12th Annual

PIMS Young Researchers Conference

in Mathematics and Statistics

(PIMS YRC 2015)

University of Calgary

May 27 - May 29, 2015

Schedule and Abstracts

Please fill out a presentation feedback form for student speakers that request feedback.

Some feedback forms may be found in your conference materials, and more can be obtained from thesession moderators.

To encourage participation, prizes will be randomly drawn at each plenary talk and event.

After the conference, please fill out the survey at http://goo.gl/forms/8vXBlJFnh8.

Organizers and Sponsors

• Organizing Committee at the University of Calgary:

– Mark W. Girard (primary organizer)

– MohanaGowri Arumugam

– Melanie Foerster

– Kunlin Hao

– Heather Hardeman

– Muhammad Khan

– Ji Ruan

– Haotian Song

The organizing committee would like to express their sincere gratitude to Melissa Wrubleski, Betty Teare,Aprile LaBerge, and Wan Lin for their indispensable assistance in organizing the 12th PIMS YRC, andwould like to thank the following sponsors for their support.

• Sponsors

– University of Calgary Department of Mathematics and Statistics

– Pacific Institute for the Mathematical Sciences (PIMS)

– University of British Columbia Math Graduate Committee

– Canadian Mathematical Society Student Committee (CMS Studc)

– Maplesoft

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Wednesday, May 27th

08:00-09:00 Registration and coffee (ST 125)

09:00-10:00 Plenary talk (ST 140)

Special orthogonal matrices and applicationsHadi Kharaghani, University of Lethbridge

10:00-10:30 Coffee break (ST 125)

10:30-12:00 Student presentations

Session A (ST 127)

10:30 Inference for Two Component Mixture Model: An Estimation Based on Nonparametric CDFTasnima Abedin, University of Calgary

11:00 Competitive spatially distributed population dynamics models: does diversity in diffusion strate-gies promote coexistence?Md Kamrujjaman, University of Calgary

11:30 A system of reaction-diffusion model for radiation-induced bystander signalsOluwole Olobatuyi, University of Alberta

Session B (ST 129)

10:30 Semidistributivity and Sublattices of Free LatticesBrian Chan, University of Calgary

11:00 CSPs and k-pebble gamesMaximiliano Liprandi, University of Calgary

11:30 Balance and Clusterability of Portfolio Signed GraphsShahid Khan, University of Calgary

12:00-13:30 Lunch

13:30-15:00 Skills Workshop (ST 140)

Skills Workshop: The Art of Oral Presentations in MathematicsKristine Bauer, University of Calgary

15:00-15:30 Coffee break (ST 125)

15:30-16:30 Student presentations

Session A (ST 127)

15:30 Quantification methods of posttranslational modifications of histone H1Carlos Contreras, University of Alberta

16:00 Feature selection for cancer classification using microarray gene expression dataWenyan Zhong, University of Calgary

Session B (ST 129)

15:30 Distribution of Squares Modulo a Composite NumberFarzad Aryan, University of Lethbridge

16:00 Fermat’s Last Theorem over Real Quadratic FieldsMichael Wanless, University of Calgary

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16:30-17:00 Coffee break (ST 125)

17:00-18:00 Student presentations

Session A (ST 127)

17:00 An Statistical Model for the Temporarily Dependent Extreme ValuesQicheng Zhang, University of Calgary

17:30 Semiparametric Estimation of a Two-component Mixture ModelXiaofan Zhou, University of Calgary

Session B (ST 129)

17:00 The Use of the Sinc Collocation Method in Computing Energy Eigenvalues of the SchrodingerEquationTyler Cassidy, University of Alberta

17:30 Algorithms for SU(n) Boson Realizations and D-functionsIsh Dhand, University of Calgary

18:00-18:30 Break

18:30-21:00 Banquet (Last Defence Lounge MSC 350 – third floor of MacEwan Student Centre)

Join us for food and drinks in the graduate student pub! If you are unfamiliar with the University ofCalgary campus, some organizers will lead the way starting from the break room (ST 125) at 18:30.

