Contributed Papers
Org: Luc Bélair and François Bergeron (UQAM) [PDF]
 VAHID H. ANVARI, University of Saskatchewan, 106 Wiggins Road, Saskatoon, SK, Canada S7N 5E6
The Fuzzy Modeling Approach for Qualitative Description of Biological Systems
[PDF] 
It is believed that most of biological procedures cannot be fully
described by quantitative dynamical models, since biological systems
are hierarchical and highly interconnected and the size of a
quantitative model grows with the complexity of the system. On the
other hand, restricting the model to a small set of variables
inevitably leads to an often unacceptable level of uncertainty in the
inference. Modeling of complex systems involves two kinds of
uncertainty, one type is randomness which models stochastic
variability; the other is fuzziness which models measurement
imprecision due to incomplete information or linguistic structure.
Numerous biological phenomena is described and explained linguistically by human observers. The derivation of suitable mathematical models is a necessary step in order to study these phenomena in a systematic
manner. Fuzzy modeling is the most effective approach for transforming
linguistic data into mathematical formulas and vice versa. This talk
demonstrates the advantages of using fuzzy modeling to analyze,
simulate, test the influence of parameters, and predict the behavior of the system.
 MAHSHID ATAPOUR, University of Saskatchewan, 106 Wiggins Road, Saskatoon, SK S7N 5E6
Asymptotic Behavior of the Linking Probability of 2Component Links in a Lattice Tube
[PDF] 
In this talk we will explore the homological linking probability of
ring polymers confined to a tube. We model a pair of polymers by two
selfavoiding polygons (2SAP) which span a tubular sublattice of
Z^{3}. Then we use the linking number of the 2SAP to
determine whether the two polygons are linked. We prove a pattern
theorem for 2SAPs and establish a lower bound (with probability one) on the rate of increase of their linking number. As a result, we show that the linking probability of 2SAPs approaches one as the size of the 2SAP goes to infinity. We also show that the linking number of an nstep
2SAP is at most linear in n.
 MHENNI BENGHORBAL, Concordia University, Montreal, QC, Canada
Unified Formulas for Integer and Fractional Order Symbolic Derivatives and AntiDerivatives of the PowerInverse Trigonometric Class
[PDF] 
This is a contination of a series of papers introduces a complete solution to the problem of symbolic differentiation and integration of any order (integer, fractional, real, or symbolic) for most of elementary and special functions by introducing unified formulas in
terms of the Fox Hfunction which can be simplified in many cases
to less general functions such as the Meijer Gfunction and the
Hypergeometric function. In this talk, we illustrate the idea on the
powerinverse trigonometric class. In particular, the
powerinverse sine class
\tag1 
ì í
î

f(x):f(x) = 
l å
j=0

p_{j} (x^{aj}) arcsin(b_{j} x^{gj}), a_{i} Î C, b_{i} Î C \{0}, g_{i} Î R \{0} 
ü ý
þ

, 
 (1) 
the powerinverse cos class
\tag2 
ì í
î

f(x):f(x) = 
l å
j=0

p_{j} (x^{aj}) arccos(b_{j} x^{gj}), a_{i} Î C, b_{i} Î C \{0}, g_{i} Î R \{0} 
ü ý
þ

, 
 (2) 
and the powerinverse tangengial class
\tag3 
ì í
î

f(x):f(x) = 
l å
j=0

p_{j} (x^{aj}) arctan(b_{j} x^{gj}), a_{i} Î C, b_{i} Î C \{0}, g_{i} Î R \{0} 
ü ý
þ

