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The Persistent Homology Transform (PHT) was introduced in the field of Topological Data Analysis about 10 years ago, and has since been proven to be a very powerful descriptor of Euclidean shapes. The PHT consists of scanning a shape from all possible directions $v\in S^{n-1}$ and then computing the persistent homology of sublevel set filtrations of the respective height functions $h_v$; this results in a sufficient and continuous descriptor of Euclidean shapes. We introduce a generalisation of the PHT in which we consider arbitrary parameter spaces and sublevel sets with respect to any function. In particular, we study transforms, defined on the Grassmannian $\mathbb{A}\mathbb{G}(m,n)$ of affine subspaces of $\mathbb{R}^n$, that allow to scan a shape by probing it with all possible affine $m$-dimensional subspaces $P\subset \mathbb{R}^n$, for fixed dimension $m$, and by computing persistent homology of sublevel set filtrations of the function $\mathrm{dist}(\cdot, P)$ encoding the distance from the flat $P$. We call such transforms "distance-from-flat" PHTs. We show that these transforms are injective and continuous and that they provide computational advantages over the classical PHT. In particular, we show that it is enough to compute homology only in degrees up to $m-1$ to obtain injectivity; for $m=1$ this provides a very powerful and computationally advantageous tool for examining shapes, which in a previous work by a subset of the authors has proven to significantly outperform state-of-the-art neural networks for shape classification tasks., Comment: 38 pages, 7 Figures

Persistent homology (PH) is one of the main methods used in Topological Data Analysis. An active area of research in the field is the study of appropriate notions of PH representatives, which allow to interpret the meaning of the information provided by PH, making it an important problem in the application of PH, and in the study of its interpretability. Computing optimal PH representatives is a problem that is known to be NP-hard, and one is therefore interested in developing context-specific optimality notions that are computable in practice. Here we introduce time-optimal PH representatives for time-varying data, allowing one to extract representatives that are close in time in an appropriate sense. We illustrate our methods on quasi-periodic synthetic time series, as well as time series arising from climate models, and we show that our methods provide optimal PH representatives that are better suited for these types of problems than existing optimality notions, such as length-optimal PH representatives., Comment: 30 pages, 19 figures

Shocked POst-starburst Galaxies (SPOGs) exhibit both emission lines suggestive of shock-heated gas and post-starburst-like stellar absorption, resulting in a unique subset for galaxy evolution studies. We have observed 77 galaxies that fulfilled the SPOGs criteria selection using the DeVeny Spectrograph on the Lowell Discovery Telescope. Our long-slit minor axis spectra detect H$\alpha$ and [O III] in some SPOGs out to 6 kpc above the galactic plane. We find extraplanar ionized gas in 31 targets of our sample overall. Using their internal and external kinematics, we argue that 22 galaxies host outflows with ionized gas masses ranging from $10^2 M_{\odot}$ to $10^5 M_{\odot}$. The rest are likely extended diffuse ionized gas. A positive correlation exists between AGN luminosity and the extraplanar gas extent, velocity dispersion, and mass$\unicode{x2013}\unicode{x2013}$suggesting that the AGN may indeed drive the outflows detected in AGN hosts. The low masses of the extraplanar gas suggest that these outflows are not depleting each galaxy's gas reserves. The outflows, therefore, are not likely a significant quenching mechanism in these SPOGs., Comment: 27 pages, 11 figures, ApJ accepted

