Cuts for circular proofs: semantics and cut-elimination

One of the authors introduced in [Santocanale, FoSSaCS, 2002] a calculus of circular proofs for studying the computability arising from the following categorical operations: finite products, finite coproducts, initial algebras, final coalgebras. The calculus presented [Santocanale, FoSSaCS, 2002] is cut-free; even if sound and complete for provability, it lacked an important property for the semantics of proofs, namely fullness w.r.t. the class of intended categorical models (called mu-bicomplete categories in [Santocanale, ITA, 2002]). In this paper we fix this problem by adding the cut rule to the calculus and by modifying accordingly the syntactical constraint ensuring soundness of proofs. The enhanced proof system fully represents arrows of the canonical model (a free mu-bicomplete category). We also describe a cut-elimination procedure as a a model of computation arising from the above mentioned categorical operations. The procedure constructs a cut-free proof-tree with possibly infinite branches out of a finite circular proof with cuts

Flux rope, hyperbolic flux tube, and late EUV phases in a non-eruptive circular-ribbon flare

We present a detailed study of a confined circular flare dynamics associated with 3 UV late phases in order to understand more precisely which topological elements are present and how they constrain the dynamics of the flare. We perform a non-linear force free field extrapolation of the confined flare observed with the HMI and AIA instruments onboard SDO. From the 3D magnetic field we compute the squashing factor and we analyse its distribution. Conjointly, we analyse the AIA EUV light curves and images in order to identify the post-flare loops, their temporal and thermal evolution. By combining both analysis we are able to propose a detailed scenario that explains the dynamics of the flare. Our topological analysis shows that in addition to a null-point topology with the fan separatrix, the spine lines and its surrounding Quasi-Separatix Layers halo (typical for a circular flare), a flux rope and its hyperbolic flux tube (HFT) are enclosed below the null. By comparing the magnetic field topology and the EUV post-flare loops we obtain an almost perfect match 1) between the footpoints of the separatrices and the EUV 1600~\AA{} ribbons and 2) between the HFT's field line footpoints and bright spots observed inside the circular ribbons. We showed, for the first time in a confined flare, that magnetic reconnection occured initially at the HFT, below the flux rope. Reconnection at the null point between the flux rope and the overlying field is only initiated in a second phase. In addition, we showed that the EUV late phase observed after the main flare episode are caused by the cooling loops of different length which have all reconnected at the null point during the impulsive phase.Comment: Astronomy & Astrophysics, in pres

The chromosphere above a δ\delta-sunspot in the presence of fan-shaped jets

$\delta$-sunspots are known to be favourable locations for fast and energetic events like flares and CMEs. The photosphere of this type of sunspots has been thoroughly investigated in the past three decades. The atmospheric conditions in the chromosphere are not so well known, however. his study is focused on the chromosphere of a $\delta$-sunspot that harbours a series of fan-shaped jets in its penumbra . The aim of this study is to establish the magnetic field topology and the temperature distribution in the presence of jets in the photosphere and the chromosphere. We use data from the Swedish 1-m Solar Telescope (SST) and the Solar Dynamics Observatory. We invert the spectropolarimetric FeI 6302~\AA\ and CaII ~8542~\AA\ data from the SST using the the non-LTE inversion code NICOLE to estimate the magnetic field configuration, temperature and velocity structure in the chromosphere. A loop-like magnetic structure is observed to emerge in the penumbra of the sunspot. The jets are launched from the loop-like structure. Magnetic reconnection between this emerging field and the pre-existing vertical field is suggested by hot plasma patches on the interface between the two fields. The height at which the reconnection takes place is located between $\log \tau_{500} = -2$ and $\log \tau_{500} = -3$. The magnetic field vector and the atmospheric temperature maps show a stationary configuration during the whole observation.Comment: 12 pages, 15 figures. Recommended for publication in A&

A spatial likelihood analysis for MAGIC telescope data

Context. The increase in sensitivity of Imaging Atmospheric Cherenkov Telescopes (IACTs) has lead to numerous detections of extended $\gamma$-ray sources at TeV energies, sometimes of sizes comparable to the instrument's field of view (FoV). This creates a demand for advanced and flexible data analysis methods, able to extract source information by utilising the photon counts in the entire FoV. Aims. We present a new software package, "SkyPrism", aimed at performing 2D (3D if energy is considered) fits of IACT data, possibly containing multiple and extended sources, based on sky images binned in energy. Though the development of this package was focused on the analysis of data collected with the MAGIC telescopes, it can further be adapted to other instruments, such as the future Cherenkov Telescope Array (CTA). Methods. We have developed a set of tools that, apart from sky images (count maps), compute the instrument response functions (IRFs) of MAGIC (effective exposure throughout the FoV, point spread function (PSF), energy resolution and background shape), based on the input data, Monte-Carlo simulations and the pointing track of the telescopes. With this information, the presented package can perform a simultaneous maximum likelihood fit of source models of arbitrary morphology to the sky images providing energy spectra, detection significances, and upper limits. Results. We demonstrate that the SkyPrism tool accurately reconstructs the MAGIC PSF, on and off-axis performance as well as the underlying background. We further show that for a point source analysis with MAGIC's default observational settings, SkyPrism gives results compatible with those of the standard tools while being more flexible and widely applicable.Comment: 13 pages, 10 figure

Machine-learning identification of galaxies in the WISExSuperCOSMOS all-sky catalogue

The two currently largest all-sky photometric datasets, WISE and SuperCOSMOS, were cross-matched by Bilicki et al. (2016) (B16) to construct a novel photometric redshift catalogue on 70% of the sky. Galaxies were therein separated from stars and quasars through colour cuts, which may leave imperfections because of mixing different source types which overlap in colour space. The aim of the present work is to identify galaxies in the WISExSuperCOSMOS catalogue through an alternative approach of machine learning. This allows us to define more complex separations in the multi-colour space than possible with simple colour cuts, and should provide more reliable source classification. For the automatised classification we use the support vector machines learning algorithm, employing SDSS spectroscopic sources cross-matched with WISExSuperCOSMOS as the training and verification set. We perform a number of tests to examine the behaviour of the classifier (completeness, purity and accuracy) as a function of source apparent magnitude and Galactic latitude. We then apply the classifier to the full-sky data and analyse the resulting catalogue of candidate galaxies. We also compare thus produced dataset with the one presented in B16. The tests indicate very high accuracy, completeness and purity (>95%) of the classifier at the bright end, deteriorating for the faintest sources, but still retaining acceptable levels of 85%. No significant variation of classification quality with Galactic latitude is observed. Application of the classifier to all-sky WISExSuperCOSMOS data gives 15 million galaxies after masking problematic areas. The resulting sample is purer than the one in B16, at a price of lower completeness over the sky. The automatic classification gives a successful alternative approach to defining a reliable galaxy sample as compared to colour cuts.Comment: 12 pages, 15 figures, accepted for publication in A&A. Obtained catalogue will be included in the public release of the WISExSuperCOSMOS galaxy catalogue available from http://ssa.roe.ac.uk/WISExSCO

WoodCircus, Underpinning the vital role of the forest-based sector in the Circular Bioeconomy. D2.2 Resource Efficiency, Side Streams and Value Chain Analysis – WP2 Final Report

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Quasi-Parallel Segments and Characterization of Unique Bichromatic Matchings

Given n red and n blue points in general position in the plane, it is well-known that there is a perfect matching formed by non-crossing line segments. We characterize the bichromatic point sets which admit exactly one non-crossing matching. We give several geometric descriptions of such sets, and find an O(nlogn) algorithm that checks whether a given bichromatic set has this property.Comment: 31 pages, 24 figure