Global Numerical Constraints on Trees

We introduce a logical foundation to reason on tree structures with constraints on the number of node occurrences. Related formalisms are limited to express occurrence constraints on particular tree regions, as for instance the children of a given node. By contrast, the logic introduced in the present work can concisely express numerical bounds on any region, descendants or ancestors for instance. We prove that the logic is decidable in single exponential time even if the numerical constraints are in binary form. We also illustrate the usage of the logic in the description of numerical constraints on multi-directional path queries on XML documents. Furthermore, numerical restrictions on regular languages (XML schemas) can also be concisely described by the logic. This implies a characterization of decidable counting extensions of XPath queries and XML schemas. Moreover, as the logic is closed under negation, it can thus be used as an optimal reasoning framework for testing emptiness, containment and equivalence

Shingle 2.0: generalising self-consistent and automated domain discretisation for multi-scale geophysical models

The approaches taken to describe and develop spatial discretisations of the domains required for geophysical simulation models are commonly ad hoc, model or application specific and under-documented. This is particularly acute for simulation models that are flexible in their use of multi-scale, anisotropic, fully unstructured meshes where a relatively large number of heterogeneous parameters are required to constrain their full description. As a consequence, it can be difficult to reproduce simulations, ensure a provenance in model data handling and initialisation, and a challenge to conduct model intercomparisons rigorously. This paper takes a novel approach to spatial discretisation, considering it much like a numerical simulation model problem of its own. It introduces a generalised, extensible, self-documenting approach to carefully describe, and necessarily fully, the constraints over the heterogeneous parameter space that determine how a domain is spatially discretised. This additionally provides a method to accurately record these constraints, using high-level natural language based abstractions, that enables full accounts of provenance, sharing and distribution. Together with this description, a generalised consistent approach to unstructured mesh generation for geophysical models is developed, that is automated, robust and repeatable, quick-to-draft, rigorously verified and consistent to the source data throughout. This interprets the description above to execute a self-consistent spatial discretisation process, which is automatically validated to expected discrete characteristics and metrics.Comment: 18 pages, 10 figures, 1 table. Submitted for publication and under revie

A Tree Logic with Graded Paths and Nominals

Regular tree grammars and regular path expressions constitute core constructs widely used in programming languages and type systems. Nevertheless, there has been little research so far on reasoning frameworks for path expressions where node cardinality constraints occur along a path in a tree. We present a logic capable of expressing deep counting along paths which may include arbitrary recursive forward and backward navigation. The counting extensions can be seen as a generalization of graded modalities that count immediate successor nodes. While the combination of graded modalities, nominals, and inverse modalities yields undecidable logics over graphs, we show that these features can be combined in a tree logic decidable in exponential time

Structurally Tractable Uncertain Data

Many data management applications must deal with data which is uncertain, incomplete, or noisy. However, on existing uncertain data representations, we cannot tractably perform the important query evaluation tasks of determining query possibility, certainty, or probability: these problems are hard on arbitrary uncertain input instances. We thus ask whether we could restrict the structure of uncertain data so as to guarantee the tractability of exact query evaluation. We present our tractability results for tree and tree-like uncertain data, and a vision for probabilistic rule reasoning. We also study uncertainty about order, proposing a suitable representation, and study uncertain data conditioned by additional observations.Comment: 11 pages, 1 figure, 1 table. To appear in SIGMOD/PODS PhD Symposium 201

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

Systems Biology Markup Language (SBML) Level 2: Structures and Facilities for Model Definitions

Not applicabl