Effects of Paramuricea clavata (Risso, 1826) (Anthozoa: Plexauridae) forests on settlement of benthic species: an experimental approach

Rationale: Coralligenous habitat is considered the second most important subtidal “hot spot” of species diversity in the Mediterranean Sea after the Posidonia oceanica meadows. It can be defined as a typical Mediterranean biogenic hard bottom, mainly produced by the accumulation of calcareous encrusting algae that, together with other builder organisms, form a multidimensional framework with a high micro-spatial variability. The development of this habitat depends on physical factors (i.e. light, hydrodynamism, nutrients, etc.), but also biologic interactions can play a relevant role in structuring the benthic assemblages. This great environmental heterogeneity allows several different assemblages to coexist in a reduced space. One of the most beautiful is that characterised by the Mediterranean gorgonian Paramuricea clavata (Risso, 1826) that can contribute to above 40% of total biomass of the community and brings significant structural complexity into the coralligenous habitat. In sites moderately exposed to waves and currents, P. clavata can form high-density populations (up to 60 colonies m-2) between 20 – 70 m in depth. Being a suspension feeder, where it forms dense populations, P. clavata plays a significant role in transferring energy from planktonic to benthic system. The effects of the branched colonies of P. clavata could be comparable to those of the forests on land. They can affect the micro scale hydrodynamism and light, promoting or inhibiting the growth of other species. Unfortunately, gorgonians are threatened by several anthropogenic disturbance factors (i.e. fishing, pollution, tourism) and by climatic anomalies, linked to the global changes, that are responsible of thermal stress, development of mucilage and enhanced pathogens activity, leading to mass mortality events in last decades. Till now, the possible effects of gorgonian forest loss are largely unknown. Our goal was to analyse the ecological role of these sea fan forests on the coralligenous benthic assemblages. Experimental setup and main results: The influence of P. clavata in the settlement and recruitment of epibenthic organisms was analysed by a field experiment carried out in two randomly selected places: Tavolara island and Portofino promontory. The experiment consisted in recreate the presence and absence of the gorgonian forest on recruitment panels, arranged in four plots per type (forested and non-forested), interspersed each other, and deployed at the same depth. On every forested panel 3 gorgonian colonies about 20 cm height were grafted with the use of Eppendorf tubes and epoxy resin bicomponent simulating a density of 190 sea fans per m-2. This density corresponds to a mean biomass of 825 g DW m-2,3 which is of the same order of magnitude of the natural high-density populations. After about 4 months, the panels were collected and analysed in laboratory in order to estimate the percent cover of all the species that have colonized the substrata. The gorgonian forest effects were tested by multivariate and univariate permutational analyses of the variance (PERMANOVA). Recruited assemblages largely differed between the two study sites, probably due to different environmental conditions including water quality and turbidity. On overall, the presence of P. clavata reduced the settlement and recruitment of several algae: the shadow caused by the gorgonian might reduce light availability and therefore their growth. This effect might be greater in places where the waters are on average more clear, since at Portofino it is less visible and could be masked by the high turbidity of the water. The same pattern was registered for forams, more abundant outside gorgonian forest, probably linked with algal distribution, shadowing effect or alimentary competition. The last one hypothesis could be valid also for serpulids polychaetes that growth mainly on non-forested panels. An opposite trend, was showed by a species of bryozoan and by an hydroid that is facilitated by the presence of P. clavata, probably because it attenuates irradiance level and hydrodynamism. Species diversity was significantly reduced by the presence of P. clavata forests at both sites. This seems in contrast with what we expected, but the result may be influenced by the large algal component on non-forested panels. The analysis confirmed the presence of differences in the species diversity among plots and between sites respectively due to natural high variability of the coralligenous system and to different local environment conditions. The reduction of species diversity due to the presence of gorgonians appeared related to a worst evenness rather than to less species richness. With our experiment it is demonstrated that the presence of P. clavata forests can significantly alter local coralligenous assemblages patterns, promoting or inhibiting the recruitment of some species, modifying trophic relationships and adding heterogeneity and complexity to the habitat. Moreover, P. clavata could have a stabilising effect on the coralligenous assemblages.

