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This is the first announcement of the n-th Annual Combinatorial Potlatch, which will be hosted by the University of Victoria on Saturday, November 18, 2017 in Victoria, BC.
 
We are close to finalizing the program.  That, and other information, will be added to the conference page soon, and will also be contained in the second announcement.  Information on lodging is available now.
 
 Main Potlatch Page:
 http://buzzard.ups.edu/potlatch/index.html
 
 2017 Conference Page:
 http://faculty.wwu.edu/sarkara/potlatch2017.html
 
There is no advance registration required, nor any registration fee.  The first talk will be mid to late morning, to allow for travel, followed by a no-host lunch, and two talks later in the afternoon.  Many participants choose to stay for dinner locally.
 
Combinatorial Potlatches have been held for many years at various locations around Puget Sound and southern British Columbia, and are an opportunity for combinatorialists in the region to gather informally for a day of invited talks and conversation. While most who attend work in, or near, the Puget Sound basin, all are welcome.
 
Please forward this announcement to anyone, especially graduate students, that might be interested and are not on our list.  Our apologies if you receive more than one copy of this.
 

• Program Committee: Nancy Neudauer, Pacific University 
• Communications Committee: Amites Sarkar, Western Washington University
•  Local Arrangements Committee: Gary MacGillivray, University of Victoria

Spectral graph theory usually studies the relations between a graph and a corresponding matrix, which can be the adjacency matrix, the Laplacian matrix, the normalised Laplacian matrix, or other matrices.  For each graph G, these matrices belong to the family S(G) of symmetric matrices whose i,j-entry with i != j is nonzero whenever {i,j} is an edge and zero otherwise.  (Diagonal entries can be either zero or nonzero.)  The inverse eigenvalue problem studies the ``general property'' of S(G) and aims to find all possible spectra appeared in S(G).  We will go through many graph concepts such as the diameter, the domination number, and the graph minor theory, and then discuss their relations to matrices.

Abstract: One can construct a stationary system where the objects in
question are rooted graphs and the shift operation is a random walk step.
Another equivalent way to say this is to say that the graph satisfies an
intrinsic "mass transport principle”. I will explain why this is an
important idea and survey some recent results. Based on some results of
Benjamini and Curien and some joint work of myself with Omer Angel, Tom
Hutchcroft and Asaf Nachmias.

This will be Part II of two consecutive lectures.

Scott Sheffield introduced a connection between weighted random planar graphs and an inventory accumulation problem in a burger factory, generalizing an earlier work on Bernardi. This connection has applications on models of random graphs which approximate certain 2 dimensional quantum gravity models coming from physics. Consequently this led to a series of work on the continuum side (primarily by Miller and Sheffield) and settle some longstanding conjectures. This connection is popularly now known as the "hamburger cheeseburger bijection". I will focus on this bijection in this talk and try to convince you why it is important

Abstract: We will discuss several notions of graded C*-algebras. We will 
in particular explain how we got interested in the topic, and what we 
have learned about it.

Abstract : The one-dimensional Landau-Lifshitz equation describes the dynamics of 
the magnetization in a ferromagnetic material. It has travelling-wave 
solutions called solitons.

In this talk, I first review previous result of the global 
existence and orbital stability of solitons. Then, I will focus on the 
asymptotic stability in the energy space of non-zero speed solitons. 
More precisely, I will show that any solution corresponding to an initial 
datum close to a soliton with non-zero speed, is weakly convergent in 
the energy space as time goes to infinity, to a soliton with a possible 
different non-zero speed, up to the geometric invariances of the 
equation. The proof relies on the ideas developed by Martel and Merle 
for the generalized Korteweg-de Vries equations. We will finish by the 
case of multi-solitons. The solitons have non-zero speed, are ordered 
according to their speeds and have sufficiently separated initial 
positions. We will show that they are asymptotically stable.


The talk is based on my PhD work at Ecole polytechnique in 
France under the supervision of Philippe Gravejat and Raphael Cote.

The UVic Mathematics Competition is held annually in the fall. The 19th competition will be held on Tuesday, September 26, 2017 between 4:00-6:00 pm in the Harry Hickman Building 110. There are monetary prizes. To participate, just show up. The competition is open to all undergraduate students at UVic, including first year students. In the past some prizes were won by first year students.

