the existence and uniqueness of the normalized potential representation of an MRF. We capitalize on this theoretical result to develop a new theory of correctness and consistency of LAP estimators corresponding to different local graph neighborhoods. This theory also establishes a general condition on composite likelihood decompositions of MRFs that guarantees the global consistency of distributed estimators, provided the local estimators are consistent. We introduce a conditional variant of LAP that enables us to attack parameter estimation of fully observed models of arbitrary connectivity, including fully connected Boltzmann distributions. We show consistency for this distributed estimator, and relate it to distributed pseudo-likelihood estimators. Finally, for linear and non-linear inverse problems with a sparse forward operator, we present a new algorithm, named iLAP, which decomposes the inverse problem into a set of smaller dimensional inverse problems that can be solved independently.
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Uriya First
UBC
Thu 6 Nov 2014, 3:30pm
Number Theory Seminar
room MATH 126
Rational isomorphism of quadratic forms and related objects
room MATH 126
Thu 6 Nov 2014, 3:30pm-4:30pm

Abstract

Let R be a discrete valuation ring with fraction field F. Two algebraic objects (say, quadratic forms) defined over R are said to be rationally isomorphic if they become isomorphic after extending scalars to F. In the case of unimodular quadratic forms, it is a classical result that rational isomorphism is equivalent to isomorphism. This has been recently extended to "almost umimodular" forms by Auel, Parimala and Suresh. I will present further generalizations to related objects: hermitian forms over involutary R-algebras, quadratic spaces equipped with a group action ("G-forms"), and systems of quadratic forms. The results can be regarded as versions of the Grothendieck–Serre conjecture for certain non-reductive groups. (Joint work with Eva Bayer–Fluckiger.)
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