What is Sound?

(Abstract to follow

Projective geometries in exponentially dense matroids. II

We show for each positive integer $a$ that, if $\mathcal{M}$ is a minor-closed class of matroids not containing all rank-$(a+1)$ uniform matroids, then there exists an integer $c$ such that either every rank-$r$ matroid in $\mathcal{M}$ can be covered by at most $r^c$ rank-$a$ sets, or $\mathcal{M}$ contains the GF$(q)$-representable matroids for some prime power $q$ and every rank-$r$ matroid in $\mathcal{M}$ can be covered by at most $cq^r$ rank-$a$ sets. In the latter case, this determines the maximum density of matroids in $\mathcal{M}$ up to a constant factor

Agricultural pest destruction movement in New Zealand

New Zealand could be regarded as an acclimatization laboratory, i.e., the consequence of a wide range of animal introductions in the period 1840-1907. Species introduced ranged from camels to hedgehogs, ostriches to sky larks. Fortunately, many failed to survive. The majority of these liberations were made by Acclimatization Societies or private individuals, often with Government approval and protection. The most damaging species were several species of deer, rabbits, Australian opossums, goats, pigs, tahr, wallabies, and chamois. Pastoral land development in the early days usually consisted of firing large tracts of indigenous forest and native grassland and this practice assisted the dispersion of some animals, particularly the rabbit. The impact of these animals was to upset the natural stability of habitat and damage soil and water values. Organizations constituted by Government with the responsibility of conducting control have in recent years made dramatic progress in reducing some animal populations to tolerable levels. This has only been achieved by positive policy changes over the years, plus the development and utilization of more effective control techniques, especially in the field of poisoning. Discussion of current species of concern includes the European rabbit, brush-tailed possum, rook, and wallabies. Control methods are briefly summarized

Projective geometries in exponentially dense matroids. I

We show for each positive integer $a$ that, if \cM is a minor-closed class of matroids not containing all rank-$(a+1)$ uniform matroids, then there exists an integer $n$ such that either every rank-$r$ matroid in \cM can be covered by at most $r^n$ sets of rank at most $a$, or \cM contains the \GF(q)-representable matroids for some prime power $q$, and every rank-$r$ matroid in \cM can be covered by at most $r^nq^r$ sets of rank at most $a$. This determines the maximum density of the matroids in \cM up to a polynomial factor