1999 APICS Mathematics/Statistics
and Computer Science Conference Schedule
Memorial University of Newfoundland
October 2224, 1999
Friday

What 
Where 
When 
Web Warehouse Tutorial 
EN4002 
10:00 a.m. 1:00 p.m. 
REGISTRATION 
Lobby: HenriettaHarvey (Math) Building 
1:00 p.m.5:00 p.m. 
CS Competition 
EN2036 
1:30 p.m. 6:30 p.m. 
APICS Computing Science Committee Meeting 
EN2022 
2:30 p.m.4:30 p.m. 
APICS Math/Stats Committee Meeting 
Dean of Science Board Room: C2001 
2:30 p.m.4:00 p.m. 
Trends in Differential Equations
and Dynamical Systems 
EN4002 
3:00 p.m.5:30 p.m. 
AARMS Business Meeting 
Dean of Science Board Room: C2001 
4:00 p.m.5:00 p.m. 
Mathematics Competition 
Lobby of HenriettaHarvey (Math) Building 
2:15 p.m. 
Pizza party for competitions' participants
hosted by Memorial's Dean of Graduate Studies 
University Club  Arts and Administration Building 
6:00 p.m. 7:30 p.m. 
Official Welcome: Dr. Robert Lucas, Dean of Science,
Memorial University 
SN2109 
7:30 p.m. 
Blundon Lecture: Tom Archibald 
SN2109 
7:40 p.m. 8:30 p.m. 
Wine & Cheese 
University Club, Arts and Administration Building 
8:30 p.m.10:30 p.m. 
Saturday

What 
Where 
When 
REGISTRATION 
Atrium  Arts & Administration Building 
9:00 a.m.12:00 p.m. 
Trends in Differential Equations and Dynamical Systems 
AA1046 
9:00 a.m.11:40 a.m. 
Sanjay Kumar Madria 
SN2109 
9:00 a.m.10:00 a.m. 
Recreational Mathematics Display 
AA1045 
9:00 a.m. 2:00 p.m. 
Coffee and Book Exhibits 
Arts Atrium 
9:00 a.m. 3:00 p.m. 
Student Paper Sessions 
AA1043 (Math)
AA1049 (CS) 
10:00 a.m.12:00 p.m. 
Lunch & Awards 
University Club  Arts and Administration Building 
12:00p.m. 2:00p.m. 
Frederick Rickey 
SN2109 
2:00p.m. 3:00p.m. 
Trends in Differential Equations and
Dynamical Systems 
AA1046 
3:00 p.m. 5:25 p.m. 
Contributed Papers 
AA1045 (Math)
AA1049 (CS) 
3:15 p.m. 5:15 p.m. 
Recreational Math: John GrantMcLoughlin 
AA1043 
3:15 p.m. 5:00 p.m. 
Sunday

