Extended modular operad

This paper is a sequel to [LoMa] where moduli spaces of painted stable curves were introduced and studied. We define the extended modular operad of genus zero, algebras over this operad, and study the formal differential geometric structures related to these algebras: pencils of flat connections and Frobenius manifolds without metric. We focus here on the combinatorial aspects of the picture. Algebraic geometric aspects are treated in [Ma2].Comment: 38 pp., amstex file, no figures. This version contains additional references and minor change

MYC functions are specific in biological subtypes of breast cancer and confers resistance to endocrine therapy in luminal tumours.

BACKGROUND: MYC is amplified in approximately 15% of breast cancers (BCs) and is associated with poor outcome. c-MYC protein is multi-faceted and participates in many aspects of cellular function and is linked with therapeutic response in BCs. We hypothesised that the functional role of c-MYC differs between molecular subtypes of BCs. METHODS: We therefore investigated the correlation between c-MYC protein expression and other proteins involved in different cellular functions together with clinicopathological parameters, patients' outcome and treatments in a large early-stage molecularly characterised series of primary invasive BCs (n=1106) using immunohistochemistry. The METABRIC BC cohort (n=1980) was evaluated for MYC mRNA expression and a systems biology approach utilised to identify genes associated with MYC in the different BC molecular subtypes. RESULTS: High MYC and c-MYC expression was significantly associated with poor prognostic factors, including grade and basal-like BCs. In luminal A tumours, c-MYC was associated with ATM (P=0.005), Cyclin B1 (P=0.002), PIK3CA (P=0.009) and Ki67 (P<0.001). In contrast, in basal-like tumours, c-MYC showed positive association with Cyclin E (P=0.003) and p16 (P=0.042) expression only. c-MYC was an independent predictor of a shorter distant metastases-free survival in luminal A LN+ tumours treated with endocrine therapy (ET; P=0.013). In luminal tumours treated with ET, MYC mRNA expression was associated with BC-specific survival (P=0.001). In ER-positive tumours, MYC was associated with expression of translational genes while in ER-negative tumours it was associated with upregulation of glucose metabolism genes. CONCLUSIONS: c-MYC function is associated with specific molecular subtypes of BCs and its overexpression confers resistance to ET. The diverse mechanisms of c-MYC function in the different molecular classes of BCs warrants further investigation particularly as potential therapeutic targets

Nef divisors for moduli spaces of complexes with compact support

In [BM14b], the first author and Macr\`i constructed a family of nef divisors on any moduli space of Bridgeland-stable objects on a smooth projective variety X. In this article, we extend this construction to the setting of any separated scheme Y of finite type over a field, where we consider moduli spaces of Bridgeland-stable objects on Y with compact support. We also show that the nef divisor is compatible with the polarising ample line bundle coming from the GIT construction of the moduli space in the special case when Y admits a tilting bundle and the stability condition arises from a \theta-stability condition for the endomorphism algebra. Our main tool generalises the work of Abramovich--Polishchuk [AP06] and Polishchuk [Pol07]: given a t-structure on the derived category D_c(Y) on Y of objects with compact support and a base scheme S, we construct a constant family of t-structures on a category of objects on YxS with compact support relative to S.Comment: 36 pages. In memory of Johan Louis Dupont. V2: updated following comments from the referee and from Joe Karmazyn who gave a counterexample to a false claim in version 1. To appear in Selecta Mat

Simulative Analysis of a Truncated Octahedral DNA Nanocage Family Indicates the Single-Stranded Thymidine Linkers as the Major Player for the Conformational Variability

Three nanocages composed of 12 DNA double helices, linked by single strand thymidine linkers made by 3, 5, and 7 nucleotides, have been characterized through classical molecular dynamics simulation to evaluate in silico the specific structural and conformational features generated by the use of a thymidine bridge of different length. The three simulated nanocages are stable, and their dynamics is characterized by a slight rotational motion of the double helices, induced by the conformational variations of the thymidine linkers. Despite this rotation the helices maintain a B-DNA structure as indicated by the values of their geometrical parameters. The thymidine strands are the elements having the largest displacement from the initial 3D model and give a significant contribution to the organization of the scaffold geometry throughout definite arrangements of base stacking and hydrogen bonds between the bases. Comparative analysis indicates that the linker length modulates the interactions occurring between the thymidines conferring a conformational variability larger in the 5T and 7T than in the 3T cage