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Funder: Cambridge Commonwealth, European and International Trust; doi: http://dx.doi.org/10.13039/501100003343, Funder: Engineering and Physical Sciences Research Council; doi: http://dx.doi.org/10.13039/501100000266, Funder: Trinity College, University of Cambridge; doi: http://dx.doi.org/10.13039/501100000727, For a prime number p, let $$A_3(p)= | \{ m \in \mathbb {N}: \exists m_1,m_2,m_3 \in \mathbb {N}, \frac{m}{p}=\frac{1}{m_1}+\frac{1}{m_2}+\frac{1}{m_3} \} |$$ A 3 ( p ) = | { m ∈ N : ∃ m 1 , m 2 , m 3 ∈ N , m p = 1 m 1 + 1 m 2 + 1 m 3 } | . In 2019 Luca and Pappalardi proved that $$x (\log x)^3 \ll \sum _{p \le x} A_{3}(p) \ll x (\log x)^5$$ x ( log x ) 3 ≪ ∑ p ≤ x A 3 ( p ) ≪ x ( log x ) 5 . We improve the upper bound, showing $$\sum _{p \le x} A_{3}(p) \ll x (\log x)^3 (\log \log x)^2$$ ∑ p ≤ x A 3 ( p ) ≪ x ( log x ) 3 ( log log x ) 2 .

In the last 15 years, the mesocercariae of Alaria alata have frequently been reported in the wild boar during routine Trichinella inspections made compulsory for the trade of venison meat in Europe. If these studies have focused primarily on mesocercariae isolated from meat, few works have been done so far to understand the circulation of the parasite in natural conditions especially in the intermediate hosts. This study focuses on the second intermediate hosts of this parasite assessing the suitability of two amphibian groups-brown frogs and water frogs sensu lato-for mesocercarial infection on an area where A. alata has already been identified in water snails and wild boars. During this study, both groups showed to be suitable for mesocercarial infection, with high prevalence and parasite burdens. Prevalence was higher in the brown frog group (56.9 versus 11.54 % for water frogs) which would indicate that it is a preferential group for infection on the study area, though reasons for this remain to be investigated. No significant difference among prevalences was observed between tadpoles and frogs. This study, the first focusing on A. alata in these amphibians in Europe, provides further information on circulation of this parasite in natura.

The presence of the mesocercarial stage of Alaria alata (Goeze, 1792) in wild boar meat represents a potential risk for human, but little is known about the circulation of mesocercaria in wild boar populations. Routine Trichinella inspection, mandatorily performed in wild boar in France, also allowed detecting mesocercaria. We analyzed the results of this detection in the carcasses of 27,582 wild boars hunted in 2007-2011, in 502 hunting areas of the Rhine valley. Prevalence was globally low (0.6%), but 12% of the hunting areas were affected. These were clustered in lowlands of the Rhine valley, and prevalence strongly decreased with increasing elevation. In the lowlands, prevalence doubled between 2007 and 2011. This time trend and the geographic aggregation of positive wild boars suggest risk management measures based on targeted surveillance, control and prevention.

Alaria alata (Goeze, 1792), a trematode that parasitizes canids, usually needs two intermediate hosts to complete its life cycle: an aquatic freshwater snail and an amphibian. Although many studies have been undertaken on the wild boar's role as paratenic host, owing to the potential threat to human health, few have sought to identify the snails that act as first intermediate hosts in natural conditions. Adopting a molecular approach, with specific markers for a portion of the second internal transcribed spacer (ITS-2), we detected haplotypes of A. alata furcocercariae in two snail species (Planorbis planorbis and Anisus vortex), identified by molecular analysis (ribosomal 18S, mitochondrial 16S and COI). This study provides the first description of snails naturally emitting A. alata furcocercaria in Western Europe.

The trematode Alaria alata is a cosmopolite parasite found in red foxes (Vulpes vulpes), the main definitive host in Europe. In contrast only few data are reported in wild boars (Sus scrofa), a paratenic host. The aim of this paper is to describe the importance and distribution of Alaria alata mesocercariae in wild boars, information is given by findings of these larvae during Trichinella mandatory meat inspection on wild boars’ carcasses aimed for human consumption. More than a hundred cases of mesocercariae positive animals are found every year in the East of France. First investigations on the parasite’s resistance to deep-freezing in meat are presented in this work.

A general consensus that an increased logK(ow) led to an increase in xenobiotic uptake and bioaccumulation is accepted. In this study we compared the toxicokinetics of two chemically different xenobiotics, i.e. benzo[a]pyrene and fipronil in female green frogs. Surprisingly, the uptake rates and the bioconcentration factors (BCF) of the two contaminants were not predicted by their logK(ow). The uptake rates obtained were of the same order of magnitude for the two contaminants and the BCFs measured for fipronil were about 3-fold higher than those obtained for benzo[a]pyrene. Fipronil appeared to be more recalcitrant than benzo[a]pyrene to detoxification processes leading to the accumulation of sulfone-fipronil especially in the ovaries. This phenomenon may explain reproductive influence of this contaminant described in other studies. Detoxification processes, including metabolism and the excretion of pollutants, are of importance when considering their persistence in aquatic organisms and trying to quantify their risks.

Resume La Cour europeenne des droits de l'homme utilise frequemment l'arbitraire dans la motivation de ses decisions. L'etude de sa jurisprudence permet de preciser les contours de cette notion, aujourd'hui encore ambigue et floue : illegalite, mauvaise foi, obscurite des processus decisionnels sont des elements de l'arbitraire qui se manifestent lorsqu'une autorite, affranchie a la fois de toute contrainte et de toute rationalite, jouit temporairement d'une liberte de decision « absolue. » En la forcant a rendre des comptes et a expliciter les fondements juridiques et rationnels de ses decisions, la motivation semble etre le moyen le plus sur de prevenir l'arbitraire.