Here are some recent question papers: 2016 2015 2014 2013 2012 2011 2010 2009 2008 2007 2006.

I’m going to step in tomorrow and talk about something current. I’ll
finish a little bit early and we can chat about who might like to talk
this term, and when. Please give this little thought so that we can, at
least, have someone lined up for  next Thursday.  If you need more than
one session, please feel free to request.

Abstract:  I will discuss optimal design of experiments in statistics.  Optimal designs can be constructed for various optimality criteria, which are often determined by research problems and experimental conditions. I will focus on block designs and fractional factorial designs to explain several concepts including statistical models, estimation methods and commonly used optimality criteria.

Abstract:

By a result of Glimm, we know that classifying representations of 
non-type-I C ∗ -algebras up to
unitary equivalence is difficult problem. Instead of this, one either 
restricts to a tractable subclass or
weakens the invariant. In the theory of free semigroup algebras, the 
latter is achieved for representations
of Toeplitz-Cuntz algebras.
Two key results in the theory that enable this are a theorem of 
Davidson, Katsoulis and Pitts on
the 2 × 2 structure of free semigroup algebras, and the Lebesuge-von 
Neumann-Wold decomposition
theorem of Kennedy.
This second talk continues the first and is based on joint work with Ken 
Davidson and Boyu Li.
We explain how we generalize the theory of free semigroup algebras to 
the context of weak operator
topology closed algebras arising from representations of 
Toeplitz-Cuntz-Krieger algebras associated to
a directed graph G. We prove a structure theorem akin to that of 
Davidson, Katsoulis and Pitts, and
obtain a Lebesuge-von Neumann Wold decomposition. We apply our results 
to obtain reflexivity, a
Kaplansky density theorem and classification results for free 
semigroupoid algebras.

Abstract: "We consider a thin-film equation with linear mobility and 
zero contact angle at the free boundary, that is, at the contact line 
where liquid, gas, and solid meet. Previous results on stability and 
well-posedness of this equation have focused on perturbations of 
equilibrium-stationary or self-similar profiles, the latter eventually 
wetting the whole surface. These solutions have their counterparts for 
the second-order porous-medium equation. Both porous-medium and 
thin-film equation are degenerate-parabolic, but the porous-medium 
equation additionally fulfills a comparison principle while the 
thin-film equation does not.

In this talk, we consider receding traveling waves describing 
de-wetting, a phenomenon genuinely linked to the fourth-order nature of 
the thin-film equation and not encountered in the porous-medium case as 
it violates the comparison principle. The linear stability analysis 
leads to a linear fourth-order degenerate-parabolic operator for which 
we prove maximal-regularity estimates with arbitrary regularity in a 
right-neighborhood of the contact line. This leads to a well-posedness 
and stability result for the corresponding nonlinear equation. As the 
linearized evolution has different scaling as at the contact line and in 
the bulk, the analysis is more intricate than in related previous works. 
We believe that our analysis is a natural step towards investigating 
other situations in which the comparison principle is violated, such as 
rupture of droplets.

The talk is based on joint work with Slim Ibrahim (University of 
Victoria, BC) and Nader Masmoudi (Courant Institute, NYU)."

Transport phenomena can be studied by investigating underlying dynamical
systems from a “probabilistic” or “mass transfer” point of view. Insight
can sometimes be gained from the dominant parts of the spectrum of
associated transfer operators. Modern computer power makes practical
studies of these objects feasible in a plethora of application areas; it
is natural to consider whether inferences from numerically approximated
transfer operators are mathematically plausible. These are classic
questions of “stochastic stability”.

Progress this decade has been significant, with advances in the
multiplicative ergodic theory of non-autonomous (or “driven” or “random”)
dynamical systems. This talk will report some current joint work with Gary
Froyland (UNSW) and Cecilia Gonzalez-Tokman (UQ) about non-autonomous
interval maps in which we obtain a fully quenched stochastic stability
result under an “eventually expanding on average condition” (with only
ergodicity of the driving process).