Thursday, May 28th

08:00-09:00 Registration and coffee (ST 126)

09:00-10:00 Plenary talk (ST 140)

Seeing through a mathematical lensKaren Kopciuk, Alberta Health Services

10:00-10:30 Group photo (near the Science B picnic area)

10:00-10:30 Coffee break (ST 126)

10:30-12:00 Student presentations

Session A (ST 139)

10:30 Estimation of Partly Linear Additive Hazards ModelArfan Afzal, University of Calgary

11:00 Group Selection in Accelerated Failure Time ModelLonglong Huang, University of Calgary

11:30 SML Program at University of AlbertaJia-Huai You, University of Alberta

Session B (ST 132)

10:30 Reverse Time Migration With an Improved Forward Wavefield PropagationSalam Alnabulsi, University of Calgary

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11:00 Anelastic linearized reflectivities and AVO inversionShahpoor Moradi, University of Calgary

11:30 The third order FVTD scheme for 3D Maxwell’s EquationsMarina Kotovshchikova, University of Manitoba

12:00-13:30 Lunch

13:30-14:30 Student presentations

Session A (ST 139)

13:30 Efficient Hedging for Defaultable Securities and its Application to Equity-Linked Life InsuranceContractsAmir Nosrati, University of Alberta

14:00 Valuation of a natural gas storageMobolaji Ogunsolu, University of Calgary

Session B (ST 132)

13:30 The X-ray Conjecture of convex bodiesMuhammad Khan, University of Calgary

14:00 Galois Theory and its GeneralizationsAdam Gerlings, University of Calgary

14:30-15:00 Coffee break (ST 126)

15:00-16:00 Student presentations

Session A (ST 139)

15:00 Equivariant LS-category of torus manifoldsSoumen Sarkar, University of Regina

15:30 The central configurations of the curved N -body problemSimon Zhu, University of Victoria

Session B (ST 132)

15:00 p-Norm Mixed Integer Cutting Planes in the Branch and Cut FrameworkSarah Couzens, University of Calgary

15:30 Multiple Change Points Detection for High Dimensional DataZixiang Guan, University of Calgary

16:00-17:00 Coffee break (ST 126)

17:00-18:30 Panel discussion (ST 140)

Job Search Tips for Mathematics and Statistics StudentsChad Ayers, Azamed Gezahagne, Clifford Kitchen, Mark Wylie, Lei Xiong,

18:30-21:00 Barbecue picnic (Science B picnic area)

Join us for some deliciously grilled foods while enjoying the warm summer weather!

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Friday, May 29th

08:00-09:00 Coffee (ST 126)

09:00-10:00 Plenary talk (ST 140)

From the Heisenberg uncertainty principle to the theory of majorization and quantum informationGilad Gour, University of Calgary

10:00-10:30 Coffee break (ST 126)

10:30-11:30 Student presentations

Session A (ST 127)

10:30 Semi-parametric time series modelling with autocopulasIlnaz Asadzadeh, University of Calgary

11:00 Comparing models for time series of countsBoyko Zlatev, University of Alberta

Session B (ST 129)

10:30 Theoretical packing densities and lattice parameters of cubic lithium garnet solid electrolytesSamuel Reid, University of Calgary

11:00 An Introduction to Mathematical BilliardsMelanie Foerster, University of Calgary

11:30-12:30 Plenary talk (ST 140)

The Leaning Tower of PingalaRichard Guy, University of Calgary

12:30-13:00 Closing remarks (ST 140)

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Plenary Talks

Special orthogonal matrices and applicationsHadi Kharaghani – University of Lethbridge (09:00 Wednesday, May 27 – ST 140)

A brief tour of the following topics will be presented:

• Hadamard matrices

• Generalized Balanced Weighing matrices

• Twin symmetric designs

• Association schemes from twin designs

• A brief review of applications in Quantum Information Theory

• Some open problems

There will be plenty of examples to describe each of the topics.

Seeing through a mathematical lensKaren Kopciuk – Alberta Health Services (09:00 Thursday, May 28 – ST 140)

Using mathematical tools and reasoning provides deeper insights into our everyday world — from bulletholes in WWII airplanes to winning the lottery. In this talk, I will describe some approaches to understandmissing information, correlation, linear and non-linear relations and expectation in specific historic andpresent-day applications and the insights these mathematical approaches provide.

From the Heisenberg uncertainty principle to the theory of majorization andquantum informationGilad Gour – University of Calgary (09:00 Friday, May 29 – ST 140)

Quantum information science is concerned with the manipulation, computation, and communication ofinformation, where the information is encoded in two (or more) level quantum systems called “qubits”,unlike classical information, which is encoded in Boolean “bits”. The devices used in this science aregoverned by the principles of quantum mechanics, which opens the possibility for a large range of appli-cations. In this talk I will give a gentle review of this exciting field with the focus on its mathematicsand the fascinating role the Uncertainty Principle plays in quantum information. I will start with a briefhistory of the discovery of non-intuitive quantum correlations (i.e. entanglement) and then show thatquantum entanglement, besides being of interest from a fundamental point of view, is a valuable resourcefor many quantum information tasks such as quantum teleportation and superdense coding. I will endby showing that with entanglement one can eliminate the uncertainty principle.

