How large is a Riemann surface: the type problem

The uniformization theorem asserts that a simply-connected non-compact Riemann surface S is conformally equivalent to precisely one of the unit disk D or the finite complex plane C. While this result (nearly a century old) closes one chapter in the theory of analytic functions of one complex variable, it opens another: given a surface S described in some explicit manner, determine from intrinsic considerations which of the conformal types S is. While this subject reached a zenith of activity in the 1930s, recent developments and the availability of new tools suggest a resurgence of interest.National Science Foundatio

Asymptotic Values of Meromorphic Functions of Finite Order.

The asymptotic values of a meromorphic function (of any order) defined in the complex plane form a Suslin analytic set. Moreover, given an analytic set A we construct a meromorphic function of finite order and minimal growth having A as its precise set of asymptotic values

Valores asintóticos de funciones meromorfas enteras

Dado un conjunto analítico A ⊂ C ∪ {∞} y un número 0 ≤ ρ ≤ ∞ existe una función meromorfa f, definida en C de orden de crecimiento ρ tal que el conjunto de valores asintóticos de f es precisamente A

Asymptotic values of entire meromorphic functions.

Let f : C → C ∪ {∞} meromorphic, a is an asymptotic value for f if there exists a continuous curve γ such that lim: f (z) = a ∈ C ∪ {∞} z→∞ z∈

The Six1 oncoprotein downregulates p53 via concomitant regulation of RPL26 and microRNA-27a-3p

TP53 is mutated in 50% of all cancers, and its function is often compromised in cancers where it is not mutated. Here we demonstrate that the pro-tumorigenic/metastatic Six1 homeoprotein decreases p53 levels through a mechanism that does not involve the negative regulator of p53, MDM2. Instead, Six1 regulates p53 via a dual mechanism involving upregulation of microRNA-27a and downregulation of ribosomal protein L26 (RPL26). Mutation analysis confirms that RPL26 inhibits miR-27a binding and prevents microRNA-mediated downregulation of p53. The clinical relevance of this interaction is underscored by the finding that Six1 expression strongly correlates with decreased RPL26 across numerous tumour types. Importantly, we find that Six1 expression leads to marked resistance to therapies targeting the p53–MDM2 interaction. Thus, we identify a competitive mechanism of p53 regulation, which may have consequences for drugs aimed at reinstating p53 function in tumours

Breast cancer epithelial-to-mesenchymal transition: examining the functional consequences of plasticity

The epithelial-to-mesenchymal transition (EMT) is a critical developmental process that has recently come to the forefront of cancer biology. In breast carcinomas, acquisition of a mesenchymal-like phenotype that is reminiscent of an EMT, termed oncogenic EMT, is associated with pro-metastatic properties, including increased motility, invasion, anoikis resistance, immunosuppression and cancer stem cell characteristics. This oncogenic EMT is a consequence of cellular plasticity, which allows for interconversion between epithelial and mesenchymal-like states, and is thought to enable tumor cells not only to escape from the primary tumor, but also to colonize a secondary site. Indeed, the plasticity of cancer cells may explain the range of pro-metastatic traits conferred by oncogenic EMT, such as the recently described link between EMT and cancer stem cells and/or therapeutic resistance. Continued research into this relationship will be critical in developing drugs that block mechanisms of breast cancer progression, ultimately improving patient outcomes