Hidden Schrödinger symmetry in FLRW and Bianchi I minisuperspace models of cosmology and black holes Schwarzschild dynamics

A broad sector of literature focuses on the relationship between fluid dynamics and gravitational systems. This thesis presents results that suggest the existence of a new kind of fluid/gravity duality not based on the holographic principle. The goal is to provide tools that allow us to systematically unearth hidden symmetries for reduced models of cosmology. The focus is on the field space of these models, i.e. the superspace. In fact, conformal isometries of the supermetric leave geodesics in the field space unaltered; this leads to symmetries of the models. An innovative aspect is the use of the Eisenhart-Duval’s lift. Using this method, systems constrained by a potential can be treated as free ones. Moreover, charges explicitly dependent on time, i.e. dynamical, can be found. A detailed analysis is carried out on three basic models of homogenous cosmology: i) flat Friedmann-Lemaître-Robertson-Walker’s isotropic universe filled with a massless scalar field; ii) Schwarzschild’s black hole mechanics and its extension to vacuum (A)dS gravity; iii) Bianchi’s anisotropic type I universe with a massless scalar field. The results show the presence of a hidden Schrödinger’s symmetry which, being intrinsic to both Navier-Stokes’ and Schrödinger’s equations, indicates a correspondence between cosmology and hydrodynamics. Furthermore, the central extension of this algebra explicitly relates two concepts. The first is the number of particles coming from the fluid picture; while the second is the ratio between the IR and UV cutoffs that weighs how much a theory has of “classical” over “quantum”. This suggests a spacetime that emerges from an underlying world which is described by quantum building blocks. These quanta statistically conspire to appear as gravitational phenomena from a macroscopic point of view.

Assessing the relationship between bee/flower diversity and vegetation structural heterogeneity through UAV photogrammetry

The ecosystem services provided by bees are very important. Factors as habitat fragmentation, intensive agriculture and climate change are contributing to the decline of bee populations. The use of remote sensing could be a useful tool for the recognition of sites with a high diversity, before performing a more expensive survey in the field. In this study the ability of Unmanned Aerial Vehicles (UAV) images to estimate biodiversity at local scale has been analysed testing the concept of the Height Variation Hypothesis (HVH). This approach states that, the higher the vegetation height heterogeneity (HH) measured by remote sensing information, the higher the vertical complexity and the higher vegetation species diversity. In this thesis the concept has been brought to a higher level, in order to understand if the vegetation HH can be considered a proxy also of bee species diversity and abundance. We tested this approach collecting field data on bees/flowers and RGB images through an UAV campaign in 30 grasslands in the South of the Netherlands. The Canopy Height Model (CHM) were derived through the photogrammetry technique "Structure from Motion" (SfM) with resolutions of 10cm, 25cm, 50cm. Successively, the HH assessed on the CHM using the Rao's Q heterogeneity index was correlated to the field data (bee abundance, diversity and bee/flower species richness). The correlations were all positive and significant. The highest R2 values were found when the HH was calculated at 10cm and correlated to bee species richness (R2 = 0.41) and Shannon’s H index (R2 = 0.38). Using a lower spatial resolution the goodness of fit slightly decreases. For flower species richness the R2 ranged between 0.36 to 0.39. Our results suggest that methods based on the concept behind the HVH, in this case deriving information of HH from UAV data, can be developed into valuable tools for large-scale, standardized and cost-effective monitoring of flower diversity and of the habitat quality for bees.

Flower cover and bee diversity estimate by drone RGB images

Worldwide, biodiversity is decreasing due to climate change, habitat fragmentation and agricultural intensification. Bees are essential crops pollinator, but their abundance and diversity are decreasing as well. For their conservation, it is necessary to assess the status of bee population. Field data collection methods are expensive and time consuming thus, recently, new methods based on remote sensing are used. In this study we tested the possibility of using flower cover diversity estimated by UAV images (FCD-UAV) to assess bee diversity and abundance in 10 agricultural meadows in the Netherlands. In order to do so, field data of flower and bee diversity and abundance were collected during a campaign in May 2021. Furthermore, RGB images of the areas have been collected using Unmanned Aerial Vehicle (UAV) and post-processed into orthomosaics. Lastly, Random Forest machine learning algorithm was applied to estimate FCD of the species detected in each field. Resulting FCD was expressed with Shannon and Simpson diversity indices, which were successively correlated to bee Shannon and Simpson diversity indices, abundance and species richness. The results showed a positive relationship between FCD-UAV and in-situ collected data about bee diversity, evaluated with Shannon index, abundance and species richness. The strongest relationship was found between FCD (Shannon Index) and bee abundance with R2=0.52. Following, good correlations were found with bee species richness (R2=0.39) and bee diversity (R2=0.37). R2 values of the relationship between FCD (Simpson Index) and bee abundance, species richness and diversity were slightly inferior (0.45, 0.37 and 0.35, respectively). Our results suggest that the proposed method based on the coupling of UAV imagery and machine learning for the assessment of flower species diversity could be developed into valuable tools for large-scale, standardized and cost-effective monitoring of flower cover and of the habitat quality for bees.