Reduction and isogenies of elliptic curves

Let $R$ be a complete discrete valuation ring with fraction field $K$ and perfect residue field $k$ of characteristic $p>0$. Let $E/K$ be an elliptic curve with a $K$-rational isogeny of prime degree $\ell$. In this article, we study the possible Kodaira types of reduction that $E/K$ can have. We also prove some related results for elliptic curves over $\mathbb{Q}$.Comment: Preprint. Submitted for publicatio

Universal quadratic forms and Dedekind zeta functions

We study universal quadratic forms over totally real number fields using Dedekind zeta functions. In particular, we prove an explicit upper bound for the rank of universal quadratic forms over a given number field $K$, under the assumption that the codifferent of $K$ is generated by a totally positive element. Motivated by a possible path to remove that assumption, we also investigate the smallest number of generators for the positive part of ideals in totally real numbers fields.Comment: 12 pages. Preprin

A Deep Learning Pipeline for the Synthesis of Graphic Novels

peer reviewedIn this paper, we present what is to the best of our knowledge, the first deep learning pipeline to produce a synthetic graphic novel. Our method can synthesize from scratch engaging sequences of graphic novel pages, focusing on the Manga genre. To achieve this, we extract images and text from around 670 thousand Manga pages, which we use separately in order to train state-of-the-art generative architectures, such as GPT-2 for text generation and StyleGAN2 for image synthesis. Using these as sources of synthetic content, we develop a set of algorithmic aesthetic rules in order to bring together complete and continuous Manga pages

Analysis of SAA1 gene polymorphisms in the Greek population: rheumatoid arthritis and FMF patients relative to normal controls. Homogeneous distribution and low incidence of AA amyloidosis

Objective. To address whether or not the rarity of amyloidosis in Greek patients with rheumatoid arthritis (RA) is related to specific alleles of single nucleotide polymorphisms (SNPs) in the 5’-flanking region and the exon 3 of the SSA1 gene. Methods. The genotypes of the - 13T/C SNP in the 5’-flanking region of the SAA1 gene and the two SNPs within exon 3 of SAA1 (2995C/T and 3010C/T polymorphisms) were determined in 88 Greek patients with RA, 14 patients with familial Mediterranean fever (IMF) and 110 healthy controls. Linkage disequilibrium and haplotype frequencies involving - 13T/C, 2995C/T and 3010C/T in these populations were tested and estimated, respectively. Results. The genotypic distribution and allelic frequencies were similar in all groups tested. SNPs 2995 and 3010 were in linkage disequilibrium for all study populations (p < 0.05), whereas SNP - 13 was not in linkage disequilibrium with either 2995 or 3010 (p >= 0.05). Two major haplotypes presented in all patients with RA and FMF and controls: - 13C; 2995T; 3010C (- 13C; alpha) and - 13C; 2995C; 3010T (- 13C; beta). The - 13T allele was linked with the 7 haplotype in Greek patients with RA and controls. The frequency of the - 13T allele was found to be very rare in all groups tested. Conclusions. In conclusion, the rarity of the putative amyloidogenic - 13T allele in Greek populations may be related to low prevalence of AA amyloidosis development in Greek RA patients