The Department of Mathematics and Statistics of the University of Victoria is hosting their second annual CMS Math Camp on July 3-7th, 2012. The CMS Math Camps are designed to provide students in grades 9 through 11, who have demonstrated a talent for mathematics, with a variety of enrichment activities in a fun and rewarding environment. With last year’s inaugural Camp getting a very positive response, we are looking forward to making the 2012 edition a unique and rewarding experience for all the participants. While the Camp's 2012 schedule is being finalized, as a sample please see last year's schedule (PDF) and description of the sessions (PDF).

Participation in the Camp is by invitation only. High school teachers who have an excellent student in mind are invited to complete the nomination form and return it by mail or e-mail to the address specified on the form no later than Tuesday June 5th, 2012. Since space is limited, it may not be possible to invite all the nominated students. Successful applicants will be informed through their teachers by Tuesday June 12th, 2012.

The generous support from University of Victoria and the Canadian Mathematical Society (CMS) will enable us to cover the majority of the food, supplies and other costs. However, a registration fee of $50.00 will be necessary to offset some of the expense. If you have any questions or need further details, please contact the Camp Organizer, Kseniya Garaschuk, directly at  kgarasch@uvic.ca.

PIMS Distinguished Speaker

Prof. Philip Maini is Director of the Centre for Mathematical Biology, University of Oxford, UK
He co-authored a Bellman Prize winning paper (1997), was awarded a Royal Society Leverhulme Trust Senior Research Fellowship for 2001-2 and a Royal Society-Wolfson Research Merit Award (2006-11). In 2009 he was awarded the LMS Naylor Prize and Lectureship.

Abstract:
This talk will present a range of mathematical modelling approaches we have used recently to model aspects of solid tumour growth. We will consider a very simple ordinary differential equation model for homeostasis in intestinal crypts, a more complicated cell-based hybrid model for crypt dynamics, a partial differential equation model for the acid-mediated invasion hypothesis and a compartmental model for acid-buffer handling in the body. Results from the mathematical analyses will be interpreted in the biological context to try to shed light on some fundamental processes and suggest therapies.

Speaker: Lorraine Dame*, University of Victoria

Title: Student Readiness and Success in Entry Level Undergraduate Mathematics

Which elements of a student's preparation are predictors of success in
entry level undergraduate math (ELUM) courses? This report describes
recent research which includes studies of the relationships between ELUM
course outcomes, high school grades and diagnostic test scores. It shows
that higher grades in secondary school English and Math go together with
a greater probability of retention and higher grades in ELUM courses.
The results of an in-house developed diagnostic test show that students
identified as at-risk were significantly more likely to fail or drop an ELUM course.

* Joint work with G. MacGillivray

The Final Oral Examination for the Degree of
DOCTOR OF PHILOSOPHY (Department of Mathematics and Statistics)

ANGUS ARGYLE

Title: Statistical methods for species richness estimation using count data from multiple sampling units

Please note:  The room that the defense is being held in is quite small and the seats have all been allocated to committee members and invited guests.

Announcement and Abstract (PDF)

Speaker: Timothy D. Johnson (U.Michigan)

Title: A Nonparametric Bayesian Spatial Point Process Approach to Neuroimaging Meta Analysis

Abstract: As the discipline of functional neuroimaging grows there is an increasing interest in meta analysis of brain imaging studies. A typical neuroimaging meta analysis collects peak activation coordinates (foci) from several studies and identifies areas of consistent activation. In our illustrative example, our colleagues collected 219 emotion studies consisting of five distinct emotion types: sad, happy, anger, fear, disgust. One psychological theory states that all emotions utilize the same functional brain regions, to varying degrees. Thus, the expected number of foci in these regions, across emotion types, should be correlated. To date, all imaging meta analysis methods have been developed to analyze a single population of studies. Furthermore, most imaging meta analysis methods do not provide an interpretable fitted model. To overcome these limitations, we propose a nonparametric Bayesian spatial point process model that generalizes the Poisson/gamma random field model (Wolpert and Ickstadt, 1998) in a hierarchical fashion. Our model simultaneously fits multi-type point pattern data, accounts for the (positive) correlation across the various types of point patterns and results in an easily interpretable posterior intensity function. Furthermore, our model can be used to accurately predict the emotion type from a new study---something of great interest to our collaborators.

The Final Oral Examination for the Degree of
DOCTOR OF PHILOSOPHY (Mathematics)

Susana Weiler

April 5th, 2012, at 3:30 p.m. University Centre, room A207a

Announcement (PDF file)

Abstract
A Smale space is a chaotic dynamical system with canonical co-ordinates of contracting and expanding directions. The basic sets for Smale’s Axiom A systems are a key class of examples. R.F. Williams considered the special case where the basic set had a totally disconnected contracting set and a Euclidean expanding one. He provided a construction using inverse limits of such examples and also proved that (under appropriate hypotheses) all such basic sets arose from this construction. We will be working in the purely topological setting of Smale spaces, but the goal is to extend Williams’ results by removing all hypotheses on the unstable sets. We give criteria on a stationary inverse limit which ensures the result is a Smale space. We also prove that any irreducible Smale space with totally disconnected local stable sets is obtained through this construction.

Speaker: Wael Bahsoun (Loughborough)

Title: Metastability of Interval Maps

Abstract: Gonzalez-Tokman, Hunt and Wright studied a metastable
expanding system which is described by a piecewise smooth and
expanding interval map. It is assumed that the metastable map has
two invariant sub-intervals and exactly two ergodic invariant
densities. Due to small perturbations, the system starts to allow
for infrequent leakage through subsets (called holes) of the
initially invariant sub-intervals, forcing the two invariant
sub-systems to merge into one perturbed system which has exactly
one invariant density. It is proved that the unique invariant
density of the perturbed interval map can be approximated by a
particular convex combination of the two invariant densities of
the original interval map, with the weights in the combination
depending on the sizes of the holes. In this talk I will present
analogous results in two cases: 1. intermittent interval maps; 2.
Randomly perturbed expanding maps. In the random case, if time
permits, I will also present random versions of Keller-Liverani
escape rate formulae. This is joint work with Sandro Vaienti.

Speaker: Kathleen Barnetson

She will present her work on Searching for Class Uniformly Resolvable Partial Coverings, also known as a place where scheduling golf vacations meets combinatorial designs.

Speaker: Kelly Burkett, Simon Fraser University

Markov chain Monte Carlo sampling of gene genealogies conditional on observed genetic data

The gene genealogy is a tree structure describing the ancestral relationships among genes sampled from unrelated individuals. Knowledge of the tree is useful for inference of population-genetic parameters such as the mutation or recombination rate. It also has potential application in gene mapping, as individuals with similar trait values will tend to be more closely related genetically at the location of a trait-influencing mutation. However, since the time scale of the genealogy is on the order of thousands of years, the true tree cannot be known.

