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We develop an analytical approach for the description of quantum many-body scars in PXP models. We show that the scarred dynamics in the PXP model on a complete bipartite graph can be interpreted as a one-dimensional chiral scattering problem, and solve this problem analytically. The insights from this analysis allow us to predict that dynamical signatures of scars in PXP models can be enhanced by spin squeezing the initial states. We show numerically that this stabilization mechanism applies not only to the complete bipartite graph but also to one- and two-dimensional lattices, which are relevant for Rydberg atom array experiments. Moreover, our findings provide a physical motivation for Hamiltonian deformations reminiscent of those known to produce perfect scars., Comment: 12 pages, 6 figures

Regularization is used in many different areas of optimization when solutions are sought which not only minimize a given function, but also possess a certain degree of regularity. Popular applications are image denoising, sparse regression and machine learning. Since the choice of the regularization parameter is crucial but often difficult, path-following methods are used to approximate the entire regularization path, i.e., the set of all possible solutions for all regularization parameters. Due to their nature, the development of these methods requires structural results about the regularization path. The goal of this article is to derive these results for the case of a smooth objective function which is penalized by a piecewise differentiable regularization term. We do this by treating regularization as a multiobjective optimization problem. Our results suggest that even in this general case, the regularization path is piecewise smooth. Moreover, our theory allows for a classification of the nonsmooth features that occur in between smooth parts. This is demonstrated in two applications, namely support-vector machines and exact penalty methods.

The two sources AGC 226178 and NGVS 3543, an extremely faint, clumpy, blue stellar system and a low surface brightness dwarf spheroidal, are adjacent systems in the direction of the Virgo cluster. Both have been studied in detail previously, with it being suggested that they are unrelated normal dwarf galaxies or that NGVS 3543 recently lost its gas through ram pressure stripping, and that AGC 226178 formed from this stripped gas. However, with HST ACS imaging we demonstrate that the stellar population of NGVS 3543 is inconsistent with being at the distance of the Virgo cluster, and that it is likely a foreground object at approximately 10 Mpc. Whereas the stellar population of AGC 226178 is consistent with it being a very young (10-100 Myr) object in the Virgo cluster. Through a re-analysis of the original ALFALFA HI detection we show that AGC 226178 likely formed from gas stripped from the nearby dwarf galaxy VCC 2034, a hypothesis strengthened by the high metallicity measured with MUSE VLT observations. However, it is unclear whether ram pressure or a tidal interaction is responsible for stripping the gas. AGC 226178 is one of at least five similar objects now known towards Virgo. These objects are all young and unlikely to remain visible for over ~500 Myr, suggesting that they are continually produced in the cluster., Comment: Accepted to ApJL

Perfusion imaging is an interesting new modality for evaluation and assessment of the liver cancer treatment. C-Arm CT provides a possibility to perform perfusion imaging scans intra-operatively for even faster evaluation. The slow speed of the C-Arm CT rotation and the presence of the noise, however, have an impact on the reconstruction and therefore model based approaches have to be applied. In this work we apply the Time separation technique (TST), to denoise data, speed up reconstruction and improve resulting perfusion images. We show on animal experiment data that Dynamic C-Arm CT Liver Perfusion Imaging together with the processing of the data based on the TST provides comparable results to standard CT liver perfusion imaging., Comment: 5 pages, 8 figures, published in Proceedings of the 16th Virtual International Meeting on Fully 3D Image Reconstruction in Radiology and Nuclear Medicine 2021 arXiv:2110.04143

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: Some material in Sections 3 and 4 have reordered to emphasize the main result of each section. Other small changes throughout based on referee feedback. To appear in the Electronic Journal of Combinatorics