Quantum field theory of (p,0)-forms on kaehler manifolds

In questa tesi abbiamo studiato la quantizzazione di una teoria di gauge di forme differenziali su spazi complessi dotati di una metrica di Kaehler. La particolarità di queste teorie risiede nel fatto che esse presentano invarianze di gauge riducibili, in altre parole non indipendenti tra loro. L'invarianza sotto trasformazioni di gauge rappresenta uno dei pilastri della moderna comprensione del mondo fisico. La caratteristica principale di tali teorie è che non tutte le variabili sono effettivamente presenti nella dinamica e alcune risultano essere ausiliarie. Il motivo per cui si preferisce adottare questo punto di vista è spesso il fatto che tali teorie risultano essere manifestamente covarianti sotto importanti gruppi di simmetria come il gruppo di Lorentz. Uno dei metodi più usati nella quantizzazione delle teorie di campo con simmetrie di gauge, richiede l'introduzione di campi non fisici detti ghosts e di una simmetria globale e fermionica che sostituisce l'iniziale invarianza locale di gauge, la simmetria BRST. Nella presente tesi abbiamo scelto di utilizzare uno dei più moderni formalismi per il trattamento delle teorie di gauge: il formalismo BRST Lagrangiano di Batalin-Vilkovisky. Questo metodo prevede l'introduzione di ghosts per ogni grado di riducibilità delle trasformazioni di gauge e di opportuni “antifields" associati a ogni campo precedentemente introdotto. Questo formalismo ci ha permesso di arrivare direttamente a una completa formulazione in termini di path integral della teoria quantistica delle (p,0)-forme. In particolare esso permette di dedurre correttamente la struttura dei ghost della teoria e la simmetria BRST associata. Per ottenere questa struttura è richiesta necessariamente una procedura di gauge fixing per eliminare completamente l'invarianza sotto trasformazioni di gauge. Tale procedura prevede l'eliminazione degli antifields in favore dei campi originali e dei ghosts e permette di implementare, direttamente nel path integral condizioni di gauge fixing covarianti necessari per definire correttamente i propagatori della teoria. Nell'ultima parte abbiamo presentato un’espansione dell’azione efficace (euclidea) che permette di studiare le divergenze della teoria. In particolare abbiamo calcolato i primi coefficienti di tale espansione (coefficienti di Seeley-DeWitt) tramite la tecnica dell'heat kernel. Questo calcolo ha tenuto conto dell'eventuale accoppiamento a una metrica di background cosi come di un possibile ulteriore accoppiamento alla traccia della connessione associata alla metrica.

Differential forms on Carnot groups

The main goal of this thesis is to understand and link together some of the early works by Michel Rumin and Pierre Julg. The work is centered around the so-called Rumin complex, which is a construction in subRiemannian geometry. A Carnot manifold is a manifold endowed with a horizontal distribution. If further a metric is given, one gets a subRiemannian manifold. Such data arise in different contexts, such as: - formulation of the second principle of thermodynamics; - optimal control; - propagation of singularities for sums of squares of vector fields; - real hypersurfaces in complex manifolds; - ideal boundaries of rank one symmetric spaces; - asymptotic geometry of nilpotent groups; - modelization of human vision. Differential forms on a Carnot manifold have weights, which produces a filtered complex. In view of applications to nilpotent groups, Rumin has defined a substitute for the de Rham complex, adapted to this filtration. The presence of a filtered complex also suggests the use of the formal machinery of spectral sequences in the study of cohomology. The goal was indeed to understand the link between Rumin's operator and the differentials which appear in the various spectral sequences we have worked with: - the weight spectral sequence; - a special spectral sequence introduced by Julg and called by him Forman's spectral sequence; - Forman's spectral sequence (which turns out to be unrelated to the previous one). We will see that in general Rumin's operator depends on choices. However, in some special cases, it does not because it has an alternative interpretation as a differential in a natural spectral sequence. After defining Carnot groups and analysing their main properties, we will introduce the concept of weights of forms which will produce a splitting on the exterior differential operator d. We shall see how the Rumin complex arises from this splitting and proceed to carry out the complete computations in some key examples. From the third chapter onwards we will focus on Julg's paper, describing his new filtration and its relationship with the weight spectral sequence. We will study the connection between the spectral sequences and Rumin's complex in the n-dimensional Heisenberg group and the 7-dimensional quaternionic Heisenberg group and then generalize the result to Carnot groups using the weight filtration. Finally, we shall explain why Julg required the independence of choices in some special Rumin operators, introducing the Szego map and describing its main properties.

Real forms of Lie algebras and Lie superalgebras

In questa tesi abbiamo studiato le forme reali di algebre e superalgebre di Lie. Il lavoro si suddivide in tre capitoli diversi, il primo è di introduzione alle algebre di Lie e serve per dare le prime basi di questa teoria e le notazioni. Nel secondo capitolo abbiamo introdotto le algebre compatte e le forme reali. Abbiamo visto come sono correlate tra di loro tramite strumenti potenti come l'involuzione di Cartan e relativa decomposizione ed i diagrammi di Vogan e abbiamo introdotto un algoritmo chiamato "push the button" utile per verificare se due diagrammi di Vogan sono equivalenti. Il terzo capitolo segue la struttura dei primi due, inizialmente abbiamo introdotto le superalgebre di Lie con relativi sistemi di radici e abbiamo proseguito studiando le relative forme reali, diagrammi di Vogan e abbiamo introdotto anche qua l'algoritmo "push the button".