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

Placing student voices at the heart of institutional dialogue

This article is based on a workshop delivered by the two authors at the SEDA Spring Conference 2008 on Engaging with Student Expectations (Flint and Oxley, 2008)

Learning from Internal Change Academy processes

A 2007/8 Research and Development Grant from SEDA under its Supporting and Leading Educational Change programme provided Sheffield Hallam University with the opportunity to undertake an extremely interesting and timely piece of work on learning from Internal Change Academy processes. A presentation to the SEDA Spring Conference 2009 focused on understanding the value of Internal Change Academies as a model for leading educational change and demonstrated how a simple benchmarking exercise may provide a rich source of data in leading change processes. This article focuses on the broader lessons learnt about change rather than on the practicalities and the different models of running an Internal Change Academy. That information is available in the project final report (Flint and Oxley, 2009)

A notion of minor-based matroid connectivity

For a matroid $N$, a matroid $M$ is $N$-connected if every two elements of $M$ are in an $N$-minor together. Thus a matroid is connected if and only if it is $U_{1,2}$-connected. This paper proves that $U_{1,2}$ is the only connected matroid $N$ such that if $M$ is $N$-connected with $|E(M)| > |E(N)|$, then $M \backslash e$ or $M / e$ is $N$-connected for all elements $e$. Moreover, we show that $U_{1,2}$ and $M(\mathcal{W}_2)$ are the only connected matroids $N$ such that, whenever a matroid has an $N$-minor using $\{e,f\}$ and an $N$-minor using $\{f,g\}$, it also has an $N$-minor using $\{e,g\}$. Finally, we show that $M$ is $U_{0,1} \oplus U_{1,1}$-connected if and only if every clonal class of $M$ is trivial.Comment: 13 page

Generalized Laminar Matroids

Nested matroids were introduced by Crapo in 1965 and have appeared frequently in the literature since then. A flat of a matroid $M$ is Hamiltonian if it has a spanning circuit. A matroid $M$ is nested if and only if its Hamiltonian flats form a chain under inclusion; $M$ is laminar if and only if, for every $1$-element independent set $X$, the Hamiltonian flats of $M$ containing $X$ form a chain under inclusion. We generalize these notions to define the classes of $k$-closure-laminar and $k$-laminar matroids. This paper focuses on structural properties of these classes noting that, while the second class is always minor-closed, the first is if and only if $k \le 3$. The main results are excluded-minor characterizations for the classes of 2-laminar and 2-closure-laminar matroids.Comment: 12 page

The improvement of zinc electrodes for electrochemical cells

Zinc electrode improvement for silver-zinc storage batter

Ten Things We Should Know About Time Series

Time series data affect many aspects of our lives. This paper highlights ten things we should all know about time series, namely: a good working knowledge of econometrics and statistics, an awareness of measurement errors, testing for zero frequency, seasonal and periodic unit roots, analysing fractionally integrated and long memory processes, estimating VARFIMA models, using and interpreting cointegrating models carefully, choosing sensibly among univariate conditional, stochastic and realized volatility models, not confusing thresholds, asymmetry and leverage, not underestimating the complexity of multivariate volatility models, and thinking carefully about forecasting models and expertise.Unit roots; fractional integration; long memory; VARFIMA; cointegration; volatility; thresholds; asymmetry; leverage; forecasting models and expertise

The Emergence and Evolution of Regional Convergence Clusters in China’s Energy Markets

Employing the new regression tests for Convergence, Club Convergence and Clustering proposed by Phillips and Sul (2007), this paper models and analyzes the behavior of China‘s energy sectors. Energy market =convergence clusters‘ are identified using new price data and their regional spatial distributions are mapped for four major fuel types; coal, gasoline, diesel and electricity. It is found that: i) as yet, there are no fully integrated national energy markets in China as more than one convergence cluster is identified for all four fuels; ii) some regional energy markets can be regarded as =quite mature‘ as evidenced by the existence of some highly concentrated convergence clusters connected geographically; iii) some regional markets remain in a =state of transition‘ as witnessed by convergence clusters that are scattered geographically and growing in membership; vi) it seems that there is more regional-based integration for coal and electricity than for gasoline and diesel as more convergent clusters were identified for coal and electricity than for gasoline and diesel v) Overall, China still appears to be in the process of energy market integration as demonstrated by the number and evolution of convergence clusters over time.China; Energy market; Convergence cluster