The isometry degree of a computable copy of ℓp\ell^p

When $p$ is a computable real so that $p \geq 1$, the isometry degree of a computable copy $\mathcal{B}$ of $\ell^p$ is defined to be the least powerful Turing degree that computes a linear isometry of $\ell^p$ onto $\mathcal{B}$. We show that this degree always exists and that when $p \neq 2$ these degrees are precisely the c.e. degrees

Optimal Oracles for Point-To-Set Principles

The point-to-set principle characterizes the Hausdorff dimension of a subset $E\subseteq\R^n$ by the effective dimension of its individual points. This characterization has been used to prove several results in classical, i.e., without any computability requirements, analysis. Recent work has shown that algorithmic techniques can be fruitfully applied to Marstrand's projection theorem, a fundamental result in fractal geometry. In this paper, we introduce an extension of point-to-set principle - the notion of optimal oracles for subsets $E\subseteq\R^n$. One of the primary motivations of this definition is that, if $E$ has optimal oracles, then the conclusion of Marstrand's projection theorem holds for $E$. We show that every analytic set has optimal oracles. We also prove that if the Hausdorff and packing dimensions of $E$ agree, then $E$ has optimal oracles. Thus, the existence of optimal oracles subsume the currently known sufficient conditions for Marstrand's theorem to hold. Under certain assumptions, every set has optimal oracles. However, assuming the axiom of choice and the continuum hypothesis, we construct sets which do not have optimal oracles. This construction naturally leads to a new, algorithmic, proof of Davies theorem on projections

First-principles investigation of Ag-Cu alloy surfaces in an oxidizing environment

In this paper we investigate by means of first-principles density functional theory calculations the (111) surface of the Ag-Cu alloy under varying conditions of pressure of the surrounding oxygen atmosphere and temperature. This alloy has been recently proposed as a catalyst with improved selectivity for ethylene epoxidation with respect to pure silver, the catalyst commonly used in industrial applications. Here we show that the presence of oxygen leads to copper segregation to the surface. Considering the surface free energy as a function of the surface composition, we construct the convex hull to investigate the stability of various surface structures. By including the dependence of the free surface energy on the oxygen chemical potential, we are able compute the phase diagram of the alloy as a function of temperature, pressure and surface composition. We find that, at temperature and pressure typically used in ethylene epoxidation, a number of structures can be present on the surface of the alloy, including clean Ag(111), thin layers of copper oxide and thick oxide-like structures. These results are consistent with, and help explain, recent experimental results.Comment: 10 pages, 6 figure

Electron attachment to SF6 and lifetimes of SF6- negative ions

We study the process of low-energy electron capture by the SF6 molecule. Our approach is based on the model of Gauyacq and Herzenberg [J. Phys. B 17, 1155 (1984)] in which the electron motion is coupled to the fully symmetric vibrational mode through a weakly bound or virtual s state. By tuning the two free parameters of the model, we achieve an accurate description of the measured electron attachment cross section and good agreement with vibrational excitation cross sections of the fully symmetric mode. An extension of the model provides a limit on the characteristic time of intramolecular vibrational relaxation in highly-excited SF6-. By evaluating the total vibrational spectrum density of SF6-, we estimate the widths of the vibrational Feshbach resonances of the long-lived negative ion. We also analyse the possible distribution of the widths and its effect on the lifetime measurements, and investigate nonexponential decay features in metastable SF6-.Comment: 22 pages, 10 figures, submitted to Phys. Rev.

Cost Utility of Omalizumab Compared with Standard of Care for the Treatment of Chronic Spontaneous Urticaria.

BACKGROUND: Chronic spontaneous urticaria (CSU) negatively impacts patient quality of life and productivity and is associated with considerable indirect costs to society. OBJECTIVE: The aim of this study was to assess the cost utility of add-on omalizumab treatment compared with standard of care (SOC) in moderate or severe CSU patients with inadequate response to SOC, from the UK societal perspective. METHODS: A Markov model was developed, consisting of health states based on Urticaria Activity Score over 7 days (UAS7) and additional states for relapse, spontaneous remission and death. Model cycle length was 4 weeks, and total model time horizon was 20 years in the base case. The model considered early discontinuation of non-responders (response: UAS7 ≤6) and retreatment upon relapse (relapse: UAS7 ≥16) for responders. Clinical and cost inputs were derived from omalizumab trials and published sources, and cost utility was expressed as incremental cost-effectiveness ratios (ICERs). Scenario analyses included no early discontinuation of non-responders and an altered definition of response (UAS7 <16). RESULTS: With a deterministic ICER of £3183 in the base case, omalizumab was associated with increased costs and benefits relative to SOC. Probabilistic sensitivity analysis supported this result. Productivity inputs were key model drivers, and individual scenarios without early discontinuation of non-responders and adjusted response definitions had little impact on results. ICERs were generally robust to changes in key model parameters and inputs. CONCLUSIONS: In this, the first economic evaluation of omalizumab in CSU from a UK societal perspective, omalizumab consistently represented a treatment option with societal benefit for CSU in the UK across a range of scenarios

The Effect of the Environment on alpha-Al_2O_3 (0001) Surface Structures

We report that calculating the Gibbs free energy of the alpha-Al_2O_3 (0001) surfaces in equilibrium with a realistic environment containing both oxygen and hydrogen species is essential for obtaining theoretical predictions consistent with experimental observations. Using density-functional theory we find that even under conditions of high oxygen partial pressure, the metal terminated surface is surprisingly stable. An oxygen terminated alpha-Al_2O_3 (0001) surface becomes stable only if hydrogen is present on the surface. In addition, including hydrogen on the surface resolves discrepancies between previous theoretical work and experimental results with respect to the magnitude and direction of surface relaxations.Comment: 4 pages including 2 figures. Submitted to Phys. Rev. Lett. Related publications can be found at http://www.fhi-berlin.mpg.de/th/paper.htm

Alloy surface segregation in reactive environments: A first-principles atomistic thermodynamics study of Ag3Pd(111) in oxygen atmospheres

We present a first-principles atomistic thermodynamics framework to describe the structure, composition and segregation profile of an alloy surface in contact with a (reactive) environment. The method is illustrated with the application to a Ag3Pd(111) surface in an oxygen atmosphere, and we analyze trends in segregation, adsorption and surface free energies. We observe a wide range of oxygen adsorption energies on the various alloy surface configurations, including binding that is stronger than on a Pd(111) surface and weaker than that on a Ag(111) surface. This and the consideration of even small amounts of non-stoichiometries in the ordered bulk alloy are found to be crucial to accurately model the Pd surface segregation occurring in increasingly O-rich gas phases.Comment: 13 pages including 6 figures; related publications can be found at http://www.fhi-berlin.mpg.de/th/th.htm