Semivariogram methods for modeling Whittle-Mat\'ern priors in Bayesian inverse problems

We present a new technique, based on semivariogram methodology, for obtaining point estimates for use in prior modeling for solving Bayesian inverse problems. This method requires a connection between Gaussian processes with covariance operators defined by the Mat\'ern covariance function and Gaussian processes with precision (inverse-covariance) operators defined by the Green's functions of a class of elliptic stochastic partial differential equations (SPDEs). We present a detailed mathematical description of this connection. We will show that there is an equivalence between these two Gaussian processes when the domain is infinite -- for us, $\mathbb{R}^2$ -- which breaks down when the domain is finite due to the effect of boundary conditions on Green's functions of PDEs. We show how this connection can be re-established using extended domains. We then introduce the semivariogram method for estimating the Mat\'ern covariance parameters, which specify the Gaussian prior needed for stabilizing the inverse problem. Results are extended from the isotropic case to the anisotropic case where the correlation length in one direction is larger than another. Finally, we consider the situation where the correlation length is spatially dependent rather than constant. We implement each method in two-dimensional image inpainting test cases to show that it works on practical examples

THE TOOLS AND MONTE CARLO WORKING GROUP Summary Report from the Les Houches 2009 Workshop on TeV Colliders

This is the summary and introduction to the proceedings contributions for the Les Houches 2009 "Tools and Monte Carlo" working group.Comment: 144 Pages. Workshop site http://wwwlapp.in2p3.fr/conferences/LesHouches/Houches2009/ . Conveners were Butterworth, Maltoni, Moortgat, Richardson, Schumann and Skand

Lilith: a tool for constraining new physics from Higgs measurements

The properties of the observed Higgs boson with mass around 125 GeV can be affected in a variety of ways by new physics beyond the Standard Model (SM). The wealth of experimental results, targeting the different combinations for the production and decay of a Higgs boson, makes it a non-trivial task to assess the compatibility of a non-SM-like Higgs boson with all available results. In this paper we present Lilith, a new public tool for constraining new physics from signal strength measurements performed at the LHC and the Tevatron. Lilith is a Python library that can also be used in C and C++/ROOT programs. The Higgs likelihood is based on experimental results stored in an easily extensible XML database, and is evaluated from the user input, given in XML format in terms of reduced couplings or signal strengths. The results of Lilith can be used to constrain a wide class of new physics scenarios.Comment: 57 pages, 11 figures; v2: minor corrections, references added; v3: extended discussions on the validity of the approach, matches the published version; the code can be found at http://lpsc.in2p3.fr/projects-th/lilith

Beyond definition: Organising semantic information in bilingual dictionaries

This paper considers the process of organising semantic information in bilingual dictionaries with diachronic coverage, from selecting the textual source-material to designing the entries. The discussion centres on practical aspects of ancient Greek lexicography. First, the traditional semantic frameworks are described. Then, more recent approaches are noted, notably those of Adrados and of Chadwick, both of which aim to integrate contextual data within a semantic framework. Since the relevance of contextual information varies with lemma part of speech, different configurations are required for entries describing nouns, adjectives, and verbs. These are illustrated by three entries from a Greek-English dictionary currently being written at Cambridge. In order to organise data to this level of specificity, stylistic templates are indispensable, and digital software provides a means of providing them. However, systems designed for writing new dictionaries require different features from those designed for encoding pre-existing texts. A description is given of how the lexicographic requirements of the Cambridge dictionary were met by a user-designed system