One way to incorporate genealogical trees in genetic applications is to sample them conditional ongenetic data observed at present. In this presentation, I will describe ourMarkov chain Monte Carlo based genealogy sampler. We first implemented a sampler that conditions on haplotype data; however, commonly used genotyping technology does not provide haplotypes and therefore the true haplotypes are also not known. I will describe how we extended the sampler to handle missing haplotype data and I will discuss its performance in estimating haplotypes in simulated datasets. Finally, I will also describe our experiences with simulated tempering as a means to improve mixing of the sampler.

Speaker: Richard Montgomery (Department of Mathematics, UC Santa Cruz)

Richard Montgomery became famous after the publication of
a paper in the Annals of Mathematics in the year 2000 in which
he proved the existence of the "figure eight" solution in the 3-body
problem (3 bodies of equal masses chase each other along a common
orbit that looks like the figure 8, all numerical experiments
suggesting that the orbit is stable). Richard's research interests
are in celestial mechanics and differential geometry.


Title: Reducing and regularizing everything for the N-body problem


Abstract: What does the phase space look like when we reduce by all the symmetries,
regularize all the binary collisions and blow up the triple collisions using McGehee
transformations?  We show how to perform these transformations`democratically' with
respect to interchange of the bodies, and explain the results  for the planar 3-body
problem. Can we do it for the spatial 3-body problem? For the planar  4-body problem? 
We show the results of some preliminary investigations as well.

Speaker: Dhavide Aruliah (U. of Ontario Inst. of Tech., Canada)

Title: A Parallel Adaptive Method for Pseudo-Arclength Continuation

Abstract: Pseudo-arclength continuation is a well-established framework for
generating a curve of numerical solutions of nonlinear equations. The
usual predictor-corrector scheme uses a prediction of a prescribed
step-length along a tangent direction followed by correction steps
(typically using Newton's method) in a hyperplane containing the
prediction point. In many complicated high-dimensional systems, the
corrections steps can be extremely costly to compute; as a result, the
step-length of the original prediction step must be chosen carefully
to avoid prohibitively many failed steps and corresponding wasted CPU
cycles.

In this talk, I present a parallel method for adapting the step-length
of pseudo-arclength continuation (jointly developed at UOIT with
Alexander Dubitski and Lennaert van Veen). Our method employs several
predictor-corrector sequences run concurrently on distinct processors
with differing step-lengths. Our parallel framework permits
intermediate results of unconverged correction sequences to seed new
predictor-corrector sequences with longer step-lengths; the goal is to
amortise the cost of corrector steps to make further progress along
the underlying numerical curve.

I shall describe the essence of the parallel algorithm and provide
evidence from numerical experiments to support its efficacy. Results
from numerical experiments suggest that a three-fold speed-up is
attainable when the continuation curve sought has great topological
complexity and the corrector steps require significant processor time.
Our implementation can be used without extensive experience with
High-Performance Computing (HPC); users need only supply a routine for
computing the corrector steps.

Title: Journey Into Chronological Rectangle Digraph County
Speaker: Josh Manzer

Abstract: We define a reflexive digraph D = (V, A) to be a chronological rectangle digraph if there exists a collection {R_v}, v in V, of closed rectangles in the plane such that uv is an arc of D if and only if R_u contains the lower left corner of R_v. I will motivate this definition with a brief survey, as this is a natural generalization of chronological interval digraphs analogous to the generalization of interval graphs to graphs with boxicity 2.  There will be lots of examples and some preliminary results on this class of digraphs.  Based on work with Jing Huang.

Speaker: Tom Meyerovitch (UBC)

Title: Stationary Markov random fields and Gibbs measures

Abstract: Markov random fields are higher-dimensional processes
with a conditional independence, which can be viewed as analogs
of Markov-chains in ine dimension. The Hammersley-Clifford
theorem states that Markov Random fields are Gibbs measures with
a nearest neighbor interaction, under an assumption on the
support: the existence of a ``safe symbol''. In this talk I will
present joint work (in progress) with Nishant Chandgotia,
Guangyue Han, Brian Marcus and Ronnie Pavlov, investigating
Markov random fields without assuming a ``safe symbol'' in the
support.

Speaker: Tron Omland, Norwegian University of Science and Technology

Title: Primitivity and primeness of twisted group C*-algebras.

Abstract: For a discrete group G and a multiplier (2-cocycle) \sigma on
G, we define the full and reduced twisted group C*-algebra
corresponding
to the pair (G,\sigma) and give conditions for which these C*-algebras
are prime or primitive.

Speaker: Stephen Finbow (St. Francis Xavier)

Title: Discharging from the point of view of a fire extinguisher

Abstract:
The firefighter problem models the spread of a fire or virus through out a network as firefighters or defenders try to limit it's impact on the network. The expected damage from a random instance of this problem is called the surviving rate of the graph.  We will discuss the firefighter problem and how the discharging method can be used to obtain results on the surviving rate in planar graphs.

Speaker: Susie Wieler (UVic)

Title: Hyperbolic dynamical systems via inverse limits

Abstract: A Smale space is a dynamical system with canonical
coordinates of contracting and expanding directions.  The basic
sets for Smale’s Axiom A systems are a key class of examples.  We
will give a brief overview of R.F. Williams' work on expanding
attractors. In this case, the local stable sets are totally
disconnected and the local unstable sets  are Euclidean. Williams
gave a description of such a system as a stationary inverse
limit, where the space in the limit is a branched manifold. We
consider Smale spaces with totally disconnected local stable sets
and no restrictions on the unstable sets. We give criteria on a
topological stationary inverse limit which ensures the result is
a Smale space and give examples. We also prove that any such
Smale space is obtained through this construction.

Speaker: Matias Salibian-Barrera, University of British Columbia

Title: On robust functional principal components

Abstract:
In this talk we study robust estimates of principal components for functional data. This work was motivated by a problem of outlier detection in atmospheric data collected by weather balloons launched into the atmosphere and stratosphere. Since principal components give best (in the $L_2$ sense) finite-dimensional approximation to random elements over separable Hilbert spaces, we consider the problem of robustly estimating these finite-dimensional approximating subspaces. We obtain some general optimality results and discuss a new family of estimators that we call S-estimators and compare their properties with those of previously proposed estimators that can be used in this setting. This is joint work with Graciela Boente.

Speaker: Pierre Marechal  (Toulouse France & UVic)

Title: A digression about ill-posed problems, intertwining relationships and spectral functions

Abstract: A function of matrix or operator argument is said to be spectral if its output depends on the spectral values of the argument only, which is generally equivalent to some group invariance of the function. The convexity properties of such functions then reduce, in essence, to those of their restrictions to diagonal arguments. This fact has been explored in various settings, mostly for matrix (finite dimensional) arguments but also, more recently, in infinite dimensions. In this talk, we will consider the infinite dimensional non-symmetric case.

