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Quantum signal processing (QSP) relies on a historically costly pre-processing step, "QSP-processing/phase-factor finding." QSP-processing is now a developed topic within quantum algorithms literature, and a beginner accessible review of QSP-processing is overdue. This work provides a whirlwind tour through QSP conventions and pre-processing methods, beginning from a pedagogically accessible QSP convention. We then review QSP conventions associated with three common polynomial types: real polynomials with definite parity, sums of reciprocal/anti-reciprocal Chebyshev polynomials, and complex polynomials. We demonstrate how the conventions perform with respect to three criteria: circuit length, polynomial conditions, and pre-processing methods. We then review the recently introduced Wilson method for QSP-processing and give conditions where it can succeed with bound error. Although the resulting bound is not computationally efficient, we demonstrate that the method succeeds with linear error propagation for relevant target polynomials and precision regimes, including the Jacobi-Anger expansion used in Hamiltonian simulation algorithms. We then apply our benchmarks to three QSP-processing methods for QSP circuits and show that a method introduced by Berntson and S\"underhauf outperforms both the Wilson method and the standard optimization strategy for complex polynomials.

In this paper, we investigate the degree of $h$-polynomials of edge ideals of finite simple graphs. In particular, we provide combinatorial formulas for the degree of the $h$-polynomial for various fundamental classes of graphs such as paths, cycles, and bipartite graphs. To the best of our knowledge, this marks the first investigation into the combinatorial interpretation of this algebraic invariant. Additionally, we characterize all connected graphs in which the sum of the Castelnuovo-Mumford regularity and the degree of the $h$-polynomial of an edge ideal reaches its maximum value, which is the number of vertices in the graph., Comment: 19 pages, 7 figures

Quantum signal processing (QSP) and its extensions are increasingly popular frameworks for developing quantum algorithms. Yet QSP implementations still struggle to complete a classical pre-processing step ('QSP-processing') that determines the set of $SU(2)$ rotation matrices defining the QSP circuit. We introduce a method of QSP-processing for complex polynomials that identifies a solution without optimization or root-finding and verify the success of our methods with polynomials characterized by floating point precision coefficients. We demonstrate the success of our technique for relevant target polynomials and precision regimes, including the Jacobi-Anger expansion used in QSP Hamiltonian Simulation. For popular choices of sign and inverse function approximations, we characterize regimes where all known QSP-processing methods should be expected to struggle without arbitrary precision arithmetic., Comment: 11 pages, 6 figures. IEEE International Conference on Quantum Computing and Engineering (QCE24) technical paper

To learn more about the properties of the Vela Supercluster (VSCL) located behind the Milky Way at $cz\sim 18000$~km~s$^{-1}$, we determined the $K_s$-band Luminosity Function (LF) of VC04, the richest known galaxy cluster in the VSCL, and two other VSCL clusters (VC02 and VC08). The galaxy sample is based on NIR observations which are complete to an extinction-corrected absolute magnitude of $M_{Ks}^o<-21.5$ mag ($\sim 2.5$ mag below $M_K^*$), within the clustercentric radius of $r_c<1.5~$Mpc ($\sim 70 \%$ of the Abell radius). For VC04 we obtained 90 new spectroscopic redshifts of galaxies observed with the 11-m Southern African Large Telescope. We found the Schechter parameters of the VC04 LF to be $M^*=-24.41\pm 0.44$ mag, $\alpha=-1.10\pm 0.20$ and $\phi^*=8.84\pm 0.20$. Both the redshift data and the LF confirm VC04 to be a rich, not yet fully relaxed cluster. We independently determined the LF of VC04 on membership defined by the Red-Sequence method and demonstrated that this method can be used in the absence of high spectroscopic coverage over a cluster. This allowed us to determine the LFs of VC02 and VC08. We also derived the LFs of the Coma, Norma and Virgo clusters to similar depth and extent as the VSCL clusters. We found that the Schechter parameters of VC04 are within $1\sigma$ uncertainties of these local clusters, as well as VC02 and VC08. We do not find significant differences between the LFs in the different cluster environments probed in this work down to $M_K^*+2.5$ mag., Comment: 19 pages, 12 figures and 9 tables. Accepted for publication in ApJ

