The Parametric Ordinal-Recursive Complexity of Post Embedding Problems

Post Embedding Problems are a family of decision problems based on the interaction of a rational relation with the subword embedding ordering, and are used in the literature to prove non multiply-recursive complexity lower bounds. We refine the construction of Chambart and Schnoebelen (LICS 2008) and prove parametric lower bounds depending on the size of the alphabet.Comment: 16 + vii page

Observations of the low-mode internal tide and its interaction with mesoscale flow south of the Azores

Understanding the temporal variability of internal tides plays a crucial role in identifying sources and sinks of energy in the ocean. Using a 10-month-long time series from moored instruments inside a tidal beam south of the Azores, the magnitude and the underlying causes of temporal variability in the first two modes of the internal tide energy flux was studied. We analyzed changes of the direction and coherence of the energy flux, its modal structure, and the impact of two eddies. Semidiurnal energy fluxes were further compared with estimates from a 1/10° ocean global circulation model, as well as with fluxes derived from satellite altimetry. All energy fluxes correlate reasonably well in direction, deviations from its fixed phase relation to astronomical forcing, and modal composition while model and satellite underestimate the total energy flux. A pronounced damping of the in situ fluxes coincides with the passing of two eddies. In the presence of a surface-intensified eddy, the coherent part of the energy flux in the first two modes is lowered by more than 40, a subsurface eddy coincides with a decrease of the energy flux mainly in the second mode. These observations support the hypothesis that eddy interactions increase the incoherent part of the energy flux and transfer energy from low modes into higher modes, which can lead to increased local dissipation. It remains an open question how much of the energy converted from lower to higher modes results in local dissipation, a crucial part in creating energetically consistent ocean-climate models. © 2020. The Authors

Impact of Borderline Resectability in Pancreatic Head Cancer on Patient Survival: Biology Matters According to the New International Consensus Criteria

Background: International consensus criteria (ICC) have redefined borderline resectability for pancreatic ductal adenocarcinoma (PDAC) according to three dimensions: anatomical (BR-A), biological (BR-B), and conditional (BR-C). The present definition acknowledges that resectability is not just about the anatomic relationship between the tumour and vessels but that biological and conditional dimensions also are important. Methods: Patients’ tumours were retrospectively defined b

A formally verified abstract account of Gödel's incompleteness theorems

We present an abstract development of Gödel’s incompleteness theorems, performed with the help of the Isabelle/HOL theorem prover. We analyze sufficient conditions for the theorems’ applicability to a partially specified logic. In addition to the usual benefits of generality, our abstract perspective enables a comparison between alternative approaches from the literature. These include Rosser’s variation of the first theorem, Jeroslow’s variation of the second theorem, and the S ́wierczkowski–Paulson semantics-based approach. As part of our framework’s validation, we upgrade Paulson’s Isabelle proof to produce a mech- anization of the second theorem that does not assume soundness in the standard model, and in fact does not rely on any notion of model or semantic interpretation