Events
All upcoming and recent events from the past six months:
Title: Ahmed Fest
Date and time:
06 Dec 2018,
10:00am -
5:00pm
Location: David Strong Building C116
Event type: Conferences and workshops
Read full description
Mark your calendars! On Thursday December 6th we will be having a day of activities to celebrate the works of Emeritus Professor Ahmed Sourour. Laurent Marcoux and Heydar Radjavi from the University of Waterloo will be giving research talks covering Sourour's scientific contributions. Sourour's former PhD student Maria Inez Cardoso Gonçalves from the Federal University of Santa Catarina, Brazil will also be joining us. We will also have a problem-solving session in recognition of Sourour's contributions to the annual UVic Math Contest and Putnam competitions. Please see the Ahmed Fest website for more detailed information.
Title: Gabor frames, Heisenberg modules and vector bundles
Speaker: Ulrik Enstad, University of Oslo
Date and time:
05 Dec 2018,
3:30pm -
4:45pm
Location: David Strong building C128
Event type: Operator theory seminar
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Abstract: In time-frequency analysis, some of the central objects of study are Gabor frames. A sequence consisting of time-frequency translates of a single function in the Hilbert space of square-integrable functions on the real line is called a Gabor system. The Balian-Low theorem, a fundamental theorem about Gabor systems, implies that for sufficiently nice functions, their associated Gabor systems can never be orthonormal bases. A solution to this is to settle with (Gabor) frames, which can be overcomplete in general.
The theory of Gabor frames is available in the Hilbert space of square-integrable functions on any locally compact abelian group, but has so far been investigated mostly for "elementary" groups such as the real numbers, the circle and the integers. As first discovered by F. Luef, Gabor frames in this setting are related to M. Rieffel's Heisenberg modules over twisted group C*-algebras. In this talk I will show how the Balian-Low theorem might or might not generalize to the locally compact abelian setting, and that the answer depends on the structure of certain Heisenberg modules, or equivalently, certain line bundles associated to the group in question.
Title: A lower bound for the gap between the first and second Lyapunov exponents for a class of cocycles of Perron-Frobenius operators
Speaker: Joseph Horan, University of Victoria
Date and time:
05 Dec 2018,
2:15pm -
3:20pm
Location: ELL 062
Event type: Dynamics seminar
Read full description
Abstract: Lyapunov exponents provide a generalization to cocycles of
operators (“random” compositions of operators) of the spectrum for single
operators. This spectral data allows us to understand expansion and decay
rates of parts of the space on which the operators act; when applied in
the case of Perron-Frobenius operators related to dynamics on a space, it
helps us to understand how mass evolves under the dynamics and decay rates
of transients in terms of spectral gaps. The problem of computing
Lyapunov exponents is generally acknowledged to be a hard one.
In this series of three talks, we will see how we can find a lower bound
on the gap between the first and second Lyapunov exponents for certain
Perron-Frobenius operator cocycles: those that preserve and contract
(somehow) a nice cone of functions. The proof begins with a general
theorem about cocycles of operators and cones where the hypotheses are
checkable and the numbers are, in principle, computable. Applications to
concrete examples require specific tools if they are not “toy” problems.
We will develop one such tool, a specialized Lastota-Yorke inequality, and
use it to estimate the gap for our specific example. We will also use
this analysis to study the situation where the system passes under
perturbation from multiple equilibria to a unique equilibrium with a small
spectral gap.
In this third and last talk, we will recap the setup of the problem and
specific example of a cocycle of paired tent maps, and then discuss the
existence and lower bound for the spectral gap in the example. An
asymptotic result about how the spectral gap shrinks with a scaling
parameter will also be shown.
Title: Semi-complete chordal digraphs
Speaker: Kevin Hsu, University of Victoria
Date and time:
29 Nov 2018,
10:00am -
11:20am
Location: Maclaurin D107
Event type: Discrete math seminar
Read full description
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Title: Moment Equations for the Enskog-Vlasov Equation
Speaker: Henning Struchtrup, Mechanical Engineering, UVic
Date and time:
28 Nov 2018,
3:30pm -
4:20pm
Location: CLE A205
Event type: Applied math seminar
Read full description
Abstract:
The Enskog-Vlasov equation extends the Boltzmann equation by accounting for the attractive forces between, and the finite volume of, the gas particles. Hence, it gives a van-der-Waals-like description of a non-ideal gas, including liquid-vapor phase change. Specifically, the equation describes the liquid phase, the vapor phase, and a diffusive transition region connecting both phases. While not the most accurate model, solutions of the Enskog-Vlasov equation exhibit all relevant phenomena occurring in the evaporation and condensation of rarefied or dense vapors.
Our interest here is to derive macroscopic transport equations—moment equations—from the Enskog-Vlasov equation, which describe liquid vapor and transition region in terms of a few macroscopic properties. To this end, we use Grad’s moment method to derive a closed set of 26 moment equations. In the appropriate limits, these reduce to the Navier-Stokes-Fourier system for liquid and vapor. Our main interest is to study non-hydrodynamic effects, in particular transport in and across the transition region, and the interplay between the transition region and Knudsen layers. We will present first results of this program, including the closed transport equations for 26 moments, discussion of the limits, and solutions in simple geometries.
Title: Amenability for Fell bundles extended from free semigroups
Speaker: Camila Fabre Sehnem, Federal University of Santa Catarina, Brazil
Date and time:
28 Nov 2018,
3:30pm -
4:45pm
Location: DSB C128
Event type: Operator theory seminar
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Abstract: Fell bundles may be viewed as generalised partial group actions. Under mild assumptions, a Fell bundle comes from a partial group action, and if it is saturated, the action is global. Amenability for Fell bundles is defined so that it generalises amenability of groups. In this talk, we will introduce a notion of Fell bundles extended from positive cones of quasi-lattice orders. That is, they arise from certain actions of semigroups. This includes semi-saturated Fell bundles over $\mathbb{Z}$ and semi-saturated and orthogonal Fell bundles over free groups as considered by Exel. We will describe cross sectional $\mathrm{C}^*$-algebras of Fell bundles extended from free semigroups and from Baumslag--Solitar semigroups as relative Cuntz--Pimsner algebras. We then use uniqueness theorems for relative Cuntz--Pimsner algebras to prove amenability for such Fell bundles.