Fast and reliable monitoring of volumetric heat distribution during MRI-guided tumor ablation is an urgent clinical need. In this work, we introduce a method for generating 2.5D thermometry maps from uniformly distributed 2D MRI phase images rotated around the applicator's main axis. The images can be fetched directly from the MR device, reducing the delay between image acquisition and visualization. For reconstruction, we use a weighted interpolation on a cylindric coordinate representation to calculate the heat value of voxels in a region of interest. A pilot study on 13 ex vivo bio protein phantoms with flexible tubes to simulate a heat sink effect was conducted to evaluate our method. After thermal ablation, we compared the measured coagulation zone extracted from the post-treatment MR data set with the output of the 2.5D thermometry map. The results show a mean Dice score of 0.75+-0.07, a sensitivity of 0.77+-0.03, and a reconstruction time within 18.02ms+-5.91ms. Future steps should address improving temporal resolution and accuracy, e.g., incorporating advanced bioheat transfer simulations., Comment: 11 pages and 4 figures, submitted to and accepted by the 24th International Conference on Medical Image Computing and Computer Assisted Intervention (MICCAI 2021)

Footprints are left, or obtained, in a variety of scenarios from crime scenes to anthropological investigations. Determining the sex of a footprint can be useful in screening such impressions and attempts have been made to do so using single or multi landmark distances, shape analyses and via the density of friction ridges. Here we explore the relative importance of different components in sexing two-dimensional foot impressions namely, size, shape and texture. We use a machine learning approach and compare this to more traditional methods of discrimination. Two datasets are used, a pilot data set collected from students at Bournemouth University (N=196) and a larger data set collected by podiatrists at Sheffield NHS Teaching Hospital (N=2677). Our convolutional neural network can sex a footprint with accuracy of around 90% on a test set of N=267 footprint images using all image components, which is better than an expert can achieve. However, the quality of the impressions impacts on this success rate, but the results are promising and in time it may be possible to create an automated screening algorithm in which practitioners of whatever sort (medical or forensic) can obtain a first order sexing of a two-dimensional footprint.

Despite decades of clinical research, sepsis remains a global public health crisis with high mortality, and morbidity. Currently, when sepsis is detected and the underlying pathogen is identified, organ damage may have already progressed to irreversible stages. Effective sepsis management is therefore highly time-sensitive. By systematically analysing trends in the plethora of clinical data available in the intensive care unit (ICU), an early prediction of sepsis could lead to earlier pathogen identification, resistance testing, and effective antibiotic and supportive treatment, and thereby become a life-saving measure. Here, we developed and validated a machine learning (ML) system for the prediction of sepsis in the ICU. Our analysis represents the largest multi-national, multi-centre in-ICU study for sepsis prediction using ML to date. Our dataset contains $156,309$ unique ICU admissions, which represent a refined and harmonised subset of five large ICU databases originating from three countries. Using the international consensus definition Sepsis-3, we derived hourly-resolved sepsis label annotations, amounting to $26,734$ ($17.1\%$) septic stays. We compared our approach, a deep self-attention model, to several clinical baselines as well as ML baselines and performed an extensive internal and external validation within and across databases. On average, our model was able to predict sepsis with an AUROC of $0.847 \pm 0.050$ (internal out-of sample validation) and $0.761 \pm 0.052$ (external validation). For a harmonised prevalence of $17\%$, at $80\%$ recall our model detects septic patients with $39\%$ precision 3.7 hours in advance.

The steadily increasing luminosity of the LHC requires an upgrade with high-rate and high-resolution detector technology for the inner end cap of the ATLAS muon spectrometer: the New Small Wheels (NSW). In order to achieve the goal of precision tracking at a hit rate of about 15 kHz/cm$^2$ at the inner radius of the NSW, large area Micromegas quadruplets with 100\,\microns spatial resolution per plane have been produced. % IRFU, from the CEA research center of Saclay, is responsible for the production and validation of LM1 Micromegas modules. The construction, production, qualification and validation of the largest Micromegas detectors ever built are reported here. Performance results under cosmic muon characterisation will also be discussed., Comment: To be submitted to NIMA

