GALOIS THEORY OF ITERATED MORPHISMS ON REDUCIBLE ELLIPTIC CURVES AND ABELIAN SURFACES WITH REAL MULTIPLICATION

Let $F$ be a number field and let $A$ be an abelian algebraic group defined over $F$. For a prime $\ell$ and a point $\alpha \in A(F)$, we obtain the tower of extensions $F([\ell^n]^{-1}(\alpha))$ by adjoining to $F$ the coordinates of all the preimages of $\alpha$ under multiplication by $[\ell^n]$. This tower contains the coordinates of all of the $\ell$-power torsion points of $A$ along with a Kummer-type extension. The Galois groups of these extensions encode information about the density of primes \cP in the ring of integers of $F$ for which the order of $\alpha$ (mod \cP) is not divisible by $\ell$. In this thesis, we determine these Galois groups and explicitly compute the associated density for the cases where $A$ is (1) a reducible elliptic curve; (2) a product of elliptic curves with complex multiplication; (3) an abelian surface with real multiplication

Monitoring biomass in two heterogeneous mountain pasture communities by image based 3D point cloud derived predictors

Abstract Primary productivity is a robust indicator of ecosystem functioning because of its close relationships with the stability of the ecological systems. In ecological research, the above ground biomass (AGB) is the most commonly used proxy of primary productivity. However, despite their ecological relevance, the estimates of primary productivity are not addressed by current protocols for monitoring the conservation status of the habitats of Community interest. In this paper, we analyse the accuracy of AGB measurements obtained by image-derived 3D reconstructions of two contrasting mountain grasslands listed as habitats of Community interest in the Annex I of the Habitats Directive. More specifically, we compared the accuracy of the AGB estimates provided by four models, based on four different predictors (height, volume, volume adjusted, and cover volume), in order to evaluate their robustness against within- and between-community heterogeneity. Our study revealed that AGB measures computed from 3D vegetation reconstructions can be an effective way to evaluate primary productivity in herbaceous communities with complex structure and composition patterns. In particular, the vegetation height showed to have the highest correlation with direct AGB measurements. However, the vegetation volume, once adjusted by the coefficient of density, resulted to be the most effective proxy due to the lowest error level. Therefore, such a parameter could be routinely used as a non-destructive indicator for monitoring habitats of particular conservation concern. As a major limitation for this approach, we detected some loss of predictivity power at very low productivity rates

Late-Developing Supernumerary Premolars: Analysis of Different Therapeutic Approaches

This case series describes the different potential approaches to late-developing supernumerary premolars (LDSP). LDSP are supernumerary teeth (ST) formed after the eruption of the permanent dentition; usually they develop in the premolar region of the upper and lower jaw. The choice to extract or to monitor the LDSP depends on many factors and has to be carefully planned due to the several risks that either the monitoring or the extraction could provoke. These four cases of LDSP showed different treatment plan alternatives derived from a scrupulous assessment of the clinical and radiographic information

Late-Developing Supernumerary Premolars: Analysis of Different Therapeutic Approaches

This case series describes the different potential approaches to late-developing supernumerary premolars (LDSP). LDSP are supernumerary teeth (ST) formed after the eruption of the permanent dentition; usually they develop in the premolar region of the upper and lower jaw.The choice to extract or to monitor the LDSP depends on many factors and has to be carefully planned due to the several risks that either the monitoring or the extraction could provoke. These four cases of LDSP showed different treatment plan alternatives derived from a scrupulous assessment of the clinical and radiographic information. 1. Introductio

HLA and killer cell immunoglobulin-like receptor (KIRs) genotyping in patients with acute viral encephalitis

Introduction: The HLA genes, as well as the innate immune KIR genes, are considered relevant determinants of viral outcomes but no study, to our knowledge, has evaluated their role in the clinical setting of acute viral encephalitis. Results: Subjects with acute viral encephalitis in comparison to subjects without acute viral encephalitis showed a significantly higher frequency of 2DL1 KIR gene and AA KIR haplotypes and of HLA-C2 and HLA-A-Bw4 alleles. Subjects without acute viral encephalitis showed a higher frequency of interaction between KIR2DL2 and HLAC1. Multiple logistic regression analysis showed the detrimental effect of HLA-A haplotype and HLA-C1, HLA-A-BW4 HLA-B-BW4T alleles, whereas multiple logistic regression showed a protective effect of AB+BB KIR haplotype and a detrimental effect of interaction between KIR3DL1 and HLA-A-Bw4. Discussion: Our findings of a lower frequency of activating receptors in patients with acute encephalitis compared to controls could result in a less efficient response of NK cells. This finding could represent a possible pathogenetic explanation of susceptibility to acute symptomatic encephalitis in patients with viral infection from potentially responsible viruses such as Herpes virus. Materials and Methods: 30 Consecutive patients with symptomatic acute viral encephalitis and as controls, 36 consecutive subjects without acute encephalitis were analyzed. The following KIR genes were analyzed, KIR2DL1, 2DL2, 2DL3, 2DL5, 3DL1, 3DL2, 3DL3, 2DL4, 2DS1, 2DS2, 2DS3, 2DS4, 2DS5, 3DS1, 2 pseudogenes (2DP1 and 3DP1) and the common variants of KIR2DL5 (KIR2DL5A, KIR2DL5B)