What 
Where 
When 
AARMS Session: Trends Differential Equations and Dynamical Systems 
AA1046 
9:00 a.m.11:45 a.m. 
Friday Morning, 10:00 a.m.1:00 p.m., EN4002
Abstract. In this tutorial, I will talk about design issues in building a
warehouse of web data. We materialize web views and store them in our
warehouse. Web views are instances of user query graph. We manipulate
these web views to garner more useful information using web algebra. We
also discover some knowledge such as visible sites, luminious paths and
pages from the stored web views. We refresh web views using our change
detection system. Briefly, we talk about web data mining issues.
Computing Science: 1:30 p.m.  6:30 p.m.
Mathematics: 3:00 p.m. 6:00 p.m.
The Computing Science Competition is FIVE HOURS in duration
this year, hence the early start (and late conclusion).
Students intending to write this competitition
may either proceed directly to the
Engineering Building, Room EN2046, the location of the exam for
the 1:30 p.m. start or, if uncertain of directions, meet in the
lobby of the HenriettaHarvey (Math) Building at 1:15 p.m. SHARP
to meet a guide.
The Mathematics Competition is a three hour affair, from
3:00 p.m. until 6:00 p.m. Students writing this competition
should meet in the
lobby of the HenriettaHarvey (Math) Building at 2:15 p.m. SHARP.
As has become the custom, the
Mathematics Competition will again be
a competition for teams of TWO students.
Friday Evening, 7:40 p.m. 8:30 p.m., SN2109
Title 
The Rise (and Fall?) of Pure Mathematics 
While puremathematical studies date to antiquity, the modern enterprise
of pure mathematics only took its characteristic form in the nineteenth
century. One famous statement of the renewed importance of pure
mathematics is Jacobi's remark, in response to Fourier, that mathematical
research was undertaken not for application but `for the honour of the
human spirit.' At the time this remark was made (around 1828) this was a
rather revolutionary view, opposing the dominant tendencies in
mathematics in France (think of Laplace, Poisson, Ampère, Fresnel,
Liouville), in Germany (Gauss) and elsewhere.
Yet by 1900 pure mathematics was the dominant form of the science,
which we can see in a number of ways. Who were the best
mathematicians, what were the most important areas of research? What
problems were most pressing and most important to solve? What were
the areas of growth in the fields of university teaching and research?
This view of the central importance of pure mathematics dominated
activity in much of the world for the first three quarters of the twentieth
century, though the last twentyfive years have seen a slight
destabilization of these values and what some perceive as a shift in the
prestige structure of the discipline.
The purpose of this talk is to examine some of the events that led pure
mathematics to gain in importance internationally during the nineteenth
century, thus showing how the stage was set for twentiethcentury
developments. If time permits a few remarks about more recent
developments will offer us a prospect for the twentyfirst century.

Saturday Morning, 9:00 a.m.10:00 a.m., SN2109
Title 
Approximate Query Processing and Summarized Databases
in a Mobile Computing Environment 
We present a queryprocessing model for mobile computing using summary
databases (database stored in some predefined condensed form). We use
concept hierarchies to generate summary databases from the main database in
various ways. Traditional database management systems are correct in that
they are able to provide answers to queries that are both sound and complete
with respect to the source data. In a mobile environment, it may be
advantageous to relax one or other of these criteria to enhance availability
through the use of summary databases. This would provide a more optimal use
of data during periods of disconnection and to enable efficient utilization
of low bandwidth and restricted memory size. The model for query processing
proposed uses concept hierarchies and summary databases at run time to
return approximate queries when access to the main database is either
undesirable or unavailable. We present a model that is able to provide
varying levels of approximate answer to queries that occur at a mobile host
using the summary database stored either locally at mobile host (MH) or
remotely at mobile service stations (MSS). 
Saturday Afternoon, 2:00 p.m.3:00 p.m., SN2109
Title 
Archimedes Palimpsest 
On 29 October 1998, Christie's auction house in New York City sold a
tenth century manuscript that contained several works of Archimedes,
including the unique surviving copy of his wonderful work that we call
"The Method." This talk will focus on the remarkable history of this
manuscript, including, a description of its discovery and publication by
Heiburg early in this century, its sale at Christie's, its display this
summer at the Walter's Art Gallery in Baltimore, and what will happen to
the manuscript next. The manuscript itself will be described as well as
its contents. Enough information about the work of Archimedes will be
given so that you can decide for yourself whether or not he discovered
the calculus.

Saturday, 9:00 a.m.2:00 p.m., AA1045
A wide range of mathematical puzzles, activities and challenges will be
featured at a recreational math exhibit. The games are intended for a
diverse public audience ranging from elementary students to adults.
Saturday Morning, 10:00 a.m.12:00 p.m.: AA1043
Accepted papers:
Title 
Stability Analysis of Two Scalar Field
Cosmological Models with Exponential Potentials 
Presenter 
Laura Filion, St. Francis Xavier University 
We investigate the dynamics of a class RobertsonWalker spacetimes containing
two scalar fields and ordinary barotropic
matter. The potentials for the scalar fields are assumed to be of an
exponential form that are multiplicatively coupled.
We find that the powerlaw inflationary solution is the global attractor if
the sum of the squares of the slopes of the
potentials is less than 2. If sum of the squares of the slopes of the
potentials is greater than two, then we find that the
curvature scaling solution is the global attractor for the open or negatively
curved models. A variety of behaviours are
possible in the zero curvature case.

