The computability path ordering

This paper aims at carrying out termination proofs for simply typed higher-order calculi automatically by using ordering comparisons. To this end, we introduce the computability path ordering (CPO), a recursive relation on terms obtained by lifting a precedence on function symbols. A first version, core CPO, is essentially obtained from the higher-order recursive path ordering (HORPO) by eliminating type checks from some recursive calls and by incorporating the treatment of bound variables as in the com-putability closure. The well-foundedness proof shows that core CPO captures the essence of computability arguments \'a la Tait and Girard, therefore explaining its name. We further show that no further type check can be eliminated from its recursive calls without loosing well-foundedness, but for one for which we found no counterexample yet. Two extensions of core CPO are then introduced which allow one to consider: the first, higher-order inductive types; the second, a precedence in which some function symbols are smaller than application and abstraction

Low Temperature Photo-oxidation of Chloroperoxidase Compound II

Oxidation of the heme-thiolate enzyme chloroperoxidase (CPO) from Caldariomyces fumago with peroxynitrite (PN) gave the Compound II intermediate, which was photo-oxidized with 365 nm light to give a reactive oxidizing species. Cryo-solvents at pH ≈ 6 were employed, and reactions were conducted at temperatures as low as − 50 °C. The activity of CPO as evaluated by the chlorodimedone assay was unaltered by treatment with PN or by production of the oxidizing transient and subsequent reaction with styrene. EPR spectra at 77 K gave the amount of ferric protein at each stage in the reaction sequence. The PN oxidation step gave a 6:1 mixture of Compound II and ferric CPO, the photolysis step gave an approximate 1:1 mixture of active oxidant and ferric CPO, and the final mixture after reaction with excess styrene contained ferric CPO in 80% yield. In single turnover reactions at − 50 °C, styrene was oxidized to styrene oxide in high yield. Kinetic studies of styrene oxidation at − 50 °C displayed saturation kinetics with an equilibrium constant for formation of the complex of Kbind = 3.8 × 104 M− 1 and an oxidation rate constant of kox = 0.30 s− 1. UV–Visible spectra of mixtures formed in the photo-oxidation sequence at ca. − 50 °C did not contain the signature Q-band absorbance at 690 nm ascribed to CPO Compound I prepared by chemical oxidation of the enzyme, indicating that different species were formed in the chemical oxidation and the photo-oxidation sequence

Exchange Interactions in a Dinuclear Manganese (II) Complex with Cyanopyridine-N-oxide Bridging Ligands

The structure and magnetic properties of oligonuclear manganese complex [Mn(hfa)2cpo]2 (where hfa is hexafluoroacetylacetonate dehydrate and cpo is 4-cyanopyridine-N-oxide) are presented. In the unit cell, the dinuclear molecules are well isolated from each other. The non-monotonous dependence of magnetic susceptibility is explained in terms of the hierarchy of exchange parameters by using exact diagonalization. The thermodynamic behavior of pure cpo and [Mn(hfa)2(cpo)]2 is simulated numerically in a dimer approximation by an extrapolation to spin S = 5/2. The Mn-Mn exchange integral is evaluated.Comment: Final corrected version, pdf, 12 page

The impact of celestial pole offset modelling on VLBI UT1 Intensive results

Very Long Baseline Interferometry (VLBI) Intensive sessions are scheduled to provide operational Universal Time (UT1) determinations with low latency. UT1 estimates obtained from these observations heavily depend on the model of the celestial pole motion used during data processing. However, even the most accurate precession-nutation model, IAU 2000/2006, is not accurate enough to realize the full potential of VLBI observations. To achieve the highest possible accuracy in UT1 estimates, a celestial pole offset (CPO), which is the difference between the actual and modelled precession-nutation angles, should be applied. Three CPO models are currently available for users. In this paper, these models have been tested and the differences between UT1 estimates obtained with those models are investigated. It has been shown that neglecting CPO modelling during VLBI UT1 Intensive processing causes systematic errors in UT1 series of up to 20 microarcseconds. It has been also found that using different CPO models causes the differences in UT1 estimates reaching 10 microarcseconds. Obtained results are applicable to the satellite data processing as well.Comment: 8 pp., accepted for publication in Journal of Geodes

Transition probability generating function of a transitionless quantum parametric oscillator

The transitionless tracking (TT) algorithm enables the exact tracking of quantum adiabatic dynamics in an arbitrary short time by adding a counterdiabatic Hamiltonian to the original adiabatic Hamiltonian. By applying Husimi's method originally developed for a quantum parametric oscillator (QPO) to the transitionless QPO achieved using the TT algorithm, we obtain the transition probability generating function with a time-dependent parameter constituted with solutions of the corresponding classical parametric oscillator (CPO). By obtaining the explicit solutions of this CPO using the phase-amplitude method, we find that the time-dependent parameter can be reduced to the frequency ratio between the Hamiltonians without and with the counterdiabatic Hamiltonian, from which we can easily characterize the result achieved by the TT algorithm. We illustrate our theory by showing the trajectories of the CPO on the classical phase space, which elucidate the effect of the counterdiabatic Hamiltonian of the QPO.Comment: 13 pages, 3 figure

Balancing efficiencies by squeezing in realistic eight-port homodyne detection

We address measurements of covariant phase observables (CPOs) by means of realistic eight-port homodyne detectors. We do not assume equal quantum efficiencies for the four photodetectors and investigate the conditions under which the measurement of a CPO may be achieved. We show that balancing the efficiencies using an additional beam splitter allows us to achieve a CPO at the price of reducing the overall effective efficiency, and prove that it is never a smearing of the ideal CPO achievable with unit quantum efficiency. An alternative strategy based on employing a squeezed vacuum as a parameter field is also suggested, which allows one to increase the overall efficiency in comparison to the passive case using only a moderate amount of squeezing. Both methods are suitable for implementantion with current technology.Comment: 8 pages, 5 figures, revised versio

Operator Mixing in Large NN Superconformal Field Theories on S4\mathbb{S}^4 and Correlators with Wilson loops

We find a general formula for the operator mixing on the $\mathbb{S}^4$ of chiral primary operators (CPO) for the ${\cal N}=4$ theory at large $N$ in terms of Chebyshev polynomials. As an application, we compute the correlator of a CPO and a Wilson loop, reproducing an earlier result by Giombi and Pestun obtained from a two-matrix model proposal. Finally, we discuss a simple method to obtain correlators in general ${\cal N}=2$ superconformal field theories in perturbation theory in terms of correlators of the ${\cal N}=4$ theory.Comment: 15 pages, no figure