Volume II, Issue 1

Bounding the Fat Shattering Dimension of a Composition Function Class Built Using a Continuous Logic Connective

Hubert Duan, University of Ottawa The paper deals with an important combinatorial parameter of a function class, the Fat Shattering dimension. An important known result in statistical learning theory is that a function class is distribution-free Probably Approximately Correct learnable if it has finite Fat Shattering dimension on every scale.
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Integers With A Predetermined Prime Factorization

Eric Naslund, University of British Columbia
A classic question in analytic number theory is, given integers x and k, to find asymptotics for the numbers n less than or equal to x with exactly k prime factors. This problem was originally resolved by Landau in 1900, and much work was subsequently done where k is allowed to vary. In this paper we look at a similar question about integers with a specific prime factorization. Download the article

Rotterdam Must Die: Triangular Finite Volume Methods Applied To The Shallow Water Equations

Luke Bovard and Katharine Hyatt, University of Waterloo In this paper we apply the method of finite volumes using a triangular mesh with a Roe solver to solve the shallow water wave equations. In order to demonstrate the advantages of using a triangular mesh, we solve two problems that are not easily solved using rectangular finite volume methods. We first solve the classic problem of a broken circular dam and then apply the scheme to the Maeslantkering, a movable barrier along the Nieuwe Waterweg in Holland used to regulate water flow from storms into the shipping canal, to demonstrate the complicated geometry that triangular meshes are able to model.
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