A focus on focal surfaces

We make a systematic study of the focal surface of a congruence of lines in the projective space. Using differential techniques together with techniques from intersection theory, we reobtain in particular all the invariants of the focal surface (degree, class, class of its hyperplane section, sectional genus and degrees of the nodal and cuspidal curve). We study in particular the congruences of chords to a smooth curve and the congruences of bitangents or flexes to a smooth surface. We find that they possess unexpected components in their focal surface, and conjecture that they are the only ones with this property.Comment: Plain TeX, 33 pages with no figure

Belowground environmental effects of transgenic crops: a soil microbial perspective

Experimental studies investigated the effects of transgenic crops on the structure, function and diversity of soil and rhizosphere microbial communities playing key roles in belowground environments. Here we review available data on direct, indirect and pleiotropic effects of engineered plants on soil microbiota, considering both the technology and the genetic construct utilized. Plants modified to express phyto-pathogen/phytoparasite resistance, or traits beneficial to food industries and consumers, differentially affected soil microorganisms depending on transformation events, experimental conditions and taxa analyzed. Future studies should address the development of harmonized methodologies by taking into account the complex interactions governing soil lif

The quest for Magrathea planets I: formation of second generation exoplanets around double white dwarfs

The evolution of binaries that become double white dwarf (DWD) can cause the ejection of high amounts of dust and gas. Such material can give rise to circumbinary discs and become the cradle of new planets, yet no studies so far have focused on the formation of circumbinary planets around DWDs. These binaries will be the main sources of gravitational waves (GWs) detectable by the ESA Laser Interferometer Space Antenna (LISA) mission, opening the possibility to detect circumbinary planets around short-period DWDs everywhere in the Milky Way. We investigate the formation of Magrathea planets by simulating multiple planet formation tracks to explore how seeds growing first by pebble accretion, and then by gas accretion, are affected by the disc environments surrounding DWDs. We present both planetary formation tracks taking place in steady-state discs, and formation tracks taking place in discs evolving with time. The time-dependent tracks account for both the disc accretion rate onto the central binary and the disc photoevaporation rate caused by stellar irradiation. Our results show that planetary formation in circumbinary discs around DWDs can be possible. In particular, the extreme planetary formation environment implies three main significant results: (i) the accretion rate and the metallicity of the disc should be high in order to form sub-stellar objects with masses up to 31 M$_J$, this is achieved only if planet formation starts soon after the onset of the disc and if first generation seeds are present in the disc; (ii) seeds formed within 0.1 Myr, or within 1 Myr, from the onset of the disc can only produce sub-Neptune and Neptunian planets, unless the disc accommodates first generation seeds with mass 10 M$_{\oplus}$; (iii) most of the planets are finally located within 1 au from the disc centre, while they are still undergoing the gas accretion phase.Comment: Accepted for publication in A&A on 05/04/2023, abstract shortened, 28 pages, 11 figures, 14 table

Camera re-calibration after zooming based on sets of conics

We describe a method to compute the internal parameters (focal and principal points) of a camera with known position and orientation, based on the observation of two or more conics on a known plane. The conics can even be degenerate (e.g. pairs of lines). The proposed method can be used to re-estimate the internal parameters of a fully calibrated camera after zooming to a new, unknown, focal length. It also allows estimating the internal parameters when a second, fully calibrated camera observes the same conics. The parameters estimated through the proposed method are coherent with the output of more traditional procedures that require a higher number of calibration images. A deep analysis of the geometrical configurations that influence the proposed method is also reported

The rank of trifocal grassmann tensors

Grassmann tensors arise from classical problems of scene reconstruction in computer vision. Trifocal Grassmann tensors, related to three projections from a projective space of dimension k onto view spaces of varying dimensions, are studied in this work. A canonical form for the combined projection matrices is obtained. When the centers of projections satisfy a natural generality assumption, such canonical form gives a closed formula for the rank of trifocal Grassmann tensors. The same approach is also applied to the case of two projections, confirming a previous result obtained with different methods in [M. Bertolini, G. Besana, and C. Turrini, Ann. Mat. Pura Appl. (4), 196 (2016), pp. 539-553]. The rank of sequences of tensors converging to tensors associated with degenerate configurations of projection centers is also considered, giving concrete examples of a wide spectrum of phenomena that can happen

Marine anthraquinones: Pharmacological and toxicological issues

The marine ecosystem, populated by a myriad of animals, plants, and microorganisms, is an inexhaustible reservoir of pharmacologically active molecules. Among the multiple secondary metabolites produced by marine sources, there are anthraquinones and their derivatives. Besides being mainly known to be produced by terrestrial species, even marine organisms and the uncount-able kingdom of marine microorganisms biosynthesize anthraquinones. Anthraquinones possess many different biological activities, including a remarkable antitumor activity. However, due to their peculiar chemical structures, anthraquinones are often associated with toxicological issues, even relevant, such as genotoxicity and mutagenicity. The aim of this review is to critically describe the an-ticancer potential of anthraquinones derived from marine sources and their genotoxic and mutagenic potential. Marine-derived anthraquinones show a promising anticancer potential, although clinical studies are missing. Additionally, an in-depth investigation of their toxicological profile is needed before advocating anthraquinones as a therapeutic armamentarium in the oncological area

Diversity of a phosphate transporter gene among species and isolates of arbuscular mycorrhizal fungi

Arbuscular mycorrhizal fungi (AMF) are a key group of beneficial obligate biotrophs, establishing a mutualistic symbiosis with the roots of most land plants. The molecular markers generally used for their characterization are mainly based on informative regions of nuclear rDNA (SSU-ITS-LSU), although protein-encoding genes have also been proposed. Within functional genes, those encoding for phosphate transporters (PT) are particularly important in AMF, given their primary ability to take up Pi from soil, and to differentially affect plant phosphate nutrition. In this work, we investigated the genetic diversity of PT1 gene sequences and sequences of the taxonomically relevant SSU-ITS-LSU region in two isolates of the species Funneliformis coronatus, three isolates of the species Funneliformis mosseae and two species of the genus Rhizoglomus, originated from geographically distant areas and cultured in vivo. Our results showed that partial PT1 sequences not only successfully differentiated AMF genera and species like ribosomal gene sequences but also highlighted intraspecific diversity among F. mosseae and F. coronatus isolates. The study of functional genes related to the uptake of key mineral nutrients for the assessment of AMF diversity represents a key step in the selection of efficient isolates to be used as inocula in sustainable agriculture

Optical mapping of neuronal activity during seizures in zebrafish

Mapping neuronal activity during the onset and propagation of epileptic seizures can provide a better understanding of the mechanisms underlying this pathology and improve our approaches to the development of new drugs. Recently, zebrafish has become an important model for studying epilepsy both in basic research and in drug discovery. Here, we employed a transgenic line with pan-neuronal expression of the genetically-encoded calcium indicator GCaMP6s to measure neuronal activity in zebrafish larvae during seizures induced by pentylenetretrazole (PTZ). With this approach, we mapped neuronal activity in different areas of the larval brain, demonstrating the high sensitivity of this method to different levels of alteration, as induced by increasing PTZ concentrations, and the rescuing effect of an anti-epileptic drug. We also present simultaneous measurements of brain and locomotor activity, as well as a high-throughput assay, demonstrating that GCaMP measurements can complement behavioural assays for the detection of subclinical epileptic seizures, thus enabling future investigations on human hypomorphic mutations and more effective drug screening methods. Notably, the methodology described here can be easily applied to the study of many human neuropathologies modelled in zebrafish, allowing a simple and yet detailed investigation of brain activity alterations associated with the pathological phenotype