Abstract: By a result of Glimm, we know that classifying representations of non-type-I C ∗ -algebras up to unitary equivalence is essentially impossible (at least with countable structures). Instead of this, one
either restricts to a tractable subclass or weakens the invariant. In the theory of free semigroup algebras, the former is achieved for atomic and finitely correlated 
representations of Toeplitz-Cuntz algebras.
In this first talk, based on joint work with Ken Davidson and Boyu Li, we introduce free semigroupoid
algebras and discuss generalizations of the above results to representations of Toeplitz-Cuntz-Krieger
algebras associated to a directed graph G. We prove a classification theorem akin to that of Davidson
and Abstract: By a result of Glimm, we know that classifying representations of non-type-I C ∗ -algebras up to unitary equivalence is essentially impossible (at least with countable structures). Instead of this, one
either restricts to a tractable subclass or weakens the invariant. In the theory of free semigroup algebras, the former is achieved for atomic and finitely correlated 
representations of Toeplitz-Cuntz algebras.
In this first talk, based on joint work with Ken Davidson and Boyu Li, we introduce free semigroupoid
algebras and discuss generalizations of the above results to representations of Toeplitz-Cuntz-Krieger
algebras associated to a directed graph G. We prove a classification theorem akin to that of Davidson
and Pitts on atomic representations, and show how the road coloring theorem from graph theory gives
us a large class of directed graphs for which the free semigroupoid algebra is in fact self-adjoint. Pitts on atomic representations, and show how the road coloring theorem from graph theory gives
us a large class of directed graphs for which the free semigroupoid algebra is in fact self-adjoint.

The Final Oral Examination for the Degree of Master of Science (Department of Mathematics & Statistics)

Xiaozhi CHEN 2013 University of Victoria BS.C-Honours

“ROC Curve and Generalized Linear Mixed Models Analysis of Environmental DNA”

Friday August 18, 2017 10:30am

DSB C108

Supervisory Committee:

Dr. M. Lesperance, Department of Mathematics & Statistics, UVic (Supervisor)

Dr. C. Helbing, Department of Biochemistry and Microbiology, UVic (Committee Member)

Chair of Oral Examination:

Dr. Kieka Mynhardt, Department of Mathematics & Statistics, UVic

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

BONNIE-JEAN ROBERT BSc (Vancouver Island University, 2013)

“A Pipeline for Differential Expression Analysis of RNA-seq Data and The Effect of Filter Cutoff on Performance”

Department of Mathematics and Statistics

Tuesday, August 15th, 2017 1:00 P.M.

Human and Social Development Building Room A250

Supervisory Committee:

Dr. Mary Lesperance, Department of Mathematics and Statistics, University of Victoria (Supervisor)

Dr. Julie Zhou, Department of Mathematics and Statistics, UVic (Member) External Examiner:

Dr. Caren Helbing, Department of Biochemistry and Microbiology, UVic Chair of Oral Examination:

Dr. Martin Farnham, Department of Economics, UVic

Abstract

RNA sequencing is a powerful new approach to analyzing differential expression of transcripts between treatments. Many statistical methods are now available to test for differential expression, each one reports results differently. This paper presents a workflow of five popular methods and discusses the results. A pipeline was built in the R language to analyze four of these packages using a real RNA-seq dataset.

At present, researchers must prepare RNA-seq data prior to analysis to achieve reliable results. Filtering is a necessary preparatory step in which transcripts exhibiting low levels of genetic expression are removed from further analysis. Yet, little research is available to guide researchers on how best to choose this threshold. This paper introduces a study designed to determine if the choice of filter threshold has a significant effect on individual package performance. Increasing the filtering threshold was shown to decrease the sensitivity and increase the specificity of the four statistical methods studied.

The Final Oral Examination for the Degree of Master of Science (Department of Mathematics & Statistics)

Yi SHEN

2013 Jiangxi University of Finance and Economics B.A 2015 University of Victoria BS.C

“Analysis of Volatility Models for Financial Time Series”

Date: Tuesday, August 15th, 2017 Time: 10:00 am-12: 50 pm

Location: HSD A270

Supervisory Committee:

Dr. J. Zhou, Department of Mathematics & Statistics, UVic (Co-Supervisor)

Dr. M. Tsao, Department of Mathematics & Statistics, UVic (Co-Supervisor) Chair of Oral Examination:

Dr. L. Cowen, Department of Mathematics & Statistics, UVic

The Final Oral Examination for the Degree of Master of Science (Department of Mathematics & Statistics)

