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We propose a construction of $d^2$ complex equiangular lines in $\mathbb{C}^d$, also known as SICPOVMs, which were conjectured by Zauner to exist for all d. The construction gives a putatively complete list of SICs with Weyl-Heisenberg symmetry in all dimensions d > 3. Specifically, we give an explicit expression for an object that we call a ghost SIC, which is constructed from the real multiplication values of a special function and which is Galois conjugate to a SIC. The special function, the Shintani-Faddeev modular cocycle, is a tuple of meromorphic functions indexed by a congruence subgroup of $\mathrm{SL}_2(\mathbb{Z})$. We prove that our construction gives a valid SIC in every case assuming two conjectures: the order 1 abelian Stark conjecture for real quadratic fields and a special value identity for the Shintani-Faddeev modular cocycle. The former allows us to prove that the ghost and the SIC are Galois conjugate over an extension of $\mathbb{Q}(\sqrt{\Delta})$ where $\Delta = (d+1)(d-3)$, while the latter allows us to prove idempotency of the presumptive fiducial projector. We provide computational tests of our SIC construction by cross-validating it with known exact solutions, with the numerical work of Scott and Grassl, and by constructing four numerical examples of inequivalent SICs in d=100, three of which are new. We further consider rank-r generalizations called r-SICs given by equichordal configurations of r-dimensional complex subspaces. We give similar conditional constructions for r-SICs for all r, d such that r(d-r) divides $(d^2-1)$. Finally, we study the structure of the field extensions conjecturally generated by the r-SICs. If $K$ is any real quadratic field, then either every abelian Galois extension of $K$, or else every abelian extension for which 2 is unramified, is generated by our construction; the former holds for a positive density of field discriminants., Comment: 183 pages (133 main + 50 appendices), 6 figures. Feedback welcome! Source code available at https://github.com/sflammia/Zauner.jl

This paper presents a case study on the development of Auto-AdvER, a specialised named entity recognition schema and dataset for text in the car advertisement genre. Developed with industry needs in mind, Auto-AdvER is designed to enhance text mining analytics in this domain and contributes a linguistically unique NER dataset. We present a schema consisting of three labels: "Condition", "Historic" and "Sales Options". We outline the guiding principles for annotation, describe the methodology for schema development, and show the results of an annotation study demonstrating inter-annotator agreement of 92% F1-Score. Furthermore, we compare the performance by using encoder-only models: BERT, DeBERTaV3 and decoder-only open and closed source Large Language Models (LLMs): Llama, Qwen, GPT-4 and Gemini. Our results show that the class of LLMs outperforms the smaller encoder-only models. However, the LLMs are costly and far from perfect for this task. We present this work as a stepping stone toward more fine-grained analysis and discuss Auto-AdvER's potential impact on advertisement analytics and customer insights, including applications such as the analysis of market dynamics and data-driven predictive maintenance. Our schema, as well as our associated findings, are suitable for both private and public entities considering named entity recognition in the automotive domain, or other specialist domains., Comment: 11 pages, 1 figure, 3 tables

Effective monitoring of wildlife is critical for assessing biodiversity and ecosystem health, as declines in key species often signal significant environmental changes. Birds, particularly ground-nesting species, serve as important ecological indicators due to their sensitivity to environmental pressures. Camera traps have become indispensable tools for monitoring nesting bird populations, enabling data collection across diverse habitats. However, the manual processing and analysis of such data are resource-intensive, often delaying the delivery of actionable conservation insights. This study presents an AI-driven approach for real-time species detection, focusing on the curlew (Numenius arquata), a ground-nesting bird experiencing significant population declines. A custom-trained YOLOv10 model was developed to detect and classify curlews and their chicks using 3/4G-enabled cameras linked to the Conservation AI platform. The system processes camera trap data in real-time, significantly enhancing monitoring efficiency. Across 11 nesting sites in Wales, the model achieved high performance, with a sensitivity of 90.56%, specificity of 100%, and F1-score of 95.05% for curlew detections, and a sensitivity of 92.35%, specificity of 100%, and F1-score of 96.03% for curlew chick detections. These results demonstrate the capability of AI-driven monitoring systems to deliver accurate, timely data for biodiversity assessments, facilitating early conservation interventions and advancing the use of technology in ecological research.