The initial motivation for this work was not only to carry out an extension to the body of theory on convex spectral functions, but also to study an optimization problem which plays some role in the theory of ill-posed inverse problems, namely the caracterization of what we call approximate pseudo-commutants. Given to operators R and C, an operator X is said to be a pseudo-commutant of C with respect to R if RC=XR. The latter equation is then referred to as an intertwining relationship. A pseudo-commutant may not exist, in which case it makes sense to define an approximate pseudo-commutant as a minimizer of the operator norm of the difference RC-XR. We show that, in essence, the solution RCR+ (in which R+ denotes the Moore-Penrose pseudo-inverse of R) remains a solution if, in the aforementioned  problem, the norm is replaced by any continuous convex spectral function.

Speaker: Ian Putnam, UVic

Title: Orbit equivalence for Cantor minimal dynamics

Abstract: I will give a survey of the main results and ideas for
orbit equivalence of minimal dynamical systems on the Cantor set.
The talk may continue next week, depending on how far I get.

The Faculty of Science is sponsoring the following upcoming Café Scientifique talk:

Title: Before Tragedy Strikes: The Quest to Predict Megadisasters
Speaker: Dr. Florian Diacu, Dept of Mathematics & Statistics, University of Victoria 
Date/Time/Place: Tuesday, March 13, 2012 at 7:00 pm - Solstice Café 529 Pandora Street

Abstract:

Can we predict tsunamis, earthquakes, hurricanes, volcanic eruptions, sudden climate changes, cosmic impacts, deadly pandemics, and stock market crashes? In the past it would have been impossible to give a positive answer to this question. But in the mean time science has made a lot of progress, and we can now better grasp some of the secrets such catastrophes hide. Still there is a lot to do to understand them in detail. This talk is about whether we can foretell extreme events and how individuals could prepare to shield themselves from megadisasters.

Speakers: David Holloway (Math, BCIT) and Patrick von Aderkas (Biology, UVic)

Title: Exploiting phenotypic variation to explain lateral organ formation in embryos

Abstract:
One of the difficulties in studying the intitiation and spacing of organs
is finding tractable eukaryotic systems. We investigated phenotypic
variation of physiological and morphological traits in cloned embryos of
Larix x marschlinsii (hybrid larch)and Pseudotsuga menziesii
(Douglas-fir). Embryos are multiplied in vitro and then matured in a
stepwise controlled manner. By raising the embryos in different
expermimental conditions their physiology, biochemistry and morphology can
be altered. Since genotypic variation has been eliminated in such cloned
systems, the variation we see is almost entirely phenotypic. We focused on
the initiation and differentiation of cotyledons, which are the first
lateral organs in the plant embryo. These appear simultaneously as a whorl
of organs. We established treatments that reliably varied the number of
lateral organs per whorl. By focusing on phenotype, we can use these
studies to test physico-chemical models for the spatial patterning
underlying morphogenesis. Our data indicate that cotyledon spacing is
controlled by a wave-forming mechanism. We discuss the experimental
results in terms of our ongoing mathematical and computational work on
reaction-diffusion dynamics in growing systems.

Speaker: Alejandro Erickson (UVic Computer Science)

Abstract: A \em{brick tiling} of the $n\times m$ grid is a
rearrangement of bricks in a horizontal bond of the same grid, while
maintaining the obvious structural advantage of having no "+" shapes
in the mortar.  This is a highly visual presentation, showing how to
derive the generating polynomials which enumerate brick tilings for
the $n\times n$ square grid with exactly $k$ horizontal tiles.  The
polynomials factor into (cyclotomic polynomials)(mystery factor).  The
mystery factor seems very predictable, appears to be irreducible,
produces beautiful complex root plots, and yet a precise description
and a geometric interpretation of it eludes us. Joint work with Frank Ruskey.

Speaker: Antoine Julien (UVic)

Title: Metric properties of tiling space.

Abstract: I will describe how the usual distance on tiling space
provides a nice approach for some properties of the tiling,
namely its complexity.  In some example, the complexity and the
Hausdorff dimension of the space are closely related. I will also
describe some results on bi-Lipschitz embedding which were
obtained with Jean Savinien and Jean Bellissard.

See http://www.pims.math.ca/educational/math-mania for more information about Mathmania!

Title: Topology of Musical Data

Speaker: William Sethares (U. Wisconsin)

Abstract: Techniques for discovering topological structures in large data sets are now becoming practical. This talk argues why the musical realm is a particularly promising arena in which to expect to find nontrivial topological features. The analysis is able to recover three important topological features in music: the circle of notes, the circle of fifths, and the rhythmic repetition of timelines, often pictured in the necklace notation.

Speaker: Jiahua Chen, Canadian Research Chair, Tier I, University of British Columbia

Advances in EM-test for Finite Mixture Models

Making valid and effective inferences for finite mixture models is known to be technically challenging. Due to the non-regularity, the likelihood ratio test was found to diverge to infinite if the parameter space is not artificially confined to a compact space. Even under compact assumption, the limiting distribution is often a function of the supremum of some Gaussian processes. Such results are of theoretical interest but not useful in applications. Recently, many new tests have been proposed to address this problem.  The EM-test has been found superior in many respects. For many classes of finite mixture models, we have tailor-designed EM-tests that have easy to use limiting distributions. The simulation indicates that the limiting distributions have good precision at approximating the finite sample distributions in the examples investigated. A general procedure for choosing the tuning parameter has also been developed.

Luke Bornn (Department of Statistics, University of British Columbia) will be giving a teaching demonstration on March 7 at 11:30 in Cornett A125 and a colloquium talk on Nonstationary Modeling Through Dimension Expansion at 2:30 in DSB C112. All members of the department are welcome to attend both presentations.

Teaching Demonstration: 11:30-12:20 in Cornett A125

Meet the speaker/coffee: 2:00-2:30 in the Departmental Common Room SSM A514

Colloquium: 2:30-3:30 in DSB C112

Title: Nonstationary Modeling Through Dimension Expansion

Abstract
If atmospheric, agricultural, and other environmental systems share one underlying theme it is complex spatial structures, being influenced by such features as topography and weather. Ideally we might model these effects directly; however, information on the underlying causes is often not routinely available. Hence, when modeling environmental systems there exists a need for a class of spatial models which does not rely on the assumption of stationarity.
In this talk, we propose a novel approach to modeling nonstationary spatial fields. The proposed method works by expanding the geographic plane over which these processes evolve into higher dimensional spaces, transforming and clarifying complex patterns in the physical plane. By combining aspects of multi-dimensional scaling, group lasso, and latent variable models, a dimensionally sparse projection is found in which the originally nonstationary field exhibits stationarity. Following a comparison with existing methods in a simulated environment, dimension expansion is studied on a classic test-bed data set historically used to study nonstationary models. Following this, we explore the use of dimension expansion in modeling air pollution in the United Kingdom, a process known to be strongly influenced by rural/urban effects, amongst others, which gives rise to a nonstationary field.