We compare the star-forming properties of satellites around Milky Way (MW) analogs from the Stage~II release of the Satellites Around Galactic Analogs Survey (SAGA-II) to those from the APOSTLE and Auriga cosmological zoom-in simulation suites. We use archival GALEX UV imaging as a star-formation indicator for the SAGA-II sample and derive star-formation rates (SFRs) to compare with those from APOSTLE and Auriga. We compare our detection rates from the NUV and FUV bands to the SAGA-II H$\alpha$ detections and find that they are broadly consistent with over $85\%$ of observed satellites detected in all three tracers. We apply the same spatial selection criteria used around SAGA-II hosts to select satellites around the MW-like hosts in APOSTLE and Auriga. We find very good overall agreement in the derived SFRs for the star-forming satellites as well as the number of star-forming satellites per host in observed and simulated samples. However, the number and fraction of quenched satellites in the SAGA-II sample are significantly lower than those in APOSTLE and Auriga below a stellar mass of $M_*\sim10^{8}\,M_{\odot}$, even when the SAGA-II incompleteness and interloper corrections are included. This discrepancy is robust with respect to the resolution of the simulations and persists when alternative star-formation tracers are employed. We posit that this disagreement is not readily explained by vagaries in the observed or simulated samples considered here, suggesting a genuine discrepancy that may inform the physics of satellite populations around MW analogs., Comment: Accepted for publication in ApJ Letters after minor changes to text

We establish asymptotic properties of $M$-estimators, defined in terms of a contrast function and observations from a continuous-time locally stationary process. Using the stationary approximation of the sequence, $\theta$-weak dependence, and hereditary properties, we give sufficient conditions on the contrast function that ensure consistency and asymptotic normality of the $M$-estimator. As an example, we obtain consistency and asymptotic normality of a localized least squares estimator for observations from a sequence of time-varying L\'evy-driven Ornstein-Uhlenbeck processes. Furthermore, for a sequence of time-varying L\'evy-driven state space models, we show consistency of a localized Whittle estimator and an $M$-estimator that is based on a quasi maximum likelihood contrast. Simulation studies show the applicability of the estimation procedures.

We introduce a general theory on stationary approximations for locally stationary continuous-time processes. Based on the stationary approximation, we use $\theta$-weak dependence to establish laws of large numbers and central limit type results under different observation schemes. Hereditary properties for a large class of finite and infinite memory transformations show the flexibility of the developed theory. Sufficient conditions for the existence of stationary approximations for time-varying L\'evy-driven state space models are derived and compared to existing results. We conclude with comprehensive results on the asymptotic behavior of the first and second order localized sample moments of time-varying L\'evy-driven state space models.

We adapt the classical definition of locally stationary processes in discrete-time to the continuous-time setting and obtain equivalent representations in the time and frequency domain. From this, a unique time-varying spectral density is derived using the Wigner-Ville spectrum. As an example, we investigate time-varying L\'evy-driven state space processes, including the class of time-varying L\'evy-driven CARMA processes. First, the connection between these two classes of processes is examined. Considering a sequence of time-varying L\'evy-driven state space processes, we then give sufficient conditions on the coefficient functions that ensure local stationarity with respect to the given definition.

We have followed up two ultra-diffuse galaxies (UDGs), detected adjacent to stellar streams, with Hubble Space Telescope (HST) imaging and HI mapping with the Jansky Very Large Array (VLA) in order to investigate the possibility that they might have a tidal origin. With the HST F814W and F555W images we measure the globular cluster (GC) counts for NGC 2708-Dw1 and NGC 5631-Dw1 as $2^{+1}_{-1}$ and $5^{+1}_{-2}$, respectively. NGC 2708-Dw1 is undetected in HI down to a 3$\sigma$ limit of $\log (M_\mathrm{HI}/\mathrm{M_\odot}) = 7.3$, and there is no apparent HI associated with the nearby stellar stream. There is a 2$\sigma$ HI feature coincident with NGC 5631-Dw1. However, this emission is blended with a large gaseous tail emanating from NGC 5631 and is not necessarily associated with the UDG. The presence of any GCs and the lack of clear HI connections between the UDGs and their parent galaxies strongly disfavor a tidal dwarf galaxy origin, but cannot entirely rule it out. The GC counts are consistent with those of normal dwarf galaxies, and the most probable formation mechanism is one where these UDGs were born as normal dwarfs and were later tidally stripped and heated. We also identify an over-luminous ($M_\mathrm{V} = -11.1$) GC candidate in NGC 2708-Dw1, which may be a nuclear star cluster transitioning to an ultra-compact dwarf as the surrounding dwarf galaxy gets stripped of stars., Comment: Accepted to ApJ

