Marquette University 2009 Commencement Address

ABOUT THE TALK: Dick Enberg presented the Commencement address to Marquette University\u27s graduating Class of 2009 on May 17, 2009. He spoke to an audience of more than 2000 graduating students, their family and friends, and members of the Marquette community. The event took place at the Bradley Center in Milwaukee. ABOUT THE SPEAKER: Dick Enberg is an award-winning sports journalist who has covered nearly every major sporting event since his debut on NBC in 1975. Enberg is the only person to win an Emmy as a sportscaster, writer and producer, having received 14 Emmys, including a Lifetime Achievement Emmy. He was inducted into the National Sportscasters and Sportswriters Hall of Fame in 1995 Enberg began his broadcast career while a student at Indiana University, doing play by play for football and basketball games while earning his master’s and doctoral degrees in health sciences

Binomial Difference Ideal and Toric Difference Variety

In this paper, the concepts of binomial difference ideals and toric difference varieties are defined and their properties are proved. Two canonical representations for Laurent binomial difference ideals are given using the reduced Groebner basis of Z[x]-lattices and regular and coherent difference ascending chains, respectively. Criteria for a Laurent binomial difference ideal to be reflexive, prime, well-mixed, perfect, and toric are given in terms of their support lattices which are Z[x]-lattices. The reflexive, well-mixed, and perfect closures of a Laurent binomial difference ideal are shown to be binomial. Four equivalent definitions for toric difference varieties are presented. Finally, algorithms are given to check whether a given Laurent binomial difference ideal I is reflexive, prime, well-mixed, perfect, or toric, and in the negative case, to compute the reflexive, well-mixed, and perfect closures of I. An algorithm is given to decompose a finitely generated perfect binomial difference ideal as the intersection of reflexive prime binomial difference ideals.Comment: 72 page

Difference Balanced Functions and Their Generalized Difference Sets

Difference balanced functions from $F_{q^n}^*$ to $F_q$ are closely related to combinatorial designs and naturally define $p$-ary sequences with the ideal two-level autocorrelation. In the literature, all existing such functions are associated with the $d$-homogeneous property, and it was conjectured by Gong and Song that difference balanced functions must be $d$-homogeneous. First we characterize difference balanced functions by generalized difference sets with respect to two exceptional subgroups. We then derive several necessary and sufficient conditions for $d$-homogeneous difference balanced functions. In particular, we reveal an unexpected equivalence between the $d$-homogeneous property and multipliers of generalized difference sets. By determining these multipliers, we prove the Gong-Song conjecture for $q$ prime. Furthermore, we show that every difference balanced function must be balanced or an affine shift of a balanced function.Comment: 17 page

Introduction: The difference that makes a difference

This article introduces TripleC’s Special Issue on The Difference That Makes a Difference, containing papers arising from a workshop of the same name that ran in Milton Keynes in September 2011. The background to the workshop is explained, workshop sessions are summarised, and the content of the papers introduced. Finally, some provisional outcomes from the workshop and the Special Issue are described

Difference-making grounds

We define a notion of difference-making for partial grounds of a fact in rough analogy to existing notions of difference-making for causes of an event. Using orthodox assumptions about ground, we show that it induces a non-trivial division with examples of partial grounds on both sides. We then demonstrate the theoretical fruitfulness of the notion by applying it to the analysis of a certain kind of putative counter-example to the transitivity of ground recently described by Jonathan Schaffer. First, we show that our conceptual apparatus of difference-making enables us to give a much clearer description than Schaffer does of what makes the relevant instances of transitivity appear problematic. Second, we suggest that difference-making is best seen as a mark of good grounding-based explanations rather than a necessary condition on grounding, and argue that this enables us to deal with the counter-example in a satisfactory way. Along the way, we show that Schaffer's own proposal for salvaging a form of transitivity by moving to a contrastive conception of ground is unsuccessful. We conclude by sketching some natural strategies for extending our proposal to a more comprehensive account of grounding-based explanations