Title: A lower bound for the gap between the first and second Lyapunov exponents for a class of cocycles of Perron-Frobenius operators
Speaker: Joseph Horan, University of Victoria
Date and time:
28 Nov 2018,
2:15pm -
3:20pm
Location: ELL 062
Event type: Dynamics seminar
Read full description
Title: A lower bound for the gap between the first and second Lyapunov
exponents for a class of cocycles of Perron-Frobenius operators preserving
a cone.
Abstract: Lyapunov exponents provide a generalization to cocycles of
operators (“random” compositions of operators) of the spectrum for single
operators. This spectral data allows us to understand expansion and decay
rates of parts of the space on which the operators act; when applied in
the case of Perron-Frobenius operators related to dynamics on a space, it
helps us to understand how mass evolves under the dynamics and decay rates
of transients in terms of spectral gaps. The problem of computing
Lyapunov exponents is generally acknowledged to be a hard one.
In this series of three talks, we will see how we can find a lower bound
on the gap between the first and second Lyapunov exponents for certain
Perron-Frobenius operator cocycles: those that preserve and contract
(somehow) a nice cone of functions. The proof begins with a general
theorem about cocycles of operators and cones where the hypotheses are
checkable and the numbers are, in principle, computable. Applications to
concrete examples require specific tools if they are not “toy” problems.
We will develop one such tool, a specialized Lastota-Yorke inequality, and
use it to estimate the gap for our specific example. We will also use
this analysis to study the situation where the system passes under
perturbation from multiple equilibria to a unique equilibrium with a small
spectral gap.
In this second talk, we will describe a new Lasota-Yorke inequality that
is
well-adapted for cocycles of paired tent maps, and we will explain why we
need
this new inequality, recalling some facts about cones and the Cocycle
Perron-Frobenius theorem.
Title: Population persistence in a source-sink metapopulation
Speaker: Julien Arino, University of Manitoba
Date and time:
22 Nov 2018,
3:00pm -
4:20pm
Location: Meet and Greet in DTB A514 then talk in CLE A202
Event type: PIMS lectures
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Please join us for a meet and greet at 3 pm in DTB A514, refreshments will be served. The talk will take place at 3:30 pm after the meet and greet.
ABSTRACT:
The problem of source-sink dynamics in mathematical ecology originated with a 1969 paper of Levins. The idea is that a species lives in an environment that is heterogeneous: some locations are favourable to the species persistence (sources), while others are unfavourable and can only be populated if there is an inflow of individuals to these locations (sinks). This setup has been studied extensively in the case of so-called Levins-type metapopulation models, which count the number of locations (patches) in various states and couple them implicitly. The case of metapopulation models with explicit movement, where individuals move between locations, is less known.
In this talk, I will discuss the solution to a simple problem set in the latter context: is there a critical number of the number of patches that are sources such that the population persists in the entire system when the number of sources is above the threshold? An existence result is provided that relies heavily on matrix analysis, illustrating the power of linear algebra in this type of large scale problem. In a particular case, the principle of equitable partitions allows us to obtain an explicit form for the threshold. This is joint work with Nicolas Bajeux (University of Manitoba) and Steve Kirkland (University of Manitoba).
Download poster (PDF)
Title: Elizebeth Smith Friedman, Pioneer Cryptanalyst - a brief glimpse of the career of one of America's heroines of WW1 and WW2.
Speaker: Kieka Mynhardt, University of Victoria
Date and time:
22 Nov 2018,
10:00am -
11:20am
Location: Maclaurin D107
Event type: Discrete math seminar
Read full description
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Title: Duration of the "stochastic" phase of an epidemic
Speaker: Julien Arino, University of Manitoba
Date and time:
21 Nov 2018,
3:30pm -
4:30pm
Location: CLE A205
Event type: Applied math seminar
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Abstract:
Epidemics of infectious pathogens of humans go through several stages. First comes
an initial "stochastic" phase, during which case counts remain low and vary apparently
at random. This initial phase is followed by a period of exponential growth of the number
of new cases per unit time (the incidence). As more and more individuals become
infected, the number of susceptible individuals in the population decreases; incidence
consequently goes through a plateau then starts to decrease, a characteristic of the
final stage of the epidemic, which typically concludes with the extinction or near
extinction of the outbreak.
In this work, we focus on the initial stochastic phase of the epidemic, which, contrary to
later stages, is badly captured by deterministic models. We consider a very simple
random walk on the number of infectious individuals in the population, allowing us to
obtain estimates of the duration of the stochastic phase. We then extend the model to
two connected spatial locations. This is joint work with Jason Rose (University of Manitoba) and Evan Milliken (Arizona
State University).
Title: Fourier-Mukai Duality and K-theory (Part 2 of 2)
Speaker: Heath Emerson, University of Victoria
Date and time:
21 Nov 2018,
3:30pm -
4:45pm
Location: David Strong building C128
Event type: Operator theory seminar
Read full description
Abstract: Problems in K-theory of crossed products by infinite groups
(like the integers) are addressed by a technique in KK-theory called the
`Dirac-dual-Dirac-method.' In the second of my two talks I will
explain how this works in the case of the integers. The main tool is the
Dirac operator -id/dx on the real line. The important feature of this
operator is its translation-invariance (it commutes with group translation
on R), and, formally, it determines, an equivariant KK-class. Since the
integers are abelian, a special situation, it turns out that this KK-class
can be described in entirely topological terms: as a K-theory
correspondence. In fact this correspondence has already appeared in
algebraic geometry, where it induces a certain duality called Fourier-Mukai
duality, a type of T-duality (a duality important in string theory in physics).