The Leaning Tower of PingalaRichard Guy – University of Calgary (11:30 Friday, May 29 – ST 140)

A simple second order recurrence leads to a tower of polynomials. If you put your head on one side,the coefficients will be seen to form Pascals triangle, which was known to Chinese, Indian and Arabicmathematicians up to two millenia ago, including Pingala, around 200BC. From the tower we can read offmany familiar and less familiar sequences, including Mersenne numbers, Fibonacci numbers, the so-calledPell numbers (probably known to the Babylonians), Jacobsthal numbers, and Chebyshev polynomials. Itis easy to deduce formulas for all of these, and to notice that all the sequences are divisibility sequences.Moreover, they often count combinatorial objects, such as matchings and spanning trees. But there areseveral things we don’t know about them!

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Workshop

Skills Workshop: The Art of Oral Presentations in MathematicsKristine Bauer – University of Calgary (13:30 Wednesday, May 27 – ST 140)

In mathematics, oral presentations are one of the most important ways in which ideas are disseminated.Oral presentations are often a more efficient means of disseminating mathematics (for example, becausethey are not subject to a lengthy peer-review process) and also more effective (for example, when thepresentation explains the idea behind a solution and is not mired in the technical details). For this reason,young researchers and teachers in mathematics need to make it a priority to actively develop and improvetheir presentation skills.In this workshop, we will endeavour to give participants the tools they need to identify their currentskill level in oral presentations, and provide some concrete advice about how to improve their skills. Theworkshop will primarily focus on these four topics:

Being heard and seen: The essential components of public speaking

Content: Simplicity and detail

Preparation: Organization and Flexibilty

Techniques: Chalk talks and slides

The workshop will end with an opportunity for students to ask questions or seek advice.

Panel discussion

Job Search Tips for Mathematics and Statistics StudentsChad Ayers, Azamed Gezahagne, Clifford Kitchen, Mark Wylie, Lei Xiong – (17:00 Thursday,May 28 – ST 140)

Some former mathematics graduate students, who have jobs outside of academia in various industries,will relay their experiences to current grad students who might be looking to get a job in industry.Presentations will be followed by an interactive discussion.Invited Panelists:

• Azamed Gezahagne, Quantitative Analyst, TransAlta Corporation

• Lei Xiong, Analyst – Market Analytics and Market Simulation, Alberta Electric System Operator

• Chad Ayers, Lead Analyst – Generation, Forecasting & Market Analytics, Alberta ElectricSystemOperator

• Clifford Kitchen, Associate Director, Commodity Derivatives, National Bank of Canada

• Mark Wylie

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Student Presentations

Inference for Two Component Mixture Model: An Estimation Based on Non-parametric CDFTasnima Abedin – University of Calgary (10:30 Wednesday, May 27 – ST 127)

Many biomedical assays involve classifying samples into one of two groups according to whether someoutput variable (e.g. optical density, parasite density, amount of radioactive label) exceeds a given cutoff.Many such assays do not classify samples correctly because there is an overlap in the output variablebetween the two groups. This problem can be considered as decomposing mixtures of two components.Suppose there is a sample from a mixture population (1− λ)F + λG and independently another samplefrom the first component F , where λ is the unknown mixing proportion and F and G are two unknowndistribution functions. The goal is to estimate λ, treating F and G as nuisance parameters. We consideredan estimation based on nonparametric distribution estimators. Simulation studies and application of thismethod on a real data set is also presented to assess its performance.

Estimation of Partly Linear Additive Hazards ModelArfan Afzal – University of Calgary (10:30 Thursday, May 28 – ST 139)

In contrast to the Cox proportional hazards model, the additive hazards model describes a different aspectof the association between covariates and the failure times, and has been used in many applications.Lin and Ying (1994) developed simple procedures with high efficiencies for making inference about theregression parameters under the linear additive hazards model with left truncated and right censored data.In this paper, we consider the additive hazards model with a semiparametric risk function that has apartially linear structure; we call it the partly linear additive hazards model. We construct a pseudoscorefunction to estimate the coefficients of the linear covariates and approximate the nonlinear functions usingpolynomial splines. The proposed estimators are asymptotically normal under the assumption that truenonparametric functions are B-spline functions whose knot locations and number of knots are held fixed.We conduct simulation studies to empirically examine the finite-sample performance of the proposedmethod and also use real data for illustration.

Reverse Time Migration With an Improved Forward Wavefield PropagationSalam Alnabulsi – University of Calgary (10:30 Thursday, May 28 – ST 132)

Reverse time migration (RTM) is considered one of the most efficient migration methods. Which providean estimate of angle dependent reflection coefficients in addition to structural image. Estimating theincident wave of the reflection coefficient require having forward propagating wave without reflections.The idea of absorbing condition can be used between the interfaces of the interior of the Earth to have theleast amount of reflections and hence more accurate incident. Applying this approach on the viscoelasticmedium lead to obtain more realistic approach.