Speaker: Takafumi Akahori (Shizuoka University, Japan)

Title: Existence of a ground state and scattering for a nonlinear Schroedinger equation with critical growth

Abstract:

This talk concerns the focusing energy-critical nonlinear Schroedinger equation with a mass-supercritical and energy-subcritical perturbation. 
In particular, we consider the existence of a ground state and  the scattering problem in the spirit of Kenig-Merle (Invent. Math. 166 (2006)).
This is a joint work with Ibrahim, Kikushi and Nawa

Speaker: Jane Wodlinger (Simon Fraser University)

Title: Wavelength Isolation Sequence Pairs: New Progress on an Abandoned Problem

In the early 1950s, Golay considered the problem of measuring
radiation of a particular wavelength in the presence of background
radiation, and defined a type of binary sequence pair that could be
used in the design of a suitable detection system. However, the
scarcity of examples of such pairs led Golay to speculate that none
more exist, and to turn his attention to an alternative solution to
the design problem. In this talk, we present examples of these
sequence pairs, which we call wavelength isolation sequence pairs, for
two new lengths. Further, we establish some structural constraints on
these pairs and describe a method whereby each of the known examples
can be constructed from a perfect Golomb ruler.

Speaker: Siri-Malén Høynes

Title: Toeplitz dynamical systems and their K-theory

Abstract: We will show that the family of Toeplitz systems can be
associated to simple dimension groups with non-trivial rational
subdimension groups. Furthermore, we will present a class of
examples which has a particularly nice Bratteli diagram
presentation.

Speaker: Patrick Gill, U. Toronto

Learning to Cope with Incomplete Sensory Data by Studying Neurons: The Brain as a Compressive Sensor

One remarkable quality of sensory brain areas is their ability to persevere in the face of incomplete information. Our cochleas have damaged hair cells and our retinas have blind spots, yet our hearing and vision suffer minimally from substantial levels of damage and undercompleteness. What tricks are brains using to achieve this robustness?

I will present evidence that this robustness comes from a variant of a newly-discovered regularization trick called compressive sensing (CS). CS is the recovery of a compressible signal (sparse in some basis) from an undercomplete set of measurements in some other basis. When there are comfortably more measurements than the signal's sparsity, CS yields a quickly-solvable convex optimization problem whose solution is the original signal.

The hypothesis that brains use CS has already lead me to invent a neuromimetic algorithm, the "in-crowd algorithm," that is the fastest solver for certain large CS problems resembling the type brains might encounter. I will present this algorithm and some of the problems it solves, then construct a case for how understanding CS can explain the physiology of the neurochemical acetylcholine in humans and its role in normal age-related cognitive decline. Finally, I will highlight some of the differences between CS as it currently stands and as it's implemented in biology, with an eye to the possibility of mimicking more algorithmic good ideas based on brain architecture.

Dr. Elif F. Acar (Department of Mathematics and Statistics, McGill University) will be giving a  colloquium talk on Nonparametric Covariate Adjustment in Copula-based Dependence Models at 2:30 on Thursday, March 1 in DSB 112.

Meet the speaker/coffee: 2:00-2:30 in the Departmental Common Room SSM A514

Colloquium: 2:30 - 3:30, DSB C112

Abstract
Adjusting statistical dependence for covariates via conditional copulas is an active area of research where model fitting and validation are currently in early development. In this talk, I will present a unified framework to assess and infer covariate effects on the dependence structure of random variables in bivariate or multivariate models. In conditional copulas, the copula parameter is deterministically linked to a covariate via the calibration function. To estimate the latter, I will introduce a nonparametric estimation procedure based on local likelihood and use the proposed estimator as a diagnostic tool for testing a parametric formulation of the calibration function against a general alternative. Cross-validation techniques for model tuning and copula family selection will be outlined within the proposed framework. I will demonstrate the estimation and test procedures using subsets of the Matched Multiple Birth and Framingham Heart Study datasets. Multivariate extensions via pair-copula constructions will also be addressed in the talk.

Dr. Qian (Michelle) Zhou from Harvard School of Public Health, Department of Biostatistics, will be speaking on Model Misspecification in Statistical Analysis on Tuesday, February 28, 2012 from 2:30 - 3:30 in DSB C108.  All are welcome!

There will be an opportunity to meet the speaker for coffee from 2:00-2:30 in the Departmental Common Room SSM A514

Abstract:

In general, model misspecification can lead to invalid inference for parameter estimation and risk prediction. In the context of quasi-likelihood inference, most of the existing statistical methods primarily focus on assessing the validity of the mean structure. However, limited work addresses the adequacy of the variance/covariance (Var/Cov) structure, and more specifically, there lacks a powerful systematic statistical test for model misspecification in Var/Cov. In this talk, I will introduce a novel and unified framework for testing such misspecification. Our method shows substantial improvement and is more robust in comparison to several popular existing statistical methods.
In the context of risk prediction, I will talk about some challenges that arise in the evaluation of the incremental value in prediction accuracy by adding new biomarkers. In light of these challenges, we have proposed novel statistical procedures for systematically identifying potential subgroups that can benefit from the measurement of additional markers. Notably, our method is robust against possible model misspecification. Finally, I will discuss developing and evaluating absolute risk prediction models with newly identified biomarkers under nested case-control sampling design; here, measurement of biomarkers on the whole study population is neither feasible nor cost-effective.

Speaker: Kathleen Barnetson

Monday, February 27, 10AM in DSB C-114.

Abstract: She'll talk about results from the paper "The Wonderful Walecki Construction" by Brian Alspach.

Organizer: 
S. 
Ibrahim: 

 ibrahims@uvic.ca

Program

8:30­-9:00 
Welcome

9:00‐9:50
 H. 
Bahouri
(Paris):
 On the lack of compactness of Sobolev embedding in Orlicz space

10:00­-10:30 
Coffee
break

10:30‐11:20
 S.
 Gustafson
(UBC):
 On the blow-up of equivariant heat and Schroedinger flows into the sphere

11:30‐12:20 
G. 
Perelman(Paris)
: 
Contracting sphere blow up solutions for the 3D cubic NLS

12:30­-1:30 
Lunch
break

1:30‐2:20
 T.‐P.
 Tsai
 (UBC)
: Classification of asymptotic profiles for nonlinear Schroedinger
equations with many excited states

2:30‐3:20

 I.
 Zwiers
(UBC)
: Local dynamics near unstable branches of NLS solitons

3:30‐4:20 

S. 
Ibrahim
(UVic)
: Blow
 up 
versus 
Scattering 
for
 the
 perturbed
 energy
 critical 
NLS

Speaker: John, Phillips, UVic

Date: Wednesday, February 22, 2012

Time: 3:30 - 5:500 PM

Room: DSB C114

Title:  The Non-unital Local Index Theorem:
What does it say in the case of Spectral Dimension 1.


Abstract: We revisit the index theorems of Gohberg-Krein, Lesch and
Phillips-Raeburn in this context.