Title 
Skolem Labellings of Ladders 
Presenter 
Patrick Kergin, Mount Allison University 
A Skolem sequence is an integer sequence of length 2n in which each
of the integers 1,...,n occurs twice, and, for each 1 <= i <= n, the two occurrences of i
are distance i apart. These sequences lend themselves to obvious generalizations to other
types of graphs. In particular, we can label twodimensional arrays according to the Skolem
property. In this presentation, we will give necessary and sufficient conditions for the
existence of these Skolem arrays, as well as provide an exponential lower bound for the
number of Skolem arrays.

Title 
Parametric and Nonparametric Approaches to
Cyclic Designs 
Presenter 
Crystal Linkletter, Acadia University 
This paper looks at cyclic designs as a method for allocating
treatments to blocks in an incomplete block design. The null
hypothesis that the rankings are independent is tested using both a
nonparametric and a normal based statistic. The power of each
statistic is compared using data from a variety of distributions.

Title 
Qualitative Analysis of some Viscous Cosmological Models 
Presenter 
Bill MacMillan, St. Francis Xavier University 
Viscous fluid cosmological models are a sexy alternative to the standard
cosmological model. This presentation will
examine four theories—a perfect fluid with zero viscosity; a viscous fluid
satisfying a first order theory of thermodynamics,
put forth by Eckart; a viscous fluid satisfying a truncated second order
theory of thermodynamics, put forth by Israel and
Stewart; and a nontruncated second order theory of thermodynamics. We shall
use a firstorder approximation of the
viscosity coefficient proposed by Caderni and Fabri, thought to be valid
during the early universe. A qualitative
comparison of the four models will then be made.

Saturday Morning, 10:00 a.m.12:00 p.m.: AA1049
Accepted papers:
Title 
Graphical Database for Category (GDCT) 
Presenter 
Jeremy Bradbury, Mount Allison University 
This is a Java application. It allows for the creation, editing, and
storage of finitely presented categories. Categories can be opened
from and saved to local (text) files or loaded from a specified
server. Once a category file is in memory it can be selected for a
three dimensional display of its underlying graph. This display can be
manipulated and a chosen shape saved. The display can be printed.
There are several tools available to study a category. Some of the
tools are make confluent, equality of composites, make dual, initial
object, sum, and terminal object. GDCT also allows for functors
between finitely presented categories to be created and stored.
Functors in memory display their domain and codomain categories, and
their action is shown by an animated display.

Title 
A Comparison of Two Genetic Encoding Schemes for
Solving Shortest Path Problems with Genetic Algorithms 
Presenter 
Cedric Davies 
Authors 
Cedric Davies and Pawan Lingras, St. Mary's University 
The standard shortest path problem can already be solved in polynomial time with
conventional algorithms. However, the shortest path problem forms a basis for many
other relevant problems to which noknown algorithm exist. Examples include:
shortest paths in dynamic and stochastic networks, multiple objective shortest
path problems, nonlinear objective shortest path problems,
multiple fuzzy objective shortest path problem, network flow problems,
and shortest path based network analysis and optimization problems.
Applying Genetic Algorithms to the standard shortest path problem
may lead to search techniques for these similar but difficult problems.
One of the important issues in applying Genetic Algorithms to the shortest
path problem is how to encode a path in a graph into a chromosome.
In general, for any problem there are many possible encoding schemes
that exist. Unfortunately, comparisons of successful encoding schemes are
not frequent in the literature. We compare two successful encoding schemes to
the shortest path problem.
Gen et al.1 proposed a priority based encoding scheme, which can be decoded
with a O(n2) algorithm. Gen et al. show that their path growth procedure
will produce a path for every encoding and every path has a corresponding
encoding. More recently, Davies and Lingras2 considered using Genetic Algorithms
to reroute shortest paths in dynamic and stochastic networks. Davies and
Lingras proposed a different encoding scheme that followed directly
from the definition of a walk. However, in this encoding scheme not every
encoding corresponds to a legal walk. Davies and Lingras consequently
provided representationspecific genetic operators to assure that
chromosomes represented legal points in the solution space.
We compare and contrast the advantages and disadvantages of each approach
supplemented with experimental results.
References
1. Gen, M., Cheng, R., and Wang, D.: Genetic Algorithms for Solving Shortest
Path Problems. Proceedings of 1997 IEEE International Conference on Evolutionary Computing, (1997) 401406.
2. Davies, C. and Lingras, P.: Genetic Algorithms for Rerouting Shortest Paths in
Dynamic and Stochastic Networks (1999), to appear

