POPLMark reloaded: Mechanizing proofs by logical relations

We propose a new collection of benchmark problems in mechanizing the metatheory of programming languages, in order to compare and push the state of the art of proof assistants. In particular, we focus on proofs using logical relations (LRs) and propose establishing strong normalization of a simply typed calculus with a proof by Kripke-style LRs as a benchmark. We give a modern view of this well-understood problem by formulating our LR on well-typed terms. Using this case study, we share some of the lessons learned tackling this problem in different dependently typed proof environments. In particular, we consider the mechanization in Beluga, a proof environment that supports higher-order abstract syntax encodings and contrast it to the development and strategies used in general-purpose proof assistants such as Coq and Agda. The goal of this paper is to engage the community in discussions on what support in proof environments is needed to truly bring mechanized metatheory to the masses and engage said community in the crafting of future benchmarks

First Physics Results at the Physical Pion Mass from Nf=2N_f = 2 Wilson Twisted Mass Fermions at Maximal Twist

We present physics results from simulations of QCD using $N_f = 2$ dynamical Wilson twisted mass fermions at the physical value of the pion mass. These simulations were enabled by the addition of the clover term to the twisted mass quark action. We show evidence that compared to previous simulations without this term, the pion mass splitting due to isospin breaking is almost completely eliminated. Using this new action, we compute the masses and decay constants of pseudoscalar mesons involving the dynamical up and down as well as valence strange and charm quarks at one value of the lattice spacing, $a \approx 0.09$ fm. Further, we determine renormalized quark masses as well as their scale-independent ratios, in excellent agreement with other lattice determinations in the continuum limit. In the baryon sector, we show that the nucleon mass is compatible with its physical value and that the masses of the $\Delta$ baryons do not show any sign of isospin breaking. Finally, we compute the electron, muon and tau lepton anomalous magnetic moments and show the results to be consistent with extrapolations of older ETMC data to the continuum and physical pion mass limits. We mostly find remarkably good agreement with phenomenology, even though we cannot take the continuum and thermodynamic limits.Comment: 45 pages, 15 figure

Collective modes in the charge-density wave state of K0.3_{0.3}MoO3_3: The role of long-range Coulomb interactions revisited

We re-examine the effect of long-range Coulomb interactions on the collective amplitude and phase modes in the incommensurate charge-density wave ground state of quasi-one-dimensional conductors. Using an effective action approach we show that the longitudinal acoustic phonon protects the gapless linear dispersion of the lowest phase mode in the presence of long-range Coulomb interactions. Moreover, in Gaussian approximation amplitude fluctuations are not affected by long-range Coulomb interactions. We also calculate the collective mode dispersions at finite temperatures and compare our results with the measured energies of amplitude and phase modes in K$_{0.3}$MoO$_3$. With the exception of the lowest phase mode, the temperature dependence of the measured mode energies can be quantitatively described within a multi-phonon Fr\"{o}hlich model neglecting long-range Coulomb interactions

An Improved Implementation and Abstract Interface for Hybrid

Hybrid is a formal theory implemented in Isabelle/HOL that provides an interface for representing and reasoning about object languages using higher-order abstract syntax (HOAS). This interface is built around an HOAS variable-binding operator that is constructed definitionally from a de Bruijn index representation. In this paper we make a variety of improvements to Hybrid, culminating in an abstract interface that on one hand makes Hybrid a more mathematically satisfactory theory, and on the other hand has important practical benefits. We start with a modification of Hybrid's type of terms that better hides its implementation in terms of de Bruijn indices, by excluding at the type level terms with dangling indices. We present an improved set of definitions, and a series of new lemmas that provide a complete characterization of Hybrid's primitives in terms of properties stated at the HOAS level. Benefits of this new package include a new proof of adequacy and improvements to reasoning about object logics. Such proofs are carried out at the higher level with no involvement of the lower level de Bruijn syntax.Comment: In Proceedings LFMTP 2011, arXiv:1110.668

Zero-voltage conductance peak from weak antilocalization in a Majorana nanowire

We show that weak antilocalization by disorder competes with resonant Andreev reflection from a Majorana zero-mode to produce a zero-voltage conductance peak of order e^2/h in a superconducting nanowire. The phase conjugation needed for quantum interference to survive a disorder average is provided by particle-hole symmetry - in the absence of time-reversal symmetry and without requiring a topologically nontrivial phase. We identify methods to distinguish the Majorana resonance from the weak antilocalization effect.Comment: 13 pages, 8 figures. Addendum, February 2014: Appendix B shows results for weak antilocalization in the circular ensemble. (This appendix is not in the published version.