In the first talk, I will explain Fourier-Mukai duality in K-theory, and
especially the effect it has on geometric cycles for torii, using the framework
of K-theory correspondences due intially to Connes and Skandalis, and
developed further by myself and Ralf Meyer. This analysis
gives some insight into what Baum-Connes is doing, geometrically.
The latter work is joint with Dan Hudson.
Title: A lower bound for the gap between the first and second Lyapunov exponents for a class of cocycles of Perron-Frobenius operators
Speaker: Joseph Horan, University of Victoria
Date and time:
21 Nov 2018,
2:15pm -
3:20pm
Location: ELL 062
Event type: Dynamics seminar
Read full description
Full Title:
A lower bound for the gap between the first and second Lyapunov
exponents for a class of cocycles of Perron-Frobenius operators preserving
a cone.
Abstract: Lyapunov exponents provide a generalization to cocycles of
operators (“random” compositions of operators) of the spectrum for single
operators. This spectral data allows us to understand expansion and decay
rates of parts of the space on which the operators act; when applied in
the case of Perron-Frobenius operators related to dynamics on a space, it
helps us to understand how mass evolves under the dynamics and decay rates
of transients in terms of spectral gaps. The problem of computing
Lyapunov exponents is generally acknowledged to be a hard one.
In this series of three talks, we will see how we can find a lower bound
on the gap between the first and second Lyapunov exponents for certain
Perron-Frobenius operator cocycles: those that preserve and contract
(somehow) a nice cone of functions. The proof begins with a general
theorem about cocycles of operators and cones where the hypotheses are
checkable and the numbers are, in principle, computable. Applications to
concrete examples require specific tools if they are not “toy” problems.
We will develop one such tool, a specialized Lastota-Yorke inequality, and
use it to estimate the gap for our specific example. We will also use
this analysis to study the situation where the system passes under
perturbation from multiple equilibria to a unique equilibrium with a small
spectral gap.
In the first lecture, we will set the problem in context, remind ourselves
of the relevant theorems, and provide some examples and motivation for our
particular solution to the problem.
Title: Estimating Precipitation Extremes using the Log-Histospline
Speaker: Whitney Huang, University of Victoria
Date and time:
09 Nov 2018,
2:30pm -
3:20pm
Location: DSB C126
Event type: Statistics seminar
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One of the commonly used approaches to modeling extremes is the peaks-overthreshold (POT) method. The POT method models exceedances over a threshold that is sufficiently high so that the exceedance has approximately a generalized Pareto distribution (GPD). This method requires the selection of a threshold that might affect the estimates. Here we propose an alternative method, the Log-Histospline (LHSpline), to explore modeling the tail behavior and the remainder of the density in one step using the full range of the data. LHSpline applies a smoothing spline model to a finely binned histogram of the log transformed data to estimate its log density. By construction, a LHSpline estimation is constrained to have polynomial tail behavior, a feature commonly observed in daily rainfall observations. We illustrate the LHSpline method by analyzing precipitation data collected in Houston, Texas.
Title: List homomorphism problems
Speaker: Jing Huang, University of Victoria
Date and time:
08 Nov 2018,
10:00am -
11:20am
Location: Mac D107
Event type: Discrete math seminar
Read full description
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Title: A mathematical model of the population dynamics of disease-transmitting vectors with spatial consideration
Speaker: Nourridine Siewe, UBC Okanagan
Date and time:
07 Nov 2018,
3:30pm -
4:20pm
Location: CLE A205
Event type: Applied math seminar
Read full description
A deterministic model with spatial consideration for a class of human disease-transmitting vectors is presented and analyzed. The model takes the form of a nonlinear system of delayed ordinary differential equations in a compartmental framework. Using the model, existence conditions of a non-trivial steady-state vector population are obtained when more than one breeding site and human habitat site are available. Model analysis confirms the existence of a non-trivial steady state, uniquely determined by a threshold parameter, R_0^j, whose value depends on the distribution and distance of breeding site j to human habitats. Results are based on the existence of a globally and asymptotically stable non-trivial steady-state human population.
Title: Fourier-Mukai Duality and K-theory (Part 1 of 2)
Speaker: Heath Emerson, University of Victoria
Date and time:
07 Nov 2018,
3:30pm -
4:45pm
Location: David Strong Building C128
Event type: Operator theory seminar
Read full description
Problems in K-theory of crossed products by infinite groups
(like the integers) are addressed by a technique in KK-theory called the
`Dirac-dual-Dirac-method.' In the second of my two talks I will
explain how this works in the case of the integers. The main tool is the
Dirac operator -id/dx on the real line. The important feature of this
operator is its translation-invariance (it commutes with group translation
on R), and, formally, it determines, an equivariant KK-class. Since the
integers are abelian, a special situation, it turns out that this KK-class
can be described in entirely topological terms: as a K-theory
correspondence. In fact this correspondence has already appeared in
algebraic geometry, where it induces a certain duality called Fourier-Mukai
duality, a type of T-duality (a duality important in string theory in physics).
In the first talk, I will explain Fourier-Mukai duality in K-theory, and
especially the effect it has on geometric cycles for torii, using the framework
of K-theory correspondences due intially to Connes and Skandalis, and
developed further by myself and Ralf Meyer. This analysis
gives some insight into what Baum-Connes is doing, geometrically.
The latter work is joint with Dan Hudson.
Title: Minimal dynamical systems on inhomogenous spaces
Speaker: Ian Putnam, University of Victoria
Date and time:
07 Nov 2018,
2:15pm -
3:20pm
Location: ELL 062
Event type: Dynamics seminar
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A homeomorphism of a compact metric space is minimal if every
orbit is dense. Examples include irrational rotations of the circle, of
higher dimensional odd spheres (Fathi-Herman) and odometers, which are
homeomorphisms of the Cantor. In many basic examples such as these, the
spaces involved are rather homomogeneous: any two points have
neighbourhoods which are homeomorphic. E. Floyd give an example of a
minimal homeomorphism of a space failing to have this property. We will
describe a more general version of Floyd's construction. The two basic
ingredients are the Bratteli-Vershik model for Cantor minimal systems
and iterated function systems. I will not assume any familiarity with
either. This is joint work with Robin Deeley and Karen Strung.