Distribution of Squares Modulo a Composite NumberFarzad Aryan – University of Lethbridge (15:30 Wednesday, May 27 – ST 129)

For q square-free, we call an integer s a square modulo q when s is a square modulo p for all primes pdividing q. Let p be a prime number, then

Prob(s is a square modp) =p+ 1

2p≈ 1

2.

The “probability” of a random integer being a square modulo q is approximately is1

2ω(q), where ω(q) is

the number of prime divisors of q.Fix h and let X : {1, 2, · · · , q} → N, be a random variable, given by

X (i) = #{s ∈ [i, i+ h] : s is a square moduloq}.

For the mean of X we have that E(X ) ≈ h2ω(q) . The trivial upper bound on the variance is E2(X ). Here

we prove thatVar(X ) ≤ E1+ε(X ).

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Semi-parametric time series modelling with autocopulasIlnaz Asadzadeh – University of Calgary (10:30 Friday, May 29 – ST 127)

In this paper we present a new approach for finding the distribution of financial time series showingstochastic increasing (decreasing) dependency. Due to the existence of linear and serial dependenciesin the series we develop an application of so-called autocopulas for such data. The linear and non-linear dependencies in the series are unknown thus we cannot use standard copula models to capturethem. Instead we apply empirical copulas and use the inverse distribution function method to generatetime series. Our approach here is semi-parametric and is characterized by a non-parametric copula andparametric marginals. One advantage of using autocopulas is that they represent the lag dependency ofthe time series well, and make it possible to study the interdependence of values of the series at differentextremes separately. The time series that we study represents daily cash flows derived from the productof daily natural gas price and daily temperature deviations from normal levels. In addition we deal withseasonality by means of a time dependent normal inverse Gaussian (NIG) distribution fitted to the rawvalues.

The Use of the Sinc Collocation Method in Computing Energy Eigenvalues ofthe Schrodinger EquationTyler Cassidy – University of Alberta (17:00 Wednesday, May 27 – ST 129)

The Coulombic anharmonic oscillator potential has generated considerable interest in the study of theSchrodinger equation due to the ability to model interaction between charged particles. Specifically, theenergy eigenvalues of the Schrodinger equation have been of interest. Until recently, there has been abeautiful diversity in the approaches to numerically obtaining these eigenvalues. We present the doubleexponential SINC-collocation method for computing eigenvalues. This approach is an alternative methodto numerically evaluate the eigenvalue problem. The crux of the method is the use of finitely manySINC functions to estimate the wave-function. This estimation is composed with a double exponentialtransformation to improve convergence. This improved method then produces accelerated convergenceto known eigenvalues when compared with other methods.

Semidistributivity and Sublattices of Free LatticesBrian Chan – University of Calgary (10:30 Wednesday, May 27 – ST 129)

A lattice is a partial order and an algebra. Consequently, one can construct a free lattice given a set ofgenerators. As opposed to determining subgroups of free groups, determining sublattices of free latticesappears to be much harder ; according to decades of research. A conjecture made by B. Jonsson spawnedmuch research for around 20 years (until it was proven by J.B. Nation in 1980.) It states that a finitelattice is a sublattice of a free lattice if and only if it is semidistributive and satisfies P. Whitmanscondition. Combining two similar past approaches to this problem, a (probably new) characterizationof this result (being a slightly weaker assertion than a characterization known to G. Gaskill, H. Gratzerand C.R. Platt) will be described. The infinite case of this problem, which infinite lattices are sublatticesof free lattices, is not well-known. How stronger variants of semidistributivity (staircase-distributivity,*-distributivity, from J. Reinhold et. al. and distributivity) relate to and could contribute to this largelyunsolved problem will be discussed.

Quantification methods of posttranslational modifications of histone H1Carlos Contreras – University of Alberta (15:30 Wednesday, May 27 – ST 127)

Posttranslational modification of proteins have different effects on the mobility and pathways of proteins.Quantification of this effect on certain experimentally modified proteins helps in the understanding of suchproteins. Here we study methods to quantify the effect of acetylation on histone H1, a protein responsiblefor the highly complex structure in which DNA is condensed. Specifically, we study the change on thebinding affinity of histone H1 with the DNA.

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p-Norm Mixed Integer Cutting Planes in the Branch and Cut FrameworkSarah Couzens – University of Calgary (15:00 Thursday, May 28 – ST 132)

Mixed integer programming (MIP) is a type of optimization problem where select variables are constrainedto take integer values. In the mid-1990s, Gomory cutting planes and the branch and bound frameworkwere combined to effectively determine optimal solutions; the resulting branch and cut algorithm has sincebecome an integral feature of state of the art MIP solvers such as Gurobi. We consider the possibilityof including novel p-norm (i.e. moment based) cutting planes within this branch and cut framework,motivated by the structure of MIP formulations used to recover optimal cancer radiotherapy treatmentplans. Preliminary implementations of this method in C++/Gurobi demonstrate more than a 30%decrease in computational time, as compared to Gurobis default cutting planes and MIP solver settings.