, 
 (3) 
The approach does not depend on the integration techniques. Arbitrary order of differentiation is found according to the RiemannLiouville definition, whereas we adopt the generalized Cauchy nfold integral definition for arbitrary order of integration. Many examples will be given using a Maple code developed by the author.
 LUKE BORNN, University of British Columbia
Residualbased approaches for structural health monitoring
[PDF] 
The use of statistical methods for anomaly detection has become of
interest to researchers in many subject areas. Structural health
monitoring in particular has benefited from the versatility of
statistical damagedetection techniques. I will present residualbased approaches for damagedetection, in particular some novel methods
relying on nonlinear autoregressive ideas to improve model fit and
detection rate. I will also discuss ideas for combining sensory output to increase detection power.
 CLAUDIA DANIELA CALIN, University of Alberta, Department of Mathematical and Statistical Sciences, 632 CAB, Edmonton, Alberta, T6G 2G1
Similarity Solutions for Coagulation Equations
[PDF] 
Similarity or group invariant solutions play a distinguished role in
the analysis of qualitative properties of solutions of several nonlinear problems. In this talk I will present two generalized methods that determine similarity solutions for the coagulation equations that describe the evolution of the size distribution function of a system of particles. Analytical solutions to the coagulation equations and explicit formulas for the moments of solutions are only known for a restricted class of coagulation rates (coefficients).
Similarity solutions are interesting particular solutions that describe the behavior of the general solutions of the coagulation equations. The first is an indirect method applied to a partial differential equation associated with a new modified form of the coagulation equation. This method determines a local Lie group of point transformations that leaves the PDE invariant. The second method is a new generalized version of the direct methods that determine the symmetry group of the point transformations to integrodifferential equations. We apply this second method to the coagulation equation directly. These methods provide us with a new family of exact and asymptotic solutions to the coagulation equations which can be further used for numerical studies. The advantage of these methods over previous methods is that in some special cases the expression of the total mass of particles does not need to be known in advance.
 CHRISTINA CHRISTARA, University of Toronto, Dept. Comp. Sci., 10 King's College Road, Toronto, Ontario, Canada
Quartic spline collocation for fourthorder boundary value problems on rectangles with an application to the biharmonic Dirichlet problem
[PDF] 
Biquartic spline collocation methods for the numerical solution of fourthorder boundary value problems on rectangular domains are presented. A particular instance of these methods is applied to the biharmonic Dirichlet problem.
The biquartic spline collocation methods use the midpoints of a uniform partition, the boundary midpoints and the corners as collocation points. While the standard biquartic spline method provides secondorder approximations, two biquartic spline collocation methods, the onestep (extrapolated) and the threestep (deferredcorrection) methods, produce approximations which are sixth order at gridpoints and midpoints, and fifth order at other points.
Both are based on high order perturbations of the differential and boundary conditions operators.
The properties of the threestep method matrices arising from a restricted class of problems are studied. Analytic formulae for the eigenvalues and eigenvectors are developed, and related to those arising from quadraticspline collocation matrices. These properties lead to a fast solver for the biharmonic Dirichlet problem on rectangles. The fast solver is based on Fast Fourier Transforms applied to an auxiliary biharmonic problem with Dirichlet and second derivative boundary conditions along the two opposite boundaries, and on preconditioned GMRES applied to a problem related to the two opposite boundaries. By analyzing the eigenvalues of the preconditioned matrix, the solver is shown to have complexity O(N^{2} logN) on a N ×N partition. Numerical experiments from a variety of problems,
including practical applications and problems more general than the analysis assumes, verify the accuracy of the discretization scheme and the effectiveness of the fast solver.
Joint work with Jingrui Zhang.
 FRANÇOIS GILBERT, Université de Montréal, 2920 Chemin de la Tour, Montréal, QC H3T 1J4
Network design under a discrete choice: a bilevel programming approach
[PDF] 
Network design problems fit the Stackelberg game framework. Two types
of players are involved: leader and follower. A single leader plays
first and has perfect knowledge of the followers' strategy, while the
followers only responds to whatever action the leader has taken. In our case the leader's goal is to maximize his revenue by setting tolls and capacities on some of the network links. This forms the basis of the generic revenue management problem. The followers' response will be
described by an entropy minimization based discrete choice model