Title: Adjusted Interval Digraphs and Invertible Pairs
Speaker: Kevin Hsu, University of Victoria
Date and time:
01 Nov 2018,
10:00am -
11:20am
Location: Maclaurin D107
Event type: Discrete math seminar
Read full description
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Title: On Marketing Models for Homogeneous Populations: Pricing, Valuation, Utility, and Demand
Speaker: Reinhard Illner, University of Victoria
Date and time:
31 Oct 2018,
3:30pm -
4:30pm
Location: CLE A205
Event type: Applied math seminar
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This is where mathematics and economics meet. I will introduce and explain the terms given in the title, discuss their meaning and relations, and introduce models of kinetic type and their use. The classical Bass model is a special case.
Title: Unitary orbits via transportation theory
Speaker: Karen Strung, Radboud University
Date and time:
31 Oct 2018,
3:30pm -
4:35pm
Location: DSB C128
Event type: Operator theory seminar
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Abstract: Results from the Elliott classification programme can be used
to translate theorems of optimal transport into calculations of the
distance between unitary orbits of normal elements in well-behaved
C*-algebras. In particular, in certain simple Jiang—Su stable
C*-algebras with real rank zero and trivial K_1, the distance between
full-spectrum unitaries can be computed in terms of spectral data. This
talk is based on joint work with Bhishan Jacelon and Alessandro Vignati.
Title: Higher-rank Toeplitz noncommutative solenoids and equilibrium states
Speaker: Zahra Asfar, Sydney University
Date and time:
31 Oct 2018,
2:15pm -
3:20pm
Location: ELL 062
Event type: Dynamics seminar
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Abstract: We consider a family of higher-dimensional noncommutative
tori, which
are twisted analogues of the algebras of continuous functions on ordinary
tori, and their Toeplitz extensions. Just as solenoids are inverse limits
of
tori, our Toeplitz noncommutative solenoids are direct limits of the
Toeplitz
extensions of noncommutative tori. We consider natural dynamics on these
Toeplitz algebras, and compute the equilibrium states for these dynamics.
We find a large simplex of equilibrium states at each positive inverse
temper-
ature, parametrised by the probability measures on an (ordinary) solenoid.
This is a joint work with Astrid an Huef, Iain Raeburn and Aidan Sims.
Title: Limited strength broadcast domination in graphs with maximum degree 3
Speaker: Frank Yang, University of Victoria
Date and time:
25 Oct 2018,
10:00am -
11:20am
Location: Maclaurin D107
Event type: Discrete math seminar
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Title: Ramp Approximations of Finitely Steep Sigmoids in Soft-Switching ODE Networks
Speaker: Graham Quee, University of Victoria
Date and time:
24 Oct 2018,
3:30pm -
4:20pm
Location: CLE A205
Event type: Applied math seminar
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Differential equations which model biological regulatory networks are made impenetrable by the sigmoidal interactions the involved molecular species exhibit. The body of theory for gene control networks has been developed over many years based on Glass networks; a dynamical system model for the level of chemical species involved in the control of one isolated gene network. These arise from the limiting case in which the behaviour of the control network switches infinitely fast. Problems with these models, which include discontinuities and non-uniqueness of solutions, have been studied in depth. This talk will explore an alternative method of approximating the Michaelis-Menton type and Hill functions, which model the individual interactions, using linear ramp functions to soften the switching behaviour. We believe this presents a more accurate approximation of the biological behaviour, which also restores continuity to the vector field, but at the cost of tractability in som!
e regions of phase space. A characterization can be given for a class of these networks that will remain tractable, which includes simple feedback loops. Existence of equilibria and periodic solutions can be shown on in this case, conditional on the sign pattern of switching terms and the eigenvalues of the Jacobian at the equilibria.
Title: Kemeny's Constant for Markov Chains
Speaker: Stephen Kirkland, University of Manitoba
Date and time:
18 Oct 2018,
3:30pm -
4:20pm
Location: Clearihue A308
Event type: PIMS lectures
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There will be refreshments at a 3:00 pm reception prior to the talk.
Abstract:
Markov chains are a much-studied class of stochastic processes, and it is well- known that if the transition matrix A associated with a Markov chain possesses a certain property (called primitivity), then the long-term behaviour of the Markov chain is described by a particular eigenvector of A, known as the stationary distribution vector. Rather less well-known is Kemeny’s constant for a Markov chain, which can be interpreted in terms of the expected number of time steps taken to arrive at a randomly chosen state, starting from initial state i. In particular, if Kemeny’s constant is small, then we can think of the Markov chain as possessing good mixing properties.
In this talk, we will give a short overview of Kemeny’s constant, and discuss some results dealing with the problem of minimising Kemeny’s constant over transition matrices that are subject to various constraints. We will also describe some results showing that Kemeny’s constant can exhibit surprising behaviour when the transition matrix is perturbed. Throughout, the techniques used rely on matrix theory and graph theory.
Download poster (PDF)
Title: Semigroup C*-algebras associated with number fields (Part 2 of 2)
Speaker: Chris Bruce, University of Victoria
Date and time:
17 Oct 2018,
3:30pm -
4:45pm
Location: David Strong building C128
Event type: Operator theory seminar
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Abstract: I will introduce a new class of semigroup C*-algebras associated with algebraic number fields. After explaining the construction, I will discuss several initial results, including an explicit description of the primitive ideals of these C*-algebras, and, time permitting, a phase transition theorem.
