Incorporating Nuisance Parameters in Likelihoods for Multisource Spectra

We describe here the general mathematical approach to constructing likelihoods for fitting observed spectra in one or more dimensions with multiple sources, including the effects of systematic uncertainties represented as nuisance parameters, when the likelihood is to be maximized with respect to these parameters. We consider three types of nuisance parameters: simple multiplicative factors, source spectra "morphing" parameters, and parameters representing statistical uncertainties in the predicted source spectra.Comment: Presented at PHYSTAT 2011, CERN, Geneva, Switzerland, January 2011, to be published in a CERN Yellow Repor

Candidate constructional volcanic edifices on Mercury

[Introduction] Studies using MESSENGER data suggest that Mercury’s crust is predominantly a product of effusive volcanism that occurred in the first billion years following the planet’s formation. Despite this planet-wide effusive volcanism, no constructional volcanic edifices, characterized by a topographic rise, have hitherto been robustly identified on Mercury, whereas constructional volcanoes are common on other planetary bodies in the solar system with volcanic histories. Here, we describe two candidate constructional volcanic edifices we have found on Mercury and discuss how these edifices may have formed

Preliminary observations of Rustaveli basin, Mercury

Rustaveli basin on Mercury (82.76° E, 52.39° N) is a 200.5 km diameter peak-ring basin. Since the approval of its name on April 24, 2012, it has not featured prominently in the literature. It is a large and important feature within the Hokusai (H5) quadrangle of which we are currently producing a 1:2M scale geological map. Here, we describe our first observations of Rustaveli

Preliminary findings from geological mapping of the Hokusai (H5) quadrangle of Mercury

Quadrangle geological maps from Mariner 10 data cover 45% of the surface of Mercury at 1:5M scale. Orbital MESSENGER data, which cover the entire planetary surface, can now be used to produce finer scale geological maps, including regions unseen by Mariner 10. Hokusai quadrangle (0–90° E; 22.5–66° N) is in the hemisphere unmapped by Mariner 10. It contains prominent features which are already being studied, including: Rachmaninoff basin, volcanic vents within and around Rachmaninoff, much of the Northern Plains and abundant wrinkle ridges. Its northern latitude makes it a prime candidate for regional geological mapping since compositional and topographical data, as well as Mercury Dual Imaging System (MDIS) data, are available for geological interpretation. This work aims to produce a map at 1:2M scale, compatible with other new quadrangle maps and to complement a global map now in progress

New Duality Relations for Classical Ground States

We derive new duality relations that link the energy of configurations associated with a class of soft pair potentials to the corresponding energy of the dual (Fourier-transformed) potential. We apply them by showing how information about the classical ground states of short-ranged potentials can be used to draw new conclusions about the nature of the ground states of long-ranged potentials and vice versa. They also lead to bounds on the T=0 system energies in density intervals of phase coexistence, the identification of a one-dimensional system that exhibits an infinite number of ``phase transitions," and a conjecture regarding the ground states of purely repulsive monotonic potentials.Comment: 11 pages, 2 figures. Slightly revised version that corrects typos. This article will be appearing in Physical Review Letters in a slightly shortened for

Relaxed Bell inequalities and Kochen-Specker theorems

The combination of various physically plausible properties, such as no signaling, determinism, and experimental free will, is known to be incompatible with quantum correlations. Hence, these properties must be individually or jointly relaxed in any model of such correlations. The necessary degrees of relaxation are quantified here, via natural distance and information-theoretic measures. This allows quantitative comparisons between different models in terms of the resources, such as the number of bits, of randomness, communication, and/or correlation, that they require. For example, measurement dependence is a relatively strong resource for modeling singlet state correlations, with only 1/15 of one bit of correlation required between measurement settings and the underlying variable. It is shown how various 'relaxed' Bell inequalities may be obtained, which precisely specify the complementary degrees of relaxation required to model any given violation of a standard Bell inequality. The robustness of a class of Kochen-Specker theorems, to relaxation of measurement independence, is also investigated. It is shown that a theorem of Mermin remains valid unless measurement independence is relaxed by 1/3. The Conway-Kochen 'free will' theorem and a result of Hardy are less robust, failing if measurement independence is relaxed by only 6.5% and 4.5%, respectively. An appendix shows the existence of an outcome independent model is equivalent to the existence of a deterministic model.Comment: 19 pages (including 3 appendices); v3: minor clarifications, to appear in PR