parametrise by the leader's policy. This setup is most naturally formulated as a bilevel mathematical program. The resulting revenue maximization problem is differentiable but nonconcave and does not directly lend itself to global resolution tools such as the combinatorial techniques often used for network design problem.
We first consider the pricing problem, where capacities are fixed. In order to find good toll policies we formulate and solve to
optimality several mixed integer approximate formulations. Approximation schemes involve piecewise linear, or quadratic,
approximations of the nonlinear terms involved in the followers' flow
distribution. These approaches are combined with local methods taking further advantage of the problem differentiability. Getting optimality certificates on the original problem is in general out of the question. Yet an upper bound is obtained which does give some guaranty of
global optimality. The case where tolls and capacities are both decision variables is the focus of the last section of the talk and involves solving a restriction of the problem to a discrete set of candidate capacities.
 QIANG GUO, York University
Adaptive splitting wavelet method for atmospheric problems
[PDF] 
Aerosol particles in the atmosphere have big significance due to their
effects on climate change and human health. A new and robust
waveletbased splitting method has been developed to solve the general
aerosol equations. The considered models are the nonlinear
integropartial differential equations on time, size and space, which
describe different processes of atmospheric aerosols including
condensation, nucleation, coagulation, deposition, sources as well as
turbulent mixing.
Wavelet technique has been a great tool for adaptivity and
multiresolution schemes to obtain solutions of systems which vary
dynamically both in space.
The proposed method reduces the complex general aerosol dynamic
equation to two directional splitting equations. Because there are
steeply varying number densities across a size range, we develop the
adaptive technique in which the solution is represented and computed in a dynamically evolved adaptive grid. Numerical experiments are given to show the effective performance of the method.
 SABER HAMIMID, UMBB, avenue de l'Indépendance, 35000 Boumerdes, Algérie
Numerical simulation of electrically conducting liquid flows in an external magnetic field
[PDF] 
The present study is devoted to the problem of onset of oscillatory
instability in convective flow of an electrically conducting fluid
under an externally imposed timeindependent uniform magnetic field.
Convection of a lowPrandtlnumber fluid in a laterally heated
twodimensional horizontal cavity is considered. Fixed values of the
aspect ratio (height/width=1) and Prandtl number (Pr = 0.015), which are associated with the horizontal Bridgman crystal growth process and are commonly used for benchmarking purposes, are considered. The effect of a uniform magnetic field with different magnitudes and orientations on the stability of the two distinct branches (with a singlecell or a
twocell pattern) of the steady state flows is investigated. The combined effects of the magnetic field and the surface tension are
presented graphically in terms of isotherm and streamline plots. The
effects of varying the physical parameters on the rate of heat transfer from the heated surface of the enclosure are also depicted.
 LARBI HAMMADI, 1 Laboratoire de rhéologie, transport et traitement des fluides complexes et Laboratoire de matière et système complexes (MSC), Paris 7 France
Effet de traitement thermique sur le comportement physicochimique et rhétorique des boues activées de station d'épuration
[PDF] 
Le traitement des eaux, qu'il s'agisse de production d'eau potable où d'épuration d'eau usée d'origine urbaine ou industrielle, conduit
toujours à la formation de boues que l'on sépare et de l'eau traitée. Ces boues se présentent à la sortie de la station d'épuration comme un liquide à forte teneur en eau. La teneur élevée en substance polluantes interdit le plus souvent leur rejet dans le milieu naturel sans précaution. Pour évaluer l'aptitude de ces boues au traitement, déterminer quels traitements leur faire subir, estimer les risques de pollution et enfin connaître leurs possibilités de réutilisation (agricole, énergétique ou
autre). Dans ce cadre que étant défini l'objet de cette étude. L'étude consiste à étudier l'effet de traitement thermique sur le comportement physicochimique et rhétorique des boues activées de station d'épuration. Le traitement thermique des boues activées montre que l'augmentation de la température provoque une augmentation du pH et une diminution de la demande chimique en oxygène (DCO), et du rapport entre matières volatiles en suspension et matière en suspension (MVS/MES). Concert l'aspect rhéologies pour les boues étudiées, le seuil de contraint diminue avec l'augmentation de la température dans le même temps la viscosité apparent des boues diminue suivant une loi de puissance avec l'augmentation de la température.
 JIALIN LI, University of Manitoba, Department of Electrical and Computer Engineering
Liquid Level Measurement Using Guided Wave Radar Approach
[PDF] 
In many industrial processes, measuring and monitoring liquid level in
tanks definitely ranks high in importance above many other parameters
