Mathematicians and physicists have long wondered why the Octionic Projective Plane (OP2), the Freudenthal – Tits Magic Square, or Magic Triangle and certain functions of the Octonions and Sedenions abruptly end. This paper lays out the various elements included in this conundra, with the assumption that irregularities and undiscovered relationships between these structures account for the anoma...

There are several locations within the paper that refer to the incorrect Supporting Information file. The locations of the errors and the correct Supporting Information files are as follows: In the Results and Discussion section, the eighth sentence of the first paragraph under the subheading “Tyramine, octopamine and dopamine evoke complex direct-currents (ID) in OA/TAMac injected oocytes” sho...

The carboxy-terminal domain (CTD) of RNA polymerase II (Pol II) consists of heptad repeats with the consensus motif Y1-S2-P3-T4-S5-P6-S7. Dynamic phosphorylation of the CTD coordinates Pol II progression through the transcription cycle. Here, we use genetic and mass spectrometric approaches to directly detect and map phosphosites along the entire CTD. We confirm phosphorylation of CTD residues ...

I. Supplementary methods and results ........................................................................S1 II. Supplementary figures (5) .......................................................................................S7 III. Supplementary tables (5)........................................................................................S12 IV. Supplementary notes (literature cited) ....

S1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 S2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 S3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 S4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 S5 . ...

INTRODUCTION Hormone receptor (HR)-positive metastatic breast cancer (MBC) is usually treated with hormone therapy. In postmenopausal females, aromatase inhibitors (AIs) are usually used as first-line therapy, and fulvestrant is used subsequently. The optimal treatment beyond fulvestrant has not been established. We experienced two cases in which high-dose toremifene (hdTOR) was effective after...

We show that in a finite semimodular lattice, the ordering of joinirreducible congruences is done in a special type of sublattice, we call a tight S7.