This document is comprised of a collection of updated preliminary parameters for the key parts of the muon collider. The updated preliminary parameters follow on from the October 2023 Tentative Parameters Report. Particular attention has been given to regions of the facility that are believed to hold greater technical uncertainty in their design and that have a strong impact on the cost and power consumption of the facility. The data is collected from a collaborative spreadsheet and transferred to overleaf.

This paper considers the asymptotic behaviour of deterministically and stochastically forced linear pantograph equations. The asymptotic behaviour is studied in the case when all solutions of the pantograph equation without forcing tend to a trivial equilibrium. In all cases, we give necessary and sufficient conditions on the forcing terms which enable all solutions to converge to the equilibrium of the unforced equation, and which enable solutions to remain bounded. In the deterministic case, we give sharp conditions on forcing terms which enable the solutions of the forced equations to inherit the power law behaviour of the unforced equation, as well as slower rates of decay or growth not present in the unforced equation., Comment: 19 pages

This is the first of a two-part paper which determines necessary and sufficient conditions on the asymptotic behaviour of forcing functions so that the solutions of additively pertubed linear differential equations obey certain growth or decay estimates. Part I considers deterministic equations, and part II It\^o-type stochastic differential equations. Results from part I are used to deal with deterministically and stochastically forced equations in the second part. Results apply to both scalar and multi-dimensional equations, and connect the asymptotic behaviour of time averages of the forcing terms on finite intervals with the growth or decay rate of the solution. Mainly, results deal with large perturbations, but some indications of how results extend to tackle subdominant perturbations are also sketched., Comment: 40 pages

In circular particle accelerators, storage rings, or colliders, mitigating beam losses is critical to ensuring optimal performance, particularly for rings that include superconducting magnets. A thorough understanding of beam-halo dynamics is essential for this purpose. This paper presents recent results for the measurement of the nonlinear diffusion process of the beam halo at the CERN Large Hadron Collider (LHC). The novel approach used in this paper is based on the analytical framework of the Nekhoroshev theorem, which provides a functional form for the diffusion coefficient. By monitoring the beam loss signal during controlled movements of the collimator jaws, we determine the beam losses at equilibrium for various amplitudes and analyze the beam-halo distribution. Post-processing of these measurements provides the nonlinear diffusion coefficient, which is found to be in excellent agreement with the theoretical assumptions. Measurements from an experiment investigating the effectiveness of beam-beam compensation using beam-beam compensation wires also provide a direct assessment of the compensation's effectiveness on beam-tail diffusion.

The structure of the low redshift Universe is dominated by a multi-scale void distribution delineated by filaments and walls of galaxies. The characteristics of voids; such as morphology, average density profile, and correlation function, can be used as cosmological probes. However, their physical properties are difficult to infer due to shot noise and the general lack of tracer particles used to define them. In this work, we construct a robust, topology-based void finding algorithm that utilizes Persistent Homology (PH) to detect persistent features in the data. We apply this approach to a volume limited sub-sample of galaxies in the SDSS I/II Main Galaxy catalog with the $r$-band absolute magnitude brighter than $M_r=-20.19$, and a set of mock catalogs constructed using the Horizon Run 4 cosmological $N$-body simulation. We measure the size distribution of voids, their averaged radial profile, sphericity, and the centroid nearest neighbor separation, using conservative values for the threshold and persistence. We find $32$ topologically robust voids in the SDSS data over the redshift range $0.02 \leq z \leq 0.116$, with effective radii in the range $21 - 56 \, h^{-1} \, {\rm Mpc}$. The median nearest neighbor void separation is found to be $\sim 57 \, h^{-1} \, {\rm Mpc}$, and the median radial void profile is consistent with the expected shape from the mock data., Comment: Accepted for publication in ApJ

We test whether Lyman alpha emitters (LAEs) and Lyman-break galaxies (LBGs) can be good tracers of high-z large-scale structures, using the Horizon Run 5 cosmological hydrodynamical simulation. We identify LAEs using the Ly{\alpha} emission line luminosity and its equivalent width, and LBGs using the broad-band magnitudes at z~2.4, 3.1, and 4.5. We first compare the spatial distributions of LAEs, LBGs, all galaxies, and dark matter around the filamentary structures defined by dark matter. The comparison shows that both LAEs and LBGs are more concentrated toward the dark matter filaments than dark matter. We also find an empirical fitting formula for the vertical density profile of filaments as a binomial power-law relation of the distance to the filaments. We then compare the spatial distributions of the samples around the filaments defined by themselves. LAEs and LBGs are again more concentrated toward their filaments than dark matter. We also find the overall consistency between filamentary structures defined by LAEs, LBGs, and dark matter, with the median spatial offsets that are smaller than the mean separation of the sample. These results support the idea that the LAEs and LBGs could be good tracers of large-scale structures of dark matter at high redshifts., Comment: 20 pages, 15 figures, 2 tables, accepted for publication in ApJ (affiliations are updated in v2)

