Effective guessing has unlikely consequences

Funding: EPSRC Grant number EP/P015638/1.A classic result of Paul, Pippenger, Szemeredi and Trotter states that DTIME(n) ⊊ NTIME(n). The natural question then arises: could the inclusion DTIME(t (n)) ⊆ NTIME(n) hold for some superlinear time-constructible function t (n)? If such a function t (n) does exist, then there also exist effective nondeterministic guessing strategies to speed up deterministic computations. In this work, we prove limitations on the effectiveness of nondeterministic guessing to speed up deterministic computations by showing that the existence of effective nondeterministic guessing strategies would have unlikely consequences. In particular, we show that if a subpolynomial amount of nondeterministic guessing could be used to speed up deterministic computation by a polynomial factor, then P ⊊ NTIME(n). Furthermore, even achieving a logarithmic speedup at the cost of making every step nondeterministic would show that SAT ∈ NTIME(n) under appropriate encodings. Of possibly independent interest, under such encodings we also show that SAT can be decided in O(n log n) steps on a nondeterministic multitape Turing machine, improving on the well-known O(n(log n)c) bound for some constant but undetermined exponent c ≥ 1.Publisher PDFPeer reviewe

Superlinear lower bounds based on ETH

Andras Z. Salamon acknowledges support from EPSRC grants EP/P015638/1 and EP/V027182/1.We introduce techniques for proving superlinear conditional lower bounds for polynomial time problems. In particular, we show that CircuitSAT for circuits with m gates and log(m) inputs (denoted by log-CircuitSAT) is not decidable in essentially-linear time unless the exponential time hypothesis (ETH) is false and k-Clique is decidable in essentially-linear time in terms of the graph's size for all fixed k. Such conditional lower bounds have previously only been demonstrated relative to the strong exponential time hypothesis (SETH). Our results therefore offer significant progress towards proving unconditional s uperlinear time complexity lower bounds for natural problems in polynomial time.Postprin

FARS2 mutations presenting with pure spastic paraplegia and lesions of the dentate nuclei.

Mutations in FARS2, the gene encoding the mitochondrial phenylalanine-tRNA synthetase (mtPheRS), have been linked to a range of phenotypes including epileptic encephalopathy, developmental delay, and motor dysfunction. We report a 9-year-old boy with novel compound heterozygous variants of FARS2, presenting with a pure spastic paraplegia syndrome associated with bilateral signal abnormalities in the dentate nuclei. Exome sequencing identified a paternal nonsense variant (Q216X) lacking the catalytic core and anticodon-binding regions, and a maternal missense variant (P136H) possessing partial enzymatic activity. This case confirms and expands the phenotype related to FARS2 mutations with regards to clinical presentation and neuroimaging findings

Potentials of a Harmonised Database for Agricultural Market Modelling

The study analysed existing databases for agricultural market data on errors and discrepancies and to elaborate the possibilities to harmonise datasets for policy modelling. The study supports DG AGRI in improving quality and timely availability of data for market modelling and ensuring that data from different sources are consistent. This study aims to provide a structure for a consolidated database for policy modelling which does not alter existing databases. Within this report, existing databases are analysed to derive key insights for setting-up a harmonised metabase. As available databases comprise statistical databases as well as scientific model databases, both groups are studied. For the purpose of this study, statistical databases are defined as providers of the information that international institutes receive from their reporters, while the reporters are required to provide harmonised, complete, consistent, and where possible, timely data series for establishing models or other quantitative methods. Nevertheless, a statistical database can also serve as a model database, such as e.g. PS&D. Statistical databases from international institutions (FAO, USDA, Eurostat), as well as model databases (AGLINK/COSIMO, AGMEMOD, CAPRI/CAPSIM, ESIM, FAPRI, GTAP, FARM, IMPACT), were studied to find ways of consolidating data and providing insights that allow for a better comparison of model results. For this reason, various classification schemes used in agricultural statistics were reviewed (country, product, balance item, year, unit), as was the manner in which the different modelling groups have dealt with these classifications in their databases. Besides a common classification, a harmonised database for market modelling purposes will require further efforts to be applied to a consolidation effort for the original data. Such a procedure must be supplemented by methods dealing with completion and balancing.JRC.J.5-Agriculture and Life Sciences in the Econom

Influence of Morphological Changes in a Source Material on the Growth Interface of 4H-SiC Single Crystals

In this study, the change of mass distribution in a source material is tracked using an in situ computer tomography (CT) setup during the bulk growth of 4H- silicon carbide (SiC) via physical vapor depostion (PVT). The changing properties of the source material due to recrystallization and densification are evaluated. Laser flash measurement showed that the thermal properties of different regions of the source material change significantly before and after the growth run. The Si-depleted area at the bottom of the crucible is thermally insulating, while the residual SiC source showed increased thermal conductivity compared to the initially charged powder. Ex situ CT measurements revealed a needle-like structure with elongated pores causing anisotropic behavior for the heat conductivity. Models to assess the thermal conductivity are applied in order to calculate the changes in the temperature field in the crucible and the changes in growth kinetics are discussed

Residual Tumor Confers a 10-Fold Increased Risk of Regrowth in Clinically Nonfunctioning Pituitary Tumors.

ObjectiveWe evaluated tumor recurrence and regrowth rates following endoscopic transnasal transsphenoidal (TNTS) surgical removal in a consecutive series of clinically nonfunctioning pituitary adenomas (CNFTs).DesignRetrospective chart review of clinical, biochemical, and sellar MRI findings in all TNTS surgeries in patients with CNFT, performed by a single surgeon, between 2008 and 2015 (n = 280).PatientsNinety-three patients met eligibility criteria, with complete clinical, biochemical, and imaging follow-up for a 3-year minimum.ResultsOf 85 patients who were not irradiated, 3-month postsurgical MRI demonstrated no residual tumor in 58 of 85 (68.2%), equivocal findings in 12 of 85 (14.1%), and definite residual tumor in 15 of 85 (17.6%) patients. Six of 85 (7.1%) demonstrated tumor regrowth by 3 years, and 2 further patients demonstrated true tumor recurrence at 3 and 6 years after surgery, respectively, for a total recurrence rate of 9.4% (8 of 85). Eight of the 93 patients were irradiated between 3 months and 4 years after pituitary surgery. In 3 patients with tumor regrowth, 2 exhibited residual tumor and 1 had no residual findings at the 3-month postoperative imaging. Overall, Ki-67 labeling index or Knosp grading did not predict recurrence.ConclusionTumor recurrence at 3 years was low (1 of 58; 1.7%) if the 3-month postoperative MRI showed no residual tumor. The findings support a less frequent imaging schedule for this group. Patients with definite residual tumor visible at 3 months harbor the greatest risk for tumor growth, but regrowth does not occur in all patients (6 of 15; 40%)

Quaternionic structures

Any oriented 4-dimensional real vector bundle is naturally a line bundle over a bundle of quaternion algebras. In this paper we give an account of modules over bundles of quaternion algebras, discussing Morita equivalence, characteristic classes and K-theory. The results have been used to describe obstructions for the existence of almost quaternionic structures on 8-dimensional Spinc manifolds and may be of some interest, also, in quaternionic and algebraic geometry.Comment: 19 page