Avian malaria is absent in juvenile colonial herons (Ardeidae) but not Culex pipiens mosquitoes in the Camargue, Southern France

Apicomplexan blood parasites Plasmodium and Haemoproteus (together termed “Avian malaria”) and Leucocytozoon are widespread, diverse vector-transmitted blood parasites of birds, and conditions associated with colonial nesting in herons (Ardeidae) and other waterbirds appear perfect for their transmission. Despite studies in other locations reporting high prevalence of parasites in juvenile herons, juvenile Little Egrets (Egretta garzetta) previously tested in the Camargue, Southern France, had a total absence of malaria parasites. This study tested the hypotheses that this absence was due to insufficient sensitivity of the tests of infection; an absence of infective vectors; or testing birds too early in their lives. Blood was sampled from juveniles of four species shortly before fledging: Little Egret (n = 40), Cattle Egret (Bubulcus ibis; n = 40), Black-crowned Night-Heron (Nycticorax nycticorax, n = 40), and Squacco Heron (Ardeola ralloides; n = 40). Sensitive nested-Polymerase Chain Reaction was used to test for the presence of parasites in both birds and host-seeking female mosquitoes captured around the colonies. No malaria infection was found of in any of the heron species. Four different lineages of Plasmodium were detected in pooled samples of female Culex pipiens mosquitoes, including two in potentially infective mosquitoes. These results confirm that the absence of malaria parasites previously demonstrated in Little Egret is not due to methodological limitations. Although the prevalence of infection in mosquitoes was low, conditions within the colonies were suitable for transmission of Plasmodium. These colonial heron species may have evolved strategies for resisting malaria infection through physiological or behavioral mechanisms

A few thoughts on the aesthetics of mathematics in research and teaching.

Mathematical aesthetic, having a variety of forms, is commonly experienced by mathematicians as a genuine reality and is available at every level of study. This short essay in hopefully moving beyond standardised hermeneutic critique attests to its authenticity through the words of some mathematical proponents, and reminds us that it should be promoted to children and students as a phenomenon that is as accessible as it is incontestable.N/

A new formulation of a result by McLaughlin for an arbitrary dimension 2 matrix power

We obtain an existing 2004 result of J. McLaughlin which gives explicit entries for a general dimension 2 matrix raised to an arbitrary power. Our formulation employs so called Catalan polynomials related to the crucial parameter of McLaughlin’s statement, and is a new one running along a different line of argument

On the notion of mathematical genius: rhetoric and reality.

The existential hypothesis of mathematical ‘genius’ rests irrefutably with the affirmative. We can’t all be one of course—that sublime solopreneur in creativity—but we may still contribute to research as lesser mortals. This short essay attempts to explore what the notion means to both us and non-mathematicians.N/

Alwyn Francis Horadam, 1923-2016: A personal tribute to the man and his sequence

Having received news of the passing of Alwyn Horadam this last July, I was determined that I should write something in his honour in which my own contact with him is described and combined with some introductory details on what I feel is his major endowment to the community of mathematicians - the so called and pre-eminent Horadam sequence whose specialisations thereof are great in number

A new non-linear recurrence identity class for Horadam sequence terms.

We state, and prove by a succinct matrix method, a non-linear recurrence identity class for terms of the so called Horadam sequence. A particular instance was established (in equivalent form) over half a century ago by A.F. Horadam, which provides a starting point for the discussion and an introduction to our formulation technique.N/

On generalised multi-index non-linear recursion identities for terms of the Horadam sequence.

We state and prove a non-linear recurrence identity for terms of the so called Horadamsequence,andthenofferitsgeneralisationwhichisavailablefromthesamemethodology. We illustrate how the overarching idea may be used to sequentially produce extended versions, each in turn with an extra level of non-linearity and term index complexity. These identities can all be captured in matrix determinant form.N/

A note on two rational invariants for a particular 2 x 2 matrix.

We state and prove the invariance, with respect to matrix power, of both the diagonals and anti-diagonals ratio of a special case 2×2 matrix. The proof methodology is new, contrasting with those deployed previously in establishing anti-diagonals matrix invariants.N/