Substructure Discovery Using Minimum Description Length and Background Knowledge

The ability to identify interesting and repetitive substructures is an essential component to discovering knowledge in structural data. We describe a new version of our SUBDUE substructure discovery system based on the minimum description length principle. The SUBDUE system discovers substructures that compress the original data and represent structural concepts in the data. By replacing previously-discovered substructures in the data, multiple passes of SUBDUE produce a hierarchical description of the structural regularities in the data. SUBDUE uses a computationally-bounded inexact graph match that identifies similar, but not identical, instances of a substructure and finds an approximate measure of closeness of two substructures when under computational constraints. In addition to the minimum description length principle, other background knowledge can be used by SUBDUE to guide the search towards more appropriate substructures. Experiments in a variety of domains demonstrate SUBDUE's ability to find substructures capable of compressing the original data and to discover structural concepts important to the domain. Description of Online Appendix: This is a compressed tar file containing the SUBDUE discovery system, written in C. The program accepts as input databases represented in graph form, and will output discovered substructures with their corresponding value.Comment: See http://www.jair.org/ for an online appendix and other files accompanying this articl

Application of Bayesian graphs to SN Ia data analysis and compression

Bayesian graphical models are an efficient tool for modelling complex data and derive self-consistent expressions of the posterior distribution of model parameters. We apply Bayesian graphs to perform statistical analyses of Type Ia supernova (SN Ia) luminosity distance measurements from the joint light-curve analysis (JLA) data set. In contrast to the $\chi^2$ approach used in previous studies, the Bayesian inference allows us to fully account for the standard-candle parameter dependence of the data covariance matrix. Comparing with $\chi^2$ analysis results, we find a systematic offset of the marginal model parameter bounds. We demonstrate that the bias is statistically significant in the case of the SN Ia standardization parameters with a maximal 6 $\sigma$ shift of the SN light-curve colour correction. In addition, we find that the evidence for a host galaxy correction is now only 2.4 $\sigma$. Systematic offsets on the cosmological parameters remain small, but may increase by combining constraints from complementary cosmological probes. The bias of the $\chi^2$ analysis is due to neglecting the parameter-dependent log-determinant of the data covariance, which gives more statistical weight to larger values of the standardization parameters. We find a similar effect on compressed distance modulus data. To this end, we implement a fully consistent compression method of the JLA data set that uses a Gaussian approximation of the posterior distribution for fast generation of compressed data. Overall, the results of our analysis emphasize the need for a fully consistent Bayesian statistical approach in the analysis of future large SN Ia data sets.Comment: 14 pages, 13 figures, 5 tables. Submitted to MNRAS. Compression utility available at https://gitlab.com/congma/libsncompress/ and example cosmology code with machine-readable version of Tables A1 & A2 at https://gitlab.com/congma/sn-bayesian-model-example/ v2: corrected typo in author's name. v3: 15 pages, incl. corrections, matches the accepted versio

Graph Signal Processing: Overview, Challenges and Applications

Research in Graph Signal Processing (GSP) aims to develop tools for processing data defined on irregular graph domains. In this paper we first provide an overview of core ideas in GSP and their connection to conventional digital signal processing. We then summarize recent developments in developing basic GSP tools, including methods for sampling, filtering or graph learning. Next, we review progress in several application areas using GSP, including processing and analysis of sensor network data, biological data, and applications to image processing and machine learning. We finish by providing a brief historical perspective to highlight how concepts recently developed in GSP build on top of prior research in other areas.Comment: To appear, Proceedings of the IEE