Using deep imaging from the CANDELS and HFF surveys, we present bulge+disc decompositions with GalfitM for $\sim$17,000 galaxies over $0.2 \leq z\leq 1.5$. We use various model parameters to select reliable samples of discs and bulges, and derive their stellar masses using an empirically calibrated relation between mass-to-light ratio and colour. Across our entire redshift range, we show that discs follow stellar mass-size relations that are consistent with those of star-forming galaxies, suggesting that discs primarily evolve via star formation. In contrast, the stellar mass-size relations of bulges are mass-independent. Our novel dataset further enables us to separate components into star-forming and quiescent based on their specific star formation rates. We find that both star-forming discs and star-forming bulges lie on stellar mass-size relations that are similar to those of star-forming galaxies, while quiescent discs are typically smaller than star-forming discs and lie on steeper relations, implying distinct evolutionary mechanisms. Similar to quiescent galaxies, quiescent bulges show a flattening in the stellar mass-size relation at $\sim$10$^{10}$M$_\odot$, below which they show little mass dependence. However, their best-fitting relations have lower normalisations, indicating that at a given mass, bulges are smaller than quiescent galaxies. Finally, we obtain rest-frame colours for individual components, showing that bulges typically have redder colours than discs, as expected. We visually derive UVJ criteria to separate star-forming and quiescent components and show that this separation agrees well with component colour. HFF bulge+disc decomposition catalogues used for these analyses are publicly released with this paper., Comment: 30 pages, 18 figures, and 6 tables. Resubmitted to MNRAS after addressing a thorough and constructive referee report

This brief explains how four important system design initiatives frequently promoted by state and local education agencies for school improvement can be implemented through an intentional systematic approach for a powerful, positive impact on student outcomes. As technical assistance providers with expertise in four specific frameworks for educational system design, and with great appreciation for one another, the contributors suggest how a coordinated Stage-based Implementation process with embedded, systems level critical Equity Inquiries at every stage can enable schools to establish Universal Design for Learning (UDL) principles and guidelines within a Multi-Tiered System of Support (MTSS) for a designed experience in instructional decision making.

In recent years, strong expectations have been raised for the possible power of quantum computing for solving difficult optimization problems, based on theoretical, asymptotic worst-case bounds. Can we expect this to have consequences for Linear and Integer Programming when solving instances of practically relevant size, a fundamental goal of Mathematical Programming, Operations Research and Algorithm Engineering? Answering this question faces a crucial impediment: The lack of sufficiently large quantum platforms prevents performing real-world tests for comparison with classical methods. In this paper, we present a quantum analog for classical runtime analysis when solving real-world instances of important optimization problems. To this end, we measure the expected practical performance of quantum computers by analyzing the expected gate complexity of a quantum algorithm. The lack of practical quantum platforms for experimental comparison is addressed by hybrid benchmarking, in which the algorithm is performed on a classical system, logging the expected cost of the various subroutines that are employed by the quantum versions. In particular, we provide an analysis of quantum methods for Linear Programming, for which recent work has provided asymptotic speedup through quantum subroutines for the Simplex method. We show that a practical quantum advantage for realistic problem sizes would require quantum gate operation times that are considerably below current physical limitations., Comment: 39 pages, 8 figures

We present an overview of the CANDELS Lyman-a Emission At Reionization (CLEAR) survey. CLEAR is a 130 orbit program of the Hubble Space Telescope using the Wide Field Camera 3 (WFC3) IR G102 grism. CLEAR targets 12 pointings divided between the GOODS-N and GOODS-S fields of the Cosmic Assembly Near-IR Deep Extragalactic Legacy Survey (CANDELS). Combined with existing spectroscopic data from other programs, the full CLEAR dataset includes spectroscopic imaging of these fields over 0.8-1.7 um. In this Paper, we describe the CLEAR survey, the survey strategy, the data acquisition, reduction, processing, and science products and catalogs released alongside this paper. The catalogs include emission line fluxes and redshifts derived from the combination of the photometry and grism spectroscopy for 6048 galaxies, primarily ranging from 0.2 < z < 3. We also provide an overview of CLEAR science goals and results. In conjunction with this Paper we provide links to electronic versions of the data products, including 1D + 2D extracted spectra and emission line maps., Comment: Accepted in ApJS. 29 pages, 14 figures. The data products (1D + 2D spectra, emission line maps) and catalogs (photometric and spectroscopic catalogs of GOODS-N and GOODS-S) are available at https://archive.stsci.edu/hlsp/clear