Title: Perfect digraphs
Speaker: Kevin Hsu, University of Victoria
Date and time:
11 Oct 2018,
10:00am -
11:20am
Location: Mac D107
Event type: Discrete math seminar
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Title: Estimating extreme events in nonlinear dynamics
Speaker: David Goluskin, University of Victoria
Date and time:
10 Oct 2018,
3:30pm -
4:30pm
Location: CLE A205
Event type: Applied math seminar
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ABSTRACT: I will describe methods for bounding instantaneous extreme values over attractors of dynamical systems governed by differential equations. The methods achieve tight bounds by using computer assistance, in particular using polynomial optimization and semidefinite programming. As an example, I will show results for the chaotic Lorenz attractor. The talk will be aimed at a broad audience.
Title: Semigroup C*-algebras associated with number fields (Part 1 of 2)
Speaker: Chris Bruce, University of Victoria
Date and time:
10 Oct 2018,
3:30pm -
4:45pm
Location: David Strong building C128
Event type: Operator theory seminar
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Abstract: I will introduce a new class of semigroup C*-algebras associated with algebraic number fields. After explaining the construction, I will discuss several initial results, including an explicit description of the primitive ideals of these C*-algebras, and, time permitting, a phase transition theorem.
Title: Roughness of square ice
Speaker: Gourab Ray, University of Victoria
Date and time:
10 Oct 2018,
2:15pm -
3:20pm
Location: Elliott 062
Event type: Dynamics seminar
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Abstract: A homomorphism height function on a finite graph is a
integer-valued function on the set of vertices constrained to have
adjacent vertices take adjacent integer values. In this article, we
consider the uniform distribution over all such functions defined on a
finite subgraph of Z^2 with predetermined values at some fixed boundary
vertices. This model is equivalent to the height function of the
six-vertex model with a = b = c = 1, i.e. to the height function of
square-ice. Our main result is that in a subgraph of Z^2 with zero
boundary conditions, the variance grows logarithmically in the distance to
the boundary. This establishes a strong form of roughness of the planar
uniform homomorphisms.
Joint work with: Hugo Duminil Copin, Matan Harel, Benoit Laslier and Aran
Raoufi.
Title: RR tournaments, rainbow paths and a coloring problem. How to kill three birds with one proof
Speaker: Moishe Rosenfeld, University of Washington
Date and time:
04 Oct 2018,
10:00am -
11:20am
Location: Mac D107
Event type: Discrete math seminar
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Title: The number of non-isomorphic ultrapowers of a separable C*-algebra (part 2 of 2)
Speaker: Chris Eagle, University of Victoria
Date and time:
03 Oct 2018,
3:30pm -
4:45pm
Location: David Strong building C128
Event type: Operator theory seminar
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Abstract: The ultrapower construction takes a C*-algebra $A$ and an ultrafilter $\mathcal{U}$, and produces a new C*-algebra $A^{\mathcal{U}}$ that shares many features with $A$, but also satisfies precise versions of some properties that $A$ only satisfies approximately. While the construction appears to depend on both the C*-algebra and the ultrafilter, it is not easy to distinguish the ultrapowers obtained by using the same C*-algebra with different ultrafilters.
In the first talk I will describe the ultrapower construction and some of its properties, and also discuss the connection between ultrapowers and model theory. In the second talk I will show that the question ``Does $A^{\mathcal{U}}$ depend on $\mathcal{U}$?” cannot be answered on the basis of the standard set-theoretic foundations of mathematics, by sketching proofs that if the Continuum Hypothesis holds then the answer is “no” (Ge-Hadwin, 2001) while if the Continuum Hypothesis fails then the answer is (in a very strong way) “yes” (Farah-Hart-Sherman, 2010).
Title: Vector Colourings of Graphs (with Application)
Speaker: Brendan Rooney, University of Waterloo
Date and time:
27 Sep 2018,
10:00am -
11:20am
Location: Maclaurin D107
Event type: Discrete math seminar
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Abstract: A vector colouring of a graph $X$ is a map from $V(X)$ to vectors on the unit sphere in $\mathbb{R}^m$. The goal is to map adjacent vertices to vectors that are far apart. The vector chromatic number of $X$ is the smallest $t\geq 1$ so that there is a vector colouring $\phi$ for which the inner product of $\phi(u)$ and $\phi(v)$ is at most $-1/(t-1)$, whenever $u$ and $v$ are adjacent.
We look at vector colourings given by representations of a graph on its least eigenspace, and identify a class of graphs for which these colourings are optimal. As an application we give a new proof that the Kneser graphs $K_{n:r}$ for $n\geq 2r+1$ and $q$-Kneser graphs $qK_{n:r}$ for $n\geq 2r+1$ are cores; in particular, a proof that does not require application of the Erd{\H o}s-Ko-Rado Theorem.
Title: The number of non-isomorphic ultrapowers of a separable C*-algebra (part 1 of 2)
Speaker: Chris Eagle, University of Victoria
Date and time:
26 Sep 2018,
3:30pm -
4:45pm
Location: David Strong building C128
Event type: Operator theory seminar
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Abstract: The ultrapower construction takes a C*-algebra $A$ and an ultrafilter $\mathcal{U}$, and produces a new C*-algebra $A^{\mathcal{U}}$ that shares many features with $A$, but also satisfies precise versions of some properties that $A$ only satisfies approximately. While the construction appears to depend on both the C*-algebra and the ultrafilter, it is not easy to distinguish the ultrapowers obtained by using the same C*-algebra with different ultrafilters.
In the first talk I will describe the ultrapower construction and some of its properties, and also discuss the connection between ultrapowers and model theory. In the second talk I will show that the question ``Does $A^{\mathcal{U}}$ depend on $\mathcal{U}$?” cannot be answered on the basis of the standard set-theoretic foundations of mathematics, by sketching proofs that if the Continuum Hypothesis holds then the answer is “no” (Ge-Hadwin, 2001) while if the Continuum Hypothesis fails then the answer is (in a very strong way) “yes” (Farah-Hart-Sherman, 2010).