measured in the seal environment. Over time, mechanical level detection devices have given way to newer technologies, with accurate readings,
wide rang of detection capability, and wide variations in operating
temperature and pressure and low dielectric constants. With many of
these features, microwavebased technology now has become firmly
established and improved mainly consisting in the development of the
excitation and data acquisition electronics. Guided Wave Radar (GWR) is one of the applications using microwave radar technology detecting
liquid level changes. The basis for GWR is TDR (Time Domain
Reflectometry). In this application, TDR technology achieves its nonmechanical level detection by measuring the flight time of a single sharp waveform. When the pulse of radar energy reaches the liquid
level where a change in impedance occurs, part of the signal is
reflected back to the transmitter. At the data acquisition stage,
sampling electronics employs ETS (Equivalent Time Sampling), obtain
repetitive signals data and measure the duration between transmitter
and reflected signal. In the meantime, system must be sensitive to
small level changes (less than 5mm).
The project involves designing a prototype level sensor including the
excitation and data acquisition electronics to meet specifications and
requirements aforementioned. Some basic mathematical analysis of the
behavior of electrical transmission lines (GWR) is discussed. The
distance versus resolution relationship is developed, as well as the
verification in simulation models. The excitation circuit is designed
and also simulated using SPICE software together with some measurement
results presented to show the resolution and accuracy.
 JESSICA McDONALD, University of Waterloo
Achieving maximum chromatic index in multigraphs
[PDF] 
The chromatic index of a multigraph M, denoted by c¢(M), is the minimum number of colours needed to colour the edges of M such that such that adjacent edges receive different colours. Shannon (1949), Vizing (1964) and Goldberg (1984) have all established wellknown upper bounds for the chromatic index of M. In this talk we ask: when is c¢(M) maximum? That is, when does c¢(M) achieve a particular upper bound?
Our main result in this talk is to characterize those multigraphs which achieve Goldberg's upper bound, generalizing a 1968 result of Vizing which characterizes those multigraphs which achieve Shannon's upper bound. There is no known characterization for those multigraphs which achieve Vizing's upper bound, however we will discuss some partial results towards this, and address the issue of the complexity of this problem.
 ABAS SABOUNI, University of Manitoba
Hybrid optimization method for microwave breast cancer detection
[PDF] 
Breast cancer has long been one of the most common forms of cancer in
women. One of the challenges facing the medical community is the early
detection and treatment of breast cancer. Microwavebased imaging
techniques offer a number of benefits, including improved contrast of
malignant lesions and safety. Microwave imaging is the process by which radiofrequency electromagnetic waves are used to generate an image of
the body to enable physicians to diagnose disease. In an effort to
improve this imaging strategy, a variety of mathematical method has
been developed in the literatures. Recently, the microwave tomography
method has been developed by solving Maxwell's partial differential
equations with FiniteDifference TimeDomain (FDTD) as well as solving
nonlinear reconstruction problem using iterative algorithms.
In this talk, we consider an accurate numerical model for breast
phantom derived from Magnetic Resonance Imaging (MRI) data that
incorporates water content and frequency dependency of dielectric
properties for breast tissues. The microwave tomography method based on FDTD and hybrid Genetic Algorithm (GA) was applied to phantoms derived
from this data in order to locate, characterize, monitor, and treat the breast cancer.
With contributions from Mr. Ali Ashtari, Prof. Sima Noghanian and Prof. Stephen Pistorius (all from University of Manitoba).
 SEYED JAFAR SADJADI, Iran University of Science and Technology
A new mathematical modeling and a genetic algorithm search for milk run problem
[PDF] 
The idea of milk run has been used in the context of logistic and
supply chain problems in order to manage the transportation of
materials. In this paper, we propose a new milk run method, as a mixed
integer approach, to manage supply chain problems. Since the resulted
problem formulation is NPhard we use some metaheuristic and compare
the results with the optimal solutions of the proposed milk run method.
The mathematical modeling of this paper is purposely customized for a
special case of an auto industry. We implement the mathematical
formulation and the metaheuristic using some actual data and compare
the results with the current strategy. The preliminary results indicate
that the proposed method could provide a practical tool to
significantly reduce the cost of logistic.
 SEYED JAFAR SADJADI, Islamic Azad University, Science and Research Branch
A Robust Optimization Model for Resource Allocation Problem with Different Time Cycles
[PDF] 
In many resource allocation problems, we are faced with the
environments that change continuously. The existing uncertainties may
