On two classes of nearly binary matroids

We give an excluded-minor characterization for the class of matroids M in which M\e or M/e is binary for all e in E(M). This class is closely related to the class of matroids in which every member is binary or can be obtained from a binary matroid by relaxing a circuit-hyperplane. We also provide an excluded-minor characterization for the second class.Comment: 14 pages, 4 figures. This paper has been accepted for publication in the European Journal of Combinatorics. This is the final version of the pape

A matroid extension result

Adding elements to matroids can be fraught with difficulty. In the V\'amos matroid $V_8$, there are four independent sets $X_1,X_2, X_3,$ and $X_4$ such that $(X_1 \cup X_2,X_3 \cup X_4)$ is a $3$-separation while exactly three of the local connectivities $\sqcap(X_1,X_{3})$, $\sqcap(X_1,X_{4})$, $\sqcap(X_2,X_{3})$, and $\sqcap(X_2,X_{4})$ are one, with the fourth being zero. As is well known, there is no extension of $V_8$ by a non-loop element $p$ such that $X_j \cup p$ is a circuit for all $j$. This paper proves that a matroid can be extended by a fixed element in the guts of a $3$-separation provided no V\'amos-like structure is present

Constructing internally 4-connected binary matroids

This is the post-print version of the Article - Copyright @ 2013 ElsevierIn an earlier paper, we proved that an internally 4-connected binary matroid with at least seven elements contains an internally 4-connected proper minor that is at most six elements smaller. We refine this result, by giving detailed descriptions of the operations required to produce the internally 4-connected minor. Each of these operations is top-down, in that it produces a smaller minor from the original. We also describe each as a bottom-up operation, constructing a larger matroid from the original, and we give necessary and su fficient conditions for each of these bottom-up moves to produce an internally 4-connected binary matroid. From this, we derive a constructive method for generating all internally 4-connected binary matroids.This study is supported by NSF IRFP Grant 0967050, the Marsden Fund, and the National Security Agency

Unavoidable parallel minors of regular matroids

This is the post-print version of the Article - Copyright @ 2011 ElsevierWe prove that, for each positive integer k, every sufficiently large 3-connected regular matroid has a parallel minor isomorphic to M (K_{3,k}), M(W_k), M(K_k), the cycle matroid of the graph obtained from K_{2,k} by adding paths through the vertices of each vertex class, or the cycle matroid of the graph obtained from K_{3,k} by adding a complete graph on the vertex class with three vertices.This study is partially supported by a grant from the National Security Agency

Matroids with at least two regular elements

For a matroid $M$, an element $e$ such that both $M\backslash e$ and $M/e$ are regular is called a regular element of $M$. We determine completely the structure of non-regular matroids with at least two regular elements. Besides four small size matroids, all 3-connected matroids in the class can be pieced together from $F_7$ or $S_8$ and a regular matroid using 3-sums. This result takes a step toward solving a problem posed by Paul Seymour: Find all 3-connected non-regular matroids with at least one regular element [5, 14.8.8]

Modular elimination in matroids and oriented matroids

We introduce a new axiomatization of matroid theory that requires the elimination property only among modular pairs of circuits, and we present a cryptomorphic phrasing thereof in terms of Crapo's axioms for flats. This new point of view leads to a corresponding strengthening of the circuit axioms for oriented matroids.Comment: 6 pages; v2: text modified in order to better reflect the published version, references update

Achieving Effective Trade liberalization in APEC: The Trade Limitations of “Open Regionalism”

Until there is a substantial degree of consensus over the strategic issues and a greater body of work on the issues of liberalization, trade liberalization of APEC will yield slight results. This paper argues the need for intensive discussion and research about the modalities of successful trade liberalization. Long process of pre-negotiation is needed to establish the terms, target and modalities of negotiating reductions. All it requires is time.trade sector, liberalization, APEC

Laminar Matroids

A laminar family is a collection $\mathscr{A}$ of subsets of a set $E$ such that, for any two intersecting sets, one is contained in the other. For a capacity function $c$ on $\mathscr{A}$, let $\mathscr{I}$ be \{I:|I\cap A| \leq c(A)\text{ for all A\in\mathscr{A}}\}. Then $\mathscr{I}$ is the collection of independent sets of a (laminar) matroid on $E$. We present a method of compacting laminar presentations, characterize the class of laminar matroids by their excluded minors, present a way to construct all laminar matroids using basic operations, and compare the class of laminar matroids to other well-known classes of matroids.Comment: 17 page

STEPS Centre research: our approach to impact

The ‘impact’ of research has seen a dramatic rise up the UK’s policy agenda in recent years. But what does ‘impact’ really mean? How do researchers and others respond to the new ‘impact agenda’ and how might we best plan, monitor and report on impact? This working paper attempts to provide answers to some of these questions by reviewing various understandings of ‘impact’ and describing the approach used by the ESRC STEPS Centre in its second five-year phase of funding. In particular, we draw on our experience of adapting and employing a down-scaled version of ‘participatory impact pathways analysis’ (PIPA) and reflect on its utility and potential as a tool for planning relatively small-scale social science/ interdisciplinary research projects conducted with partners in developing countries. In using PIPA, the STEPS Centre has adapted the idea of ‘impact pathways’ in line with its broader ‘pathways approach’, which focusses on complex and dynamic interactions between knowledge, politics and ‘social, technological and environmental pathways to sustainability’. In this way, PIPA has been useful in articulating and exploring the potential impact of STEPS Centre projects: it has helped to map out the networks known to the researchers, appreciate different perspectives held by the team members and generate an understanding of the narratives, networks and policy processes under study. Although the possibility for detailed ex ante prediction of impact pathways is limited, using PIPA has helped teams to be ready to maximise communication and engagement opportunities, and to link research across different STEPS Centre projects and beyond. The working paper also describes how PIPA may be used iteratively in a way that enables reflexive learning amongst research teams. Lastly, we speculate on the ways in which PIPA may be further developed and used in ex post impact monitoring and evaluation into the future