Karhunen-Lo\`eve expansion for a generalization of Wiener bridge

We derive a Karhunen-Lo\`eve expansion of the Gauss process $B_t - g(t)\int_0^1 g'(u)\,d B_u$, $t\in[0,1]$, where $(B_t)_{t\in[0,1]}$ is a standard Wiener process and $g:[0,1]\to R$ is a twice continuously differentiable function with $g(0) = 0$ and $\int_0^1 (g'(u))^2\,d u =1$. This process is an important limit process in the theory of goodness-of-fit tests. We formulate two special cases with the function $g(t)=\frac{\sqrt{2}}{\pi}\sin(\pi t)$, $t\in[0,1]$, and $g(t)=t$, $t\in[0,1]$, respectively. The latter one corresponds to the Wiener bridge over $[0,1]$ from $0$ to $0$.Comment: 25 pages, 1 figure. The appendix is extende

Comment on Bress et al. Effect of Intensive Versus Standard Blood Pressure Treatment According to Baseline Prediabetes Status: A Post Hoc Analysis of a Randomized Trial. Diabetes Care 2017;40:1401-1408.

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Extended X-ray Emission From a Quasar-Driven Superbubble

We present observations of extended, 20-kpc scale soft X-ray gas around a luminous obscured quasar hosted by an ultra-luminous infrared galaxy caught in the midst of a major merger. The extended X-ray emission is well fit as a thermal gas with a temperature of kT ~ 280 eV and a luminosity of L_X ~ 10^42 erg/s and is spatially coincident with a known ionized gas outflow. Based on the X-ray luminosity, a factor of ~10 fainter than the [OIII] emission, we conclude that the X-ray emission is either dominated by photoionization, or by shocked emission from cloud surfaces in a hot quasar-driven wind.Comment: Accepted for publication in ApJ, 6 pages, 2 figure

Generalization of French and Portuguese plural alternations and initial syllable protection

We present two cases of morphophonological alternations in the plural of nouns, one from French and one from Brazilian Portuguese. In both of them, monosyllabic items are protected from right-edge alternations more than polysyllabic items are, an asymmetry we attribute to privileged protection of initial syllables. We implement the analyses of the two languages using constraint-based grammars that take trends learned across the lexicon and predict the treatment of nonce words. Five large-scale nonce word tasks confirm the productivity of the trend in both languages

Rapid iododeboronation with and without gold catalysis: application to radiolabelling of arenes

Radiopharmaceuticals incorporating radioactive iodine in combination with SPECT imaging play a key role in nuclear medicine, with applications in drug development and disease diagnosis. Despite this importance, there are relatively few general methods for incorporating radioiodine into small molecules. Here we describe a rapid, air- and moisture-stable ipso-iododeboronation procedure using NIS, in the non-toxic and green solvent dimethyl carbonate. The fast reaction and mild conditions of the gold-catalysed method led to the development of a highly efficient process for radiolabelling of arenes, which constitutes the first example of an application of homogenous gold catalysis to selective radiosynthesis. This has been exemplified with an effective synthesis of radiolabelled meta-[125I]iodobenzylguanidine, a radiopharmaceutical used for the imaging and therapy of human norepinephrine transporter-expressing tumours

Constructing solutions to the Bj\"orling problem for isothermic surfaces by structure preserving discretization

In this article, we study an analog of the Bj\"orling problem for isothermic surfaces (that are more general than minimal surfaces): given a real analytic curve $\gamma$ in ${\mathbb R}^3$, and two analytic non-vanishing orthogonal vector fields $v$ and $w$ along $\gamma$, find an isothermic surface that is tangent to $\gamma$ and that has $v$ and $w$ as principal directions of curvature. We prove that solutions to that problem can be obtained by constructing a family of discrete isothermic surfaces (in the sense of Bobenko and Pinkall) from data that is sampled along $\gamma$, and passing to the limit of vanishing mesh size. The proof relies on a rephrasing of the Gauss-Codazzi-system as analytic Cauchy problem and an in-depth-analysis of its discretization which is induced from the geometry of discrete isothermic surfaces. The discrete-to-continuous limit is carried out for the Christoffel and the Darboux transformations as well.Comment: 29 pages, some figure

Efficiency optimization in a correlation ratchet with asymmetric unbiased fluctuations

The efficiency of a Brownian particle moving in periodic potential in the presence of asymmetric unbiased fluctuations is investigated. We found that there is a regime where the efficiency can be a peaked function of temperature, which proves that thermal fluctuations facilitate the efficiency of energy transformation, contradicting the earlier findings (H. kamegawa et al. Phys. Rev. Lett. 80 (1998) 5251). It is also found that the mutual interplay between asymmetry of fluctuation and asymmetry of the potential may induce optimized efficiency at finite temperature. The ratchet is not most efficiency when it gives maximum current.Comment: 10 pages, 7 figure