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

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

Bayesian Methods for Genomic Prediction and Genome-Wide Association Studies combining Information on Genotyped and Non-Genotyped Individuals

Genomic prediction involves using high-density marker genotypes to characterize the impact on performance of every region of the genome, and using that information to predict performance of genotyped selection candidates. This is a relatively new technology and is now gaining traction in personalized medicine and in various livestock industries. Our new approach promises to overcome serious limitations with existing techniques for genomic prediction

On the Optical Activity of Steroidal 5,7-Dienes

Circular dichroism (CD) data are reported of a series of 9,10- stereoisomeric steroidal 5,7-dienes. In general the effects in the longest wavelength transition (270-280 nm) are large (Mm" 10---30) and consignate with respect to the diene helicity rule. The magnitude of the CD appears to vary markedly with the substituent at C-3 and at C-17, and with solvent. In the case of the 9a,10p-H dienes, variation of solvent and temperature can affect even the sign of the Cotton effect. This is explained from a change of geometry of the diene ring: solvation, substitution and temperature can affect the average geometry of the ring including the values of the angle of twist of the diene (ef> (6-7». The relevance of the observed chiroptical data for the theoretical description of the optical activity in the So-+ Sl transition of homoannular cisoid dienes is discussed

'Unbearable suffering': a qualitative study on the perspectives of patients who request assistance in dying

BACKGROUND One of the objectives of medicine is to relieve patients' suffering. As a consequence, it is important to understand patients' perspectives of suffering and their ability to cope. However, there is poor insight into what determines their suffering and their ability to bear it. PURPOSE To explore the constituent elements of suffering of patients who explicitly request euthanasia or physician-assisted suicide (EAS) and to better understand unbearable suffering from the patients' perspective. PATIENTS AND METHODS A qualitative study using in-depth face-to-face interviews was conducted with 31 patients who had requested EAS. The grounded theory approach was used to analyse the data. RESULTS Medical, psycho-emotional, socio-environmental and existential themes contributed to suffering. Especially fatigue, pain, decline, negative feelings, loss of self, fear of future suffering, dependency, loss of autonomy, being worn out, being a burden, loneliness, loss of all that makes life worth living, hopelessness, pointlessness and being tired of living were constituent elements of unbearable suffering. Only patients with a psychiatric (co)diagnosis suffered unbearably all the time. CONCLUSIONS Unbearable suffering is the outcome of an intensive process that originates in the symptoms of illness and/or ageing. According to patients, hopelessness is an essential element of unbearable suffering. Medical and social elements may cause suffering, but especially when accompanied by psycho-emotional and existential problems suffering will become 'unbearable'. Personality characteristics and biographical aspects greatly influence the burden of suffering. Unbearable suffering can only be understood in the continuum of the patients' perspectives of the past, the present and expectations of the future.This study was supported by the Dutch Cancer Society (grant number KUN2007-03736)

How to assess the external validity of therapeutic trials: a conceptual approach

Background External validity of study results is an important issue from a clinical point of view. From a methodological point of view, however, the concept of external validity is more complex than it seems to be at first glance. Methods Methodological review to address the concept of external validity. Results External validity refers to the question whether results are generalizable to persons other than the population in the original study. The only formal way to establish the external validity would be to repeat the study for that specific target population. We propose a three-way approach for assessing the external validity for specified target populations. (i) The study population might not be representative for the eligibility criteria that were intended. It should be addressed whether the study population differs from the intended source population with respect to characteristics that influence outcome. (ii) The target population will, by definition, differ from the study population with respect to geographical, temporal and ethnical conditions. Pondering external validity means asking the question whether these differences may influence study results. (iii) It should be assessed whether the study's conclusions can be generalized to target populations that do not meet all the eligibility criteria. Conclusion Judging the external validity of study results cannot be done by applying given eligibility criteria to a single target population. Rather, it is a complex reflection in which prior knowledge, statistical considerations, biological plausibility and eligibility criteria all have plac

Improved Accuracy of Genomic Prediction for Traits with Rare QTL by Fitting Haplotypes

Genomic prediction estimates breeding values by exploiting linkage disequilibrium (LD) between quantitative trait loci (QTL) and single nucleotide polymorphisms (SNPs). High LD cannot occur when QTL and SNPs have different minor allele frequencies (MAF). Marker panels tend to use SNPs with high MAF and will have limited ability to predict rare QTL alleles. In practice, increasing SNP density has not improved prediction accuracy. A possible reason is that many traits are characterized by rare QTL. In that case, linear models fitting haplotypes could have advantage because haplotypes can be in complete LD with QTL alleles. SNP genotypes were simulated to resemble 600K chip for the bovine genome. Genomic breeding values were predicted using either SNP genotypes or non-overlapping haplotypes. When QTL had low MAF, the haplotype model had significantly higher accuracy than the SNP model. Results show that fitting haplotypes can improve the accuracy of genomic prediction for traits controlled by rare QTL

Recognising and defining a new crown clade within Stromboidea Rafinesque, 1815 (Mollusca, Gastropoda)

This paper defines a new crown clade Neostromboidea to separate the Strombidae, Rostellariidae, and Seraphsidae from their sister families Struthiolariidae and Aporrhaidae. There is significant value to understanding evolutionary processes within Stromboidea to recognise the universal similarity in the position of the eye on the end of peduncles and a diminished cephalic tentacle that arises from the middle to the end on that peduncle. This is in contrast to other members of the Stromboidea where the eye is located at the base of the cephalic tentacle. These physiological differences represent two set of organisms with divergent and independent evolutionary life histories and therefore these differences need to be identifiable within the nomenclature to bring meaning to the way we name things