Fan-extensions in fragile matroids

If S is a set of matroids, then the matroid M is S-fragile if, for every element e in E(M), either M\e or M/e has no minor isomorphic to a member of S. Excluded-minor characterizations often depend, implicitly or explicitly, on understanding classes of fragile matroids. In certain cases, when F is a minor-closed class of S-fragile matroids, and N is in F, the only members of F that contain N as a minor are obtained from N by increasing the length of fans. We prove that if this is the case, then we can certify it with a finite case-analysis. The analysis involves examining matroids that are at most two elements larger than N.Comment: Small revisions and correction

Capturing elements in matroid minors

In this dissertation, we begin with an introduction to a matroid as the natural generalization of independence arising in three different fields of mathematics. In the first chapter, we develop graph theory and matroid theory terminology necessary to the topic of this dissertation. In Chapter 2 and Chapter 3, we prove two main results. A result of Ding, Oporowski, Oxley, and Vertigan reveals that a large 3-connected matroid M has unavoidable structure. For every n exceeding two, there is an integer f(n) so that if |E(M)| exceeds f(n), then M has a minor isomorphic to the rank-n wheel or whirl, a rank-n spike, the cycle or bond matroid of K_{3,n}, or U_{2,n} or U_{n-2,n}. In Chapter 2, we build on this result to determine what can be said about a large structure using a specified element e of M. In particular, we prove that, for every integer n exceeding two, there is an integer g(n) so that if |E(M)| exceeds g(n), then e is an element of a minor of M isomorphic to the rank-n wheel or whirl, a rank-n spike, the cycle or bond matroid of K_{1,1,1,n}, a specific single-element extension of M(K_{3,n}) or the dual of this extension, or U_{2,n} or U_{n-2,n}. In Chapter 3, we consider a large 3-connected binary matroid with a specified pair of elements. We extend a corollary of the result of Chapter 2 to show the following result for any pair {x,y} of elements of a 3-connected binary matroid M. For every integer n exceeding two, there is an integer h(n) so that if |E(M)| exceeds h(n), then x and y are elements of a minor of M isomorphic to the rank-n wheel, a rank-n binary spike with a tip and a cotip, or the cycle or bond matroid of K_{1,1,1,n}

Capturing two elements in unavoidable minors of 3-connected binary matroids

Let M be a 3-connected binary matroid and let n be an integer exceeding 2. Ding, Oporowski, Oxley, and Vertigan proved that there is an integer f(n) so that if |E(M)|\u3ef(n), then M has a minor isomorphic to one of the rank-n wheel, the rank-n tipless binary spike, or the cycle or bond matroid of K3 n. This result was recently extended by Chun, Oxley, and Whittle to show that there is an integer g(n) so that if |E(M)|\u3eg(n) and xεE(M), then x is an element of a minor of M isomorphic to one of the rank-n wheel, the rank-n binary spike with a tip and a cotip, or the cycle or bond matroid of K11,1,n. In this paper, we prove that, for each i in {2,3}, there is an integer hi(n) so that if |E(M)|\u3ehi(n) and Z is an i-element rank-2 subset of M, then M has a minor from the last list whose ground set contains Z. © 2012 Elsevier Inc

Understanding Hope and Its Implications for Consumer Behavior: I Hope, Therefore I Consume

Building on prior work (MacInnis and de Mello (2005) \u27The concept of hope and its relevance to product evaluation and choice\u27. Journal of Marketing 69(January), 1-14; de Mello and MacInnis (2005) \u27Why and how consumers hope: Motivated reasoning and the marketplace\u27. Inside Consumption: Consumer Motives, Goals, and Desires, S. Ratneshwar and D. G. Mick (eds.). London/New York: Routledge, pp. 44-66), the authors argue that the concept of hope is highly relevant to consumer behavior and marketing, though its study has not yet appeared in these literatures. Complicating this study is that the definition of hope across literatures is inconsistent. The purpose of this conceptual article is to articulate the concept of hope and elucidate its relevance to consumer behavior. We do so in six sections. The first section explores the conceptual meaning of hope. A definition of hope and the constituent elements that underlie it is articulated. We compare this definition to ones provided elsewhere and differentiate hope from related terms like wishing, expectations, involvement, and faith. The second section focuses on what consumers hope for. The third section considers several important consumer relevant outcomes of hope, including biased processing and self-deception, risk taking behavior, product satisfaction, and life satisfaction and materialism. The fourth section addresses the extent to which marketers are purveyors of hope and what tactics they use to induce hope in consumers. The fifth section uses the conceptualization of hope to both discuss novel ways of measuring hope and their comparisons to existing hope measures. The final section addresses a set of interesting, yet unresolved questions about hope and consumer behavior

Capturing matroid elements in unavoidable 3-connected minors

A result of Ding, Oporowski, Oxley, and Vertigan reveals that a large 3-connected matroid M has unavoidable structure. For every n\u3e2, there is an integer f(n) so that if {pipe}E(M){pipe}\u3ef(n), then M has a minor isomorphic to the rank-n wheel or whirl, a rank-n spike, the cycle or bond matroid of K 3,n, or U 2,n or U n-2,n. In this paper, we build on this result to determine what can be said about a large structure using a specified element e of M. In particular, we prove that, for every integer n exceeding two, there is an integer g(n) so that if {pipe}E(M){pipe}\u3eg(n), then e is an element of a minor of M isomorphic to the rank-n wheel or whirl, a rank-n spike, the cycle or bond matroid of K 1,1,1,n, a specific single-element extension of M(K 3,n) or the dual of this extension, or U 2,n or U n-2,n. © 2012 Elsevier Ltd

Unavoidable Minors of Large 4-Connected Bicircular Matroids

It is known that any 3-connected matroid that is large enough is certain to contain a minor of a given size belonging to one of a few special classes of matroids. This paper proves a similar unavoidable minor result for large 4-connected bicircular matroids. The main result follows from establishing the list of unavoidable minors of large 4-biconnected graphs, which are the graphs representing the 4-connected bicircular matroids. This paper also gives similar results for internally 4-connected and vertically 4-connected bicircular matroids

Affective Forecasting and Self-Control: Why Anticipating Pride Wins Over Anticipating Shame in a Self-Regulation Context

We demonstrate that anticipating pride from resisting temptation facilitates self-control due to an enhanced focus on the self while anticipating shame from giving in to temptation results in self-control failure due to a focus on the tempting stimulus. In two studies we demonstrate the effects of anticipating pride (vs. shame) on self-control thoughts and behavior over time (Studies 1 and 2) and illustrate the process mechanism of self vs. stimulus focus underlying the differential influence of these emotions on self-control (Study 2). We present thought protocols, behavioral data (quantity consumed) and observational data (number/size of bites) to support our hypotheses