There is currently a national debate surrounding what can and cannot be taught in K-12 public schools. In this Equity Dispatch we remember that centering equity and being able to recognize, name, and address the history of systemic racism and oppression in the United States is inclusive, not divisive.

Automatic segmentation of the placenta in fetal ultrasound (US) is challenging due to the (i) high diversity of placenta appearance, (ii) the restricted quality in US resulting in highly variable reference annotations, and (iii) the limited field-of-view of US prohibiting whole placenta assessment at late gestation. In this work, we address these three challenges with a multi-task learning approach that combines the classification of placental location (e.g., anterior, posterior) and semantic placenta segmentation in a single convolutional neural network. Through the classification task the model can learn from larger and more diverse datasets while improving the accuracy of the segmentation task in particular in limited training set conditions. With this approach we investigate the variability in annotations from multiple raters and show that our automatic segmentations (Dice of 0.86 for anterior and 0.83 for posterior placentas) achieve human-level performance as compared to intra- and inter-observer variability. Lastly, our approach can deliver whole placenta segmentation using a multi-view US acquisition pipeline consisting of three stages: multi-probe image acquisition, image fusion and image segmentation. This results in high quality segmentation of larger structures such as the placenta in US with reduced image artifacts which are beyond the field-of-view of single probes., Comment: 21 pages (18 + appendix), 13 figures (9 + appendix)

This paper presents an analytical and experimental design and deployment control analysis of a hyperbolic paraboloid cable net based on clustering actuation strategies. First, the dynamics and statics for clustered tensegrity structures (CTS) are given. Then, we propose the topology design of the deployable hyperbolic paraboloid cable net. The deployability of the cable net is achieved by using clustered cables. It is shown that the clustered cables significantly reduce the number of actuators required for control. The deployment trajectory and actuation prestress in the cables are designed to ensure the tensions are feasible during the deployment process. Then, we compare the deployment analysis's open-loop and closed-loop control strategies. Finally, a lab-scale model is constructed to validate the actuation laws. We test the static performance and deployment process of the experimental model. Results show that the closed-loop control approach is more stable and smoother than the open-loop one in the deployment process. The approaches developed in this paper can also be used for various deployable tensegrity structures., Comment: 20 pages, 24 figures

This work presents an extended ordinary state-based peridynamics (XOSBPD) model for the non-spherical horizons. Based on the OSBPD, we derive the XOSBPD by introducing the Lagrange multipliers to guarantee the non-local dilatation and non-local strain energy density (SED) are equal to local dilatation and local SED, respectively. In this formulation, the XOSBPD removes the limitation of spherical horizons and is suitable for arbitrary horizon shapes. In addition, the presented XOSBPD does not need volume and surface correction and allows non-uniform discretization implementation with various horizon sizes. Three classic examples demonstrate the accuracy and capability for complex dynamical fracture analysis. The proposed method provides an efficient tool and in-depth insight into the failure mechanism of structure components and solid materials., Comment: 19 pages, 9 figures

This paper presents the equilibrium and stiffness study of clustered tensegrity structures (CTS) considering pulley sizes. We first derive the geometric relationship between clustered strings and pulleys, where the nodal vector is chosen as the generalized coordinate. Then, the equilibrium equations of the clustered tensegrity structure with pulleys based on the Lagrangian method are given. Since the stiffness of a structure is usually weakened when using clustering strings, we formulate the tangent stiffness matrix equations for analysis. It is also shown that as pulley sizes go to zero, the governing equations of the clustered tensegrity system with pulleys yield to the classical clustered tensegrity structure without pulleys, which is consistent with the existing literature. Three examples are demonstrated to validate the given theory. The proposed method allows one to conduct equilibrium, stiffness, and robustness studies of cluster tensegrity structures with pulleys. Nevertheless, the approach developed in this paper is not limited to the tensegrity structures. It can also be applied to a wide range of applications with pulley-rope systems, such as drilling rigs, ocean platform anchors, and cargo cranes., Comment: 23 pages, 16 figures