Algorithms for SU(n) Boson Realizations and D-functionsIsh Dhand – University of Calgary (17:30 Wednesday, May 27 – ST 129)

We devise an algorithm to construct boson realizations of canonical basis states of SU(n) for arbitrary n.The boson realizations are employed to calculate Wigner D-functions of SU(n) in the canonical Gelfand-Tsetlin basis. We connect these functions to outputs of multi-photon interferometry.

An Introduction to Mathematical BilliardsMelanie Foerster – University of Calgary (11:00 Friday, May 29 – ST 129)

The traditional game of billiards, particularly the trajectory of a billiard ball, is of great interest from ageometric perspective. One can consider such a trajectory in a variety of billiard tables or, in a geometricsense, domains in the plane. In this talk we discuss billiard trajectories in convex domains. Specifically,we examine billiard trajectories in convex domains of constant width.

Galois Theory and its GeneralizationsAdam Gerlings – University of Calgary (14:00 Thursday, May 28 – ST 132)

Galois Theory began as an investigation into a very concrete problem: is it possible to solve a generalquintic equation by radicals? The answer is surprisingly no and what started as a look into solvingequations a few hundred years ago has grown into a diverse field of mathematics. Galois Theory, althoughclassically being very grounded in abstract algebra, reaches into many different areas of mathematics:from algebra, to number theory, algebraic geometry, algebraic topology, and more. The first part of thistalk will provide a look into classical Galois Theory for fields, establish the Galois correspondence, anddiscuss its significance. Then we will show that the patterns we see in classical field theory can be seenin various other fields of mathematics. We will discuss some of the shortcomings of using the classicalnotions in more modern areas and how this has lead to further generalizations of Galois Theory.

Multiple Change Points Detection for High Dimensional DataZixiang Guan – University of Calgary (15:30 Thursday, May 28 – ST 132)

This presentation is concerned with the change-point problem. In our scenario, we focus on the highdimensional data where classical method does not work well. Here we propose a hard-threshold methodwhich can be divided into three steps to improve the result. We can show that the results based on ourmethod is better than traditional ones. A BIC criterion is suggested to give the estimation of changepoints. Simulation confirms our theoretical conclusion.Keywords: Change-point problem; High dimension; Least square method; Dynamic programming; BICcriterion

Group Selection in Accelerated Failure Time ModelLonglong Huang – University of Calgary (11:00 Thursday, May 28 – ST 139)

Survival analysis problems focus on estimating the covariate eects on the censored survival outcome.When covariates can be naturally grouped, group selection is important. Motivated by the group bridgeapproach proposed by Huang et al. (2009), we consider the accelerated failure time (AFT) model with a

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group bridge penalty. This method is capable to carry out feature selection at the group and within-groupindividual variable levels simultaneously. Simulation studies indicate that the group bridge approach forAFT model based on Stute’s weighted least squares could identify the correct group and correct individualvariable even with high censoring rate. Real data analysis is provided to illustrate the application of theproposed method to scientic problems.

Competitive spatially distributed population dynamics models: does diversityin diffusion strategies promote coexistence?Md Kamrujjaman – University of Calgary (11:00 Wednesday, May 27 – ST 127)

We study the interaction between different types of dispersal, intrinsic growth rates and carrying capacitiesof two competing species in a heterogeneous environment: one of them is subject to a regular diffusionwhile the other moves in the direction of most per capita available resources. If spatially heterogeneouscarrying capacities coincide, and intrinsic growth rates are proportional then competitive exclusion of aregularly diffusing population is inevitable. However, the situation may change if intrinsic growth ratesfor the two populations have different spatial forms. We also consider the case when carrying capacitiesare different. If the carrying capacity of a regularly diffusing population is higher than for the otherspecies, the two populations may coexist; as the difference between the two carrying capacities grows,competitive exclusion of the species with a lower carrying capacity occurs.

The X-ray Conjecture of convex bodiesMuhammad Khan – University of Calgary (13:30 Thursday, May 28 – ST 132)

A point x on the boundary of a convex body K is said to be ‘X-rayed’ along a line ` if the line parallelto ` and passing through x has nonempty intersection with the interior of K. The X-ray number X(K)of K is defined as the least number of lines needed to X-ray the whole boundary of K. In 1994, Bezdekand Zamfirescu conjectured that for any d-dimensional convex body K, we have X(K) ≤ 3 · 2d−2. Thisis known as the X-ray Conjecture and has generated a lot of interest due to its close connection withthe Boltyanski-Hadwiger Illumination Conjecture (1960). In this talk, we discuss recent progress on theX-ray Conjecture and show that it holds for d-dimensional d− 2-codimensional cylinders and some otherclasses of convex bodies.

