Ultrafilter spaces on the semilattice of partitions

The Stone-Cech compactification of the natural numbers bN, or equivalently, the space of ultrafilters on the subsets of omega, is a well-studied space with interesting properties. If one replaces the subsets of omega by partitions of omega, one can define corresponding, non-homeomorphic spaces of partition ultrafilters. It will be shown that these spaces still have some of the nice properties of bN, even though none is homeomorphic to bN. Further, in a particular space, the minimal height of a tree pi-base and P-points are investigated

Techniques for approaching the dual Ramsey property in the projective hierarchy

We define the dualizations of objects and concepts which are essential for investigating the Ramsey property in the first levels of the projective hierarchy, prove a forcing equivalence theorem for dual Mathias forcing and dual Laver forcing, and show that the Harrington-Kechris techniques for proving the Ramsey property from determinacy work in the dualized case as well

The modal logic of forcing

What are the most general principles in set theory relating forceability and truth? As with Solovay's celebrated analysis of provability, both this question and its answer are naturally formulated with modal logic. We aim to do for forceability what Solovay did for provability. A set theoretical assertion psi is forceable or possible, if psi holds in some forcing extension, and necessary, if psi holds in all forcing extensions. In this forcing interpretation of modal logic, we establish that if ZFC is consistent, then the ZFC-provable principles of forcing are exactly those in the modal theory known as S4.2.Comment: 31 page

Computation and Logic in the Real World

The proceedings contain 78 papers. The topics discussed include: shifting and lifting of cellular automata; learning as data compression; a classification of viruses through recursion theorems; characterizing programming systems allowing program self-reference; thin maximal antichains in the turing degrees; effective computation for nonlinear systems; time-complexity semantics for feasible affine recursions; feasible depth; a continuous derivative for real-valued functions; refocusing generalised normalisation; parameterized complexity and logic; index sets of computable structures with decidable theories; operational semantics for positive relevant logics without distribution; unique existence and computability in constructive reverse mathematics; circuit complexity of regular language; definability in the homomorphic quasiorder of finite labeled forests; and membrane systems and their application to systems biology

Obtaining Reliable RT-qPCR Results in Molecular Diagnostics—MIQE Goals and Pitfalls for Transcriptional Biomarker Discovery

In this review, we discuss the development pipeline for transcriptional biomarkers in molecular diagnostics and stress the importance of a reliable gene transcript quantification strategy. Hence, a further focus is put on the MIQE guidelines and how to adapt them for biomarker discovery, from signature validation up to routine diagnostic applications. First, the advantages and pitfalls of the holistic RNA sequencing for biomarker development will be described to establish a candidate biomarker signature. Sequentially, the RT-qPCR confirmation process will be discussed to validate the discovered biomarker signature. Examples for the successful application of RT-qPCR as a fast and reproducible quantification method in routinemolecular diagnostics are provided. Based on the MIQE guidelines, the importance of “key steps” in RT-qPCR is accurately described, e.g., reverse transcription, proper reference gene selection and, finally, the application of automated RT-qPCR data analysis software. In conclusion, RT-qPCR proves to be a valuable tool in the establishment of a disease-specific transcriptional biomarker signature and will have a great future in molecular diagnostics or personalized medicine