The degree of Gaussianity of a field offers insights into its cosmological nature, and its statistical properties serve as indicators of its Gaussianity. In this work, we examine the signatures of Gaussianity in a gravitational wave background (GWB) by analyzing the cumulants of the one- and two-point functions of the relevant observable, using pulsar timing array (PTA) simulations as a proof-of-principle. This appeals to the ongoing debate about the source of the spatially-correlated common-spectrum process observed in PTAs, which is likely associated with a nanohertz stochastic GWB. We investigate the distribution of the sample statistics of the one-point function in the presence of a Gaussian GWB. Our results indicate that, within PTAs, one-point statistics are impractical for constraining the Gaussianity of the nanohertz GWB due to dominant pulsar noises. However, our analysis of two-point statistics shows promise, suggesting that it may be possible to constrain the Gaussianity of the nanohertz GWB using PTA data. We also emphasize that the Gaussian signatures identified in the one- and two-point functions in this work are expected to be applicable to any gravitational wave background., Comment: 18 pages + refs, 9 figures, v2: discussion improved, to appear in JCAP

The International Muon Collider Collaboration (IMCC) [1] was established in 2020 following the recommendations of the European Strategy for Particle Physics (ESPP) and the implementation of the European Strategy for Particle Physics-Accelerator R&D Roadmap by the Laboratory Directors Group [2], hereinafter referred to as the the European LDG roadmap. The Muon Collider Study (MuC) covers the accelerator complex, detectors and physics for a future muon collider. In 2023, European Commission support was obtained for a design study of a muon collider (MuCol) [3]. This project started on 1st March 2023, with work-packages aligned with the overall muon collider studies. In preparation of and during the 2021-22 U.S. Snowmass process, the muon collider project parameters, technical studies and physics performance studies were performed and presented in great detail. Recently, the P5 panel [4] in the U.S. recommended a muon collider R&D, proposed to join the IMCC and envisages that the U.S. should prepare to host a muon collider, calling this their "muon shot". In the past, the U.S. Muon Accelerator Programme (MAP) [5] has been instrumental in studies of concepts and technologies for a muon collider., Comment: This document summarises the International Muon Collider Collaboration (IMCC) progress and status of the Muon Collider R&D programme

In this article we discuss the requirements needed in order to characterise the solution space of perturbed linear integro-differential Volterra convolution equations. We highlight in general how the pointwise behaviour of perturbation functions does not necessarily propagate through to the solution which the classical literature seems to suggest. To illustrate this general idea we show the Ces\`aro mean of the solution can converge even in cases when the Ces\`aro mean of the perturbation function diverges. Furthermore we provide a characterisation of when such convergence takes place and explicitly identify the limit in terms of the problem data. Additionally we prove how all results can also be applied to perturbed linear functional differential equations., Comment: 18 pages

In this article we are concerned with characterising when solutions of perturbed linear stochastic Volterra summation equations are $p$-summable along with when their continuous time counterparts, perturbed linear stochastic Volterra integrodifferential equations are $p$-integrable. In the discrete case we find it necessary and sufficient that perturbing functions are $p$-summable in order to ensure paths of the discrete equation are $p$-summable almost surely, while in the continuous case it transpires one can have almost surely $p$-integrable sample paths even with non-integrable perturbation functions. For the continuous equation the main converse is clinched by considering an appropriate discretisation and applying results from the discrete case., Comment: 24 pages

We present LinkQ, a system that leverages a large language model (LLM) to facilitate knowledge graph (KG) query construction through natural language question-answering. Traditional approaches often require detailed knowledge of complex graph querying languages, limiting the ability for users -- even experts -- to acquire valuable insights from KG data. LinkQ simplifies this process by first interpreting a user's question, then converting it into a well-formed KG query. By using the LLM to construct a query instead of directly answering the user's question, LinkQ guards against the LLM hallucinating or generating false, erroneous information. By integrating an LLM into LinkQ, users are able to conduct both exploratory and confirmatory data analysis, with the LLM helping to iteratively refine open-ended questions into precise ones. To demonstrate the efficacy of LinkQ, we conducted a qualitative study with five KG practitioners and distill their feedback. Our results indicate that practitioners find LinkQ effective for KG question-answering, and desire future LLM-assisted systems for the exploratory analysis of graph databases.

