Are there Hilbert-style Pure Type Systems?

For many a natural deduction style logic there is a Hilbert-style logic that is equivalent to it in that it has the same theorems (i.e. valid judgements with empty contexts). For intuitionistic logic, the axioms of the equivalent Hilbert-style logic can be propositions which are also known as the types of the combinators I, K and S. Hilbert-style versions of illative combinatory logic have formulations with axioms that are actual type statements for I, K and S. As pure type systems (PTSs)are, in a sense, equivalent to systems of illative combinatory logic, it might be thought that Hilbert-style PTSs (HPTSs) could be based in a similar way. This paper shows that some PTSs have very trivial equivalent HPTSs, with only the axioms as theorems and that for many PTSs no equivalent HPTS can exist. Most commonly used PTSs belong to these two classes. For some PTSs however, including lambda* and the PTS at the basis of the proof assistant Coq, there is a nontrivial equivalent HPTS, with axioms that are type statements for I, K and S.Comment: Accepted in Logical Methods in Computer Scienc

Geïntegreerde akkerbouw: vooral lagere milieubelasting

In samenspraak met een klankbordgroep van akkerbouwers in het noordelijk kleigebied berekende PPO voor verschillende bedrijfstypen (graan; pootaardappelen; consumptieaardappelen) de bedrijfseconomische en milieutechnische resultaten van een geïntegreerde bedrijfsvoering in vergelijking met de gangbare bedrijfsvoering. De verschillen betreffen vooral bemesting, gewasbescherming, arbeidsbehoefte en gewasopbrengsten. In tabellen de kosten en opbrengsten, de mineralenbalansen (overschotten voor N, P2O5 en K2O), en de milieuscores (milieubelastingpunten, MBP; blootstellingsrisicoindex, BRI; inzet van actieve stof

Sodium-glucose cotransporter 2 inhibitors:extending the indication to non-diabetic kidney disease?

This year the medical community was pleasantly surprised by the results of the first large outcome trial that primarily examined the renal effects of the sodium-glucose cotransporter 2 (SGLT2) inhibitor canagliflozin (CANA) in subjects with diabetes and impaired kidney function. The Evaluation of the Effects of Canagliflozin on Renal and Cardiovascular Outcomes in Participants With Diabetic Nephropathy (CREDENCE) trial showed that CANA, relative to placebo, reduces the risk for end-stage renal disease, doubling of creatinine or renal death by 34% [hazard ratio 0.66 (95% confidence interval 0.53-0.81]. These effects were consistent across baseline estimated glomerular filtration rate (eGFR) and haemoglobin A1c subgroups. In this review we combine the results of the CREDENCE trial with those of several cardiovascular outcome trials with SGLT2 inhibitors and show that, unexpectedly, patients with lower eGFR levels may have greater benefit with respect to cardiovascular outcome than patients with normal kidney function. The cardio- and renoprotective effects of SGLT2 inhibitors seem to be independent of their glucose-lowering effects, as shown in several post hoc analyses. In this review we discuss the alleged mechanisms of action that explain the beneficial effects of this novel class of drugs. Moreover, we discuss whether these findings indicate that this class of drugs may also be beneficial in non-diabetic chronic kidney diseases

Admixtures to d-wave gap symmetry in untwinned YBa2Cu3O7 superconducting films measured by angle-resolved electron tunneling

We report on an \textit{ab}-anisotropy of $J_{c \parallel b}/J_{c \parallel a}$ and $I_{c}R_{n \parallel b}/I_{c}R_{n \parallel a}\cong 1.2$ in ramp-edge junctions between untwinned YBa$_{2}$Cu$_{3}$O$_{7}$ and $s$% -wave Nb. For these junctions, the angle $\theta$ with the YBa$_{2}$Cu$_{3}$O$_{7}$ crystal b-axis is varied as a single parameter. The $R_{n}$A($\theta$)-dependence presents 2-fold symmetry. The minima in $I_{c}R_{n}$ at $\theta \cong 50^{\circ}$ suggest a real s-wave subdominant component and negligible $d_{xy}$-wave or imaginary s-wave admixtures. The $I_{c}R_{n}$($\theta$)-dependence is well-fitted by 83% $d_{x^{2}-y^{2}}$-, 15% isotropic $s$- and 2% anisotropic s-wave order parameter symmetry, consistent with $\Delta_{b}/\Delta_{a} \cong 1.5$.Comment: 4 pages, 3 figures, to be published in Physical Review Letter

Selection for Lean Growth Rate in a Synthetic Line of YorkshireMeishan Pigs 1. Selection Pressure Applied and Direct Response

Selection for lean growth rate (LGR) was conducted for four generations in a synthetic line of YorkshireMeishan pigs. In the select line, seven boars and 20 gilts with the highest LGR were selected from each generation to produce the subsequent generation. A contemporaneous control line was maintained by randomly selecting five boars and 15 gilts to produce the next generation. Inbreeding coefficients averaged .198 and .207 for the select and control line pigs and .173 and .162 for the select and control line dams, respectively, in the fourth generation. LGR was estimated from ultrasound measures of 10 th -rib backfat thickness and longissimus muscle area from 1,057 pigs. These pigs were sired by 58 boars and out of 133 sows. The generation interval was 13 months and the average selection differential per generation was 1.1 phenotypic standard deviation units for LGR. Heritability and response were estimated from the deviation of select line from the control line and multiple trait derivative free restricted maximum likelihood (MTDFREML) on the same material. Realized heritability was .29 ± .12 for LGR in the control line. Corresponding estimates from MTDFREML were .32 and .37. The estimate of direct genetic change per generation using the deviation from the control line was 9.4 g/day for LGR. Corresponding estimates from MTDFREML were similar but were more precisely estimated