Title 
A TwoCamera Wand Calibration Technique 
Presenter 
Darrell Matthew Lahey, Memorial University 
A technique to calibrate cameras in a twocamera optical tracking system
is presented. This technique, which uses a wand to calibrate the two
cameras simultaneously, is compared to a traditional approach that
calibrates each camera individually. The wand calibration procedure is
easier to implement and reduces setup time for extended volume
measurements while producing similar results. External and internal
parameters required to compute the locations of markers in
threedimensional space, using the image coordinates from both cameras,
are determined during the camera calibration. For the calibration
technique, a rod with a marker fastened to each end is moved through the
viewing volume of both cameras. The wand calibration algorithm determines
the parameters by minimizing the difference between the actual and
calculated length of the wand over all image frames. Test results are
given comparing the two techniques.

Title 
Fixed Polarity ReedMuller Expansions for 3valued Logic 
Presenter 
Mark MacIssac 
Authors 
Mark MacIssac (St. Francis Xavier University) and Gerhard W. Dueck (University
of New Brunswick) 

Any nvariable symmetric function can be represented by a
carrier vector of length n+1. For such functions, Suprun has
developed a method to find all fixed polarity ReedMuller (FPRM)
expansions from a simple triangle consisting of zeros and ones.
The triangle is very compact, it only requires (n+2)(n+1)/2
bits, where n is the number of variables. Butler et al.
developed an algorithm that can construct the triangle and find
the best polarity in O(n^{3}) time. This is a significant
improvement over the previous algorithm with complexity O(n^{7}).
In this paper we extend the binary case to 3valued logic. It is
not surprising, that the complexity is greatly increased. The
simple triangle becomes a complex multidimensional structure.
Nevertheless we show that using this structure, significant
savings in storage and processing time can be achieved.

Saturday Afternoon, 3:15 p.m.5:15 p.m.
MATHEMATICS: AA1045
COMPUTER SCIENCE: AA1049
Accepted Papers in Mathematics/Statistics
Title 
6Cycle Decompositions of the Cartesian Product of Two Complete Graphs 
Presenter 
Kelda Farrell 
Authors 
Kelda A. Farrell and David A. Pike, Memorial 
The cartesian product of two graphs G_{1} and G_{2},
is the graph G_{1}×G_{2}
having vertex set V(G_{1})×V(G_{2}) and in
which vertex (u_{1},u_{2}) is
adjacent to (v_{1},v_{2}) if and only if either
u_{1} = v_{1} and u_{2} is adjacent
to v_{2} in G_{2}, or u_{2} = v_{2} and
u_{1} is adjacent to v_{1} in G_{1}. A cycle
is a 2regular connected graph (or subgraph of a graph).
I will discuss the necessary and sufficient conditions on m and n for
K_{m}×K_{n}, the cartesian product of two complete graphs,
to be decomposable into cycles of length 6.