Despite decision-making being a vital goal of data visualization, little work has been done to differentiate decision-making tasks within the field. While visualization task taxonomies and typologies exist, they often focus on more granular analytical tasks that are too low-level to describe large complex decisions, which can make it difficult to reason about and design decision-support tools. In this paper, we contribute a typology of decision-making tasks that were iteratively refined from a list of design goals distilled from a literature review. Our typology is concise and consists of only three tasks: CHOOSE, ACTIVATE, and CREATE. Although decision types originating in other disciplines exist, we provide definitions for these tasks that are suitable for the visualization community. Our proposed typology offers two benefits. First, the ability to compose and hierarchically organize the tasks enables flexible and clear descriptions of decisions with varying levels of complexities. Second, the typology encourages productive discourse between visualization designers and domain experts by abstracting the intricacies of data, thereby promoting clarity and rigorous analysis of decision-making processes. We demonstrate the benefits of our typology through four case studies, and present an evaluation of the typology from semi-structured interviews with experienced members of the visualization community who have contributed to developing or publishing decision support systems for domain experts. Our interviewees used our typology to delineate the decision-making processes supported by their systems, demonstrating its descriptive capacity and effectiveness. Finally, we present preliminary findings on the usefulness of our typology for visualization design.

Dimensionality reduction techniques are widely used for visualizing high-dimensional data. However, support for interpreting patterns of dimension reduction results in the context of the original data space is often insufficient. Consequently, users may struggle to extract insights from the projections. In this paper, we introduce DimBridge, a visual analytics tool that allows users to interact with visual patterns in a projection and retrieve corresponding data patterns. DimBridge supports several interactions, allowing users to perform various analyses, from contrasting multiple clusters to explaining complex latent structures. Leveraging first-order predicate logic, DimBridge identifies subspaces in the original dimensions relevant to a queried pattern and provides an interface for users to visualize and interact with them. We demonstrate how DimBridge can help users overcome the challenges associated with interpreting visual patterns in projections.

Stochastic battery bidding in real-time energy markets is a nuanced process, with its efficacy depending on the accuracy of forecasts and the representative scenarios chosen for optimization. In this paper, we introduce a pioneering methodology that amalgamates Transformer-based forecasting with weighted constrained Dynamic Time Warping (wcDTW) to refine scenario selection. Our approach harnesses the predictive capabilities of Transformers to foresee Energy prices, while wcDTW ensures the selection of pertinent historical scenarios by maintaining the coherence between multiple uncertain products. Through extensive simulations in the PJM market for July 2023, our method exhibited a 10% increase in revenue compared to the conventional method, highlighting its potential to revolutionize battery bidding strategies in real-time markets.

We present a mixed-methods study to explore how large language models (LLMs) can assist users in the visual exploration and analysis of knowledge graphs (KGs). We surveyed and interviewed 20 professionals from industry, government laboratories, and academia who regularly work with KGs and LLMs, either collaboratively or concurrently. Our findings show that participants overwhelmingly want an LLM to facilitate data retrieval from KGs through joint query construction, to identify interesting relationships in the KG through multi-turn conversation, and to create on-demand visualizations from the KG that enhance their trust in the LLM's outputs. To interact with an LLM, participants strongly prefer a chat-based 'widget,' built on top of their regular analysis workflows, with the ability to guide the LLM using their interactions with a visualization. When viewing an LLM's outputs, participants similarly prefer a combination of annotated visuals (e.g., subgraphs or tables extracted from the KG) alongside summarizing text. However, participants also expressed concerns about an LLM's ability to maintain semantic intent when translating natural language questions into KG queries, the risk of an LLM 'hallucinating' false data from the KG, and the difficulties of engineering a 'perfect prompt.' From the analysis of our interviews, we contribute a preliminary roadmap for the design of LLM-driven knowledge graph exploration systems and outline future opportunities in this emergent design space.

