Crossing Statistic: Bayesian interpretation, model selection and resolving dark energy parametrization problem

By introducing Crossing functions and hyper-parameters I show that the Bayesian interpretation of the Crossing Statistics [1] can be used trivially for the purpose of model selection among cosmological models. In this approach to falsify a cosmological model there is no need to compare it with other models or assume any particular form of parametrization for the cosmological quantities like luminosity distance, Hubble parameter or equation of state of dark energy. Instead, hyper-parameters of Crossing functions perform as discriminators between correct and wrong models. Using this approach one can falsify any assumed cosmological model without putting priors on the underlying actual model of the universe and its parameters, hence the issue of dark energy parametrization is resolved. It will be also shown that the sensitivity of the method to the intrinsic dispersion of the data is small that is another important characteristic of the method in testing cosmological models dealing with data with high uncertainties.Comment: 14 pages, 4 figures, discussions extended, 1 figure and two references added, main results unchanged, matches the final version to be published in JCA

Detection of a variable interstellar absorption component towards δ Orionis A

Observations of δ Ori A made with the UHRF in its highest resolution mode (R≈900 000) have revealed the presence of a cool (Tk⩽350 K) variable absorption component at a heliocentric velocity of +21.3 km s−1. The component is detected in Na I D1, where clear hyperfine splitting is seen, and Ca II K. Comparison of our data with existing spectra suggests that the component has consistently increased in strength from 1966 to 1994, and subsequently reduced in intensity by 1999. Following a discussion of the possible origins of this component it is concluded that an interstellar, rather than circumstellar, origin is most likely. This is one of very few detections of variable interstellar absorption reported in the literature, and we suggest an origin within filamentary material associated with the expanding H I shell surrounding the Orion-Eridanus superbubble

Remarks on the KLS conjecture and Hardy-type inequalities

We generalize the classical Hardy and Faber-Krahn inequalities to arbitrary functions on a convex body $\Omega \subset \mathbb{R}^n$, not necessarily vanishing on the boundary $\partial \Omega$. This reduces the study of the Neumann Poincar\'e constant on $\Omega$ to that of the cone and Lebesgue measures on $\partial \Omega$; these may be bounded via the curvature of $\partial \Omega$. A second reduction is obtained to the class of harmonic functions on $\Omega$. We also study the relation between the Poincar\'e constant of a log-concave measure $\mu$ and its associated K. Ball body $K_\mu$. In particular, we obtain a simple proof of a conjecture of Kannan--Lov\'asz--Simonovits for unit-balls of $\ell^n_p$, originally due to Sodin and Lata{\l}a--Wojtaszczyk.Comment: 18 pages. Numbering of propositions, theorems, etc.. as appeared in final form in GAFA seminar note

An ultra-high-resolution study of the interstellar medium towards Orion

We report ultra-high-resolution observations graphic of Na I, Ca II, K I, CH and CH+ for interstellar sightlines towards 12 bright stars in Orion. These data enable the detection of many more absorption components than previously recognized, providing a more accurate perspective on the absorbing medium. This is especially so for the line of sight to the Orion nebula, a region not previously studied at very high resolution. Model fits have been constructed for the absorption-line profiles, providing estimates for the column density, velocity dispersion and central velocity for each constituent velocity component. A comparison between the absorption occurring in sightlines with small angular separations has been used, along with comparisons with other studies, to estimate the line-of-sight velocity structures. Comparisons with earlier studies have also revealed temporal variability in the absorption-line profile of ζ Ori, highlighting the presence of small-scale spatial structure in the interstellar medium on scales of ≈10 au. Where absorption from both Na0 and K0 is observed for a particular cloud, a comparison of the velocity dispersions measured for each of these species provides rigorous limits on both the kinetic temperature and turbulent velocity prevailing in each cloud. Our results indicate the turbulent motions to be subsonic in each case

Multiresolution analysis of active region magnetic structure and its correlation with the Mt. Wilson classification and flaring activity

Two different multi-resolution analyses are used to decompose the structure of active region magnetic flux into concentrations of different size scales. Lines separating these opposite polarity regions of flux at each size scale are found. These lines are used as a mask on a map of the magnetic field gradient to sample the local gradient between opposite polarity regions of given scale sizes. It is shown that the maximum, average and standard deviation of the magnetic flux gradient for alpha, beta, beta-gamma and beta-gamma-delta active regions increase in the order listed, and that the order is maintained over all length-scales. This study demonstrates that, on average, the Mt. Wilson classification encodes the notion of activity over all length-scales in the active region, and not just those length-scales at which the strongest flux gradients are found. Further, it is also shown that the average gradients in the field, and the average length-scale at which they occur, also increase in the same order. Finally, there are significant differences in the gradient distribution, between flaring and non-flaring active regions, which are maintained over all length-scales. It is also shown that the average gradient content of active regions that have large flares (GOES class 'M' and above) is larger than that for active regions containing flares of all flare sizes; this difference is also maintained at all length-scales.Comment: Accepted for publication in Solar Physic

The Crossing Statistic: Dealing with Unknown Errors in the Dispersion of Type Ia Supernovae

