Finding ECM-friendly curves through a study of Galois properties

In this paper we prove some divisibility properties of the cardinality of elliptic curves modulo primes. These proofs explain the good behavior of certain parameters when using Montgomery or Edwards curves in the setting of the elliptic curve method (ECM) for integer factorization. The ideas of the proofs help us to find new families of elliptic curves with good division properties which increase the success probability of ECM

Modular curves over number fields and ECM

International audienceWe construct families of elliptic curves defined over number fields and containing torsion groups Z=M1Z x Z=M2Z where (M1;M2) belongs to f(1; 11), (1; 14), (1; 15), (2; 10), (2; 12), (3; 9), (4; 8), (6; 6)g (i.e., when the corresponding modular curve X1(M1;M2) has genus 1). We provide formulae for the curves and give examples of number fields for which the corresponding elliptic curves have non-zero ranks, giving explicit generators using D. Simon's program whenever possible. The reductions of these curves can be used to speed up ECM for factoring numbers with special properties, a typical example being (factors of) Cunningham numbers bn - 1 such that M1 j n. We explain how to find points of potentially large orders on the reduction, if we accept to use quadratic twists

Working with Mycorrhizas in Forestry and Agriculture

Crop Production/Industries,

Aggregation and travelling wave dynamics in a two-population model of cancer cell growth and invasion

Funding: Engineering and Physical Sciences Research Council (UK) grant numbers EP/L504932/1 (VB), EP/K033689/1 (RE).Cells adhere to each other and to the extracellular matrix (ECM) through protein molecules on the surface of the cells. The breaking and forming of adhesive bonds, a process critical in cancer invasion and metas- tasis, can be influenced by the mutation of cancer cells. In this paper, we develop a nonlocal mathematical model describing cancer cell invasion and movement as a result of integrin-controlled cell-cell adhesion and cell-matrix adhesion, for two cancer cell populations with different levels of mutation. The partial differential equations for cell dynamics are coupled with ordinary differential equations describing the extracellular matrix (ECM) degradation and the production and decay of integrins. We use this model to investigate the role of cancer mutation on the possibility of cancer clonal competition with alternating dominance, or even competitive exclusion (phenomena observed experimentally). We discuss different possible cell aggregation patterns, as well as travelling wave patterns. In regard to the travelling waves, we investigate the effect of cancer mutation rate on the speed of cancer invasion.Publisher PDFPeer reviewe

PMC42, a breast progenitor cancer cell line, has normal-like mRNA and microRNA transcriptomes.

INTRODUCTION: The use of cultured cell lines as model systems for normal tissue is limited by the molecular alterations accompanying the immortalisation process, including changes in the mRNA and microRNA (miRNA) repertoire. Therefore, identification of cell lines with normal-like expression profiles is of paramount importance in studies of normal gene regulation. METHODS: The mRNA and miRNA expression profiles of several breast cell lines of cancerous or normal origin were measured using printed slide arrays, Luminex bead arrays, and real-time reverse transcription-polymerase chain reaction. RESULTS: We demonstrate that the mRNA expression profiles of two breast cell lines are similar to that of normal breast tissue: HB4a, immortalised normal breast epithelium, and PMC42, a breast cancer cell line that retains progenitor pluripotency allowing in-culture differentiation to both secretory and myoepithelial fates. In contrast, only PMC42 exhibits a normal-like miRNA expression profile. We identified a group of miRNAs that are highly expressed in normal breast tissue and PMC42 but are lost in all other cancerous and normal-origin breast cell lines and observed a similar loss in immortalised lymphoblastoid cell lines compared with healthy uncultured B cells. Moreover, like tumour suppressor genes, these miRNAs are lost in a variety of tumours. We show that the mechanism leading to the loss of these miRNAs in breast cancer cell lines has genomic, transcriptional, and post-transcriptional components. CONCLUSION: We propose that, despite its neoplastic origin, PMC42 is an excellent molecular model for normal breast epithelium, providing a unique tool to study breast differentiation and the function of key miRNAs that are typically lost in cancer.RIGHTS : This article is licensed under the BioMed Central licence at http://www.biomedcentral.com/about/license which is similar to the 'Creative Commons Attribution Licence'. In brief you may : copy, distribute, and display the work; make derivative works; or make commercial use of the work - under the following conditions: the original author must be given credit; for any reuse or distribution, it must be made clear to others what the license terms of this work are

A classification of ECM-friendly families using modular curves: intégré à la thèse de doctorat de Sudarshan Shinde, Sorbonne Université, 10 juillet 2020.

Validé par le jury de thèse de Sudarshan Shinde, Sorbonne Université, 10 juillet 2020.jury :Loïc Mérel (président)Jean-Marc Couveignes (rapporteur)David Zureick Brown (rapporteur)Annick ValibouzeBen SmithPierre-Voncent Koseleff (co-directeur)Razvan Barbulescu (co-drecteur)In this work, we establish a link between the classification of ECM-friendly curves and Mazur's program B, which consists in parameterizing all the families of elliptic curves with exceptional Galois image. Building upon two recent works which treated the case of congruence subgroups of prime-power level which occur for infinitely many $j$-invariants, we prove that there are exactly 1525 families of rational elliptic curves with distinct Galois images which are cartesian products of subgroups of prime-power level. This makes a complete list of rational families of ECM-friendly elliptic curves, out of which less than 25 were known in the literature. We furthermore refine a heuristic of Montgomery to compare these families and conclude that the best 4 families which can be put in $a=-1$ twisted Edwards' form are new

Development and characterisation of MSC-seeded decellularised airway scaffolds for regenerative bioengineering

Tracheal tissue engineering (TE) is a potential solution for long tracheal lesions and recent clinical experience yielded promising results but challenges remain with respect to measurable criteria for acceptance of decellularised scaffolds, optimisation of cell seeding and understanding the biology of the seeded cells post attachment. Confirming previous data from our group, I showed cellular clearance of DC scaffolds and significant reduction in total DNA levels but observed retention of residual nuclear materials within hyaline cartilage and submucosa. Evaluation of extracellular matrix components demonstrated retention of collagen and glycosaminoglycan and disrupted basement membrane components. The novel use of dynamic mechanical analysis (DMA) to measure the viscoelastic properties of tracheal cartilage in addition to tensile testing, provided the first demonstration of preservation of native viscoelastic mechanical properties after decellularisation. To overcome the limitations of passive cell seeding, I conceived partial surface dehydration (PSD) conditioning of scaffolds which significantly improved cell seeding/attachment efficiency to (96.46% 1.710) and I confirmed survival of MSCs on the scaffold in vitro. Multiphoton imaging showed limited scaffold infiltration but revealed two, distinct cell morphologies dependent on the presence or absence of adventitia. These showed different RNA transcriptomic profiles and differential gene expression. Seeded MSCs upregulated transcripts of bioactive paracrine factors associated with tissue repair, including ECM remodelling, pro-angiogenesis, antifibrosis, chemoattraction and immunomodulatory properties. Cells seeded into the adventitial layer upregulated more bioactive factors and showed lower cellular stress, suggesting a favourable effect of maintaining adventitial layer. The data presented herein form a coherent series of experiments providing novel data to the field of tracheal tissue engineering which address important GMP issues such as in-process acceptance criteria for scaffolds and data to support the rationale of autologous MSC seeding prior to implantation. These results allowed us to manufacture an improved clinical product for a compassionate case