Chanfan ZHENG B.Sc., Simon Fraser University, 2015

“Analysis of Semi-parametric Mixture Models using binary-based NBA and HDP data”

Tuesday, August 15, 2017 9:30am

HSD A250

Supervisory Committee:

Dr. M. Lesperance, Department of Mathematics & Statistics, UVic (Supervisor)

Dr. F. Nathoo, Department of Mathematics & Statistics, UVic (Member)

Chair of Oral Examination: Dr. Junling Ma, Department of Mathematics & Statistics, UVic

Notice of the Final Oral Examination

for the Degree of Master of Science of

HASSAN AL NASSER

BSc (University of Victoria, 2014)

“On Ridge Regression and Lasso”

Department of Mathematics and Statistics

Wednesday, August 2, 2017 2:00 P.M.

David Turpin Building Room A136

Supervisory Committee:

Dr. Jane Ye, Department of Mathematics and Statistics, University of Victoria (Co-Supervisor)

Dr. Julie Zhou, Department of Mathematics and Statistics, UVic (Co-Supervisor)

External Examiner: Dr. Hong-Chuan Yang, Department of Electrical and Computer Engineering,

UVic Chair of Oral Examination: Dr. Sybille Artz, School of Child and Youthcare,

UVic Dr. David Capson, Dean, Faculty of Graduate Studies

Abstract This thesis focuses on ridge regression (RR) and the lasso (least absolute shrinkage and selection operator). Ridge properties are being investigated in great detail which include studying the bias, the variance and the mean squared error as a function of the tuning parameter. We also study the convexity of the trace of the mean squared error in terms of the tuning parameter. In addition, we examined some special properties of RR for factorial experiments. Not only do we review ridge properties, we also review lasso properties because they are somewhat similar. Rather than shrinking the estimates toward zero in RR, the lasso is able to provide a sparse solution, setting many coefficient estimates exactly to zero. Furthermore, we try a new approach to solve the lasso problem by formulating it as a bilevel problem and developing a new algorithm to solve this bilevel problem.

Abstract: Gibbs states in thermodynamics are expressed as Gibbs measures on shift spaces. We apply the study of the transition classes of factor maps to investigate how Gibbs properties are transformed under factor maps from shifts of finite type.

Abstract: In this work, we deal with correlated under-reported data through INAR(1)-hidden Markov chain models. These models are very flexible and can be identified through its autocorrelation function, which has a very simple form. A naïve method of parameter estimation is proposed, jointly with the maximum likelihood method based on a revised version of the forward algorithm. The most-probable unobserved time series is reconstructed by means of the Viterbi algorithm.

Notice of the Final Oral Examination for the Degree of Doctor of Philosophy (PDF file)

In any real system, changing the control signal from one value to another will usually cause wear and tear on the system's actuators. Thus, when designing a control law, it is important to consider not only predicted system performance, but also the cost associated with changing the control action. This cost, however, is almost always ignored in the optimal control literature. In this talk, we will consider a class of optimal control problems in which the variation of the control signal is explicitly penalized in the cost function. We describe two computational methods---one based on a smooth approximation scheme and the other based on a novel transformation procedure---for solving this class of optimal control problems. We then apply these methods to solve example problems in fisheries, train control, and chemical engineering.

Notice of the Final Oral Examination for the Degree of Doctor of Philosophy of

YUE YIN

MSc (University of Victoria, 2013)

BSc (Beijing Institute of Technology, 2011)

“Theory and Algorithms for Finding Optimal Regression Design”

Department of Mathematics and Statistics

Tuesday, June 20, 2017 1:00 P.M.

David Turpin Building Room A136

Supervisory Committee:

Dr. Julie Zhou, Department of Mathematics and Statistics, University of Victoria (Supervisor)

Dr. Boualem Khouider, Department of Mathematics and Statistics, UVic (Member)

Dr. Farouk Nathoo, Department of Mathematics and Statistics, UVic (Member)

Dr. Stan Dosso, School of Earth and Ocean Sciences, UVic (Outside Member)

External Examiner: Dr. Zhide Fang, Department of Biostatistics, Louisiana State University

Chair of Oral Examination: Dr. Judith Clarke, Department of Economics, UVic

Abstract:

