..................................................................................................................................................... 1 Students vs. Skills: Partitioning Variance Explained in Learner Models ........................................... 2 The Opportunity Count Model: A Flexible Approach to Modeling Student Performance ............. 10 Enhancing the Efficiency and R...

Let ex(n,C4) denote the maximum size of a C4-free graph of order n. For an even integer or odd prime power q > 6, we prove that ex(q2 + q + 2, C4) < 1 2(q+1)(q 2+q+2), which leads to an improvement of the upper bounds on Ramsey numbers R(C4,Wq2+2), where Wn is a wheel of order n. By using a simple polarity graph Gq for a prime power q, we construct the graphs whose complements do not contain K1...

An edge e of a simple 3-connected graph G is essential if neither the deletion G\e nor the contraction G/e is both simple and 3–connected. Tutte’s Wheels Theorem proves that the only simple 3–connected graphs with no non-essential edges are the wheels. In earlier work, as a corollary of a matroid result, the authors determined all simple 3-connected graphs with at most two non-essential edges. ...

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Tutte’s Wheels-and-Whirls Theorem proves that if M is a 3-connected matroid other than a wheel or a whirl, then M has a 3-connected minor N such that |E(M)| − |E(N)| = 1. Geelen and Whittle extended this theorem by showing that when M is sequentially 4-connected, the minor N can also be guaranteed to be sequentially 4connected, that is, for every 3-separation (X, Y ) of N , the set E(N) can be ...

An essential element of a 3–connected matroid M is one for which neither the deletion nor the contraction is 3–connected. Tutte’s Wheels and Whirls Theorem proves that the only 3–connected matroids in which every element is essential are the wheels and whirls. In an earlier paper, the authors showed that a 3–connected matroid with at least one non-essential element has at least two such element...

We study the unwheeled rational Kontsevich integral of torus knots. We give a precise formula for these invariants up to loop degree 3 and show that they appear as colorings of simple diagrams. We show that they behave under cyclic branched coverings in a very simple way. Our proof is combinatorial: it uses the results of Wheels and Wheelings and new decorations of diagrams.

Acknowledgements This report was made possible by a generous grant from the Meals On Wheels Association of America Foundation and underwritten by Harrah's Foundation. We owe a special debt of gratitude to Enid Bor-den, Peggy Ingraham, and Robert Herbolsheimer of MOWAAF for their assistance and feedback through the various stages of the report. We also thank members of the MOWAAF Board of Direct...

In this paper I examine the issue of whether we can trust software systems and put forward an argument that in an absolute sense the answer must necessarily be no for a multitude of reasons. The paper then examines the question of whether this is an actual impediment to the successful application of software with particular reference to automotive applications. In particular I examine the quest...