Title 
Improving on the MLE of a Bounded Normal Mean 
Presenter 
Eric Marchand 
Authors 
Eric Marchand (New Brunswick) and François Perron (Montréal) 
We propose improvements under squared error loss to the
maximum likelihood estimator for estimating
the mean of a pvariate normal distribution when this
mean lies in a ball of radius m centered at the origin and the
covariance matrix is equal to the identity matrix.
Our construction of explicit improvements relies on conditional
risks and, although the potential gains over the mle vary, they
are seen to be possible for all problems (m,p).
We show that, for small enough m, a wide class of estimators,
including all Bayes estimators with respect to orthogonally
invariant priors, dominate the mle. When m is not so small, we
establish general sufficient conditions for dominance over the
the mle. We also study the resulting Bayes rules
for orthogonally invariant priors,
and obtain conditions of dominance involving the choice of the
prior. As well, (i) we derive an alternative estimator which
dominates the mle and we provide numerical evidence that
is fares quite well in comparison to others ; (ii) we show
that when m £ Öp the Bayes rule with respect to
a uniform prior on the boundary of the parameter space
dominates the mle, and that it is also minimax for
p £ 50 thus
extending the case p = 1 which was established by
Casella and Strawderman (1981) ; (iii) we apply our
results to the case of a uniform prior on the whole
parameter space; and, (iv) finally, numerical
comparisons of the risk functions are performed
and commented upon.

Title 
Graceful Trees from Skolem Sequences 
Presenter 
David Morgan (Memorial) 
Given a graph,
Given a graph, G, a graceful labeling of G is an injective mapping
a: V_{G} ® \mathbbZ_{EG} such that the associated
mapping b: E_{G}: ® {1, ¼, E_{G}} defined by
b({u, v}) = a(u) a(v) is bijective.
A Skolem sequence of order n is a partition, P of \mathbbZ_{2n} into
n subsets of size 2, such that for {a_{i}, b_{i}} Î P

n È
i = 1

{a_{i}  b_{i}} = {1, ¼, n}. 

We will show that the existence of a
Skolem sequence of order n implies the existence of a graceful tree on
2n vertices which exhibits a matching that excludes at most two
vertices. Moreover, two particular
constructions of graceful trees from Skolem sequences will be examined.

Title 
Prediction Intervals for the Thickness of Pipes
Subjected to Flow Accelerated Corrosion 
Presenter 
Rolf Turner (New Brunswick) 
Flow accelerated corrosion of the walls of pipes carrying heavy water
in nuclear power plants is a serious concern. A break in a pipe and
the resulting leakage of heavy water results in an extremely expensive
cleanup operation. Replacing pipes is also very expensive.
These days, the thickness of the pipes walls is monitored frequently
at a multiplicity of locations. The aim is to forecast when the
thickness of a pipe wall will fall below a specified level that
provides for a reasonable margin of safety. In a recent consulting
project I was called upon to help with the computation of prediction
intervals for the wall thicknesses.
There were several aspects to the problem that made it somewhat
nonstandard. These included a random effect from the differing
initial thickness of the walls of different pipes, and the fact that
prediction intervals were required for individual pipes rather than
for the ensemble. There was also a problem as to how to incorporate
a separate estimate of measurement error. In this talk I will
elaborate on these problems and how they were solved. The ideas are
all quite elementary and the talk should be accessible to anyone who
has taken a beginning statistics course.

Accepted Papers in Computer Science (AA1049):
Title 
Comparing Layers of Coloured Substrings 
Presenter 
Patricia Evans (New Brunswick) 
Long genetic sequences frequently have associated information about the structure
of different parts of the sequence. This includes how the pieces relate to each
other, and also how they are organized to form a threedimensional structure.
This information can be encoded in a way that can be incorporated into sequence
comparison algorithms. Colours can be superimposed onto individual sequence
symbols or onto contiguous substrings of the sequence. Single levels of such
annotation can be put together to form a hierarchy of layers that represents
a complex structure. This paper presents these methods for encoding structural
information and the comparison algorithms that compare both structure and
sequence in a hierarchical manner. The longest common subsequence, which is
the foundation of most sequence comparison measures, is used. Results for
both topdown and bottomup hierarchy comparison are discussed, showing a
tradeoff between the possible editing operations and the complexity of the
algorithm.

