On integral points of some Fano threefolds and their Hilbert schemes of lines and conics

We prove some density results for integral points on affine open sets of Fano threefolds. For instance, let Xo= P3\ D where D is the union of two quadrics such that their intersection contains a smooth conic, or the union of a smooth quadric surface and two planes, or the union of a smooth cubic surface V and a plane Π such that the intersection V∩ Π contains a line. In all these cases we show that the set of integral points of Xo is potentially dense. We apply the above results to prove that integral points are potentially dense in some log-Fano or in some log-Calabi-Yau threefold

A minimal and non-alternative realisation of the Cayley plane

The compact 16-dimensional Moufang plane, also known as the Cayley plane, has traditionally been defined through the lens of octonionic geometry. In this study, we present a novel approach, demonstrating that the Cayley plane can be defined in an equally clean, straightforward and more economic way using two different division and composition algebras: the paraoctonions and the Okubo algebra. The result is quite surprising since paraoctonions and Okubo algebra possess a weaker algebraic structure than the octonions, since they are non-alternative and do not satisfy the Moufang identities. Intriguingly, the real Okubo algebra has SU3 as automorphism group, which is a classical Lie group, while octonions and paraoctonions have an exceptional Lie group of type G2. This is remarkable, given that the projective plane defined over the real Okubo algebra is nevertheless isomorphic and isometric to the octonionic projective plane which is at the very heart of the geometric realisations of all types of exceptional Lie groups. Despite its historical ties with octonionic geometry, our research underscores the real Okubo algebra as the weakest algebraic structure allowing the definition of the compact 16-dimensional Moufang plane

Weighted Fano varieties and infinitesimal Torelli problem

We solve the infinitesimal Torelli problem for 3-dimensional quasi-smooth ℚ-Fano hypersurfaces with at worst terminal singularities. We also find infinite chains of double coverings of increasing dimension which alternatively distribute themselves in examples and counterexamples for the infinitesimal Torelli claim and which share the analogue, and in some cases the same, Hodge-diagram properties as the length 3 Gushel-Mukai chain of prime smooth Fanos of coindex 3 and degree 10

The fundamental group and torsion group of Beauville surfaces

We give a survey on the fundamental group of surfaces isogenous to a higher product. If the surfaces are regular, e.g. if they are Beauville surfaces, the first homology group is a finite group. We present a MAGMA script which calculates the first homology groups of regular surfaces isogenous to a product.Comment: 14 pages; MAGMA script included; v2: minor corrections, final version to appear in the Proceedings of the Conference "Beauville Surfaces and Groups", Newcastle University (UK), 7-9th June 201

Trypanosoma brucei brucei invasion and T-cell infiltration of the brain parenchyma in experimental sleeping sickness: timing and correlation with functional changes

Background: The timing of Trypanosoma brucei entry into the brain parenchyma to initiate the second, meningoencephalitic stage of human African trypanosomiasis or sleeping sickness is currently debated and even parasite invasion of the neuropil has been recently questioned. Furthermore, the relationship between neurological features and disease stage are unclear, despite the important diagnostic and therapeutic implications. Methodology: Using a rat model of chronic Trypanosoma brucei brucei infection we determined the timing of parasite and T-cell neuropil infiltration and its correlation with functional changes. Parasite DNA was detected using trypanosome-specific PCR. Body weight and sleep structure alterations represented by sleep-onset rapid eye movement (SOREM) periods, reported in human and experimental African trypanosomiasis, were monitored. The presence of parasites, as well as CD4+ and CD8+ T-cells in the neuropil was assessed over time in the brain of the same animals by immunocytochemistry and quantitative analyses. Principal findings: Trypanosome DNA was present in the brain at day 6 post-infection and increased more than 15-fold by day 21. Parasites and T-cells were observed in the parenchyma from day 9 onwards. Parasites traversing blood vessel walls were observed in the hypothalamus and other brain regions. Body weight gain was reduced from day 7 onwards. SOREM episodes started in most cases early after infection, with an increase in number and duration after parasite neuroinvasion. Conclusion: These findings demonstrate invasion of the neuropil over time, after an initial interval, by parasites and lymphocytes crossing the blood-brain barrier, and show that neurological features can precede this event. The data thus challenge the current clinical and cerebrospinal fluid criteria of disease staging

Fermat hypersurfaces and Subcanonical curves

We extend the classical Enriques-Petri Theorem to $s$-subcanonical projectively normal curves, proving that such a curve is $(s+2)$-gonal if and only if it is contained in a surface of minimal degree. Moreover, we show that any Fermat hypersurface of degree $s+2$ is apolar to an $s$-subcanonical $(s+2)$-gonal projectively normal curve, and vice versa.Comment: 18 pages; AMS-LaTe