Speaker: Ronnie Pavlov (Denver)

Title: Limiting entropy of d-dimensional axial powers of
subshifts

Abstract: Given any one-dimensional subshift X, the d-th axial
power of X is defined to be the Z^d-subshift obtained by
enforcing the constraints of X in every cardinal direction. For
instance, if X is the so-called golden mean shift, which consists
of all 0-1 sequences with no two consecutive 1s, then the second
axial power of X consists of all 2-dimensional 0-1 arrays with no
adjacent 1s horizontally or vertically.

Though in general, the computation of topological entropy for Z^d
subshifts is difficult (or impossible!), it turns out that for
any fixed X, the topological entropies of its axial powers
approach a limit. In current work with Tom Meyerovitch, we prove
that this limit is equal to a surprising, often
easily-computable, function of the underlying one-dimensional
subshift, called "independence entropy." I will define
independence entropy, discuss the relationship between
independence and standard topological entropies, and if time
permits, give some related open problems.

Speaker: Michelle Edwards. 

Title: The $\gamma$ graph of a tree

She'll present solutions to several of the problems raised in the talk by Steve Hedetniemi here last April. (See http://www.math.uvic.ca/faculty/gmacgill/Victoria.pdf for his slides; Michelle will talk about the solution to the first three problems). 

We are very pleased to announce that Mark Lewis has been chosen as UVic's Faculty of Science distinguished alumnus for 2012. Mark graduated from UVic in 1987 with a joint Math/Biology degree and now holds a Tier I Canada Research Chair in Math Biology at University of Alberta. Mark's research focuses on spatial ecology models, and he works on diverse problems including modeling population dynamics of polar bears, ecological succession on Mt. St. Helens, and dynamics of infectious disease. For more information on Mark's research, go to his website.

In honour of Mark's award, we are organizing a Math Biology Symposium, on Wednesday February 8th, 2012 in MacLaurin D116.

LEWIS FEST:   Wednesday February 08 2012, UVic Mac D116

PROGRAM

10.30am -12 noon   Seminar by Mark Lewis (University of Alberta) followed by a discussion

Title: First passage time: Connecting random walks to functional responses

Abstract: In this talk I will outline first passage time analysis for animals undertaking complex movement patterns, and will demonstrate how first passage time can be used to derive functional responses in predator prey systems. The result is a new approach to understanding functional responses based on a random walk model. I will extend the analysis to complex heterogeneous environments to assess the effects of man-made linear landscape features on functional responses in wolves and elk. (This work is joint with Hannah McKenzie, Evelyn Merrill and Ray Spiteri)

12-noon -1pm Lunch for registered participants in Haro Room, Caddy Commons

1pm Return to Mac D116 for the afternoon events

1.10-1.20pm  Musical interlude: J Ben Wilson (Math & Stats)

1.20pm-1.30pm Remarks by the Dean of Science

1.30pm  How far will transgenic apple pollen travel?  Rebecca Tyson (UBC Okanagan, Math & Stats)

1.50pm Extracting meaningful data from large fisheries ecology data sets: Jaimie Imrie (Interdisciplinary, CSc & Biology)

2.10pm  Models for the spread of cholera: Zhishing Shuai (Math & Stats)

2.30pm Short Break

2.40pm Bayesian hierarchical analysis of Chytrid disease in British Columbia: Jean Richardson (Biology)

3.00pm The Jolly-Seber-Tag-Loss model with group heterogeneity: Laura Cowen (Math & Stats)

3.20pm How species diversity stabilizes food webs: History, new theory & data: Brad  Anholt (Biology)

3.40-4.20pm Tea and closing of Lewis Fest

If you have any questions, please ask one of us.
Thank you from the Organizers:
Chris Bose, Rod Edwards, Junling Ma, Steve Perlman, Pauline van den Driessche, John Volpe

<a href="http://www.math.uvic.ca/local/events/LewisFest">Photos and List of Participants</a>

Time: February 6, 3:30PM

Room: HH 116

Speaker: Rebecca Tyson (UBC Okanagan)

Title: Predicting honeybee-mediated movement of transgenic pollen: A diffusion-based approach

Abstract: We present models to address two major issues surrounding
bee-pollinated crops: (1) the movement of transgenic pollen and (2) the
collapse of honeybee colonies.  Both issues are inextricably tied to bee
movement, and thus solutions can only be generated if bee foraging and
dispersal movement patterns are understood.  In this talk, we develop a
novel diffusion-based model for bee movement whose solutions capture
both the centre and tails of the bee population distribution.  We then
use this model as a basis for modelling bee-mediated pollen movement,
and validate our work with an experimental study measuring percent
transgenic seed in an apple orchard with a row of 200 transgenic source
trees. We show that the model can be used to predict the percent
transgenic seed in neighbouring conventional trees as a function of the
size of each orchard block and the distance between them.  We then
explore extensions of the bee movement model to wild bee movement and
the evaluation of pollination services these bees can provide both in
the absence of honeybees, and when honeybees are present.

Speaker: Ross Churchley.

Abstract: Ross will present some results of Natasha Komarov and Peter Winkler on a question he asked: what is the expected time needed  for a (sober) cop to catch a drunken robber (who staggers about the graph randomly).

Speaker: Cecilia Gonzalez Tokman

Title:
Ulam's method for systems with holes.

Abstract:

Ulam's method provides a way of approximating absolutely continous invariant
measures for dynamical systems. These approximations come from fixing a finite
partition of the phase space and encoding the dynamics in an inter-set
transition matrix. We review some of the existing results regarding convergence
of these approximations as the diameter of the partition goes to zero, and
present a (non-perturbative) extension of these results to the context of open
systems, or systems with holes. (Joint work with C. Bose, G. Froyland and R.
Murray.)

See http://www.pims.math.ca/educational/math-mania for more information about Mathmania!

Speaker: Boualem Khouider (UVic)

Title: Convective momentum transport and multiscale organization of tropical convection

Abstract:

I'll present some models of convective momentum
transport--that is momentum flux from unresolved convective meso-scale
systems being transported across scales and serves to force the
large-scale/resolved waves. I will also present a model for the
organization of synoptic and meso-scale waves within the MJO
envelope--MJO (Madden-Julian oscillation) refers to a planetary scale
wave/oscillation that regulates the climate variability
in the tropics on intra-seasonal (40-60 days) time scales.

Speaker: Heath Emerson

Title: Dirac classes for crossed-products (part 2)

Abstract: This is a continuation of my talks on KK-theory from the fall.
I will continue to discuss what a `noncommutative manifold’ might be.
In this and the following talk I will define `Dirac class,’ a special
kind of K-homology class for a crossed-product C*-algebra arising from a
discrete group action on a smooth manifold. The definition uses the
mechanics of equivariant KK-theory and the Baum-Connes conjecture.
After giving the definition I will discuss some basic
examples and, if time permits, a more elaborate one arising from
boundary actions of classical hyperbolic groups.

Speaker: Kathleen Barnetson.