Balance and Clusterability of Portfolio Signed GraphsShahid Khan – University of Calgary (11:30 Wednesday, May 27 – ST 129)

A signed graph is formed by assigning a + or − to each edge of a graph. A signed graph is said to bebalanced if its nodes can be partitioned into two sets such that all positive edges join nodes in the samecluster, while all negative edges join nodes in different clusters. It is said to be clusterable if its nodes canbe partitioned into two or more sets in the above manner. Here, we investigate a recent application ofsigned graphs in investment portfolio management. M. A. Khan and S. Pirzada [Clusterability of portfoliosigned graphs, in Proceedings of the Second Symposium on Games and Decisions in Reliability and Risk(GDRR), Belgirate, Italy, May 19-21, 2011] introduced the term portfolio signed graph (PSG) for a signedgraph whose nodes represent assets in an investment portfolio and whose edges represent positive ornegative correlations between assets. In this talk, we study the balance and clustering properties of PSGsin detail and establish a relationship between the predictability of a portfolio and the clustering propertiesof the corresponding PSG. This is joint work with Muhammad Ali Khan (University of Calgary).

The third order FVTD scheme for 3D Maxwell’s EquationsMarina Kotovshchikova – University of Manitoba (11:30 Thursday, May 28 – ST 132)

The Finite Volume Time-Domain (FVTD) method has demonstrated to be useful for electromagnetic(EM) problems that involve complex geometry and high dielectric contrast. An efficient implementationof third order weighted essentially non-oscillatory (WENO) finite volume scheme on tetrahedral meshesis proposed to approximate spatial derivatives in Maxwell’s equations. Non-oscillatory schemes avoidoscillations near singularities, and preserve the accuracy of the smooth part of the solution. This is use-ful for EM problems with high dielectric contrasts and discontinuous signals. Geometrical flexibility of

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FVTD method is beneficial for problems where fine geometrical structures compared to the wavelengthare embedded in large structures. In this case a high resolution mesh can be used locally near the finefeatures while cell of relatively large size can be used elsewhere. The main drawback of strong meshinhomogeneities is that the maximum allowable time-step for explicit time evolution is limited by thefinest cells with the smallest volume-area ratio. This leads to large CPU times as well as additionalerrors induces by non-optimal time-steps on large cells. To overcome this problem a third order accuratemultirate Runge-Kutta scheme with arbitrary time-step ratios is implemented to improve the computa-tional efficiency of the FVTD method. The advantages of the proposed scheme are demonstrated on 3Delectromagnetic simulations.

CSPs and k-pebble gamesMaximiliano Liprandi – University of Calgary (11:00 Wednesday, May 27 – ST 129)

A Constraint Satisfaction Problem (CSP) is a mathematical problem that asks whether a set of variablescan be assigned values so that they satisfy certain constraints or limitations. A simple example of sucha problem is a Sudoku Puzzle, where every empty square is a variable that has to be assigned a numberfrom 1 to 9 in such a way that all the constraints are satisfied. Many problems, both in mathematics andother areas, can be modeled as CSPs. This talk will give an introduction to these problems, and discussan approach to better understanding them by analyzing homomorphism games.

Anelastic linearized reflectivities and AVO inversionShahpoor Moradi – University of Calgary (11:00 Thursday, May 28 – ST 132)

Study of linearized reflectivity is very important for amplitude versus offset (AVO). Linearized reflectioncoefficients for interfaces of a low contrast, separating two isotropic, low-loss viscoelastic media are derivedusing the zeoprittz equation. We show that in low-loss viscoelastic approximation, we can obtain thetransmitted and reflected attenuations in terms of incident attenuation angle. Also by linearization ofthe snell’s law we show that the perturbation in attenuation angles can be expressed as perturbationsin elastic velocity and it’s corresponding quality factor. The ray parameter and slowness vectors areintroduced as a function of attenuation angle and incident angle. It is shown that linearized reflectivitiescan be converted to the scattering potential that is obtained in the context of Born approximation. Forall possible incident and reflected waves we show that reflection coefficient is a complex function, thatthe it’s imaginary part is due to anelasticity in medium.