cause some changes on the return values of the investment alternatives
during the planning horizon which could lead us to have even infeasible
solutions. In this talk we consider a new robust resource allocation
problem. The proposed method of this talk consider an investment
strategy where different investment alternatives may return in various
time cycles and resources can be allocated only at the beginning of
each period. We develop a mathematical formulation for the problem of
robust resource allocation. The implementation of the proposed method
is discussed through a numerical example.
 SAMIRA SADAT SAJADI, Iran University of Science and Technology, Narmak, Tehran, Iran
A statistical model to estimate information technology spending
[PDF] 
In this talk we present a statistical model to estimate demand for
Information Technology. The statistical function is based on Engle
model where demand is a model of home nonfood expenditure as well as
the size of the family. We use an Ordinary Least Square (OLS) method for our estimation and validate the model using actual information of a Middle East region country. The method is also validated using
different statistical tests.
 DMITRY TRUKHACHEV, University of Alberta, 2nd floor ECERF, Edmonton, AB, Canada T6G 2V4
Generalized Modulation
[PDF] 
Classic modulation in communication theory is based on representation
of an informationbearing signal as a linear combination of orthonormal basis waveforms. At the receiver the signal is usually passed through a bank of filters matched to the orthogonal basis waveforms and simple
post processing acquires the transmitted information. In reality,
however, specifically in modern communication systems, the transmitted
signal is rather viewed as a combination of correlated waveforms. For
example in Multiple Input Multiple Output systems the base waveforms
can deorthogonalise during the transmission and in random Code
Division Multiple Access they are chosen randomly and independently.
Therefore, fundamental understanding of general modulation and
demodulation process constitutes an important problem in modern digital communications.
We consider signals represented as a linear combination of random
waveforms with bounded average crosscorrelation. The signals are
transmitted over additive white Gaussian noise channel. It is well
known that signal reception with optimum maximumlikelihood decoders
quickly becomes impractical due to complexity constraints. On the other hand, linear signal separation via, for example, minimum meansquare
error (MMSE) filtering provides close to optimal performance only for
small information loads. We propose a modulation format introducing
redundancy and interleaving to the data at the transmitter so that at
the receiver the information can be recovered using an iterative
distributed messagepassing detection algorithm designed to solve
inference problems on graphical models. We prove that the capacity of
the channel can be approached to within less than 1 bit per dimension
as the number of base signal waveforms becomes large.
 HENRY VAN ROESSEL, University of Alberta, Edmonton
Some Exact Solutions to the Coagulation Equation with Product Kernel
[PDF] 
An important phenomenon in a wide variety of processes in physics, chemistry, biology, medicine and engineering is the coalescence or aggregation of small clusters of particles into larger ones. Examples include, but are not limited to, polymerization processes in polymer science, coagulation processes in aerosol and colloidal physics, planet and galaxy formation.
Coagulation processes are governed by integrodifferential equations known as coagulation equations. The nature of the solution of these coagulation equations will depend on the form of the coagulation kernel that appears in the equation. One interesting feature of these equations is that, depending on the coagulation kernel used, mass need not be conserved. The phenomenon whereby conservation of mass breaks down in finite time is known as "gelation" and is physically interpreted as being caused by the appearance of an infinite "gel" or "superparticle".
For certain forms of the coagulation kernel exact solutions to the coagulation equation can be found.
 RALF WITTENBERG, Simon Fraser University, Burnaby, BC
Rigorous Bounds on RayleighBénard Convection with Conductive Plates
[PDF] 
Considerable experimental and theoretical effort has been devoted to
obtaining the asymptotic scaling of the enhanced bulk heat transport in turbulent RayleighBénard convection, measured by the Nusselt number, in terms of the temperature drop across the fluid, given by the Rayleigh number; however, the usual assumption of fixed temperature
across the fluid is mathematically and experimentally inadequate.
We formulate a variational bounding principle to obtain rigorous
theoretical estimates for the Nusselt number as a function of the
Rayleigh number in finite Prandtl number turbulent convection. We are
able to treat a full range of thermal boundary conditions between the
fixed temperature and fixed flux extremes in a uniform formulation, and show that the usual fixed temperature assumption is a singular limit of the full problem. We also obtain analytical bounds in the physically
realistic case of a fluid bounded by conductive plates, and discuss
some generalizations.