In this dissertation, we investigate various theoretical properties of optimal regression designs and develop several numerical algorithms for computing optimal regression designs. The results can be applied to linear, nonlinear and generalized linear models. Our work starts from how to solve the design problems for A-, As, c-, I- and L-optimality criteria on one-response model. Theoretical results are hard to derive for many regression models and criteria, and existing numerical algorithms can not compute the results efficiently when the number of support points is large. Therefore we consider to solve the design problems based on SeDuMi program in MATLAB. SeDuMi is developed to solve semidefinite programming (SDP) problems in optimization. To apply it, we derive a general transformation to connect the design problems with SDP problems, and propose a numerical algorithm based on SeDuMi to solve these SDP problems. The algorithm is quite general under the least squares estimator (LSE) and weighted least squares estimator (WLSE) and can be applied to both linear and nonlinear regression models. We continue to study the optimal designs based on one-response model when the error distribution is asymmetric. Since the second-order least squares estimator (SLSE) is more efficient than the LSE when the error distribution is not symmetric, we study optimal designs under the SLSE. We derive expressions to characterize A- and D-optimality criteria and develop a numerical algorithm for finding optimal designs under the SLSE based on SeDuMi and CVX programs in MATLAB. Several theoretical properties are also derived for optimal designs under SLSE. To check the optimality of the numerical results, we obtain the KieferWolfowitz equivalence theorem and apply it to various applications. Finally, we discuss the optimal design problems for multi-response models. Our algorithm studied here is based on SeDuMi and CVX, and it can be used for linear, nonlinear and generalized linear models. The transformation invariance property and dependence on the covariance matrix of the correlated errors are derived. We also correct the errors in the literature caused by formulation issues. The results are very useful to construct optimal regression designs on discrete design space. They can be applied for any one-response and multi-response models, various optimality criteria, and several estimators including LSE, maximum likelihood estimator, best linear unbiased estimator, SLSE and WLSE.

Abstract: In this talk, we prove the existence of two phase quadrature domains as well as two (and multiphase) quadrature surfaces. The existence is obtained by minimizing suitable energy functional, using one-phase solutions as barrier Regularity of the associated free boundary and some qualitative properties will be discussed.

Nature-inspired meta-heuristic algorithms are increasingly studied and used in computer science and engineering disciplines to solve high-dimensional complex optimization problems in the real world. It appears that relatively few of these algorithms are used in mainstream statistics even though they are simple to implement, very flexible and frequently able to find an optimum or a nearly optimal solution to an optimization problem quickly. These general optimization methods usually do not require any assumption on the function to be optimized and the user only needs to input a few easy-to-use tuning parameters.

In this talk, I provide an overview of such algorithms and demonstrate their usefulness for finding different types of optimal designs for biomedical applications.  In particular, I will construct various types of optimal designs for the 4-parameter logistic model (Hill model) for tumor growth reduction and hard-to-find optimal designs, like maximin and standardized maximin optimal designs for some enzyme kinetic inhibition nonlinear models with 3 or 4 parameters.    This approach also has potential applications in population pharmacokinetic studies with multiple objectives. For example, in HIV and TB studies, an important design problem is the determination optimal sampling times for simultaneous estimation of PK parameters of multiple drugs used in combination therapy.

The celebrated Rudin-Osher-Fatemi scheme is a very popular  denoising method, intimately related to the mean-curvature flow which is the (L^2) gradient flow of the total variation.  In this talk we will consider the variant where the standard L^2 fidelity criterion is replaced by the Wasserstein distance. We will characterize the minimizers, study their regularity and will establish a connection with a fourth-order nonlinear evolution equation. This is a joint work with Clarice Poon (Cambridge).

An n_3 configuration consists of n "points" and n "lines", where each point is contained in 3 lines, and each line contains 3 points, and any 2 points are contained in at most one line. The Fano configuration is the smallest n_3 configuration (n=7). An n_3 configuration is geometric if it can be drawn in the real plane such that all lines are straight lines.   An example is the Desargues configuration (n=10).

Grunbaum has conjectured that any configuration which is geometric can also be drawn in the rational plane, ie, the coordinates of the points are rational numbers.

We describe a 1-point extension in an n_3 configuration to produce an (n+1)_3 configuration.  If the starting n_3 configuration has a rational coordinatization, then it is shown how to construct a rational coordinatization of the resulting (n+1)_3 configuration.