Title: Heterogeneously Coupled Maps: reconstruction of microscopic details from observations
Speaker: Matteo Tanzi, University of Victoria
Date and time:
26 Sep 2018,
2:15pm -
3:20pm
Location: Elliott 062 NEW ROOM
Event type: Dynamics seminar
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Abstract: In this talk, I will briefly review a result that justifies the
emergence of behaviour on different connectivity layers of a network of
coupled dynamical systems, and I will show how it can be used to
reconstruct details of the system from observations. In particular, I will
describe a procedure that, given observations of the dynamics at each node
of an heterogeneous network (e.g scale free), it recovers: local dynamics,
effective coupling and properties of the network such as degree
distribution and community structures. To assess the performance of the
procedure, I will present numerical simulations in various cases.
Title: UVic Math Competition
Date and time:
25 Sep 2018,
4:30pm -
6:30pm
Location: MAC D010
Event type: Education and outreach
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The UVic Mathematics Competition is held annually in the fall and is open to all UVic undergraduate students. The competition will be held on Tuesday, September 25, 2018 between 4:30-6:30 pm in MacLaurin D010. There are monetary prizes. To participate, just show up.
Here are some recent question papers: 2017 2016 2015 2014 2013 2012 2011 2010 2009 2008 2007 2006.
Title: Are Clusterings of Multiple Data Views Independent?
Speaker: Lucy Gao, University of Washington
Date and time:
21 Sep 2018,
2:30pm -
3:20pm
Location: DSB C126
Event type: Statistics seminar
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ABSTRACT: In the Pioneer 100 (P100) Wellness Project (Price and others, 2017), multiple types of data are collected on a single set of healthy participants at multiple time points, in order to characterize and optimize wellness. One way to do this is to identify clusters, or subgroups, among the participants, and then to develop personalized health recommendations tailored to each subgroup. It is tempting to cluster the participants using all of the data types and timepoints, in order to fully exploit the available information. However, clustering the participants based on multiple data views implicitly assumes that a single underlying clustering of the participants is shared across all data views. If this assumption does not hold, then clustering the participants using multiple data views will lead to spurious results. In this paper, we seek to evaluate the assumption that a single underlying clustering of the participants is shared across all data views. Specifically, we ask the question: are the clusters within each data view dependent or independent? We develop a new test for answering this question, which we then apply to clinical, proteomic, and metabolomic data, across two distinct time points, from the P100 study. We find that while the subgroups of the participants defined with respect to any single data type seem to persist across time, the clustering among the participants based on one data type (e.g. proteomic data) appears not to be associated with the clustering based on another data type (e.g. clinical data).
Title: A few new applications of classical difference sets
Speaker: Peter Dukes, University of Victoria
Date and time:
20 Sep 2018,
10:00am -
11:20am
Location: Maclaurin D107
Event type: Discrete math seminar
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Abstract: In this talk I will sketch some new constructions of mutually orthogonal latin squares and difference triangle sets that arise from intersecting classical finite-field difference sets with a subgroup. Some well-studied Diophantine equations are encountered, yet it is an unexpected property of their solutions which leads to good constructions.
Title: Cyclic homology of crossed-product algebras
Speaker: Raphael Ponge, Seoul National University
Date and time:
19 Sep 2018,
3:30pm -
4:45pm
Location:
Event type: Operator theory seminar
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Abstract: There is a great amount of work on the cyclic homology of
crossed-product algebras, by Baum-Connes, Brylinski-Nistor, Connes,
Crainic, Elliott-Natsume-Nest, Feigin-Tsygan, Getzler-Jones, Nest,
Nistor, among others. However, at the exception of the characteristic
map of Connes from the early 80s, we don’t have explicit chain maps that
produce isomorphisms at the level of homology and provide us with
geometric constructions of cyclic cycles in the case of group actions on
manifolds or varieties.
In my talk I would like to present the construction of such explicit
quasi-isomorphisms for crossed products associated with actions of
discrete groups. Along the way we recover and clarify various earlier
results (in the sense that we obtain explicit chain maps that yield
quasi-isomorphisms). In particular, we recover the spectral sequences of
Feigin-Tsygan and Getzler-Jones, and derive an additional spectral
sequence. In the case of group actions on manifolds we have an explicit
description of cyclic homology and periodic cyclic homology. In the
finite order case, the results are expressed in terms of what we call
“mixed equivariant homology”, which interpolates group homology and de
Rham cohomology. This is actually the natural receptacle for a cap
product of group homology with equivariant cohomology. As a result
taking cap products of group cycles with equivariant characteristic
classes naturally gives to a geometric construction of cyclic cycles.
For the periodic cyclic homology we recover earlier results of Connes
and Brylinski-Nistor via a Poincaré duality argument. For the
non-periodic cyclic homology the results seem to be new. In the infinite
order case, we fix and simplify the misidentification of cyclic homology
by Crainic.
Title: 1-Block factors of g measures
Speaker: Mark Piraino, University of Victoria
Date and time:
19 Sep 2018,
2:15pm -
3:20pm
Location: MacLaurin D105
Event type: Dynamics seminar
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Abstract: Measures on shifts of finite type which have conditional
probabilities that depend on a finite number of coordinates are called
Markov, by combining some states we obtain a new measure called a hidden
Markov measure. A natural generalization of a Markov measure is to allow
conditional probabilities to depend on an infinite number of coordinates
but in a continuous way (these are known as g-measures), again by
combining some of the states we obtain a new measure which we call a
1-block factor. The classical method for understanding hidden Markov
measures is to realize the measure of a cylinder set in terms of a product
of non-negative matrices. In this talk I will present a natural way of
extending this idea to 1-block factors of g measures. Using this extension
I will explain how to apply cone techniques to show that some standard
classes of g measures are closed under factors by maps which are mixing in
fibres.