The 3D-Drift And SHift (3D-DASH) program is a \textit{Hubble Space Telescope} WFC3 F160W imaging and G141 grism survey of the equatorial COSMOS field. 3D-DASH extends the legacy of HST near-infrared imaging and spectroscopy to degree-scale swaths of the sky, enabling the identification and study of distant galaxies ($z>2$) that are rare or in short-lived phases of galaxy evolution at rest-frame optical wavelengths. Furthermore, when combined with existing ACS/F814W imaging, the program facilitates spatially-resolved studies of the stellar populations and dust content of intermediate-redshift ($0.5

We report a comparative theoretical study of the \textit{Pnma} and \textit{R-3m} phases of Sb$_2$S$_3$, Bi$_2$S$_3$, and Sb$_2$Se$_3$ close to ambient pressure. Our enthalpy calculations at 0 K show that at ambient pressure the \textit{R-3m} (tetradymite-like) phase of Sb$_2$Se$_3$ is energetically more stable than the \textit{Pnma} phase, contrary to what is observed for Sb$_2$S$_3$ and Bi$_2$S$_3$, and irrespective of the exchange-correlation functional employed in the calculations. The result for Sb$_2$Se$_3$ is in contradiction to experiments where all three compounds are usually grown in the \textit{Pnma} phase. This result is further confirmed by free-energy calculations taking into account the temperature dependence of the unit-cell volumes and phonon frequencies. Lattice dynamics and elastic tensor calculations further show that both \textit{Pnma} and \textit{R-3m} phases of Sb$_2$Se$_3$ are dynamically and mechanically stable at zero applied pressure. Since these results suggest that the formation of the \textit{R-3m} phase for Sb$_2$Se$_3$ should be feasible at close to ambient conditions, we provide a theoretical crystal structure and simulated Raman and infrared spectra to help in its identification. We also discuss the results of the two published works that have claimed to have synthesized tetradymite-like Sb$_2$Se$_3$. Finally, the stability of the \textit{R-3m} phase across the three group-15 \textit{A$_2$X$_3$} sesquichalcogenides is analysed based on their van der Waals gap and X-X in-plane geometry., Comment: 17 pages, 9 figures

A number of authors have studied the question of when a graph can be represented as a Cayley graph on more than one nonisomorphic group. In this paper we give conditions for when a Cayley graph on an abelian group can be represented as a Cayley graph on a generalized dihedral group, and conditions for when the converse is true., Comment: 6 pages

We extend the analysis of Bok et al. (2020) in which the HI content of isolated galaxies from the AMIGA sample and selected paired galaxies from ALFALFA were examined as a potential driver of galaxy location on the WISE mid-infrared SFR-Mstar sequence. By further characterizing the isolated and pair galaxy samples, i.e. in terms of optical galaxy morphology, a more detailed and quantitative description of local galaxy environment by way of the local number density (eta) and tidal strength (Q) parameters, star formation efficiency (SFE(HI)), and HI integrated profile asymmetries, we present plausible pathways for the broadening of the pair sample HI deficiency distribution towards both high and low deficiencies compared to the narrower isolated galaxy sample distribution (i.e. sigma_pairs = 0.34 versus sigma_AMIGA = 0.28). We associate the gas-rich tail of the pair deficiency distribution with the highest Q values, large profile asymmetries, and low SFEs. From this we infer that merger activity is enhancing gas supplies, as well as disrupting the efficiency of star formation, via strong gravitational torques. The gas-poor wing of the deficiency distribution appears to be populated with galaxies in denser environments (with larger eta values on average), more akin to groups. Despite our gas-rich selection criterion, there is a small population of early-type galaxies in the pair sample, which primarily fall in the positive deficiency wing of the distribution. These results suggest that a combination of a denser galaxy environment, early-type morphology, and higher stellar mass, is contributing to the broadening of the deficiency distribution towards larger deficiencies.