Title 
A Performance Evaluation of the ACORN Architecture 
Presenter 
Ali Ghorbani 
Authors 
Virendra C. Bhavsar (New Brunswick), Ali Akabar Ghorbani, (New
Brunswick), Stephen Marsh (NRC), 

ACORN (Agentbased Community Oriented Retrieval Network) is a multiagent
system which uses agents to provide information across internet/intranet
networks. In this report, we adapt the ACORN
architecture for its performance evaluation on single and multiple servers,
running on single and multiple machines. In order to evaluate the performance
of ACORN, we introduce a novel concept of multiple autonomous virtual users.
The concept of multiple autonomous virtual users and our testing
philosophy is applicable to the performance evaluation of other
client/server based multiagent systems. The modified ACORN architecture has
been ported to different machines and experimental results on single processors
obtained. The processing time required by ACORN is found to be a
nonlinear function of the number of agents.

Title 
An Adaptive Intranet Search Engine 
Presenter 
Colin Cherry 
Authors 
Colin Cherry, Shawn Wallace, André Trudel (Acadia) 
This paper presents a search engine that can be used to search a specially indexed
collection of documents. This search engine is designed to be intelligent.
It keeps track of all successful queries and the frequency of record and keyword usage.
Using this information, the engine improves its accuracy and performance over time.

Saturday Afternoon, 3:15 p.m.5:00 p.m., AA1043
Title 
Mathematical INvestigations of "Open Ended Problems" 
Presenter 
John Grant McLoughlin, Memorial 
Numbers such as 256 and 169 are unusual in that the square of the sum of
the digits of one number equals the other, and viceversa. Consideration
of curious number properties defined by such algorithms leads to rich
sources of mathematical conjectures and results. Snapshots of my own
work and investigations by students will offer an invitation to become
involved in investigations as recreational mathematicians and
teachers/students of mathematics. A smorgasbord of ideas for mathematical
investigation will be served from the range of topics examined by
students: paperclip divisions, unique factorization (?), the game of
"Life", and counting triangles, for example.

Title 
On the Use of Recreational Mathematics Problems to
Develop Mathematical Knowledge Among Students 
Presenter 
Amar Sodhi, Sir Wilfred Grenfell College 
By using a recreational mathematics problem one is able to introduce, in a
natural way, certain concepts in mathematics. This paper discusses the
concepts a grade eleven student discovered when confronted with the
following famous problem of Reverend T.P. Kirkman:
"Fifteen young schoolgirls are in the habit of being in groups of three
when setting out for their daily walk. Is it possible to arrange these
girls so that no two girls will be together in a group twice in the same
week?"

Title 
Introducing the Science of Computing:
The COMPUTER SCIENCE UNPLUGGED Experience 
Presenter 
Todd Wareham 
Though computers are now commonplace and elementary computer literacy is
on the rise, it is hard to convince people that there is a science behind
computing and harder still to introduce them to key ideas in this science.
Paradoxically, the apparent ease of use of computers and the flashiness of
readilyavailable technology often obscures the simple and elegant
mathematics underlying hardware and software research and development. To
remedy this, various researchers in Canada, USA, and New Zealand have,
over the last 10 years, developed games and activities for children aged 7
to 14 that introduce many topics in computer science without using
computers. Two exemplars of this effort are the books THIS IS
MEGAMATHEMATICS by Casey and Fellows and COMPUTER SCIENCE UNPLUGGED by
Bell, Witten, and Fellows.
In this talk, I will discuss my experience in using the COMPUTER SCIENCE
UNPLUGGED materials in public presentations held at various schools in
British Columbia from 1994 to 1997. In particular, I will focus on two
activities that illustrate important points about algorithm development
and computational complexity, namely the Poor Cartographer (graph
coloring) and Muddy City (minimum spanning trees).