We present observations of CO(1--0) and CO(2--1) lines from the Institut de radioastronomie millim\'etrique (IRAM) 30m telescope toward 20 nearby, optically luminous type 2 quasars (QSO2s) and observations of [C II] 158$\mu$m line from the Stratospheric Observatory For Infrared Astronomy (SOFIA) for 5 QSO2s in the CO sample and 5 type 1 quasars (QSO1s). In the traditional evolutionary scenario explaining different types of QSOs, obscured QSO2s emerge from gas-rich mergers observed as luminous infrared galaxies (LIRGs) and then turn into unobscured QSO1s as the black holes clear out the obscuring material in a blow-out phase. We test the validity of this theoretical prediction by comparing the gas fractions and star formation efficiencies among LIRGs and QSOs. We find that CO luminosity, CO-derived gas masses and gas fractions in QSO1s are consistent with those estimated for QSO2s, while LIRGs exhibit a closer resemblance to QSO2s in terms of CO-derived gas masses and gas fractions, and [C II] luminosity. However, comparisons between [C II] luminosity and star formation tracers such as the CO and infrared luminosity imply additional sources of [C II] emission in QSO1s likely tracing neutral atomic or ionized gas. All three types of galaxies have statistically indistinguishable distributions of star formation efficiency. Our results are consistent with part of the evolutionary scenario where nearby QSO2s could emerge from LIRGs, but they are unlikely to be the precursors of nearby QSO1s., Comment: 32 pages, 10 figures, 7 tables; the complete set of Figure 1 is appended to the end of document. Under review (revisions submitted) by ApJ

We present Gemini near-infrared integral field spectrograph (NIFS) K-band observations of the central 400 pc of NGC 1266, a nearby (D$\approx$30 Mpc) post-starburst galaxy with a powerful multi-phase outflow and a shocked ISM. We detect 7 H$_2$ ro-vibrational emission lines excited thermally to $T$$\sim$2000 K, and weak Br$\gamma$ emission, consistent with a fast C-shock. With these bright H$_2$ lines, we observe the spatial structure of the shock with an unambiguous tracer for the first time. The Br$\gamma$ emission is concentrated in the central $\lesssim$100 pc, indicating that any remaining star-formation in NGC 1266 is in the nucleus while the surrounding cold molecular gas has little on-going star-formation. Though it is unclear what fraction of this Br$\gamma$ emission is from star-formation or the AGN, assuming it is entirely due to star-formation we measure an instantaneous star-formation rate of 0.7 M$_\odot$ yr$^{-1}$, though the star-formation rate may be significantly higher in the presence of additional extinction. NGC 1266 provides a unique laboratory to study the complex interactions between AGN, outflows, shocks, and star-formation, all of which are necessary to unravel the evolution of the post-starburst phase., Comment: ApJ accepted

We present the CO(1-0) maps of 28 infrared-bright galaxies from the Great Observatories All-Sky Luminous Infrared Galaxy Survey (GOALS) taken with the Combined Array for Research in Millimeter Astronomy (CARMA). We detect 100GHz continuum in 16 of 28 galaxies, which trace both active galactic nuclei (AGNs) and compact star-forming cores. The GOALS galaxies show a variety of molecular gas morphologies, though in the majority of cases, the average velocity fields show a gradient consistent with rotation. We fit the full continuum SEDs of each of the source using either MAGPHYS or SED3FIT (if there are signs of an AGN) to derive the total stellar mass, dust mass, and star formation rates of each object. We adopt a value determined from luminous and ultraluminous infrared galaxies (LIRGs and ULIRGs) of $\alpha_{\rm CO}=1.5^{+1.3}_{-0.8}~M_\odot$ (K km s$^{-1}$ pc$^2)^{-1}$, which leads to more physical values for $f_{\rm mol}$ and the gas-to-dust ratio. Mergers tend to have the highest gas-to-dust ratios. We assume the cospatiality of the molecular gas and star formation, and plot the sample on the Schmidt-Kennicutt relation, we find that they preferentially lie above the line set by normal star-forming galaxies. This hyper-efficiency is likely due to the increased turbulence in these systems, which decreases the freefall time compared to star-forming galaxies, leading to "enhanced" star formation efficiency. Line wings are present in a non-negligible subsample (11/28) of the CARMA GOALS sources and are likely due to outflows driven by AGNs or star formation, gas inflows, or additional decoupled gas components., Comment: 29 pages, 4 tables, 11 figures, Accepted by the Astrophysical Journal

Persistent homology (PH) is a method for generating topology-inspired representations of data. Empirical studies that investigate the properties of PH, such as its sensitivity to perturbations or ability to detect a feature of interest, commonly rely on training and testing an additional model on the basis of the PH representation. To gain more intrinsic insights about PH, independently of the choice of such a model, we propose a novel methodology based on the pull-back geometry that a PH encoding induces on the data manifold. The spectrum and eigenvectors of the induced metric help to identify the most and least significant information captured by PH. Furthermore, the pull-back norm of tangent vectors provides insights about the sensitivity of PH to a given perturbation, or its potential to detect a given feature of interest, and in turn its ability to solve a given classification or regression problem. Experimentally, the insights gained through our methodology align well with the existing knowledge about PH. Moreover, we show that the pull-back norm correlates with the performance on downstream tasks, and can therefore guide the choice of a suitable PH encoding.

