Topology of complements of skeletons

Given a polytopal complex $X$, we examine the topological complement of its $k$-skeleton. We construct a long exact sequence relating the homologies of the skeleton complements and links of faces in $X$, and using this long exact sequence, we obtain characterisations of Cohen-Macaulay and Leray complexes, stacked balls, and neighbourly spheres in terms of their skeleton complements. We also apply these results to CAT(0) cubical complexes, and find new similarities between such a complex and an associated simplicial complex, the crossing complex.Comment: 22 pages, 14 figure

Topology of Cut Complexes of Graphs

We define the $k$-cut complex of a graph $G$ with vertex set $V(G)$ to be the simplicial complex whose facets are the complements of sets of size $k$ in $V(G)$ inducing disconnected subgraphs of $G$. This generalizes the Alexander dual of a graph complex studied by Fr\"oberg (1990), and Eagon and Reiner (1998). We describe the effect of various graph operations on the cut complex, and study its shellability, homotopy type and homology for various families of graphs, including trees, cycles, complete multipartite graphs, and the prism $K_n \times K_2$, using techniques from algebraic topology, discrete Morse theory and equivariant poset topology.Comment: 36 pages, 10 figures, 1 table, Extended Abstract accepted for FPSAC2023 (Davis

Herschel-ATLAS: Multi-wavelength SEDs and physical properties of 250 micron-selected galaxies at z < 0.5

We present a pan-chromatic analysis of an unprecedented sample of 1402 250 micron-selected galaxies at z < 0.5 (mean z = 0.24) from the Herschel-ATLAS survey. We complement our Herschel 100-500 micron data with UV-K-band photometry from the Galaxy And Mass Assembly (GAMA) survey and apply the MAGPHYS energy-balance technique to produce pan-chromatic SEDs for a representative sample of 250 micron selected galaxies spanning the most recent 5 Gyr of cosmic history. We derive estimates of physical parameters, including star formation rates, stellar masses, dust masses and infrared luminosities. The typical H-ATLAS galaxy at z < 0.5 has a far-infrared luminosity in the range 10^10 - 10^12 Lsolar (SFR: 1-50 Msolar/yr) thus is broadly representative of normal star forming galaxies over this redshift range. We show that 250 micron-selected galaxies contain a larger mass of dust at a given infra-red luminosity or star formation rate than previous samples selected at 60 micron from IRAS. We derive typical SEDs for H-ATLAS galaxies, and show that the emergent SED shape is most sensitive to specific star formation rate. The optical-UV SEDs also become more reddened due to dust at higher redshifts. Our template SEDs are significantly cooler than existing infra-red templates. They may therefore be most appropriate for inferring total IR luminosities from moderate redshift submillimetre selected samples and for inclusion in models of the lower redshift submillimetre galaxy populations.Comment: 26 pages, 24 figures, Accepted by MNRA

Extracorporeal Membrane Oxygenation for Acute Pediatric Respiratory Failure

This article is made available for unrestricted research re-use and secondary analysis in any form or by any means with acknowledgement of the original source. These permissions are granted for the duration of the World Health Organization (WHO) declaration of COVID-19 as a global pandemic.The use of extracorporeal membrane oxygenation (ECMO) to support children with acute respiratory failure has steadily increased over the past several decades, with major advancements having been made in the care of these children. There are, however, many controversies regarding indications for initiating ECMO in this setting and the appropriate management strategies thereafter. Broad indications for ECMO include hypoxia, hypercarbia, and severe air leak syndrome, with hypoxia being the most common. There are many disease-specific considerations when evaluating children for ECMO, but there are currently very few, if any, absolute contraindications. Venovenous rather than veno-arterial ECMO cannulation is the preferred configuration for ECMO support of acute respiratory failure due to its superior side-effect profile. The approach to lung management on ECMO is variable and should be individualized to the patient, with the main goal of reducing the risk of VILI. ECMO is a relatively rare intervention, and there are likely a minimum number of cases per year at a given center to maintain competency. Patients who have prolonged ECMO runs (i.e., greater than 21 days) are less likely to survive, though no absolute duration of ECMO that would mandate withdrawal of ECMO support can be currently recommended

