Curry-Howard for sequent calculus at last!

This paper tries to remove what seems to be the remaining stumbling blocks in the way to a full understanding of the Curry-Howard isomorphism for sequent calculus, namely the questions: What do variables in proof terms stand for? What is co-control and a co-continuation? How to define the dual of Parigot's mu-operator so that it is a co-control operator? Answering these questions leads to the interpretation that sequent calculus is a formal vector notation with first-class co-control. But this is just the "internal" interpretation, which has to be developed simultaneously with, and is justified by, an "external" one, offered by natural deduction: the sequent calculus corresponds to a bi-directional, agnostic (w.r.t. the call strategy), computational lambda-calculus. Next, the duality between control and co-control is studied and proved in the context of classical logic, where one discovers that the classical sequent calculus has a distortion towards control, and that sequent calculus is the de Morgan dual of natural deduction.

Expression of histone methyltransferases as novel biomarkers for renal cell tumor diagnosis and prognostication

Renal cell tumors (RCTs) are the most lethal of the common urological cancers. The widespread use of imaging entailed an increased detection of small renal masses, emphasizing the need for accurate distinction between benign and malignant RCTs, which is critical for adequate therapeutic management. Histone methylation has been implicated in renal tumorigenesis, but its potential clinical value as RCT biomarker remains mostly unexplored. Hence, the main goal of this study was to identify differentially expressed histone methyltransferases (HMTs) and histone demethylases (HDMs) that might prove useful for RCT diagnosis and prognostication, emphasizing the discrimination between oncocytoma (a benign tumor) and renal cell carcinoma (RCC), especially the chromophobe subtype (chRCC). We found that the expression levels of three genes-SMYD2, SETD3, and NO66-was significantly altered in a set of RCTs, which was further validated in a large independent cohort. Higher expression levels were found in RCTs compared to normal renal tissues (RNTs) and in chRCCs comparatively to oncocytomas. SMYD2 and SETD3 mRNA levels correlated with protein expression assessed by immunohistochemistry. SMYD2 transcript levels discriminated RCTs from RNT, with 82.1% sensitivity and 100% specificity (AUC=0.959), and distinguished chRCCs from oncocytomas, with 71.0% sensitivity and 73.3% specificity (AUC: 0.784). Low expression levels of SMYD2, SETD3, and NO66 were significantly associated with shorter disease-specific and disease-free survival, especially in patients with non-organ confined tumors. We conclude that expression of selected HMTs and HDMs might constitute novel biomarkers to assist in RCT diagnosis and assessment of tumor aggressiveness.