Efficient Hedging for Defaultable Securities and its Application to Equity-LinkedLife Insurance ContractsAmir Nosrati – University of Alberta (13:30 Thursday, May 28 – ST 139)

In this talk, we consider the efficient hedging problem for defaultable securities with multiple defaulttimes and non-zero recovery rates. First, we convert the efficient hedging problem into a Neyman-Pearson problem with composite hypothesis against a simple alternative. Then we apply non-smoothconvex duality to provide a solution in the framework of a defaultable Black-Scholes model. Moreover,in the case of zero recovery rates, we find a closed form solution for the problem. As an application, itis shown how to use such type of results in pricing equity-linked life insurance contracts. The results arealso demonstrated by some numerical examples.

Valuation of a natural gas storageMobolaji Ogunsolu – University of Calgary (14:00 Thursday, May 28 – ST 139)

Natural gas plays an important role in energy markets, accounting for up to a quarter of North America’senergy needs. Owing to its importance, there is a need to look at the means of storage and transmissionto end users. Storage facilities have in times past been owned and maintained by major players who havethe capacity to manage such enormous structures. With the deregulation and liberalization of the naturalgas markets, market participants can now rent storage with the aim of making profit by speculation onprices. As a result, it is important to determine the fair value of storage: how much should you be willingto pay to use a storage facility for a period of time? The need for efficient mechanisms for valuation

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cannot be overemphasized.Using a two-factor gas price model, we present a model for the gas storage problem.This value problemis expressed as a stochastic control problem which is solved numerically by extending the Least SquaresMonte Carlo (LSM) approach of Longstaff and Schwartz(2001) for pricing early exercise options. Wedemonstrate this approach via a numerical example.

A system of reaction-diffusion model for radiation-induced bystander signalsOluwole Olobatuyi – University of Alberta (11:30 Wednesday, May 27 – ST 127)

It has been observed that unirradiated cells located in the neighborhood of a region irradiated at lowirradiation dosage undergo the same order of effects as those cells that are directly irradiated. Theseeffects are called radiation-induced bystander effects (RIBE). These RIBE are due to some diffusive pro-teins which are capable of reacting with the DNA of nearby cells, and thereby triggering these so-calledbystander effects. These diffusive proteins are generally referred to as bystander signals. RIBE haveimplications for radiation therapy and unfortunately, the dynamics/kinetics of the signals responsible forthese RIBEs are still largely unknown. In particular, we are interested in the signals lifespan and factorsthat can affect its longevity. In this talk, I will present a partial differential equation models that inves-tigates the lifespan of this signal and factors that may affect its longevity. I also use this model to studyits dynamics under fractionated radiation treatments and examine its impact at subsequent fractions ofirradiation. Lastly, I will examine the contribution of this signal to the region of hypersensitivity observedat low irradition dose in the traditional survival curve.

Theoretical packing densities and lattice parameters of cubic lithium garnet solidelectrolytesSamuel Reid – University of Calgary (10:30 Friday, May 29 – ST 129)

We introduce applied discrete geometry and the molecular sphere packing correspondence to provide aformula for the packing density and thus lattice parameters of the cubic lithium garnet solid electrolytesLi3+xX3M2O12, where x = 2, 4, X=Nd, Gd, Tb, Er, Lu, La, and M=Te, Nb, Ta, Sb, Bi, Zr, Hf. Wenumerically implement our formula using Shannon’s table of ionic radii and compare our results withexperimentally measured lattice parameters from x-ray and neutron diffraction.

Equivariant LS-category of torus manifoldsSoumen Sarkar – University of Regina (15:00 Thursday, May 28 – ST 139)

In this talk, I will discuss the lower bound and upper bound for LS-category and equivariant LS-category.In particular I will compute both invariants for locally standard torus manifolds. Beside I will presentthe equivariant LS-cat of product space and counterexample of previous results.

Fermat’s Last Theorem over Real Quadratic FieldsMichael Wanless – University of Calgary (16:00 Wednesday, May 27 – ST 129)

Andrew Wiles’ proof of Fermat’s Last Theorem is actually a consequence of the Modularity Theorem,which established an unprecedented connection between elliptic curves and modular forms. Freitas, Hung,and Siksek established that this connection between elliptic curves and modular forms also holds trueover real quadratic fields, but some adaptation of Wiles’ arguments is required to establish a Fermat-likeresult in these contexts. Certain cases have already been proved, and this talk examines the argumentsfor these cases and how they may be adapted for outstanding cases.

SML Program at University of AlbertaJia-Huai You – University of Alberta (11:30 Thursday, May 28 – ST 139)

Statistical ideas and statistical thinking constitute the core of the subject on machine learning. Inthis brief presentation, I’d like to introduce the Master of Science and Doctor of Philosophy degrees inStatistical Machine Learning (SML), offered jointly in the Department of Computing Science and in theDepartment of Mathematical and Statistical Sciences of the University of Alberta.

