Maximal induced paths and minimal percolating sets in hypercubes

For a graph $G$, the \emph{$r$-bootstrap percolation} process can be described as follows: Start with an initial set $A$ of "infected'' vertices. Infect any vertex with at least $r$ infected neighbours, and continue this process until no new vertices can be infected. $A$ is said to \emph{percolate in $G$} if eventually all the vertices of $G$ are infected. $A$ is a \emph{minimal percolating set} in $G$ if $A$ percolates in $G$ and no proper subset of $A$ percolates in $G$. An induced path, $P$, in a hypercube $Q_n$ is maximal if no induced path in $Q_n$ properly contains $P$. Induced paths in hypercubes are also called snakes. We study the relationship between maximal snakes and minimal percolating sets (under 2-bootstrap percolation) in hypercubes. In particular, we show that every maximal snake contains a minimal percolating set, and that every minimal percolating set is contained in a maximal snake

ARTE: Automated Generation of Realistic Test Inputs for Web APIs

Automated test case generation for web APIs is a thriving research topic, where test cases are frequently derived from the API specification. However, this process is only partially automated since testers are usually obliged to manually set meaningful valid test inputs for each input parameter. In this article, we present ARTE, an approach for the automated extraction of realistic test data for web APIs from knowledge bases like DBpedia. Specifically, ARTE leverages the specification of the API parameters to automatically search for realistic test inputs using natural language processing, search-based, and knowledge extraction techniques. ARTE has been integrated into RESTest, an open-source testing framework for RESTful APIs, fully automating the test case generation process. Evaluation results on 140 operations from 48 real-world web APIs show that ARTE can efficiently generate realistic test inputs for 64.9% of the target parameters, outperforming the state-of-the-art approach SAIGEN (31.8%). More importantly, ARTE supported the generation of over twice as many valid API calls (57.3%) as random generation (20%) and SAIGEN (26%), leading to a higher failure detection capability and uncovering several real-world bugs. These results show the potential of ARTE for enhancing existing web API testing tools, achieving an unprecedented level of automationJunta de Andalucía APOLO (US-1264651)Junta de Andalucía EKIPMENT-PLUS (P18-FR-2895)Ministerio de Ciencia, Innovación y Universidades RTI2018-101204-B-C21 (HORATIO)Ministerio de Ciencia, Innovación y Universidades RED2018-102472-

Juan de Fuca subduction zone from a mixture of tomography and waveform modeling

Seismic tomography images of the upper mantle structures beneath the Pacific Northwestern United States display a maze of high-velocity anomalies, many of which produce distorted waveforms evident in the USArray observations indicative of the Juan de Fuca (JdF) slab. The inferred location of the slab agrees quite well with existing contour lines defining the slab's upper interface. Synthetic waveforms generated from a recent tomography image fit teleseismic travel times quite well and also some of the waveform distortions. Regional earthquake data, however, require substantial changes to the tomographic velocities. By modeling regional waveforms of the 2008 Nevada earthquake, we find that the uppermost mantle of the 1D reference model AK135, the reference velocity model used for most tomographic studies, is too fast for the western United States. Here, we replace AK135 with mT7, a modification of an older Basin-and-Range model T7. We present two hybrid velocity structures satisfying the waveform data based on modified tomographic images and conventional slab wisdom. We derive P and SH velocity structures down to 660 km along two cross sections through the JdF slab. Our results indicate that the JdF slab is subducted to a depth of 250 km beneath the Seattle region, and terminates at a shallower depth beneath Portland region of Oregon to the south. The slab is about 60 km thick and has a P velocity increase of 5% with respect to mT7. In order to fit waveform complexities of teleseismic Gulf of Mexico and South American events, a slab-like high-velocity anomaly with velocity increases of 3% for P and 7% for SH is inferred just above the 660 discontinuity beneath Nevada