Abstract: Kathleen will present the (1-1/e)-approxomation algorithm  from the paper:

Leizhen Cai, Elad Verbin, Lin Yang: Firefighting on Trees: (1-1/e)-Approximation, Fixed Parameter Tractability and a Subexponential Algorithm.

Here e is the base of the natural logs rather than a poorly typeset epsilon.

Speaker: Anthony Quas

Title: Alpern theorems for higher-dimensional flows

Abstract: We discuss Alpern theorems (a generalization of Rokhlin's lemma) for R^d actions in which the `towers' are rectangular boxes of prescribed sizes, proving both sufficient and necessary conditions on the number of boxes.

Speaker: Carl James Schwarz (SFU)*

Bayesian Time-Stratified-Petersen estimators for abundance

Simple-Petersen or Stratified-Petersen methods are often used to estimate number of outgoing smolt or returning salmon. These methods are inadequate to deal with heterogeneity in catchability among strata and with missing data from strata caused by crew illness, high water flow, or other causes. We propose a Bayesian spline-based methodology to estimate abundance and run-timing which provides several compelling advantages over the more traditional estimators. The hierarchical model for capture probabilities and the spline model for the general shape of the run curve, allow information to be shared among stratra within a Bayesian framework and allows great flexibility to deal with missing data. It is self-calibrating- for strata with poor data, extensive pooling across strata take place but with strata with rich data, the information for a particular stratum takes precedence. The methodology automatically adjusts measures of precision for heterogeneity in catchability among strata (which is ignored in the simple-Petersen) and shares information from neighbouring strata (unlike the Stratified-Petersen). Examples from estimating the number of outgoing number of salmon smolt in the Trinity River, CA will be present

*Joint work with Simon Bonner, U. Kentucky.

Speaker: Jane Ye (UVic)

Title: On solving bilevel programs with a nonconvex lower level program

Abstract:

A bilevel program is a sequence of two optimization problems where the constraint region of the upper level problem is determined implicitly by the solution set to the lower level problem. Bilevel programs can be used to model a two-level hierarchical system where the two decision makers have different objectives and make their decisions on different levels of hierarchy. Bilevel programs can be used to model many situations in Economics, Engineering and Decision Science.

In this talk we consider a class of bilevel programs where the lower level program is a nonconvex minimization problem over a compact set and we discuss two issues: necessary optimality conditions and numerical algorithms. We prove some new necessary optimality conditions and design an algorithm to solve the bilevel program.

Speaker: Heath Emerson

Title: Dirac classes for crossed-products

Abstract: This is a continuation of my talks on KK-theory from the fall.

I will continue to discuss what a `noncommutative manifold’ might be.

In this and the following talk I will define `Dirac class,’ a special kind of K-homology class for a crossed-product C*-algebra arising from a discrete group action on a smooth manifold. The definition uses the mechanics of equivariant KK-theory and the Baum-Connes conjecture.

After giving the definition I will discuss some basic examples and, if time permits, a more elaborate one arising from boundary actions of classical hyperbolic groups.

Speaker: Peter Dukes

Title: The Different Pairs Problem for Latin Squares

Talk is based on work with Jared Howell.

Speaker: Salimah Ismail, University of Victoria

Title: A skew-t space-varying regression model for the spectral analysis of magnetoencephalography readings

It is known that in many neurological disorders such as Down syndrome, main brain rhythms shift their frequenciesslightly, and characterizing the spatial distribution of these shifts is ofinterest. We will explore the development of a skew-t mixed model for the spatial analysis of resting state brain activity in healthy controls and individuals with Down syndrome (DS). Magnetoencephalography (MEG) is used to record time series of oscillatory brain activity thereby providing spectral summaries for multiple sensor sites across the scalp. We consider the mean frequency of the power density, and use space-varying regression to examine associationswith age, gender and Down syndrome simultaneously across several scalp regions. A multivariate Markov random field creates a basis to incorporate spatial smoothing priors and the use of a skew-t distribution accommodates themarkedly non-Gaussian nature of the response variable. We examine a range of models representing different prior assumptions on the association structure and conduct model selection and goodness-of-fit using posterior predictive methods in a Bayesian framework. Our analysis suggests differences between healthy controls and individuals with Down syndrome, and produces smoothed maps indicating the scalp topography of the estimated differences.

Speaker: Ian Putnam

Title: (Topological) Full Groups

Abstract: Full groups were introduced in measurable dynamics by Henry
Dye about fifty years ago. The topological analogue was introduced by
Giordano, Skau and myself about a decade ago: given a homeomorphism of
the Cantor set without periodic points (or more generally a free action
of some countable group on the Cantor set), its associated full group
consists of those homeomorphisms of the space which are obtained by
partitioning the space into pieces and applying different powers of the
map to each piece.  The topological full group is obtained by
restricting to partitions into clopen sets. I will discuss the
definitions, elementary properties and some of our old results. In the
last couple of years, a number of other people have obtained some much
more interesting results on the structure of these topological full
groups and I will survey some of these.

Speaker: Cecilia Gonzalez Tokman

Title:
A semi-invertible operator Oseledets theorem

Abstract:
Semi-invertible multiplicative ergodic theorems establish the existence of an
Oseledets splitting-- a decomposition into generalized Jordan blocks-- for
cocycles of non-invertible linear operators (such as transfer operators) over
an invertible base. Using a constructive approach, we establish a
semi-invertible multiplicative ergodic theorem that for the first time can be
applied to the study of transfer operators associated to the composition of
piecewise expanding maps randomly chosen from a set of cardinality of the
continuum.
This is joint work with Anthony Quas.

Speaker: William R. Holmes (UBC)

Title: Regulatory Control of Response Thresholds during Chemotactic Polarization

Abstract
Eukaryotic cells exhibit a number of distinct chemotactic phenotypes.  Some, Dictyostelium for example, undergo random motion in the absence of stimuli.  Others, such as neutorphils, exhibit a more stable rest state and require a spatially directed stimulus to induce motion.  Yet others such as fibroblasts have been observed to switch between these two behaviours as a result of environmental and/or biochemical factors.  It is widely accepted that spatio-temporal reorganization of evolutionarily conserved regulatory molecules, Rho-GTPases and Phosphoinositides (PIs), is responsible for directing cytoskeletal reorganization and subsequent motion.  The former behaviour is indicative of an unstable, noise sensitive pattern forming (symmetry breaking) process and the latter a threshold driven process. 
In this joint modelling / experimental study, we probe the regulatory network in a model system (HeLa cells) and provide a mechanistic hypothesis for how these phenotypes can arise.  A microfluidic device is used to apply precisely controlled stimuli and pharmacological techniques are used to augment and explore the underlying biochemistry of interest.  A minimal reaction diffusion model of the relevant molecular interactions is developed.  We use a novel asymptotic technique, the Local Perturbation Analysis (LPA), to parametrically map out pattern forming regimes in this model.  It is found that it exhibits both noise sensitive and threshold behaviour, resulting from a sub-critical Turing bifurcation. The model parameter that controls the stability and response threshold is directly linked to a biochemical pathway (GEF activation of the GTPase Rac).  This pathway is directly probed in associated experiments supporting the assertion that its augmentation controls response thresholds.  We thus hypothesize that it is of primary importance in determining motility phenotype.  Further analysis shows that these results are independent of particular molecular interactions, which likely vary among cell types, and thus are more general.  A description of the experiments, the resulting model, and the LPA technique will be provided along with a discussion of the results.

