Transversely projective foliations on surfaces: existence of normal forms and prescription of the monodromy

We introduce a notion of normal form for transversely projective structures of singular foliations on complex manifolds. Our first main result says that this normal form exists and is unique when ambient space is two-dimensional. From this result one obtains a natural way to produce invariants for transversely projective foliations on surfaces. Our second main result says that on projective surfaces one can construct singular transversely projective foliations with prescribed monodromy

On the algebraic invariant curves of plane polynomial differential systems

We consider a plane polynomial vector field $P(x,y)dx+Q(x,y)dy$ of degree $m>1$. To each algebraic invariant curve of such a field we associate a compact Riemann surface with the meromorphic differential $\omega=dx/P=dy/Q$. The asymptotic estimate of the degree of an arbitrary algebraic invariant curve is found. In the smooth case this estimate was already found by D. Cerveau and A. Lins Neto [Ann. Inst. Fourier Grenoble 41, 883-903] in a different way.Comment: 10 pages, Latex, to appear in J.Phys.A:Math.Ge

Notes on the Third Law of Thermodynamics.I

We analyze some aspects of the third law of thermodynamics. We first review both the entropic version (N) and the unattainability version (U) and the relation occurring between them. Then, we heuristically interpret (N) as a continuity boundary condition for thermodynamics at the boundary T=0 of the thermodynamic domain. On a rigorous mathematical footing, we discuss the third law both in Carath\'eodory's approach and in Gibbs' one. Carath\'eodory's approach is fundamental in order to understand the nature of the surface T=0. In fact, in this approach, under suitable mathematical conditions, T=0 appears as a leaf of the foliation of the thermodynamic manifold associated with the non-singular integrable Pfaffian form $\delta Q_{rev}$. Being a leaf, it cannot intersect any other leaf $S=$ const. of the foliation. We show that (N) is equivalent to the requirement that T=0 is a leaf. In Gibbs' approach, the peculiar nature of T=0 appears to be less evident because the existence of the entropy is a postulate; nevertheless, it is still possible to conclude that the lowest value of the entropy has to belong to the boundary of the convex set where the function is defined.Comment: 29 pages, 2 figures; RevTex fil

Integrated transcriptomic and proteomic analysis of the global response of Wolbachia to doxycycline-induced stress

The bacterium Wolbachia (order Rickettsiales), representing perhaps the most abundant vertically transmitted microbe worldwide, infects arthropods and filarial nematodes. In arthropods, Wolbachia can induce reproductive alterations and interfere with the transmission of several arthropod-borne pathogens. In addition, Wolbachia is an obligate mutualist of the filarial parasites that cause lymphatic filariasis and onchocerciasis in the tropics. Targeting Wolbachia with tetracycline antibiotics leads to sterilisation and ultimately death of adult filariae. However, several weeks of treatment are required, restricting the implementation of this control strategy. To date, the response of Wolbachia to stress has not been investigated, and almost nothing is known about global regulation of gene expression in this organism. We exposed an arthropod Wolbachia strain to doxycycline in vitro, and analysed differential expression by directional RNA-seq and label-free, quantitative proteomics. We found that Wolbachia responded not only by modulating expression of the translation machinery, but also by upregulating nucleotide synthesis and energy metabolism, while downregulating outer membrane proteins. Moreover, Wolbachia increased the expression of a key component of the twin-arginine translocase (tatA) and a phosphate ABC transporter ATPase (PstB); the latter is associated with decreased susceptibility to antimicrobials in free-living bacteria. Finally, the downregulation of 6S RNA during translational inhibition suggests that this small RNA is involved in growth rate control. Despite its highly reduced genome, Wolbachia shows a surprising ability to regulate gene expression during exposure to a potent stressor. Our findings have general relevance for the chemotherapy of obligate intracellular bacteria and the mechanistic basis of persistence in the Rickettsiales

Phylotranscriptomic insights into the diversification of endothermic Thunnus tunas

Birds, mammals, and certain fishes, including tunas, opahs and lamnid sharks, are endothermic, conserving internally generated, metabolic heat to maintain body or tissue temperatures above that of the environment. Bluefin tunas are commercially important fishes worldwide, and some populations are threatened. They are renowned for their endothermy, maintaining elevated temperatures of the oxidative locomotor muscle, viscera, brain and eyes, and occupying cold, productive high-latitude waters. Less cold-tolerant tunas, such as yellowfin tuna, by contrast, remain in warm-temperate to tropical waters year-round, reproducing more rapidly than most temperate bluefin tuna populations, providing resiliency in the face of large-scale industrial fisheries. Despite the importance of these traits to not only fisheries but also habitat utilization and responses to climate change, little is known of the genetic processes underlying the diversification of tunas. In collecting and analyzing sequence data across 29,556 genes, we found that parallel selection on standing genetic variation is associated with the evolution of endothermy in bluefin tunas. This includes two shared substitutions in genes encoding glycerol-3 phosphate dehydrogenase, an enzyme that contributes to thermogenesis in bumblebees and mammals, as well as four genes involved in the Krebs cycle, oxidative phosphorylation, β-oxidation, and superoxide removal. Using phylogenetic techniques, we further illustrate that the eight Thunnus species are genetically distinct, but found evidence of mitochondrial genome introgression across two species. Phylogeny-based metrics highlight conservation needs for some of these species