It is hypothesized that short-term exposure to air pollution may influence the transmission of aerosolized pathogens such as COVID-19. We used data from 23 provinces in Italy to build a generalized additive model to investigate the association between the effective reproductive number of the disease and air quality while controlling for ambient environmental variables and changes in human mobility. The model finds that there is a positive, nonlinear relationship between the density of particulate matter in the air and COVID-19 transmission, which is in alignment with similar studies on other respiratory illnesses., Comment: Supplementary materials available at: https://jds-online.org/journal/JDS/article/549/info

Quantifying entanglement properties of mixed states in quantum field theory via entanglement of purification and reflected entropy is a new and challenging subject. In this work, we study both quantities for two spherical subregions far away from each other in the vacuum of a conformal field theory in any number of dimensions. Using lattice techniques, we find an elementary proof that the decay of both, the entanglement of purification and reflected entropy, is enhanced with respect to the mutual information behaviour by a logarithm of the distance between the subregions. In the case of the Ising spin chain at criticality and the related free fermion conformal field theory, we compute also the overall coefficients numerically for the both quantities of interest., Comment: 5 pages, 2 figures + appendices; v2: previous results unchanged, added proof of the long-distance behaviour of EoP, reorganized presentation

We present observations of the dwarf galaxies GALFA Dw3 and GALFA Dw4 with the Advanced Camera for Surveys (ACS) on the Hubble Space Telescope (HST). These galaxies were initially discovered as optical counterparts to compact HI clouds in the GALFA survey. Both objects resolve into stellar populations which display an old red giant branch, younger helium burning, and massive main sequence stars. We use the tip of the red giant branch method to determine the distance to each galaxy, finding distances of 7.61$_{-0.29}^{+0.28}$ Mpc and 3.10$_{-0.17}^{+0.16}$ Mpc, respectively. With these distances we show that both galaxies are extremely isolated, with no other confirmed objects within ~1.5 Mpc of either dwarf. GALFA Dw4 is also found to be unusually compact for a galaxy of its luminosity. GALFA Dw3 and Dw4 contain HII regions with young star clusters and an overall irregular morphology; they show evidence of ongoing star formation through both ultraviolet and H$\alpha$ observations and are therefore classified as dwarf irregulars (dIrrs). The star formation histories of these two dwarfs show distinct differences: Dw3 shows signs of a recently ceased episode of active star formation across the entire dwarf, while Dw4 shows some evidence for current star formation in spatially limited HII regions. Compact HI sources offer a promising method for identifying isolated field dwarfs in the Local Volume, including GALFA Dw3 & Dw4, with the potential to shed light on the driving mechanisms of dwarf galaxy formation and evolution., Comment: 18 pages, 7 figures, 1 table, submitted to ApJ

We present a novel algorithm that allows us to gain detailed insight into the effects of sparsity in linear and nonlinear optimization, which is of great importance in many scientific areas such as image and signal processing, medical imaging, compressed sensing, and machine learning (e.g., for the training of neural networks). Sparsity is an important feature to ensure robustness against noisy data, but also to find models that are interpretable and easy to analyze due to the small number of relevant terms. It is common practice to enforce sparsity by adding the $\ell_1$-norm as a weighted penalty term. In order to gain a better understanding and to allow for an informed model selection, we directly solve the corresponding multiobjective optimization problem (MOP) that arises when we minimize the main objective and the $\ell_1$-norm simultaneously. As this MOP is in general non-convex for nonlinear objectives, the weighting method will fail to provide all optimal compromises. To avoid this issue, we present a continuation method which is specifically tailored to MOPs with two objective functions one of which is the $\ell_1$-norm. Our method can be seen as a generalization of well-known homotopy methods for linear regression problems to the nonlinear case. Several numerical examples - including neural network training - demonstrate our theoretical findings and the additional insight that can be gained by this multiobjective approach., Comment: Accepted by IEEE TPAMI 2021

We optimize multilayered anti-reflective coatings for photovoltaic devices, using modern evolutionary algorithms. We apply a rigorous methodology to show that a given structure, which is particularly regular, emerge spontaneously in a very systematical way for a very broad range of conditions. The very regularity of the structure allows for a thorough physical analysis of how the designs operate. This allows to understand that the central part is a photonic crystal utilized as a buffer for light, and that the external layers have the purpose of reducing the impedance mismatch between the outer media and the Bloch mode supported by the photonic crystal. This shows how optimization can suggest new design rules and be considered as a source of inspiration. Finally, we fabricate these structures with easily deployable techniques.