Speaker: Michael Rempel, University of Victoria

Title: A Spatial Model for Extreme Precipitation

Max-stable processes are limiting processes for maxima of independent copies of a stochastic process. The definition of a max-stable process cannot be used directly to construct a model for extreme phenomena, but several models have been constructed that satisfy the requirements for max-stability. We present twomodels for extreme precipitation that appear in the literature. The first is constructed from uniformly distributed bivariate normal distributions and the second is constructed from Gaussian processes in R^2. We focus on the second, as it is more flexible and more representative of precipitation fields. We discuss the model fitting procedure and parameter estimation for the model,using rainfall in southwestern BC.

Speaker: Peter Dukes

Title: Efficient total dominating sets in Cayley graphs, and coverings of the reflexive complete graph

Prof. Walter Craig, McMaster University
Lower bounds on the Navier - Stokes singular set

Thursday, December 1, 2011
3:30 pm
Cornett Bldg (COR) B107

Walter holds a CRC for Mathematical Analysis and its Applications at McMaster University, and was recently elected a fellow of the Royal Society of Canada. Before moving to Canada he has been on the faculty of Caltech, Stanford University, and was chair of the Mathematics  Department at Brown University.

Abstract: The well-known result of partial regularity for solutions of the Navier-Stokes equations provides an upper bound on the size of the singular set of (suitable) weak solutions. This talk will describe complementary lower bounds, both for the the singular set and the energy (L^2 norm) concentration set, in case that they are nonempty. These bounds are microlocal in nature, and follow from a novel estimate for weak solutions of the Navier-Stokes equations. These results are, in part, joint work with M. Arnold, and the above estimate on weak solutions was originally described by A. Biryuk, S. Ibrahim and myself.

Thursday December 1, 2011 2:30-3:30
DSB C118

Speaker: Kyle Vincent, Simon Fraser University

Estimating Hard to Reach Population Sizes with Link tracing Sampling

The ability to conventionally sample members of a hard to reach population, like those comprised of injection drug users, is a difficult task as there is likely to be an absence of a sampling frame for such populations. An alternative approach is to follow the social links from accessible members of the community in order to recruit more individuals into the study. Employing capture recapture methods for estimating the sizes of populations based on such adaptive sampling designs will likely result in biased estimates since the sample is comprised of members that are selected through an incompatible probability sampling mechanism. We have developed a method for estimating population sizes based on a popular link tracing sampling design termed snowball sampling that works over a Bayesian data augmentation inferential procedure when applied to an elaborate graph model. In addition, a design based approach which utilizes an estimation procedure based on sample reorderings consistent with a sufficient statistic(s), in conjunction with some of the common capture recapture techniques, for other practical adaptive sampling designs is proposed. In this talk, these two methods are demonstrated for a simulated networked population.

Program of the Final Oral Examination for the Degree of Master of Science

DEPARTMENT OF MATHEMATICS AND STATISTICS of

SCOTT LUNNEY

“Trees with Equal Broadcast and Domination Numbers”

Wednesday, November 30th, 2011 11:30 am

University Centre Building, Room A207a

A copy of the thesis will be available for viewing in the Department of Mathematics and Statistics’ General Office at least one week prior to the oral examination.

Dr. Aaron H. Devor Dean, Faculty of Graduate Studies

Time: Monday November 28, 3:30PM

Room: CLE A311

Speaker: Our speaker this week is Caroline Cameron (Biochemestry/Microbiology, UVic)

Title: Spread of the Syphilis Spirochete, Treponema pallidum.

Abstract:
Syphilis remains a public health threat worldwide, with an estimated 15 million new infections per year and a global burden of 25 million infections.  Within the last decade there has been an increase in syphilis outbreaks in major cities around the world, with a 10-fold increase in syphilis infections documented for China and Canada and a doubling of syphilis infections in the United States.  Syphilis infections increase the risk of acquiring and transmitting HIV, and there has been a 23% increase in congenital syphilis infections, resulting from mother to child transmission in utero, in recent years within North America.  Although syphilis is curable with penicillin treatment if diagnosed early, the worldwide syphilis prevalence shows that elimination of this disease will not occur through public health control measures alone, and instead will require development of an effective syphilis vaccine. 

Development of a syphilis vaccine requires an in depth knowledge of the pathogenic mechanisms used by this highly successful pathogen.  The bacterium that causes syphilis, Treponema pallidum, is able to disseminate rapidly within the host during the early stages of infection to infect every organ and tissue.  Despite over a century of research that has been conducted on T. pallidum, the pathogenic mechanisms used by T. pallidum to undergo widespread dissemination throughout the host have remained unknown.  Our investigations have identified a protein, designated Tp0751, which is central to dissemination of T. pallidum and represents a potential vaccine candidates for prevention of syphilis infection.

Speaker: Laura Teshima

Monday, Nov 28 at 10 am in DSB C114

Title: On Forming Committees

Abstract: Laura will give a talk on this article by Penny Haxell.

Thursday November 24, 2011 2:30-3:30 DSB C118

Speaker: Farouk Nathoo, University of Victoria

Title: A Spatiotemporal Hidden Markov Model for Electromagnetic Brain Mapping

We present a new statistical approach for solving the neuroelectromagnetic inverse problem
arising in studies involving electroencephalography (EEG) and magnetoencephalography (MEG). This spatial problem involves the estimation of time-varying neural activity at a large number of locations within the brain, from time series recorded at a relatively small number of locations on or near the scalp. The underdetermined nature of this estimation problem necessitates
the use of regularization methods, either through penalization, or through the inclusion of priors in a hierarchical Bayes setting. Framing this problem within the context of variable selection in a dynamic linear model, we propose a mixture formulation, where the spatial profile of activity within the
brain is represented with a latent process governed by an autologistic model.
The autologistic model accommodates spatial clustering in brain activation,
while also allowing for the inclusion of auxiliary information derived from
alternative imaging modalities, such as fMRI. We develop a variational approach for approximate Bayesian inference, and we compare this approach with several established methods, including low-resolution electrical tomography (LORETA) and the well-known minimum norm estimate. Joint work with Arif Babul, Alexander Moiseev, Mirza Faisal Beg and Naznin Virji-Babul.

