Poincaré on the Foundation of Geometry in the Understanding

This paper is about Poincaré’s view of the foundations of geometry. According to the established view, which has been inherited from the logical positivists, Poincaré, like Hilbert, held that axioms in geometry are schemata that provide implicit definitions of geometric terms, a view he expresses by stating that the axioms of geometry are “definitions in disguise.” I argue that this view does not accord well with Poincaré’s core commitment in the philosophy of geometry: the view that geometry is the study of groups of operations. In place of the established view I offer a revised view, according to which Poincaré held that axioms in geometry are in fact assertions about invariants of groups. Groups, as forms of the understanding, are prior in conception to the objects of geometry and afford the proper definition of those objects, according to Poincaré. Poincaré’s view therefore contrasts sharply with Kant’s foundation of geometry in a unique form of sensibility. According to my interpretation, axioms are not definitions in disguise because they themselves implicitly define their terms, but rather because they disguise the definitions which imply them

ESR1 amplification is rare in breast cancer and is associated with high grade and high proliferation: a multiplex ligation-dependent probe amplification study

Background: Expression of estrogen receptor alpha (ERα) is predictive for endocrine therapy response and an important prognostic factor in breast cancer. Overexpression of ERα can be caused by estrogen receptor 1 (ESR1) gene amplification and was originally reported to be a frequent event associated with a significantly longer survival for ER-positive women treated with adjuvant tamoxifen monotherapy, which was however questioned by subsequent studies

The good, the bad and the ugly

This paper discusses the neo-logicist approach to the foundations of mathematics by highlighting an issue that arises from looking at the Bad Company objection from an epistemological perspective. For the most part, our issue is independent of the details of any resolution of the Bad Company objection and, as we will show, it concerns other foundational approaches in the philosophy of mathematics. In the first two sections, we give a brief overview of the "Scottish" neo-logicist school, present a generic form of the Bad Company objection and introduce an epistemic issue connected to this general problem that will be the focus of the rest of the paper. In the third section, we present an alternative approach within philosophy of mathematics, a view that emerges from Hilbert's Grundlagen der Geometrie (1899, Leipzig: Teubner; Foundations of geometry (trans.: Townsend, E.). La Salle, Illinois: Open Court, 1959.). We will argue that Bad Company-style worries, and our concomitant epistemic issue, also affects this conception and other foundationalist approaches. In the following sections, we then offer various ways to address our epistemic concern, arguing, in the end, that none resolves the issue. The final section offers our own resolution which, however, runs against the foundationalist spirit of the Scottish neo-logicist program

High resolution analysis of DNA copy-number aberrations of chromosomes 8, 13, and 20 in gastric cancers

DNA copy-number gains of chromosomes 8q, 13q, and 20q are frequently observed in gastric cancers. Moreover gain of chromosome 20q has been associated with lymph node metastasis. The aim of this study was to correlate DNA copy-number changes of individual genes on chromosomes 8q, 13q, and 20q in gastric adenocarcinomas to clinicopathological data. DNA isolated from 63 formalin-fixed and paraffin-embedded gastric adenocarcinoma tissue samples was analyzed by whole-genome microarray comparative genomic hybridization and by multiplex ligation-dependent probe amplification (MLPA), targeting 58 individual genes on chromosomes 8, 13, and 20. Using array comparative genomic hybridization, gains on 8q, 13q, and 20q were observed in 49 (77.8%), 25 (39.7%), and 49 (77.8%) gastric adenocarcinomas, respectively. Gain of chromosome 20q was significantly correlated with lymph node metastases (p = 0.05) and histological type (p = 0.02). MLPA revealed several genes to be frequently gained in DNA copy number. The oncogene c-myc on 8q was gained in 73% of the cancers, while FOXO1A and ATP7B on 13q were both gained in 28.6% of the cases. Multiple genes on chromosome 20q showed gains in more than 60% of the cancers. DNA copy-number gains of TNFRSF6B (20q13.3) and ZNF217 (20q13.2) were significantly associated with lymph node metastasis (p = 0.02) and histological type (p = 0.02), respectively. In summary, gains of chromosomes 8q, 13q, and 20q in gastric adenocarcinomas harbor DNA copy-number gains of known and putative oncogenes. ZNF217 and TNFRSF6B are associated with important clinicopathological variables, including lymph node status

Electrical Control of Optical Emitter Relaxation Pathways enabled by Graphene

Controlling the energy flow processes and the associated energy relaxation rates of a light emitter is of high fundamental interest, and has many applications in the fields of quantum optics, photovoltaics, photodetection, biosensing and light emission. While advanced dielectric and metallic systems have been developed to tailor the interaction between an emitter and its environment, active control of the energy flow has remained challenging. Here, we demonstrate in-situ electrical control of the relaxation pathways of excited erbium ions, which emit light at the technologically relevant telecommunication wavelength of 1.5 $\mu$m. By placing the erbium at a few nanometres distance from graphene, we modify the relaxation rate by more than a factor of three, and control whether the emitter decays into either electron-hole pairs, emitted photons or graphene near-infrared plasmons, confined to $<$15 nm to the sheet. These capabilities to dictate optical energy transfer processes through electrical control of the local density of optical states constitute a new paradigm for active (quantum) photonics.Comment: 9 pages, 4 figure