Combinatorics of CAT(0) cubical complexes, crossing complexes and co-skeletons

Thesis (Ph.D.)--University of Washington, 2023This thesis consists of three papers about cubical complexes: Chapter 1 is [Rowlands 22a], Chapter 2 is [Rowlands 23], and Chapter 3 is [Rowlands 22b]. Chapter 1 extends a result by Dancis to cubical complexes: Dancis proved that any d-dimensional simplicial manifold can be reconstructed from its (floor(d/2) + 1)-skeleton, and we prove an analogous result for d-dimensional cubical manifolds that can be embedded as a subcomplex into a cube I^N. Chapter 2 studies CAT(0) cubical complexes, using the framework of a poset with inconsistent pairs developed by Ardila et al. We introduce a simplicial complex called the "crossing complex" associated to each CAT(0) cubical complex, and study its properties. We deduce that this crossing complex holds much of the combinatorial information contained in the cubical complex: our main results relate their f-vectors, hyperplane/link structure, and balancedness. Finally, Chapter 3 studies the topology of complements of skeletons in polytopal complexes: we derive a long exact sequence involving homology of skeleton complements and links, and we characterise various topological properties of spaces in terms of skeleton complements. Our main application of this machinery is to CAT(0) cubical complexes: we conclude that these complexes also share several topological properties with their crossing complexes

A characterization of two-dimensional Buchsbaum matching complexes

The matching complex $M(G)$ of a graph $G$ is the set of all matchings in $G$. A Buchsbaum simplicial complex is a generalization of both a homology manifold and a Cohen--Macaulay complex. We give a complete characterization of the graphs $G$ for which $M(G)$ is a two-dimensional Buchsbaum complex. As an intermediate step, we determine which graphs have matching complexes that are themselves connected graphs.Comment: 22 pages. Minor changes throughout and a few results reordered for clarity of presentation. Some of the Buchsbaum families have been renamed to match the order in which they appear in the paper. Submitted for publicatio

Geology and tectonics of Neoproterozoic salt diapirs and salt sheets in the eastern Willouran Ranges, South Australia

Allochthonous salt structures and associated primary and secondary minibasins are exposed in Neoproterozoic strata of the eastern Willouran Ranges, South Australia. Detailed geologic mapping using high‐quality airborne hyperspectral remote‐sensing data and satellite imagery, combined with a qualitative structural restoration, are used to elucidate the evolution of this complex, long‐lived ( \u3e 250 Myr) salt system. Field observations and interpretations at a resolution unobtainable from seismic or well data provide a means to test published models of allochthonous salt emplacement and associated salt‐sediment interaction derived from subsurface data in the northern Gulf of Mexico. Salt diapirs and sheets are represented by megabreccias of nonevaporite lithologies that were originally interbedded with evaporites that have been dissolved and/or altered. Passive diapirism began shortly after deposition of the Callanna Group layered evaporite sequence. A primary basin containing an expulsion‐rollover structure and megaflap is flanked by two vertical diapirs. Salt flowed laterally from the diapirs to form a complex, multi‐level canopy, now partly welded, containing an encapsulated minibasin and capped by suprasalt basins. Salt and minibasin geometries were modified during the Late Cambrian–Ordovician Delamerian Orogeny (ca. 500 Ma). Small‐scale structures such as subsalt shear zones, fractured or mixed ‘rubble zones’ and thrust imbricates are absent beneath allochthonous salt and welds in the eastern Willouran Ranges. Instead, either undeformed strata or halokinetic drape folds that include preserved diapir roof strata are found directly below the transition from steep diapirs to salt sheets. Allochthonous salt first broke through the diapir roofs and then flowed laterally, resulting in variable preservation of the subsalt drape folds. Lateral salt emplacement was presumably on roof‐edge thrusts or, because of the shallow depositional environment, via open‐toed advance or extrusive advance, but without associated subsalt deformation