We propose a new statistic that has been designed to be used in situations where the intrinsic dispersion of a data set is not well known: The Crossing Statistic. This statistic is in general less sensitive than `chi^2' to the intrinsic dispersion of the data, and hence allows us to make progress in distinguishing between different models using goodness of fit to the data even when the errors involved are poorly understood. The proposed statistic makes use of the shape and trends of a model's predictions in a quantifiable manner. It is applicable to a variety of circumstances, although we consider it to be especially well suited to the task of distinguishing between different cosmological models using type Ia supernovae. We show that this statistic can easily distinguish between different models in cases where the `chi^2' statistic fails. We also show that the last mode of the Crossing Statistic is identical to `chi^2', so that it can be considered as a generalization of `chi^2'.Comment: 14 pages, 5 figures. Paper restructured and extended and new interpretation of the method presented. New results concerning model selection. Treatment and error-analysis made fully model independent. References added. Accepted for publication in JCA

Thermal treatment of nuclear fuel-containing Magnox sludge radioactive waste

Magnesium aluminosilicate and magnesium borosilicate glass formulations were developed and evaluated for the immobilisation of the radioactive waste known as Magnox sludge. Glass compositions were synthesised using two simplified bounding waste simulants, including corroded and metallic uranium and magnesium at waste loadings of up to 50 wt.%. The glasses immobilising corroded simulant waste formed heterogeneous and fully amorphous glasses, while those immobilising metallic wastes contained crystallites of UO2 and U3O8. Uranium speciation within the glass was investigated by micro-focus X-ray absorption near edge spectroscopy and it was shown that the borosilicate glass compositions were characterised by a slightly lower mean uranium oxidation state than the aluminosilicate counterparts. This had an impact upon the durability, and uranium within glasses of higher mean oxidation states was dissolved more readily. All material showed dissolution rates that were comparable to simulant high level radioactive waste glasses, while the borosilicate-based formulations melted at a temperature suitable for modern vitrification technologies used in radioactive waste applications. These data highlights the potential for vitrification of hazardous radioactive Magnox sludge waste in borosilicate or aluminosilicate glass formulations, with the potential to achieve >95 % reduction in conditioned waste volume over the current baseline plan

What Attracts Men Who Batter to Their Partners? An Exploratory Study

Men who batter, because of particular personality traits and sense of entitlement, may select partners whom they perceive will be dependent on them, meet their emotional needs, or be “objects” of physical attractiveness. During treatment intake, 181 offenders responded to the question, “What attracted you to her (your partner)?” We explored whether men who mentioned their own needs or her physical traits would engage in more frequent and severe violence and would have specific forms of personality disorder dimensions or personality traits. Six categories of attraction, including “her physical traits” and “his needs,” were derived from the men’s responses. The results showed that men who focused on their partners’ physical attractiveness were more likely to be violent after treatment. Men who cited their own needs for their attraction had higher scores on borderline personality, alcohol abuse, and psychotic thinking and lower scores on compulsive-conformingPeer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/89970/1/Saunders-Kurko-Barlow-Crane 2011 What Attracts Men Who Batter to Their Partners JIV.pd

Methods to Determine Neutrino Flux at Low Energies:Investigation of the Low ν\nu Method

We investigate the "low-$\nu$" method (developed by the CCFR/NUTEV collaborations) to determine the neutrino flux in a wide band neutrino beam at very low energies, a region of interest to neutrino oscillations experiments. Events with low hadronic final state energy $\nu<\nu_{cut}$ (of 1, 2 and 5 GeV) were used by the MINOS collaboration to determine the neutrino flux in their measurements of neutrino ($\nu_\mu$) and antineutrino (\nub_\mu) total cross sections. The lowest $\nu_\mu$ energy for which the method was used in MINOS is 3.5 GeV, and the lowest \nub_\mu energy is 6 GeV. At these energies, the cross sections are dominated by inelastic processes. We investigate the application of the method to determine the neutrino flux for $\nu_\mu$, \nub_\mu energies as low as 0.7 GeV where the cross sections are dominated by quasielastic scattering and $\Delta$(1232) resonance production. We find that the method can be extended to low energies by using $\nu_{cut}$ values of 0.25 and 0.50 GeV, which is feasible in fully active neutrino detectors such as MINERvA.Comment: 25 pages, 32 figures, to be published in European Physics Journal

Measurement of the Hadronic Photon Structure Function F_2^gamma at LEP2

The hadronic structure function of the photon F_2^gamma is measured as a function of Bjorken x and of the factorisation scale Q^2 using data taken by the OPAL detector at LEP. Previous OPAL measurements of the x dependence of F_2^gamma are extended to an average Q^2 of 767 GeV^2. The Q^2 evolution of F_2^gamma is studied for average Q^2 between 11.9 and 1051 GeV^2. As predicted by QCD, the data show positive scaling violations in F_2^gamma. Several parameterisations of F_2^gamma are in agreement with the measurements whereas the quark-parton model prediction fails to describe the data.Comment: 4 pages, 2 figures, to appear in the proceedings of Photon 2001, Ascona, Switzerlan