Proof internalization in generalized Frege systems for classical logic

We present a general method for inserting proofs in Frege systems for classical logic that produces systems that can internalize their own proofs.

The role of epistasis in the manifestation of heterosis: a systems-oriented approach

Heterosis is widely used in breeding, but the genetic basis of this biological phenomenon has not been elucidated. We postulate that additive and dominance genetic effects as well as two-locus interactions estimated in classical QTL analyses are not sufficient for quantifying the contributions of QTL to heterosis. A general theoretical framework for determining the contributions of different types of genetic effects to heterosis was developed. Additive x additive epistatic interactions of individual loci with the entire genetic background were identified as a major component of midparent heterosis. On the basis of these findings we defined a new type of heterotic effect denoted as augmented dominance effect di* that comprises the dominance effect at each QTL minus half the sum of additive x additive interactions with all other QTL. We demonstrate that genotypic expectations of QTL effects obtained from analyses with the design III using testcrosses of recombinant inbred lines and composite-interval mapping precisely equal genotypic expectations of midparent heterosis, thus identifying genomic regions relevant for expression of heterosis. The theory for QTL mapping of multiple traits is extended to the simultaneous mapping of newly defined genetic effects to improve the power of QTL detection and distinguish between dominance and overdominance.

Canonical proof nets for classical logic

Proof nets provide abstract counterparts to sequent proofs modulo rule permutations; the idea being that if two proofs have the same underlying proof-net, they are in essence the same proof. Providing a convincing proof-net counterpart to proofs in the classical sequent calculus is thus an important step in understanding classical sequent calculus proofs. By convincing, we mean that (a) there should be a canonical function from sequent proofs to proof nets, (b) it should be possible to check the correctness of a net in polynomial time, (c) every correct net should be obtainable from a sequent calculus proof, and (d) there should be a cut-elimination procedure which preserves correctness. Previous attempts to give proof-net-like objects for propositional classical logic have failed at least one of the above conditions. In Richard McKinley (2010) [22], the author presented a calculus of proof nets (expansion nets) satisfying (a) and (b); the paper defined a sequent calculus corresponding to expansion nets but gave no explicit demonstration of (c). That sequent calculus, called LK∗ in this paper, is a novel one-sided sequent calculus with both additively and multiplicatively formulated disjunction rules. In this paper (a self-contained extended version of Richard McKinley (2010) [22]), we give a full proof of (c) for expansion nets with respect to LK∗, and in addition give a cut-elimination procedure internal to expansion nets – this makes expansion nets the first notion of proof-net for classical logic satisfying all four criteria.

Ultracold Quantum Gases and Lattice Systems: Quantum Simulation of Lattice Gauge Theories

Abelian and non-Abelian gauge theories are of central importance in many areas of physics. In condensed matter physics, AbelianU(1) lattice gauge theories arise in the description of certain quantum spin liquids. In quantum information theory, Kitaev’s toric code is a Z(2) lattice gauge theory. In particle physics, Quantum Chromodynamics (QCD), the non-Abelian SU(3) gauge theory of the strong interactions between quarks and gluons, is nonperturbatively regularized on a lattice. Quantum link models extend the concept of lattice gauge theories beyond the Wilson formulation, and are well suited for both digital and analog quantum simulation using ultracold atomic gases in optical lattices. Since quantum simulators do not suffer from the notorious sign problem, they open the door to studies of the real-time evolution of strongly coupled quantum systems, which are impossible with classical simulation methods. A plethora of interesting lattice gauge theories suggests itself for quantum simulation, which should allow us to address very challenging problems, ranging from confinement and deconfinement, or chiral symmetry breaking and its restoration at finite baryon density, to color superconductivity and the real-time evolution of heavy-ion collisions, first in simpler model gauge theories and ultimately in QCD.

Quantum and classical criticality in a dimerized quantum antiferromagnet

A quantum critical point (QCP) is a singularity in the phase diagram arising because of quantum mechanical fluctuations. The exotic properties of some of the most enigmatic physical systems, including unconventional metals and superconductors, quantum magnets and ultracold atomic condensates, have been related to the importance of critical quantum and thermal fluctuations near such a point. However, direct and continuous control of these fluctuations has been difficult to realize, and complete thermodynamic and spectroscopic information is required to disentangle the effects of quantum and classical physics around a QCP. Here we achieve this control in a high-pressure, high-resolution neutron scattering experiment on the quantum dimer material TlCuCl3. By measuring the magnetic excitation spectrum across the entire quantum critical phase diagram, we illustrate the similarities between quantum and thermal melting of magnetic order. We prove the critical nature of the unconventional longitudinal (Higgs) mode of the ordered phase by damping it thermally. We demonstrate the development of two types of criticality, quantum and classical, and use their static and dynamic scaling properties to conclude that quantum and thermal fluctuations can behave largely independently near a QCP.

Influence of screw augmentation in posterior dynamic and rigid stabilization systems in osteoporotic lumbar vertebrae: a biomechanical cadaveric study.

STUDY DESIGN Biomechanical cadaveric study. OBJECTIVE To determine whether augmentation positively influence screw stability or not. SUMMARY OF BACKGROUND DATA Implantation of pedicle screws is a common procedure in spine surgery to provide an anchorage of posterior internal fixation into vertebrae. Screw performance is highly correlated to bone quality. Therefore, polymeric cement is often injected through specifically designed perforated pedicle screws into osteoporotic bone to potentially enhance screw stability. METHODS Caudocephalic dynamic loading was applied as quasi-physiological alternative to classical pull-out tests on 16 screws implanted in osteoporotic lumbar vertebrae and 20 screws in nonosteoporotic specimen. Load was applied using 2 different configurations simulating standard and dynamic posterior stabilization devices. Screw performance was quantified by measurement of screwhead displacement during the loading cycles. To reduce the impact of bone quality and morphology, screw performance was compared for each vertebra and averaged afterward. RESULTS All screws (with or without cement) implanted in osteoporotic vertebrae showed lower performances than the ones implanted into nonosteoporotic specimen. Augmentation was negligible for screws implanted into nonosteoporotic specimen, whereas in osteoporotic vertebrae pedicle screw stability was significantly increased. For dynamic posterior stabilization system an increase of screwhead displacement was observed in comparison with standard fixation devices in both setups. CONCLUSION Augmentation enhances screw performance in patients with poor bone stock, whereas no difference is observed for patients without osteoporosis. Furthermore, dynamic stabilization systems have the possibility to fail when implanted in osteoporotic bone.