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An Statistical Model for the Temporarily Dependent Extreme ValuesQicheng Zhang – University of Calgary (17:00 Wednesday, May 27 – ST 127)

The risk management is always crucial for decision makers, for instance, the 2013’s flood in Calgarycaused huge loss. All insurance fees rose. Everyone in Calgary has been involved. However, the extremevalues analysis used in risk assessment process is based on independent assumption, which is obviously notappropriate in many situations. Independence makes estimating computation and interpretation easierfor people to handle. It may also lead to underestimation of risk. In this talk, a statistical model calledGumbel Autoregressive (1) model will be introduced. The performance of some estimation methods willalso be discussed. The corresponding new interpretation of the estimated risk will be presented.

Feature selection for cancer classification using microarray gene expression dataWenyan Zhong – University of Calgary (16:00 Wednesday, May 27 – ST 127)

This talk proposes a new but simple method of selecting highly discriminative genes for cancer classifica-tion based on DNA microarray data. For two-group classification problem, the Bhattacharyya distanceand Hellinger distance are investigated to measure the dissimilarity in gene expression levels between thetwo groups. For any particular gene, we calculate the distance between the two groups based on theexpression levels of that particular gene. We use the calculated distances as a criteria to rank all thegenes. Finally, support vector machine is utilized to obtain the optimal subset of genes achieving thelowest misclassification rate. Compared with the other two methods, SWKC (supervised weighted kernelclustering) (Shim et al., 2009) and SVM-RFE (support vector machine with recursive feature elimination)(Guyon et al., 2002), the proposed method is shown to be more effective and sensitive to differentiallyexpressed genes. In the simulation study, the proposed method has much higher recovery rate than theother two methods.

Semiparametric Estimation of a Two-component Mixture ModelXiaofan Zhou – University of Calgary (17:30 Wednesday, May 27 – ST 127)

Suppose that univariate data are from a mixture of two symmetric distributions that are identical exceptfor a shift parameter. With the identifiability assumption, this model is defined by four parameters: themixing proportion λ, the two location parameters µ1 and µ2, and the infinite dimensional symmetricdistribution f defining the two components of the mixture model. We estimate the unknown symmetricdistribution f by applying an inversion operator on an appropriate nonparametric density estimator, sayh. Then we estimate the mixing proportion λ and the two location parameters µ1 and µ2 by minimizingthe profile Hellinger distance between the model with estimated f and the nonparametric density h.We propose a simple but efficient algorithm to find the estimators. A numerical study is conducted toexamine the performance of the estimators in normal mixtures and when contaminations are present.The results demonstrate that the proposed estimators have good efficiency and are robust when data arecontaminated by outlying observations.

The central configurations of the curved N-body problemSimon Zhu – University of Victoria (15:30 Thursday, May 28 – ST 139)

We first introduce the classical N -body problem, emphasizing on the central configurations, which arecritical points of the Newtonian potential defined on the configuration space. It is not known that thepotential is a Morse function or not. Then we will introduce the curved N -body problem and proposea natural definition of central configurations, which are also critical points of the so called cotangentpotential. The surprising fact is that this potential is Not a Morse function in general.

Comparing models for time series of countsBoyko Zlatev – University of Alberta (11:00 Friday, May 29 – ST 127)

Different models for time series of counts in their application to historical data are compared. Among themodels considered are autoregressive Poisson models studied by Fokianos (2010,2012), as well as theirmore parsimonious modifications, which are appropriate especially for low intensity processes. Connec-tions with underlying point processes are briefly discussed.

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List of Participants

Tasnima AbedinArfan AfzalEman AldabbasSalam AlnabulsiMohanaGowri ArumugamFarzad AryanIlnaz AsadzadehTyler CassidyBrian ChanSimone Cherry-DelisleCarlos ContreasSarah CouzensIsh DhandPeter DixonDakota DuffyQuinton FarrKai FenderDiane FentonJuan FialloMelanie FoersterAdam GerlingsMark GirardZixiang GuanKunlin HaoHeather HardemanLonglong HuangThomas HughesMd KamrujjamanMuhammad KhanShahid KhanMarina Kotovshchikova

Jixian LiMaximiliano LiprandiPrachi LoliencarReginald LybbertShahpoor MoradiAmir NosratiMobolaji OgunsoluOluwole OlobatuyiSaifa RazSamuel ReidTess RitchieWeston RodaMatthew RupertCharles SamSoumen SarkarTaylor ScoryMajid ShahabiHaotian SongNazanin TahmasebiMichael WanlessCurtis WendlandtOmar YasinJia-Huai YouQicheng ZhangWenyan ZhongXiofan ZhouHeng ZhuSimon ZhuBoyko ZlatevLin Zuo

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