In the local Universe, OH megamasers (OHMs) are detected almost exclusively in infrared-luminous galaxies, with a prevalence that increases with IR luminosity, suggesting that they trace gas-rich galaxy mergers. Given the proximity of the rest frequencies of OH and the hyperfine transition of neutral atomic hydrogen (HI), radio surveys to probe the cosmic evolution of HI in galaxies also offer exciting prospects for exploiting OHMs to probe the cosmic history of gas-rich mergers. Using observations for the Looking At the Distant Universe with the MeerKAT Array (LADUMA) deep HI survey, we report the first untargeted detection of an OHM at $z > 0.5$, LADUMA J033046.20$-$275518.1 (nicknamed "Nkalakatha"). The host system, WISEA J033046.26$-$275518.3, is an infrared-luminous radio galaxy whose optical redshift $z \approx 0.52$ confirms the MeerKAT emission line detection as OH at a redshift $z_{\rm OH} = 0.5225 \pm 0.0001$ rather than HI at lower redshift. The detected spectral line has 18.4$\sigma$ peak significance, a width of $459 \pm 59\,{\rm km\,s^{-1}}$, and an integrated luminosity of $(6.31 \pm 0.18\,{\rm [statistical]}\,\pm 0.31\,{\rm [systematic]}) \times 10^3\,L_\odot$, placing it among the most luminous OHMs known. The galaxy's far-infrared luminosity $L_{\rm FIR} = (1.576 \pm 0.013) \times 10^{12}\,L_\odot$ marks it as an ultra-luminous infrared galaxy; its ratio of OH and infrared luminosities is similar to those for lower-redshift OHMs. A comparison between optical and OH redshifts offers a slight indication of an OH outflow. This detection represents the first step towards a systematic exploitation of OHMs as a tracer of galaxy growth at high redshifts., Comment: 10 pages, 4 figures. Accepted to ApJ Letters

Re-committing to equity work means that equity-oriented educators must reflect on the impact of historical and systemic inequities on minoritized students, accepting that transformative change towards equity takes time and unrelenting and continuous hard work, and it means being willing to pursue educational equity even in the face of fierce opposition.

This "Equity by Design" brief highlights equity issues that arise in the process of reopening schools during a global pandemic. The authors examine state plans and guidance for reopening schools across states in the Midwest & Plains Equity Assistance Center (MAP EAC) region which includes the 13 states of Indiana, Illinois, Iowa, Kansas, Michigan, Minnesota, Missouri, Nebraska, North Dakota, Ohio, Oklahoma, South Dakota, and Wisconsin. The purpose of this paper is to provide explicit consideration of equity issues in the context of reopening schools and generate discussion about the topics addressed. The following topics are covered: (1) time spent in face-to-face instruction vs. virtual or hybrid learning environments and any calendar changes; (2) screening and reporting of COVID-19 symptoms and exposure; (3) social distancing, face masks and classroom set up; (4) ensuring more equitable learning for students with dis/abilities and multilingual learners; (5) access to technology; (6) opportunities and challenges in online learning, (7) communication with parent/caregivers; (8) addressing learning loss; (9) guidance on Social Emotional Learning (SEL); and (10) guidance on field trips and co-curricular and extra-curricular activities. Throughout this brief, the authors highlight equity issues that inevitably arise in the context of schooling where conditions of access are likely exacerbated by the pandemic and how one might approach and consider these issues in planning and policy. As school and district leaders review and revise policy implementation, the guidance outlined in this paper can inform the way that policy is implemented and can help highlight issues around equity that district and school personnel may not have considered in planning for reopening.

In this edition of "Equity Dispatch," we discuss equity implications around disciplinary policies in virtual learning contexts. We offer practical applications of principles of Universal Design for Learning & Culturally Responsive Pedagogy as proactive strategies for engaging students in virtual learning activities.

In this edition of "Equity Dispatch," we discuss the equity implications of the impact of online/distance learning, in the wake of the COVID-19 pandemic. As school districts are preparing to open, we argue the importance of positioning minoritized students' and families' knowledge production and lived experiences as assets in the development and delivery of online/distance learning.