Polymer brushes, coatings consisting of densely grafted macromolecules, experience an intrinsic lateral compressive pressure, originating from chain elasticity and excluded volume interactions. This lateral pressure complicates a proper definition of the interface and, thereby, the determination and interpretation of the interfacial tension and its relation to the wetting behavior of brushes. Here, we study the link between grafting-induced compressive lateral pressure in polymer brushes, interfacial tension, and brush wettability using coarse-grained molecular dynamics simulations. We focus on grafting densities and polymer-liquid affinities such that the polymer and liquid do not tend to mix. For these systems, a central result is that the liquid contact angle is independent of the grafting density, which implies that the grafting-induced lateral compressive pressure in the brush does not influence its wettability. Although the definition of brush interfacial tensions is complicated by the grafting-induced pressure, the difference in interfacial tension between wet and dry brushes is perfectly well-defined. We confirm explicitly from Young's law that this difference offers an accurate description of the brush wettability. We then explore a method to isolate the grafting-induced contribution to the lateral pressure, assuming the interfacial tension to be independent of grafting density. This scenario indeed allows to disentangle interfacial and grafting effects for a broad range of parameters, except close to the mixing point. We separately discuss the latter case in the light of autophobic dewetting.

Post-starburst galaxies (PSBs) have recently and rapidly quenched their star-formation, thus they are an important way to understand how galaxies transition from star-forming late-types to quiescent early-types. The recent discovery of large cold gas reservoirs in PSBs calls into question the theory that galaxies must lose their gas to become quiescent. Optical Integral Field Spectroscopy (IFS) surveys have revealed two classes of PSBs: central PSBs with central quenching regions and ring PSBs with quenching in their outskirts. We analyze a sample of 13 nearby (z < 0.1) PSBs with spatially resolved optical IFS data from the Mapping Nearby Galaxies at Apache Point Observatory (MaNGA) survey and matched resolution Atacama Large (sub-)Millimeter Array (ALMA) observations of $^{12}$CO(1-0). Disturbed stellar kinematics in 7/13 of our PSBs and centrally concentrated molecular gas is consistent with a recent merger for most of our sample. In galaxies without merger evidence, alternate processes may funnel gas inwards and suppress star-formation, which may include outflows, stellar bars, and minor mergers or interactions. The star-formation efficiencies of the post-starburst regions in nearly half our galaxies are suppressed while the gas fractions are consistent with star-forming galaxies. AGN feedback may drive this stabilization, and we observe AGN-consistent emission in the centers of 5/13 galaxies. Finally, our central and ring PSBs have similar properties except the ionized and molecular gas in central PSBs is more disturbed. Overall, the molecular gas in our PSBs tends to be compact and highly disturbed, resulting in concentrated gas reservoirs unable to form stars efficiently., Comment: Accepted for publication in The Astrophysical Journal

A database driven web application is a very common software solution to rising business problems. Modeling the database and the software architecture can be challenging, hence there not being one combined modeling language for database and software architecture, specifically suited for web application development. In this paper we present Database object-oriented Modeling Language (DooML) and its primary Archetype Diagram: a notation for specifying the design of a database schema and corresponding object-oriented software architecture. It combines the syntax for drawing Entity Relationship Diagrams, the Relational Model and Universal Modeling Language Class Diagrams as well to create a mixed diagram, stating database design as well as software design specifications. By default, DooML ensures that the approach of advanced web application development is model-driven and both database-oriented as well as object-oriented., Comment: 9 pages. International Journal of Software Engineering & Applications (IJSEA), Chennai, India (2022)