Expression of interferon-inducible chemokines and sleep/wake changes during early encephalitis in experimental African trypanosomiasis

Background: Human African trypanosomiasis or sleeping sickness, caused by the parasite Trypanosoma brucei, leads to neuroinflammation and characteristic sleep/wake alterations. The relationship between the onset of these alterations and the development of neuroinflammation is of high translational relevance, but remains unclear. This study investigates the expression of interferon (IFN)-γ and IFN-inducible chemokine genes in the brain, and the levels of CXCL10 in the serum and cerebrospinal fluid prior to and during the encephalitic stage of trypanosome infection, and correlates these with sleep/wake changes in a rat model of the disease. Methodology/Principal findings: The expression of genes encoding IFN-γ, CXCL9, CXCL10, and CXCL11 was assessed in the brain of rats infected with Trypanosoma brucei brucei and matched controls using semi-quantitative end-point RT-PCR. Levels of CXCL10 in the serum and cerebrospinal fluid were determined using ELISA. Sleep/wake states were monitored by telemetric recording. Using immunohistochemistry, parasites were found in the brain parenchyma at 14 days post-infection (dpi), but not at 6 dpi. Ifn-γ, Cxcl9, Cxcl10 and Cxcl11 mRNA levels showed moderate upregulation by 14 dpi followed by further increase between 14 and 21 dpi. CXCL10 concentration in the cerebrospinal fluid increased between 14 and 21 dpi, preceded by a rise in the serum CXCL10 level between 6 and 14 dpi. Sleep/wake pattern fragmentation was evident at 14 dpi, especially in the phase of wake predominance, with intrusion of sleep episodes into wakefulness. Conclusions/Significance: The results show a modest increase in Cxcl9 and Cxcl11 transcripts in the brain and the emergence of sleep/wake cycle fragmentation in the initial encephalitic stage, followed by increases in Ifn-γ and IFN-dependent chemokine transcripts in the brain and of CXCL10 in the cerebrospinal fluid. The latter parameter and sleep/wake alterations could provide combined humoral and functional biomarkers of the early encephalitic stage in African trypanosomiasis

Effects of 5-year experimental warming in the Alpine belt on soil Archaea: Multi-omics approaches and prospects

We currently lack a predictive understanding of how soil archaeal communities may respond to climate change, particularly in Alpine areas where warming is far exceeding the global average. Here, we characterized the abundance, structure, and function of total (by metagenomics) and active soil archaea (by metatranscriptomics) after 5-year experimental field warming (+1°C) in Italian Alpine grasslands and snowbeds. Our multi-omics approach unveiled an increasing abundance of Archaea during warming in snowbeds, which was negatively correlated with the abundance of fungi (by qPCR) and micronutrients (Ca and Mg), but positively correlated with soil water content. In the snowbeds transcripts, warming resulted in the enrichment of abundances of transcription and nucleotide biosynthesis. Our study provides novel insights into possible changes in soil Archaea composition and function in the climate change scenario

Molecular ions in L1544. I. Kinematics

We have mapped the dense dark core L1544 in H13CO+(1-0), DCO+(2-1), DCO+(3-2), N2H+(1-0), NTH+(3-2), N2D+(2-1), N2D+(3-2), C18O(1-0), and C17O(1-0) using the IRAM 30-m telescope. We have obtained supplementary observations of HC18O+(1-0), HC17O+(1-0), and D13CO+(2-1). Many of the observed maps show a general correlation with the distribution of dust continuum emission in contrast to C18O(1-0) and C17O(1-0) which give clear evidence for depletion of CO at positions close to the continuum peak. In particular N2D+(2-1) and (3-2) and to a lesser extent N2H+(1-0) appear to be excellent tracers of the dust continuum. We find that the tracers of high density gas (in particular N2D+) show a velocity gradient along the minor axis of the L1544 core and that there is evidence for larger linewidths close to the dust emission peak. We interpret this using the model of the L1544 proposed by Ciolek & Basu (2000) and by comparing the observed velocities with those expected on the basis of their model. The results show reasonable agreement between observations and model in that the velocity gradient along the minor axis and the line broadening toward the center of L1544 are predicted by the model. This is evidence in favour of the idea that amipolar diffusion across field lines is one of the basic processes leading to gravitational collapse. However, line widths are significantly narrower than observed and are better reproduced by the Myers & Zweibel (2001) model which considers the quasistatic vertical contraction of a layer due to dissipation of its Alfvenic turbulence, indicating the importance of this process for cores in the verge of forming a star.Comment: 24 pages, 9 figures, to be published in Ap