Title: Reconstructing the Bost--Connes semigroup actions from K-theory (Part 2 of 2)
Speaker: Takuya Takeishi, Kyoto
Date and time:
18 Sep 2018,
3:30pm -
4:50pm
Location: Clearihue D125
Event type: Operator theory seminar
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Abstract. In this talk, we give a result of the complete classification
of Bost--Connes systems. We show that two Bost--Connes C*-algebras for number fields are isomorphic if and only if the original semigroup actions are conjugate. Together with the reconstruction results in number theory by Cornelissen--de Smit--Li--Marcolli--Smit, we conclude that two Bost--Connes C*-algebras are isomorphic if and only if the original number fields are isomorphic. This talk consists of two parts. We introduce the main result and the key idea of the proof in the first week, and several technical machinery, such as the valuation homomorphisms, are explained in the second week.
Title: (j, k)-domination and efficient (j, k)-domination
Speaker: Gary MacGillivray, University of Victoria
Date and time:
13 Sep 2018,
10:00am -
11:20am
Location: MacLaurin D107
Event type: Discrete math seminar
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Title: Reconstructing the Bost--Connes semigroup actions from K-theory (Part 1 of 2)
Speaker: Takuya Takeishi, Kyoto
Date and time:
12 Sep 2018,
3:30pm -
4:50pm
Location: DSB C128
Event type: Operator theory seminar
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Abstract. In this talk, we give a result of the complete classification
of Bost--Connes systems. We show that two Bost--Connes C*-algebras for
number ?fields are isomorphic if and only if the original semigroup
actions are conjugate. Together with the reconstruction results in
number theory by Cornelissen--de Smit--Li--Marcolli--Smit, we conclude
that two Bost--Connes C*-algebras are isomorphic if and only if the
original number fields are isomorphic.This talk consists of two parts.
We introduce the main result and the key idea of the proof in the first
week, and several technical machinery, such as the valuation
homomorphisms, are explained in the second week.
Title: Training Neural Networks using Particle Swarm Optimization
Speaker: Andries Engelbrecht, University of Pretoria
Date and time:
04 Sep 2018,
2:00pm -
3:00pm
Location: MacLaurin D281
Event type: Statistics seminar
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ABSTRACT: Particle swarm optimization (PSO), a population-based, stochastic optimization algorithm, has been applied successfully in training neural networks. PSO is an attractive alternative to train neural networks, due to the simplicity of the PSO algorithm and that PSO doescnot make use of any derivative information. This talk will explore lessons learned in the application of PSO as a training algorithm. While PSO was shown to be successful in this task, it does suffer from some issues inherent to PSO: (1) the performance of PSO is very sensitive to the values of its control parameters; (2) if bounded activation functions are used, PSO causes saturation in the hidden units, (3) neural networks training results in large-dimensional optimization problems, but standard PSO does not scale well to large-dimensional problems. These issues will be discussed and solutions will be presented to address these issues.
Most applications of PSO to training neural networks are in static environments where the training data does not change over time. When training data does change over time, concept drift occurs, and the neural network weights need to be adjusted in order to efficiently cope with such concept drift. Training a neural network under the presence of concept drift can be considered as a dynamic optimization problem. The talk will illustrate how a simple adaptation of the PSO algorithm can be used to dynamically adjust the weights of a neural network in such dynamic environments. An approach will also be discussed to deal with dynamic architecture optimization in such dynamic environments.
Funding from the South Africa – Canada Research Chairs Mobility Initiative (NRF-IDRC) is acknowledged.
Title: A Combinatorial Game and an Efficiently Computable Shift Rule for the Prefer Max De Bruijn Sequence
Speaker: Yotam Svoray, Ben Gurion University of the Negev
Date and time:
21 Aug 2018,
2:30pm -
3:20pm
Location: David Strong Building C122
Event type: Discrete math seminar
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We present a two-player combinatorial game over a k -ary shift-register and analyze it. The game is defined such that, for each of the player, the only way to avoid losing is to play such that the next state of the game is the next window in the well known prefer-max De Bruijn sequence. We then proceed to solve the game, i.e., to propose efficient algorithms that compute the moves for each player. Finally, we show how these algorithms can be combined into an efficiently computable shift-rule for the prefer-max sequence.
Title: The Prediction of Random Effects and Model Selection
Speaker: Wenxue Ge, University of Victoria
Date and time:
20 Aug 2018,
1:30pm -
2:30pm
Location: DSB C114
Event type: Graduate dissertations
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The Final Oral Examination for the Degree of
Master of Science (Department of Mathematics & Statistics)
Wenxue Ge
BSc (Purdue University, 2015)
“The Prediction of Random Effects and Model Selection”
Monday, August 20, 2018 1:30 P.M.
DSB C114
Supervisory Committee:
Dr. Mary Lesperance, Department of Mathematics & Statistics, University of Victoria (Supervisor)
Dr. Xuekui Zhang, Department of Mathematics & Statistics, UVic (Member)
Chair of Oral Examination:
Dr. Julie Zhou, Department of Mathematics & Statistics, UVic
Title: Steiner triple systems with few parallel classes
Speaker: Daniel Horsley, Monash University, Melbourne
Date and time:
08 Aug 2018,
2:30pm -
3:20pm
Location: DSB C126
Event type: Discrete math seminar
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A \emph{Steiner triple system} of order $v$ (or STS$(v)$) is a pair $(V,\mathcal{B})$ where $V$ is a $v$-set and $\mathcal{B}$ is a set of $3$-subsets of $V$ (called triples) such that each pair of elements of $V$ occurs in exactly one triple in $\mathcal{B}$. Such a system exists if and only if $v=6k+1$ or $v=6k+3$ for some integer $k$. A \emph{parallel class} of an STS$(6k+3)$ is a set of its triples that forms a partition of its point set.
In 2015, Darryn Bryant and I constructed the first known infinite family of STS$(6k+3)$s without parallel classes. More recently, together with Charles Colbourn and Ian Wanless, we were able to use similar methods to find, for all $k$, STS$(6k+3)$s with ``few'' (sublinearly many in $k$) disjoint parallel classes. This talk will discuss these results and their context.