An unsolved challenge in cooking automation is designing for shared kitchen workspaces. In particular, robots struggle with dexterity in the unstructured and dynamic kitchen environment. We propose that human-machine collaboration can be achieved without robotic manipulation. We describe a novel system design using computer vision to inform intelligent cooking interventions. This human-centered approach does not require actuators and promotes dynamic, natural collaboration. We show that automation that assists user-led actions can offer meaningful cooking assistance and can generate the image databases needed for fully autonomous robotic systems of the future. We provide an open source implementation of our work and encourage the research community to build upon it., Comment: 6 pages, 7 figures. Open source repository is available at https://github.com/onionbot

Finding pure states in an enlarged Hilbert space that encode the mixed state of a quantum field theory as a partial trace is necessarily a challenging task. Nevertheless, such purifications play the key role in characterizing quantum information-theoretic properties of mixed states via entanglement and complexity of purifications. In this article, we analyze these quantities for two intervals in the vacuum of free bosonic and Ising conformal field theories using, for the first time, the~most general Gaussian purifications. We provide a comprehensive comparison with existing results and identify universal properties. We further discuss important subtleties in our setup: the massless limit of the free bosonic theory and the corresponding behaviour of the mutual information, as well as the Hilbert space structure under the Jordan-Wigner mapping in the spin chain model of the Ising conformal field theory., Comment: 31 pages, 14 figures

We exploit insights into the geometry of bosonic and fermionic Gaussian states to develop an efficient local optimization algorithm to extremize arbitrary functions on these families of states. The method is based on notions of gradient descent attuned to the local geometry which also allows for the implementation of local constraints. The natural group action of the symplectic and orthogonal group enables us to compute the geometric gradient efficiently. While our parametrization of states is based on covariance matrices and linear complex structures, we provide compact formulas to easily convert from and to other parametrization of Gaussian states, such as wave functions for pure Gaussian states, quasiprobability distributions and Bogoliubov transformations. We review applications ranging from approximating ground states to computing circuit complexity and the entanglement of purification that have both been employed in the context of holography. Finally, we use the presented methods to collect numerical and analytical evidence for the conjecture that Gaussian purifications are sufficient to compute the entanglement of purification of arbitrary mixed Gaussian states., Comment: 33 pages, supplementary Mathematica package with example notebook (as ancillary file)

In pioneering works of Meyer and of McMullen in the early 1970s, the set of Minkowski summands of a polytope was shown to be a polyhedral cone called the type cone. Explicit computations of type cones are in general intractable. Nevertheless, we show that the type cone of the product of simplices is the cone over a simplex. This remarkably simple result derives from insights about rainbow point configurations and the work of McMullen., Comment: 12 pages, 4 figures. Incorporated referee suggestions, minor edits throughout. This version focuses more on type cones of products of simplices than the previous version. Introduction has been partially rewritten to reflect this change. To appear in the Bulletin of the London Mathematical Society

The Dual-zone Aperture X-ray Solar Spectrometer (DAXSS) was flown on 2018 June18 on the NASA 36.336 sounding rocket flight and obtained the highest resolution to date for solar soft X-ray (SXR) spectra over a broad energy range. This observation was during a time with quiescent (non-flaring) small active regions on the solar disk and when the 10.7 cm radio flux (F10.7) was 75 solar flux units (1 sfu = 10-22 W/m^2/Hz). The DAXSS instrument consists of a LASP-developed dual-zone aperture and a commercial X-ray spectrometer from Amptek that measures solar full-disk irradiance from 0.5-20 keV with a resolving power of 20 near 1 keV. This paper discusses the novel design of the spectrometer and the instrument characterization techniques. Additionally,the solar measurements obtained from the 2018 sounding rocket flight are analyzed using CHIANTI spectral models to fit the temperatures, emission measures, and relative elemental abundances of the solar corona plasma. The abundance of iron was found to be 35 percent higher than expected in the quiescent sun's corona suggesting either that our spectral models require additional sophistication or that the underlying atomic database may require updates. Future long-term systematic observations of this spectral range are needed. DAXSS will fly on the INSPIRESat-1 CubeSat in late-2020, and its SXR spectral data could provide further insight into the sources of coronal heating through modeling the changes of relative elemental abundances during developments of active regions and solar flaring events., Comment: 21 pages, 12 figures, Submitted to The Astrophysical Journal

