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AARMS Session

1999 APICS Mathematics/Statistics and Computer Science Conference Schedule

Memorial University of Newfoundland

October 22-24, 1999

What Where When
Web Warehouse Tutorial EN-4002 10:00 a.m.- 1:00 p.m.
REGISTRATION Lobby: Henrietta-Harvey (Math) Building 1:00 p.m.-5:00 p.m.
CS Competition EN-2036 1:30 p.m.- 6:30 p.m.
APICS Computing Science Committee Meeting EN-2022 2:30 p.m.-4:30 p.m.
APICS Math/Stats Committee Meeting Dean of Science Board Room: C-2001 2:30 p.m.-4:00 p.m.
Trends in Differential Equations and Dynamical Systems EN-4002 3:00 p.m.-5:30 p.m.
AARMS Business Meeting Dean of Science Board Room: C-2001 4:00 p.m.-5:00 p.m.
Mathematics Competition Lobby of Henrietta-Harvey (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 SN-2109 7:30 p.m.
Blundon Lecture: Tom Archibald SN-2109 7:40 p.m.- 8:30 p.m.
Wine & Cheese University Club, Arts and Administration Building  8:30 p.m.-10:30 p.m.
What Where When
REGISTRATION Atrium - Arts & Administration Building  9:00 a.m.-12:00 p.m.
Trends in Differential Equations and Dynamical Systems AA-1046  9:00 a.m.-11:40 a.m.
Sanjay Kumar Madria SN-2109  9:00 a.m.-10:00 a.m.
Recreational Mathematics Display AA-1045  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 AA-1043 (Math)
AA-1049 (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 SN-2109  2:00p.m.- 3:00p.m.
Trends in Differential Equations and Dynamical Systems AA-1046  3:00 p.m.- 5:25 p.m.
Contributed Papers AA-1045 (Math)
AA-1049 (CS)
 3:15 p.m.- 5:15 p.m.
Recreational Math: John Grant-McLoughlin AA-1043  3:15 p.m.- 5:00 p.m.
What Where When
AARMS Session: Trends Differential Equations and Dynamical Systems AA-1046 9:00 a.m.-11:45 a.m.

Tutorial: Sanjay Kumar Madria

Friday Morning, 10:00 a.m.-1:00 p.m., EN-4002

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.

Competitions: Friday Afternoon

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 EN-2046, the location of the exam for the 1:30 p.m. start or, if uncertain of directions, meet in the lobby of the Henrietta-Harvey (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 Henrietta-Harvey (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.

Blundon Lecture: Tom Archibald

Friday Evening, 7:40 p.m.- 8:30 p.m., SN-2109

Title The Rise (and Fall?) of Pure Mathematics
While pure-mathematical 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 twenty-five 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 twentieth-century developments. If time permits a few remarks about more recent developments will offer us a prospect for the twenty-first century.

Sanjay Kumar Madria

Saturday Morning, 9:00 a.m.-10:00 a.m., SN-2109

Title Approximate Query Processing and Summarized Databases in a Mobile Computing Environment
We present a query-processing 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).

Fred Rickey

Saturday Afternoon, 2:00 p.m.-3:00 p.m., SN-2109

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.

Recreational Mathematics Exhibit

Saturday, 9:00 a.m.-2:00 p.m., AA-1045

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.

Student Paper Session in Mathematics/Statistics

Saturday Morning, 10:00 a.m.-12:00 p.m.: AA-1043

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 Robertson-Walker 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 power-law 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 two-dimensional 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 non-truncated second order theory of thermodynamics. We shall use a first-order 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.

Student Paper Session in Computer Science

Saturday Morning, 10:00 a.m.-12:00 p.m.: AA-1049

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 no-known 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 representation-specific 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) 401-406.
    2. Davies, C. and Lingras, P.: Genetic Algorithms for Rerouting Shortest Paths in Dynamic and Stochastic Networks (1999), to appear

    Title A Two-Camera Wand Calibration Technique
    Presenter Darrell Matthew Lahey, Memorial University
    A technique to calibrate cameras in a two-camera 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 three-dimensional 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 Reed-Muller Expansions for 3-valued Logic
Presenter Mark MacIssac
Authors Mark MacIssac (St. Francis Xavier University) and Gerhard W. Dueck (University of New Brunswick)
Any n-variable 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 Reed-Muller (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(n3) time. This is a significant improvement over the previous algorithm with complexity O(n7).

In this paper we extend the binary case to 3-valued logic. It is not surprising, that the complexity is greatly increased. The simple triangle becomes a complex multi-dimensional structure. Nevertheless we show that using this structure, significant savings in storage and processing time can be achieved.

Contributed Papers

Saturday Afternoon, 3:15 p.m.-5:15 p.m.

Accepted Papers in Mathematics/Statistics

    Title 6-Cycle 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 G1 and G2, is the graph G1×G2 having vertex set V(G1)×V(G2) and in which vertex (u1,u2) is adjacent to (v1,v2) if and only if either u1 = v1 and u2 is adjacent to v2 in G2, or u2 = v2 and u1 is adjacent to v1 in G1. A cycle is a 2-regular connected graph (or subgraph of a graph). I will discuss the necessary and sufficient conditions on m and n for Km×Kn, 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 p-variate 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: VG ® \mathbbZ|EG| such that the associated mapping b: EG: ® {1, ¼, |EG|} defined by b({u, v}) = |a(u) -a(v)| is bijective.

    A Skolem sequence of order n is a partition, P of \mathbbZ2n into n subsets of size 2, such that for {ai, bi} Î P

    i = 1 
    {|ai - bi} = {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 clean-up 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 non-standard. 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 (AA-1049)

    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 three-dimensional 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 top-down and bottom-up 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 (Agent-based Community Oriented Retrieval Network) is a multi-agent 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 multi-agent 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.

Recreational Math:
John Grant-McLoughlin

Saturday Afternoon, 3:15 p.m.-5:00 p.m., AA-1043

    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 vice-versa. 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 readily-available 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).