Class Numbers of Real Cyclotomic Fields of Conductor pq

The class numbers h+ of the real cyclotomic fields are very hard to compute. Methods based on discriminant bounds become useless as the conductor of the field grows and that is why other methods have been developed, which approach the problem from different angles. In this thesis we extend a method of Schoof that was designed for real cyclotomic fields of prime conductor to real cyclotomic fields of conductor equal to the product of two distinct odd primes. Our method calculates the index of a specific group of cyclotomic units in the full group of units of the field. This index has h+ as a factor. We then remove from the index the extra factor that does not come from h+ and so we have the order of h+. We apply our method to real cyclotomic fields of conductor < 2000 and we test the divisibility of h+ by all primes < 10000. Finally, we calculate the full order of the l-part of h+ for all odd primes l < 10000.</italic

On the Selmer group and rank of a family of elliptic curves

For arbitrary $m,n \in \mathbb{Z}$ with $gcd(2m , 3n) = 1$ we denote by $D = 4m^3 - 27n^2 \neq -3, -4$ the discriminants which are squarefree, and we define the family of elliptic curves $E_{D}: y^2 = x^3 + 16D$. These curves admit a rational 3-isogeny $\lambda$. In this paper we show that the rank of the $\lambda$-Selmer group of $E_{D}$ and of the $\lambda$-isogenous curves $E_{D'} = E_{-27D}$ have specific values related to the 3-rank $r_{3}(D)$ of the ideal class group of the quadratic field $K_{D} = \mathbb{Q}(\sqrt{D})$. Employing a known result on the parity of \Sha[E_{D}], we obtain that the rank of these curves is bounded below by $1$ for $D > 0$ and by $2$ for $D < -4$. Finally, we give an explicit, infinite subfamily of curves $E_{D}$ with $D = -p$, where $p$ are primes of a specific form.Comment: Submitted 26/10/2021 - Under review, 13 page

Epidemiology and risk factors for resistance to treatment of Kawasaki disease in Cyprus

Kawasaki disease (KD) is one of the most common vasculitides of early childhood. There are no previous studies on KD in Cyprus. The aim of this study was to evaluate the epidemiology of KD in Cyprus, risk factors for resistance to treatment and the development of cardiac complications. This is a retrospective multicenter study of pediatric patients with KD hospitalized between January 2000 and-December 2019. The data were collected from medical records. A total of 136 patients with KD were included in the study. 83% of patients were < 5 years of age and 10% were < 6 months. Thirty patients (22%) developed coronary artery lesions. Serum sodium ≤ 133 mmol/L, albumin ≤ 3.2 g/dl, ALT ≥ 80 U/L and neutrophils percentage ≥ 80% at diagnosis, were identified as risk factors for resistance to IVIG. Clinical and epidemiological characteristics of KD in Cyprus population were similar to those reported in the literature. Although the majority of cases received appropriate treatment in time, cardiac complications still occurred

Non-catalytic Roles of Tet2 Are Essential to Regulate Hematopoietic Stem and Progenitor Cell Homeostasis

The Ten-eleven translocation (TET) enzymes regulate gene expression by promoting DNA demethylation and partnering with chromatin modifiers. TET2, a member of this family, is frequently mutated in hematological disorders. The contributions of TET2 in hematopoiesis have been attributed to its DNA demethylase activity, and the significance of its nonenzymatic functions has remained undefined. To dissect the catalytic and non-catalytic requirements of Tet2, we engineered catalytically inactive Tet2 mutant mice and conducted comparative analyses of Tet2 mutant and Tet2 knockout animals. Tet2 knockout mice exhibited expansion of hematopoietic stem and progenitor cells (HSPCs) and developed myeloid and lymphoid disorders, while Tet2 mutant mice predominantly developed myeloid malignancies reminiscent of human myelodysplastic syndromes. HSPCs from Tet2 knockout mice exhibited distinct gene expression profiles, including downregulation of Gata2. Overexpression of Gata2 in Tet2 knockout bone marrow cells ameliorated disease phenotypes. Our results reveal the non-catalytic roles of TET2 in HSPC homeostasis

On homomorphic encryption using abelian groups: Classical security analysis

In [15], Leonardi and Ruiz-Lopez propose an additively homomorphic public key encryption scheme whose security is expected to depend on the hardness of the $\textit{learning homomorphism with noise problem}$ (LHN). Choosing parameters for their primitive requires choosing three groups $G$, $H$, and $K$. In their paper, Leonardi and Ruiz-Lopez claim that, when $G$, $H$, and $K$ are abelian, then their public-key cryptosystem is not quantum secure. In this paper, we study security for finite abelian groups $G$, $H$, and $K$ in the classical case. Moreover, we study quantum attacks on instantiations with solvable groups

The transcriptional activator Gli2 modulates T-cell receptor signalling through attenuation of AP-1 and NFκB activity

Different tissues contain diverse and dynamic cellular niches, providing distinct signals to tissue-resident or migratory infiltrating immune cells. Hedgehog (Hh) proteins are secreted inter-cellular signalling molecules, which are essential during development and are important in cancer, post-natal tissue homeostasis and repair. Hh signalling mediated by the Hh-responsive transcription factor Gli2 also has multiple roles in T-lymphocyte development and differentiation.Here, we investigate the function of Gli2 in T-cell signalling and activation. Gene transcription driven by the Gli2 transcriptional activator isoform (Gli2A) attenuated T-cell activation and proliferation following T-cell receptor (TCR) stimulation. Expression of Gli2A in T-cells altered gene expression profiles, impaired the TCR-induced Ca2+ flux and nuclear expression of NFAT2, suppressed upregulation of molecules essential for activation, and attenuated signalling pathways upstream of the AP-1 and NFκB complexes, leading to reduced activation of these important transcription factors. Inhibition of physiological Hh-dependent transcription increased NFκB activity upon TCR ligation. These data are important for nderstanding the molecular mechanisms of immunomodulation, particularly in tissues where Hh proteins or other Gli-activating ligands such as TGFβ are upregulated, including during inflammation, tissue damage and repair, and in tumour microenvironments

Nel positively regulates the genesis of retinal ganglion cells by promoting their differentiation and survival during development

Peer reviewedPublisher PD