A geometric approach to Mathon maximal arcs

In 1969 Denniston gave a construction of maximal arcs of degree d in Desarguesian projective planes of even order q, for all d dividing q. In 2002 Mathon gave a construction method generalizing the one of Denniston. We will give a new geometric approach to these maximal arcs. This will allow us to count the number of isomorphism classes of Mathon maximal arcs of degree 8 in PG(2,2^h), h prime.Comment: 20 page

Partial flocks of the quadratic cone yielding Mathon maximal arcs

N. Hamilton and J. A. Thas describe a link between maximal arcs of Mathon type and partial flocks of the quadratic cone. This link is of a rather algebraic nature. In this paper we establish a geometric connection between these two structures. We also define a composition on the flock planes and use this to work out an analogue of the synthetic version of Mathon's Theorem. Finally, we show how it is possible to construct a maximal arc of Mathon type of degree 2d, containing a Denniston arc of degree d provided that there is a solution to a certain given system of trace conditions

Perp-systems and partial geometries

A perp-system R(r) is a maximal set of r-dimensional subspaces of PG(N,q) equipped with a polarity rho, such that the tangent space of an element of R(r) does not intersect any element of R(r). We prove that a perp-system yields partial geometries, strongly regular graphs, two-weight codes, maximal arcs and k-ovoids. We also give some examples, one of them yielding a new pg(8,20,2)

Using structured eradication feasibility assessment to prioritize the management of new and emerging invasive alien species in Europe

Prioritizing the management of invasive alien species (IAS) is of global importance and within Europe integral to the EU IAS regulation. To prioritize management effectively, the risks posed by IAS need to be assessed, but so too does the feasibility of their management. While the risk of IAS to the EU has been assessed, the feasibility of management has not. We assessed the feasibility of eradicating 60 new (not yet established) and 35 emerging (established with limited distribution) species that pose a threat to the EU, as identified by horizon scanning. The assessment was carried out by 34 experts in invasion management from across Europe, applying the Non‐Native Risk Management scheme to defined invasion scenarios and eradication strategies for each species, assessing the feasibility of eradication using seven key risk management criteria. Management priorities were identified by combining scores for risk (derived from horizon scanning) and feasibility of eradication. The results show eradication feasibility score and risk score were not correlated, indicating that risk management criteria evaluate different information than risk assessment. In all, 17 new species were identified as particularly high priorities for eradication should they establish in the future, whereas 14 emerging species were identified as priorities for eradication now. A number of species considered highest priority for eradication were terrestrial vertebrates, a group that has been the focus of a number of eradication attempts in Europe. However, eradication priorities also included a diverse range of other taxa (plants, invertebrates and fish) suggesting there is scope to broaden the taxonomic range of attempted eradication in Europe. We demonstrate that broad scale structured assessments of management feasibility can help prioritize IAS for management. Such frameworks are needed to support evidence‐based decision‐making