Effective Theory and Breakdown of Conformal Symmetry in a Long-Range Quantum Chain

We deal with the problem of studying the symmetries and the effective theories of long-range models around their critical points. A prominent issue is to determine whether they possess (or not) conformal symmetry (CS) at criticality and how the presence of CS depends on the range of the interactions. To have a model, both simple to treat and interesting, where to investigate these questions, we focus on the Kitaev chain with long-range pairings decaying with distance as power-law with exponent alpha. This is a quadratic solvable model, yet displaying non-trivial quantum phase transitions. Two critical lines are found, occurring respectively at a positive and a negative chemical potential. Focusing first on the critical line at positive chemical potential, by means of a renormalization group approach we derive its effective theory close to criticality. Our main result is that the effective action is the sum of two terms: a Dirac action S-D, found in the short-range Ising universality class, and an "anomalous" CS breaking term SAN. While SD originates from low-energy excitations in the spectrum, SAN originates from the higher energy modes where singularities develop, due to the long-range nature of the model. At criticality SAN flows to zero for alpha > 2, while for alpha infinity the ELI is restored. In order to test the validity of the determined effective theory, we compared the two-fermion static correlation functions and the von Neumann entropy obtained from them with the ones calculated on the lattice, finding agreement. These results explain two observed features characteristic of long-range models, the hybrid decay of static correlation functions within gapped phases and the area-law violation for the von Neumann entropy. The proposed scenario is expected to hold in other long-range models displaying quasiparticle excitations in ballistic regime. From the effective theory one can also see that new phases emerge for alpha infinity) model, are not altered. This also shows that the long-range paired Kitaev chain provides an example of a long-range model in which the value of a where the CS is broken does not coincide with the value at which the critical exponents start to differ from the ones of the corresponding short-range model. At variance, for the second critical line, having negative chemical potential, only SAN (So) is present for 1 2). Close to this line, where the minimum of the spectrum coincides with the momentum where singularities develop, the critical exponents change where CS is broken. \ua9 2016 Elsevier Inc

Association of polymorphisms in CYP19A1 and CYP3A4 genes with lower urinary tract symptoms, prostate volume, uroflow and PSA in a population-based sample

PURPOSE: The known importance of testosterone for the development of benign prostatic hyperplasia (BPH) prompted us to test the hypothesis whether polymorphisms of two genes (CYP19A1 and CYP3A4) involved in testosterone metabolism are associated with clinical BPH-parameters. METHODS: A random sample of the population-based Herne lower urinary tract symptoms cohort was analysed. All these men underwent a detailed urological work-up. Two polymorphisms in the CYP19A1 gene [rs700518 in exon 4 (A57G); rs10046 at the 3'UTR(C268T)] and one in the 3'UTR of CYP3A4 [rs2740574 (A392G)] were determined by TaqMan assay from genomic DNA of peripheral blood. These polymorphisms were correlated to clinical and laboratory BPH-parameters. RESULTS: A total of 392 men (65.4 +/- 7.0 years; 52-79 years) were analysed. Mean International Prostate Symptom Score (IPSS; 7.5), Q (max) (15.4 ml/s), prostate volume (31 ml) and prostate specific antigen (PSA) (1.8 ng/ml) indicated a typical elderly population. Both polymorphisms in the CYP19A1 gene were not correlated to age, IPSS, Q (max), prostate volume and post-void residual volume. Serum PSA was higher in men carrying the heterozygous rs10046 genotype (2.0 +/- 0.1 ng/ml) than in those with the CC-genotype (1.7 +/- 0.2 ng/ml, P = 0.012). Men carrying one a mutated allele of the CYP3A4 gene had smaller prostates (27.0 +/- 2.0 vs. 32 +/- 0.8 ml, P = 0.02) and lower PSA levels (1.6 +/- 0.3 vs. 1.9 +/- 0.1 ng/ml). CONCLUSIONS: The inconsistent associations observed herein and for other gene polymorphisms warrant further studies. In general, the data regarding the association of gene polymorphism to BPH-parameters suggest that this disease is caused by multiple rather than a single genetic variant. A rigorous patient selection based on anatomo-pathological and hormonal profile may possible reduce the number of confounders for future studies thus enabling a more detailed assessment of the association between genetic factors and BPH-parameter