*********************************************************
Speaker: Anna Machina (UVic)
*********************************************************

Wednesday November 23 at 3:30 in CLE D132

*********************************************************
Title: Differential inclusions and piecewise models in gene regulatory networks
*********************************************************

Abstract:

We study some properties of piecewise linear differential systems describing gene regulatory networks, where the dynamics are governed by sigmoid-type nonlinearities which are close to or coincide with the step functions. To overcome the difficulty of describing the dynamics of the system near singular stationary points (belonging to the discontinuity set of the system) we use the concept of Filippov solutions. It consists in replacing discontinuous differential equations with differential inclusions.  We compare two frameworks to study singular stationary points and there stability: one is based on the Filippov theory and the other exploits singular  perturbation methods (Tikhonov theorem). We also discuss and analyse another concept of Filippov, based on non-convex differential inclusions. The latter solutions (namely, in the narrow sense)  seem to have got little attention in the literature due to the existence problem. At the same time the Filippov solutions in the general sense are in fact  “too many” for describing real-world dynamics.

Wednesday November 16 and 23 at 3:30 in DSB C114

Title: A Bratteli-Vershik model for minimal Z^2-actions on the Cantor set

Abstract: We will discuss the interrelations between: minimal Z^d Cantor
systems, Bratteli diagrams and ordered abelian groups. The first lecture
will be a survey of these topics which is accessible to non-experts. A
very satisfactory picture emerges in the case d=1. However, things are
much less clear for d > 1. In particular, it has been unclear how to
construct models for Z^2 actions from a Bratteli diagram. In the second
lecture, I will report on recent progress in this direction with Thierry
Giordano and Christian Skau.

Speaker: Garrett Flowers

Monday, Nov 21 at  10AM in DSB C114

Date & Time : Friday Nov 18, at 3:30 pm.
Location: HSD A250.

Speaker:
Antoine Julien

Title:
An alternate description of the Robinson tilings

Abstract:
The Robinson set of tiles was produced to give an example of a
two-dimensional subshift of finite type without any periodic orbits. I
will give a short introduction to the Robinson tiles: explain why they
tile, and why they can't tile periodically. Then, I will focus on the
space of all Robinson tilings that can be produced using these rules. It
has a unique minimal subspace, and this subspace can be described by
means of a substitution map.  This description has several consequences,
namely it is possible to compute topological invariants for this
subshift, and it also implies that the Robinson tilings can be obtained
by using the cut and project method.
(Joint work with F. Gähler and J.  Savinien)

Thursday November 17, 2011 2:30-3:30
DSB C118

Speaker: Weixun Lu, University of Victoria
Title: Interval Estimation of Binomial Proportions

Interval estimation is very helpful in estimating the unknown but
interested parameter in prediction. For interval estimation of a
proportion in Binomial distribution, the probabilities obtained from the
``Exact'' confidence interval are too large and overestimate the
confidence interval for a binomial test. Estimation intervals obtained
from the Wald test are too small for the binomial test. But inverting the
related Score test yields good results to the nominal confidence levels.
The true confidence levels obtained from the Score test are very close to
the nominal confidence levels. This is true even when the size of sample
is small. However, the Score test formula is difficult to remembered. For
estimating 95% confidence levels, we suggest using the adjusted Wald
interval, which adds two ``success'' and two ``failures'' to the sample
probability. Probabilities obtained from the adjusted Wald interval
provides similar result to the Score test and is easily remembered.

Wednesday November 16 at 3:30PM

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Speaker: Burt Voorhees (U of A)
*********************************************************

*********************************************************
Title: A Population Model of the Stability-Flexibility Trade-Off
*********************************************************

Abstract:

We present a population model illustrating the concept of virtual stability, that is, the idea that complex adaptive systems with the capacity for self-monitoring and adaptive change are able to maintain themselves in states that would otherwise be unstable.  The advantage gained from this is increased behavioral flexibility in the face of random environmental perturbations.  In the model presented, transition probabilities between three population types are used to emulate stability: stable types have low probabilities of making transitions to other types, unstable types have high transition probabilities.  The model itself consists of two stable types and one unstable type and conditions are explored that lead to dominance by the unstable type.  Under certain conditions the unstable type can defeat a stable type, even in an environment that always favors the stable type.

Wednesday November 16 and 23 at 3:30 in DSB C114

Title: A Bratteli-Vershik model for minimal Z^2-actions on the Cantor set

Abstract: We will discuss the interrelations between: minimal Z^d Cantor
systems, Bratteli diagrams and ordered abelian groups. The first lecture
will be a survey of these topics which is accessible to non-experts. A
very satisfactory picture emerges in the case d=1. However, things are
much less clear for d > 1. In particular, it has been unclear how to
construct models for Z^2 actions from a Bratteli diagram. In the second
lecture, I will report on recent progress in this direction with Thierry
Giordano and Christian Skau.

Time and Room: SSM A102,  Monday, November 14 at 4pm

Title: A skew-normal space-varying regression model for the spectral
analysis of magnetoencephalography readings

Abstract:

It is known that in many neurological disorders such as Down syndrome,
main brain rhythms shift their frequencies slightly, and characterizing
the patial distribution of these shifts is of interest. This paper reports
on
the development of a skew-normal mixed model for the spatial analysis of
resting state brain activity in healthy controls and individuals with Down
syndrome (DS). Magnetoencephalography (MEG) is used to record time series
of oscillatory brain activity thereby providing spectral summaries for
multiple sensor sites across the scalp. We consider the mean frequency of
the power density, and use space-varying regression to examine
associations with age, gender and Down syndrome simultaneously across
several scalp regions. A multivariate Markov random field creates a basis
to incorporate spatial smoothing priors and the use of a skew-normal
distribution accomodates the markedly non-Gaussian nature of the response
variable. We examine a range of models representing different prior
assumptions on the association structure and conduct model selection and
goodness-of-fit using posterior predictive methods in a Bayesian
framework. Our analysis suggests differences between healthy controls and
individuals with Down syndrome, and produces smoothed maps indicating the
scalp topography of the estimated differences.

Speaker: Kieka Mynhardt

Title: Where we stand on Vizing's conjecture on the domination number of Cartesian products of graphs

Monday Nov. 14 at 10 AM in David Strong Building Room C114

Time and Room: Monday November 7th at 4pm in SSM A102

Title: Equivariant embeddings

Abstract:

Let a and b be two positive real numbers whose ratio is
irrational. Let Y be the space of all partitions of the real line by
intervals of lengths a and b. Endow Y with the time-one map T that acts on
a partition of the real line by shifting each interval of the partition to
the left by one unit. Consider the space X of all bi-infinite binary
sequences, endowed with a product measure, and the shift-operator S given
by (Sx)(i) = x(i + 1) for all x in X and all integers i. Thus X is a
probability space for a bi-infinite sequence of i.i.d. coin-flips. We will
show that provided a and b are sufficiently small, there exists a subset W
of X of full-measure and an injective map F from W to Y with the property
that F is equivariant; that is, F(S(x)) = T(F(x)) for all x in W. Nothing
fancy is needed and all the necessary background will be discussed.

(This is a special case of joint work with Anthony Quas)