We present a multiwavelength study of IC 860, a nearby post-starburst galaxy at the early stage of transitioning from blue and star-forming to red and quiescent. Optical images reveal a galaxy-wide, dusty outflow originating from a compact core. We find evidence for a multiphase outflow in the molecular and neutral gas phase from the CO position-velocity diagram and NaD absorption features. We constrain the neutral mass outflow rate to be ~0.5 M$_{\odot}/$yr, and the total hydrogen mass outflow rate to be ~12 M$_{\odot}$/yr. Neither outflow component seems able to escape the galaxy. We also find evidence for a recent merger in the optical images, CO spatial distribution, and kinematics, and evidence for a buried AGN in the optical emission line ratios, mid-IR properties, and radio spectral shape. The depletion time of the molecular gas reservoir under the current star formation rate is ~7 Gyr, indicating that the galaxy could stay at the intermediate stage between the blue and red sequence for a long time. Thus the timescales for a significant decline in star formation rate ("quenching") and gas depletion are not necessarily the same. Our analysis supports the quenching picture where outflows help suppress star formation by disturbing rather than expelling the gas and shed light on possible ongoing activities in similar quenching galaxies., Comment: 31 pages, 15 figures, accepted for publication in The Astrophysical Journal. Online material will be available from the publisher

Persistent homology (PH) is one of the most popular methods in Topological Data Analysis. Even though PH has been used in many different types of applications, the reasons behind its success remain elusive; in particular, it is not known for which classes of problems it is most effective, or to what extent it can detect geometric or topological features. The goal of this work is to identify some types of problems where PH performs well or even better than other methods in data analysis. We consider three fundamental shape analysis tasks: the detection of the number of holes, curvature and convexity from 2D and 3D point clouds sampled from shapes. Experiments demonstrate that PH is successful in these tasks, outperforming several baselines, including PointNet, an architecture inspired precisely by the properties of point clouds. In addition, we observe that PH remains effective for limited computational resources and limited training data, as well as out-of-distribution test data, including various data transformations and noise. For convexity detection, we provide a theoretical guarantee that PH is effective for this task in $\mathbb{R}^d$, and demonstrate the detection of a convexity measure on the FLAVIA data set of plant leaf images. Due to the crucial role of shape classification in understanding mathematical and physical structures and objects, and in many applications, the findings of this work will provide some knowledge about the types of problems that are appropriate for PH, so that it can - to borrow the words from Wigner 1960 - ``remain valid in future research, and extend, to our pleasure", but to our lesser bafflement, to a variety of applications., Comment: Main text 10 pages; Appendices 23 pages; References 6 pages; 32 figures. To appear in Advances in Neural Information Processing Systems 35 (NeurIPS 2022). Theorem 1 guarantees that PH with respect to the tubular filtration (Definition 1, Figure 9) can detect convexity in any d-dimensional Euclidean space (Appendix A). A convexity measure is detected with PH on a real-world dataset (Appendix G)

Magnitude is an isometric invariant for metric spaces that was introduced by Leinster around 2010, and is currently the object of intense research, since it has been shown to encode many known invariants of metric spaces. In recent work, Govc and Hepworth introduced persistent magnitude, a numerical invariant of a filtered simplicial complex associated to a metric space. Inspired by Govc and Hepworth's definition, we introduce alpha magnitude and investigate some of its key properties. Heuristic observations lead us to conjecture a relationship with the Minkowski dimension of compact subspaces of Euclidean space. Finally, alpha magnitude presents computational advantages over both magnitude as well as Rips magnitude, and we thus propose it as a new measure for the estimation of fractal dimensions of real-world data sets that is easily computable., Comment: 26 pages, 8 figures