On extension-shearing bending-twisting coupled laminates

This article presents details of the development of a special class of laminate, possessing Extension-Shearing Bending-Twisting coupling, necessary for optimised passive-adaptive flexible wing-box structures. The possibility of achieving a measurable drag reduction in cruise flight, without the cost or reliability issues associated with active control mechanisms, is of significant interest for achieving increased fuel burn efficiency, and meeting associated emissions targets. The introduction of passive Bending-Twisting coupling at the wing-box level has been previously demonstrated through laminate level tailoring with Extension-Shearing coupling only, but the limited design space and the possibility for ply terminations (to produce tapered thickness) effectively rule out this special class of laminate for practical construction. The study is now broadened to consider laminates with Extension-Shearing and Bending-Twisting coupling, beyond the less well-known un-balanced and symmetric design rule or indeed balanced and symmetric designs with off-axis alignment. Results reveal a vast laminate design space with Extension-Shearing coupling that can be maximised without the unfavourable strength characteristics associated with off-axis alignment. Results also reveal that shear buckling strength can be maximised through Bending-Twisting coupling when load reversal is not a design constraint

Buckling strength improvements for Fibre Metal Laminates using thin-ply tailoring

The buckling response and load carrying capacity of thin-walled open cross-section profiles made of Fibre Metal Laminates, subjected to static axial compression loading are considered. These include thin-walled Z-shape and channel cross-section profiles adopting a 3/2 FML lay-up design, made of 3 aluminium layers. The objective of the investigation is the comparison of standard thickness Fibre Reinforced Plastic layers versus thin-ply material technology. Whilst thin ply designs differ only by the layer thickness, they offer an exponential increase in stacking sequence design freedoms, allowing detrimental coupling effects to be eliminated. The benefit of different hybrid materials are also considered. The comparisons involve semi-analytical and finite element methods, which are validated against experimental investigations

Properties of mass-loading shocks: 1. Hydrodynamic considerations

The one-dimensional hydrodynamics of flows subjected to mass loading are considered anew, with particular emphasis placed on determining the properties of mass-loading shocks. This work has been motivated by recent observations of the outbound Halley bow shock (Neubauer et al., 1990), which cannot be understood in terms of simple hydrodynamical or magnetohydrodynamical descriptions. By including mass injection at the shock, we have investigated the properties of the Rankine-Hugoniot conditions on the basis of a geometric formulation of the entropy condition. Such a condition, which is more powerful than the usual thermodynamical formulation, serves to determine those solutions to the Rankine-Hugoniot conditions which correspond to a physically realizable downstream state. On this basis a concise theoretical description of hydrodynamic mass-loading shocks is obtained. We show that mass-loading shocks have more in common with combustion shocks than with ordinary nonreacting gas dynamical shocks. It is shown that for decelerated solutions to the Rankine-Hugoniot conditions to exist, the upstream flow speed u0 must satisfy u0 > ucrit > cs, where cs is the sound speed. Besides the usual supersonic-subsonic transition, mass-loading fronts can also admit a decelerating supersonic-supersonic transition, the structure of which consists of a sharp decrease in the flow velocity preceding a recovery and an increase in the final downstream flow speed. We suggest the possibility that such structures may describe the inbound Halley bow shock (Coates et al., 1987a). Both parallel and oblique shocks are considered, the primary difference being that oblique shocks are subjected to a shearing stress due to mass loading. It is conjectured that such a shearing may destabilize the shock

Effect of bending-twisting coupling on the compression and shear buckling strength of infinitely long plates

This article describes the development of closed form polynomial equations for compression and shear buckling to assess the effect of Bending-Twisting coupling on infinitely long laminated plates with simply supported edges. The equations are used to generate contour maps, representing non-dimensional buckling factors, which are superimposed on the lamination parameter design spaces for laminates with standard ply orientations. The contour maps are applicable to two recently developed databases containing symmetric and non-symmetric laminates with either Bending-Twisting or Extension-Shearing Bending-Twisting coupling. The contour maps provide new insights into buckling performance improvements that are non-intuitive and facilitate comparison between hypothetical and practical designs. The databases are illustrated through point clouds of lamination parameter coordinates, which demonstrate the effect of applying common design heuristics, including ply angle, ply percentage and ply contiguity constraints