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Title: Decomposing complete multigraphs into stars of varying sizes
Speaker: Daniel Horsley, Monash University, Melbourne
Date and time:
30 Jul 2018,
2:30pm -
3:20pm
Location: DSB C126
Event type: Discrete math seminar
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In 1979 Tarsi showed that an edge decomposition of a complete multigraph into stars of size $k$ exists whenever the obvious necessary conditions hold. In 1996 Lin and Shyu gave necessary and sufficient conditions for the existence of an edge decomposition of a (simple) complete graph into stars of sizes $m_1,\dots,m_t$.
I will discuss the common generalisation of these problems: when does a complete multigraph admit an edge decomposition into stars of sizes $m_1, \dots ,m_t$? This problem exhibits more complicated and interesting behaviour than either of its specialisations.
Title: Stability of the Euler and Lagrange relative equilibria in the curved 3–body problem
Speaker: Ernesto Perez Chavela, ITAM Dpto. de Matemáticas, Mexico
Date and time:
24 Jul 2018,
3:00pm -
3:50pm
Location: DSB C124
Event type: Applied math seminar
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In this talk we generalize the well known Euler and Lagrange rela- tive equilibria of the classical Newtonian three body problem, to spaces of constant curvature. We also study the liner stability of them.
Title: SUMS mini-conference
Date and time:
24 Jul
to
26 Jul 2018,
3:00pm -
5:00pm
Location: CLE C112
Event type: Conferences and workshops
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SUMS is running a mini-conference this week from July 24th-26th, 3-5pm in CLE C112. Short, accessible talks on a variety of subjects will be delivered by students and a few professors. The intended audience is math undergrads, but the rest of the department is welcome, and encouraged, to attend. Refreshments will be available. Speakers and abstracts (PDF)
Title: The Replicator Dynamics for Multilevel Selection in Evolutionary Games and Indelible Signatures of Individual-Level Selection
Speaker: Daniel Cooney, Princeton University
Date and time:
19 Jul 2018,
1:30pm -
2:20pm
Location: DSB C126
Event type: Applied math seminar
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We consider a stochastic model for evolution of group-structured populations in which selection operates at two organization levels: individuals compete with other individuals in their group, while groups also compete with other groups. Individuals obtain payoff from playing a two-strategy game, either a generalized version of the Prisoner's Dilemma or of the Hawk-Dove game, against members of their group. Individual-level competition depends on individual payoff, while group-level depends on average payoff of group members. This creates a tension between the two levels of selection, as defectors are favored by at the individual level, whereas groups with cooperators outperform groups of defectors at the between-group level. In the limit of infinite group size and infinite number of groups, we derive a non-local PDE that describes the probability distribution of group compositions in the population. For special families of payoff matrices, we characterize the long-time beha!
vior of solutions of our equation, with particular emphasis placed on understanding the average and most frequent group compositions at steady state. We observe, regardless of how weak within-group selection is relative to between-group selection, that the most prevalent group composition will contain more defectors than the type of group which maximizes average group payoff if, and only if, maximum average payoff is not achieved by full cooperator groups. In such cases, the conflict between the two levels of selection cannot be decoupled, and we even observe cases in which cooperation cannot be sustained even when between-group competition favors perfect coexistence of cooperators and defectors.
Title: Mathematical model of influenza A evolution with HA protein stability
Speaker: Chadi Saad-Roy, Princeton University
Date and time:
17 Jul 2018,
1:30pm -
2:20pm
Location: DSB C126
Event type: Applied math seminar
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Influenza A H3N2 displays a tremendous capacity to adapt and evolve in response to pressure from host immune systems. The mutations that aid in immune system evasion are thought to occur largely in the viral antigen hemagglutinin (HA). Nucleoprotein (NP) is another protein of influenza A that is under significantly less selection pressure than HA. It has been shown that substitutions in NP are constrained by NP stability. That is, certain substitutions that decrease stability, but otherwise increase fitness, only occur in tandem with others that increase NP stability. In this project, we formulate a phylodynamics model of viral evolution for influenza A that incorporates HA protein stability. Our model tracks host individuals that are, respectively, infected, have strain-transcending immunity, or have lifelong antibodies against each specific strain. Our formulation also includes salient biological features such as cross-immunity between closely related strains. We!
show that important novel features emerge due to the inclusion of HA protein stability in our model. We characterize these properties through multiple approaches, illustrating the significance of protein stability in influenza A models.
Title: Optimal Regression Design under Second-Order Least Squares Estimator: Theory, Algorithm and Applications
Speaker: Chi-Kuang Yeh, University of Victoria
Date and time:
13 Jul 2018,
1:00pm -
2:00pm
Location: Clearihue Building Room B346
Event type: Graduate dissertations
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Notice of the Final Oral Examination for the Degree of Master of Science
of
CHI-KUANG YEH
BSc Hons (University of Victoria, 2016)
“Optimal Regression Design under Second-Order Least Squares Estimator: Theory, Algorithm and Applications”
Department of Mathematics and Statistics
Friday, July 13, 2018 1:00 P.M. Clearihue Building Room B346
Supervisory Committee:
Dr. Julie Zhou, Department of Mathematics and Statistics, University of Victoria (Supervisor) Dr. Xuekui Zhang, Department of Mathematics and Statistics, UVic (Member)
External Examiner:
Dr. Xiaodai Dong, Department of Electrical and Computer Engineering, UVic
Chair of Oral Examination:
Dr. Adam Ritz, Department of Physics and Astronomy, UVic
Abstract
In this thesis, we first review the current development of optimal regression designs under the second-order least squares estimator in the literature. The criteria include A- and D-optimality. We then introduce a new formulation of A-optimality criterion so the result can be extended to c-optimality which has not been studied before. Following Kiefer's equivalence results, we derive the optimality conditions for A-, c- and D-optimal designs under the second-order least squares estimator. In addition, we study the number of support points for various regression models including Peleg models, trigonometric models, regular and fractional polynomial models. A generalized scale invariance property for D-optimal designs is also explored. Furthermore, we discuss one computing algorithm to find optimal designs numerically. Several interesting applications are presented and related MATLAB code are provided in the thesis.