Chest Computational Tomography (CT) scans present low cost, speed and objectivity for COVID-19 diagnosis and deep learning methods have shown great promise in assisting the analysis and interpretation of these images. Most hospitals or countries can train their own models using in-house data, however empirical evidence shows that those models perform poorly when tested on new unseen cases, surfacing the need for coordinated global collaboration. Due to privacy regulations, medical data sharing between hospitals and nations is extremely difficult. We propose a GAN-augmented federated learning model, dubbed ST-FL (Style Transfer Federated Learning), for COVID-19 image segmentation. Federated learning (FL) permits a centralised model to be learned in a secure manner from heterogeneous datasets located in disparate private data silos. We demonstrate that the widely varying data quality on FL client nodes leads to a sub-optimal centralised FL model for COVID-19 chest CT image segmentation. ST-FL is a novel FL framework that is robust in the face of highly variable data quality at client nodes. The robustness is achieved by a denoising CycleGAN model at each client of the federation that maps arbitrary quality images into the same target quality, counteracting the severe data variability evident in real-world FL use-cases. Each client is provided with the target style, which is the same for all clients, and trains their own denoiser. Our qualitative and quantitative results suggest that this FL model performs comparably to, and in some cases better than, a model that has centralised access to all the training data., Comment: 5 pages, 1 figure, full version (15 pages, 13 figures) to be published in SPIE: Medical Imaging 2022 Proceedings

The Baldwin, Philips, & Terlevich diagram of [O III]/H$\beta$ vs. [N II]/H$\alpha$ (hereafter N2-BPT) has long been used as a tool for classifying galaxies based on the dominant source of ionizing radiation. Recent observations have demonstrated that galaxies at $z\sim2$ reside offset from local galaxies in the N2-BPT space. In this paper, we conduct a series of controlled numerical experiments to understand the potential physical processes driving this offset. We model nebular line emission in a large sample of galaxies, taken from the SIMBA cosmological hydrodynamic galaxy formation simulation, using the CLOUDY photoionization code to compute the nebular line luminosities from H II regions. We find that the observed shift toward higher [O III]/H$\beta$ and [N II]/H$\alpha$ values at high redshift arises from sample selection: when we consider only the most massive galaxies $M_* \sim 10^{10-11} M_\odot$, the offset naturally appears, due to their high metallicities. We predict that deeper observations that probe lower-mass galaxies will reveal galaxies that lie on a locus comparable to $z\sim 0$ observations. Even when accounting for sample selection effects, we find that there is a subtle mismatch between simulations and observations. To resolve this discrepancy, we investigate the impact of varying ionization parameters, H II region densities, gas-phase abundance patterns, and increasing radiation field hardness on N2-BPT diagrams. We find that either decreasing the ionization parameter or increasing the N/O ratio of galaxies at fixed O/H can move galaxies along a self-similar arc in N2-BPT space that is occupied by high-redshift galaxies., Comment: 25 pages, 15 figures. Accepted for publication in ApJ

This paper documents the seventeenth data release (DR17) from the Sloan Digital Sky Surveys; the fifth and final release from the fourth phase (SDSS-IV). DR17 contains the complete release of the Mapping Nearby Galaxies at Apache Point Observatory (MaNGA) survey, which reached its goal of surveying over 10,000 nearby galaxies. The complete release of the MaNGA Stellar Library (MaStar) accompanies this data, providing observations of almost 30,000 stars through the MaNGA instrument during bright time. DR17 also contains the complete release of the Apache Point Observatory Galactic Evolution Experiment 2 (APOGEE-2) survey which publicly releases infra-red spectra of over 650,000 stars. The main sample from the Extended Baryon Oscillation Spectroscopic Survey (eBOSS), as well as the sub-survey Time Domain Spectroscopic Survey (TDSS) data were fully released in DR16. New single-fiber optical spectroscopy released in DR17 is from the SPectroscipic IDentification of ERosita Survey (SPIDERS) sub-survey and the eBOSS-RM program. Along with the primary data sets, DR17 includes 25 new or updated Value Added Catalogs (VACs). This paper concludes the release of SDSS-IV survey data. SDSS continues into its fifth phase with observations already underway for the Milky Way Mapper (MWM), Local Volume Mapper (LVM) and Black Hole Mapper (BHM) surveys., Comment: 40 pages, 8 figures, 6 tables. In press at ApJSS (arxiv v2 corrects some minor typos and updates references)