We obtain central limit theorems for stationary random fields employing a novel measure of dependence called $\theta$-lex weak dependence. We show that this dependence notion is more general than strong mixing, i.e., it applies to a broader class of models. Moreover, we discuss hereditary properties for $\theta$-lex and $\eta$-weak dependence and illustrate the possible applications of the weak dependence notions to the study of the asymptotic properties of stationary random fields. Our general results apply to mixed moving average fields (MMAF in short) and ambit fields. We show general conditions such that MMAF and ambit fields, with the volatility field being an MMAF or a $p$-dependent random field, are weakly dependent. For all the models mentioned above, we give a complete characterization of their weak dependence coefficients and sufficient conditions to obtain the asymptotic normality of their sample moments. Finally, we give explicit computations of the weak dependence coefficients of MSTOU processes and analyze under which conditions the developed asymptotic theory applies to CARMA fields.

Given a family of lattice polytopes, two common questions in Ehrhart Theory are determining when a polytope has the integer decomposition property and determining when a polytope is reflexive. While these properties are of independent interest, the confluence of these properties is a source of active investigation due to conjectures regarding the unimodality of the $h^\ast$-polynomial. In this paper, we consider the Newton polytopes arising from two families of polynomials in algebraic combinatorics: Schur polynomials and inflated symmetric Grothendieck polynomials. In both cases, we prove that these polytopes have the integer decomposition property by using the fact that both families of polynomials have saturated Newton polytope. Furthermore, in both cases, we provide a complete characterization of when these polytopes are reflexive. We conclude with some explicit formulas and unimodality implications of the $h^\ast$-vector in the case of Schur polynomials., Comment: 37 pages, 3 tables, 4 figures; Comments Welcome; Version 2: updated references to acknowledge one result was previously known, corrected values in Table 1 and reference correct OEIS sequence; Version 3: Final Version. To appear in Electronic Journal of Combinatorics

In this article, we present an efficient descent method for locally Lipschitz continuous multiobjective optimization problems (MOPs). The method is realized by combining a theoretical result regarding the computation of descent directions for nonsmooth MOPs with a practical method to approximate the subdifferentials of the objective functions. We show convergence to points which satisfy a necessary condition for Pareto optimality. Using a set of test problems, we compare our method to the multiobjective proximal bundle method by M\"akel\"a. The results indicate that our method is competitive while being easier to implement. While the number of objective function evaluations is larger, the overall number of subgradient evaluations is lower. Finally, we show that our method can be combined with a subdivision algorithm to compute entire Pareto sets of nonsmooth MOPs.

We have obtained deep Hubble Space Telescope (HST) imaging of four faint and ultra-faint dwarf galaxy candidates in the vicinity of M101 - Dw21, Dw22, Dw23 and Dw35, originally discovered by Bennet et al. (2017). Previous distance estimates using the surface brightness fluctuation technique have suggested that these four dwarf candidates are the only remaining viable M101 satellites identified in ground based imaging out to the virial radius of M101 (D~250 kpc). Advanced Camera for Surveys imaging of all four dwarf candidates shows no associated resolved stellar populations, indicating that they are thus background galaxies. We confirm this by generating simulated HST color magnitude diagrams of similar brightness dwarfs at the distance of M101. Our targets would have displayed clear, resolved red giant branches with dozens of stars if they had been associated with M101. With this information, we construct a satellite luminosity function for M101, which is 90% complete to M_V=-7.7 mag and 50% complete to M_V=-7.4 mag, that extends into the ultra-faint dwarf galaxy regime. The M101 system is remarkably poor in satellites in comparison to the Milky Way and M31, with only eight satellites down to an absolute magnitude of M_V=-7.7 mag, compared to the 14 and 26 seen in the Milky Way and M31, respectively. Further observations of Milky Way analogs are needed to understand the halo-to-halo scatter in their faint satellite systems, and connect them with expectations from cosmological simulations., Comment: 9 Pages, 3 Figures, 1 Table, Accepted by ApJL