Algorithmic and Hardness Results for the Colorful Components Problems

In this paper we investigate the colorful components framework, motivated by applications emerging from comparative genomics. The general goal is to remove a collection of edges from an undirected vertex-colored graph $G$ such that in the resulting graph $G'$ all the connected components are colorful (i.e., any two vertices of the same color belong to different connected components). We want $G'$ to optimize an objective function, the selection of this function being specific to each problem in the framework. We analyze three objective functions, and thus, three different problems, which are believed to be relevant for the biological applications: minimizing the number of singleton vertices, maximizing the number of edges in the transitive closure, and minimizing the number of connected components. Our main result is a polynomial time algorithm for the first problem. This result disproves the conjecture of Zheng et al. that the problem is $NP$-hard (assuming $P \neq NP$). Then, we show that the second problem is $APX$-hard, thus proving and strengthening the conjecture of Zheng et al. that the problem is $NP$-hard. Finally, we show that the third problem does not admit polynomial time approximation within a factor of $|V|^{1/14 - \epsilon}$ for any $\epsilon > 0$, assuming $P \neq NP$ (or within a factor of $|V|^{1/2 - \epsilon}$, assuming $ZPP \neq NP$).Comment: 18 pages, 3 figure

Unfolding symmetric Bogdanov-Takens bifurcations for front dynamics in a reaction-diffusion system

This manuscript extends the analysis of a much studied singularly perturbed three-component reaction-diffusion system for front dynamics in the regime where the essential spectrum is close to the origin. We confirm a conjecture from a preceding paper by proving that the triple multiplicity of the zero eigenvalue gives a Jordan chain of length three. Moreover, we simplify the center manifold reduction and computation of the normal form coefficients by using the Evans function for the eigenvalues. Finally, we prove the unfolding of a Bogdanov-Takens bifurcation with symmetry in the model. This leads to stable periodic front motion, including stable traveling breathers, and these results are illustrated by numerical computations.Comment: 39 pages, 7 figure

The Common Shrew (Sorex araneus): A neglected host of tick-borne infections?

Although the importance of rodents as reservoirs for a number of tick-borne infections is well established, comparatively little is known about the potential role of shrews, despite them occupying similar habitats. To address this, blood and tick samples were collected from common shrews (Sorex araneus) and field voles (Microtus agrestis), a known reservoir of various tick-borne infections, from sites located within a plantation forest in northern England over a 2-year period. Of 647 blood samples collected from shrews, 121 (18.7%) showed evidence of infection with Anaplasma phagocytophilum and 196 (30.3%) with Babesia microti. By comparison, of 1505 blood samples from field voles, 96 (6.4%) were positive for A. phagocytophilum and 458 (30.4%) for Ba. microti. Both species were infested with the ticks Ixodes ricinus and Ixodes trianguliceps, although they had different burdens: on average, shrews carried almost six times as many I. trianguliceps larvae, more than twice as many I. ricinus larvae, and over twice as many nymphs (both tick species combined). The finding that the nymphs collected from shrews were almost exclusively I. trianguliceps highlights that this species is the key vector of these infections in this small mammal community. These findings suggest that common shrews are a reservoir of tick-borne infections and that the role of shrews in the ecology and epidemiology of tick-borne infections elsewhere needs to be comprehensively investigated

Impact de l’activité de butinage de Apis mellifera adansonii Latreille (Hymenoptera : Apidae) sur la pollinisation et la chute des jeunes fruits du karité Vitellaria paradoxa (Sapotaceae) à Ngaoundéré (Cameroun)

Afin d’estimer la valeur apicole et d’évaluer l’impact de Apis mellifera adansonii sur le rendement fruitier de Vitellaria paradoxa Gaertner (Sapotaceae) au Cameroun, les activités de butinage, l’indice de fructification et le taux de chute des fruits avant maturité ont été enregistrés dans la savane de Tchabal-Bambi et de Béka (région de l’Adamaoua – Ngaoundéré). De décembre à janvier, en 2005/2006 et 2006/2007 respectivement, 120 et 200 inflorescences divisées en deux lots selon la présence ou l’absence de protection de ces inflorescences vis-à-vis des insectes ont été déterminées. Chaque année, les butineuses ont récolté le nectar et le pollen de façon intense et permanente. Le rythme des visites de A. m. adansonii a été positivement corrélé au rythme d’épanouissement des fleurs de V. paradoxa. Les données obtenues indiquent que la sapotacée est une plante apicole très fortement nectarifère et fortement pollinifère. L’indice de fructification des inflorescences non protégées a été significativement supérieur à celui des inflorescences protégées des insectes. La contribution numérique de A. m. adansonii dans la fructification a été de 57,74% en 2005/2006 et 53,55% en 2006/2007. La contribution numérique de A. m. adansonii dans la réduction du taux de chute des jeunes fruits a été de 19,04% en 2005/2006 et 52,21% en 2006/2007. L’installation des colonies de A. m. adansonii à proximité des populations de V. paradoxa est recommandée pour accroître son rendement en fruits et augmenter la production du miel.Keywords: Vitellaria paradoxa, Apis mellifera adansonii , butinage, pollinisation, fructificatio

Exchange Bias Induced by the Fe3O4 Verwey transition

We present a study of the exchange bias in different configurations of V2O3 thin films with ferromagnetic layers. The exchange bias is accompanied by a large vertical shift in the magnetization. These effects are only observed when V2O3 is grown on top of Ni80Fe20 permalloy. The magnitude of the vertical shift is as large as 60% of the total magnetization which has never been reported in any system. X-Ray diffraction studies show that the growth conditions promote the formation of a ferrimagnetic Fe3O4 interlayer. The change in the easy magnetization axis of Fe3O4 across the Verwey transition at 120 K is correlated with the appearance of exchange bias and vertical shift in magnetization. Both phenomena disappear above 120 K, indicating for the first time a direct relationship between the magnetic signature of the Verwey transition and exchange bias.Comment: Accepted for publication Physical Review