Large energy acceptance arcs have been proposed for applications such as cancer therapy, muon accelerators, and recirculating linacs. The efficacy of charged particle therapy can be improved by reducing the energy layer switching time, however this is currently limited by the small momentum acceptance of the beam delivery system ($<\pm$1\%). A `closed-dispersion arc' with a large momentum acceptance has the potential to remove this bottleneck, however such a beamline has not yet been constructed. We have developed a design methodology for large momentum acceptance arcs with Fixed Field Accelerator optics, applying it to a demonstrator beam delivery system for protons at 0.5--3.0MeV $\pm$42\% momentum acceptance) as part of the TURBO project at the University of Melbourne. Using realistic magnetic fields, a beamline has been designed with zero dispersion at either end. An algorithm has been devised for the construction of permanent magnet Halbach arrays for this beamline with multipole error below one part in $10^4$, using commercially available magnets. The sensitivity to errors has been investigated, finding that the delivered beam is robust in realistic conditions. This study demonstrates that a closed-dispersion arc with fixed fields can achieve a large momentum acceptance, and we outline future work required to develop these ideas into a complete proof-of-principle beam delivery system that can be scaled up for a medical facility., Comment: 20 pages including references, 16 figures. For submission to PRAB

Exclusion zones in the cross-correlations between critical points (peak-void, peak-wall, filament-wall, filament-void) of the density field define quasi-standard rulers that can be used to constrain dark matter and dark energy cosmological parameters. The average size of the exclusion zone is found to scale linearly with the typical distance between extrema. The latter changes as a function of the matter content of the universe in a predictable manner, but its comoving size remains essentially constant in the linear regime of structure growth on large scales, unless the incorrect cosmology is assumed in the redshift-distance relation. This can be used to constrain the dark energy parameters when considering a survey that scans a range of redshifts. The precision of the parameter estimation is assessed using a set of cosmological simulations, and is found to be a 4$\sigma$ detection of a change in matter content of 5%, or about 3.8$\sigma$ detection of 50% shift in the dark energy parameter using a full sky survey up to redshift 0.5., Comment: 12 pages (including a 3-page appendix, 9 figures, 2 tables. Submitted to MNRAS

Content recommendation tasks increasingly use Graph Neural Networks, but it remains challenging for machine learning experts to assess the quality of their outputs. Visualization systems for GNNs that could support this interrogation are few. Moreover, those that do exist focus primarily on exposing GNN architectures for tuning and prediction tasks and do not address the challenges of recommendation tasks. We developed RekomGNN, a visual analytics system that supports ML experts in exploring GNN recommendations across several dimensions and making annotations about their quality. RekomGNN straddles the design space between Neural Network and recommender system visualization to arrive at a set of encoding and interaction choices for recommendation tasks. We found that RekomGNN helps experts make qualitative assessments of the GNN's results, which they can use for model refinement. Overall, our contributions and findings add to the growing understanding of visualizing GNNs for increasingly complex tasks.

The Upgrade II of the LHCb experiment is proposed to be installed during the CERN Long Shutdown 4, aiming to operate LHCb at 1.5x$10^{34}cm^{-2}s^{-1}$ that is 75 times its design luminosity and reaching an integrated luminosity of about $400 fb^{-1}$ by the end of the High Luminosity LHC era. This increase of the data sample at LHCb is an unprecedented opportunity for heavy flavour physics measurements. A first upgrade of LHCb, completed in 2022, has already implemented important changes of the LHCb detector and, for the Upgrade II, further detector improvements are being considered. Such a luminosity increase will have an impact not only on the LHCb detector but also on the LHC magnets, cryogenics and electronic equipment placed in the IR8. In fact, the LHCb experiment was conceived to work at a much lower luminosity than ATLAS and CMS, implying minor requirements for protection of the LHC elements from the collision debris and therefore a different layout around the interaction point. The luminosity target proposed for the Upgrade II requires to review the layout of the entire insertion region in order to ensure safe operation of the LHC magnets and to mitigate the risk of failure of the electronic devices. The objective of this paper is to provide an overview of the implications of the Upgrade II of LHCb in the experimental cavern and in the tunnel with a focus on the LHCb detector, electronic devices and accelerator magnets.

The two-point statistics of the cosmic velocity field, measured from galaxy peculiar velocity (PV) surveys, can be used as a dynamical probe to constrain the growth rate of large-scale structures in the universe. Most works use the statistics on scales down to a few tens of Megaparsecs, while using a theoretical template based on the linear theory. In addition, while the cosmic velocity is volume-weighted, the observable line-of-sight velocity two-point correlation is density-weighted, as sampled by galaxies, and therefore the density-velocity correlation term also contributes, which has often been neglected. These effects are fourth order in powers of the linear density fluctuation $\delta_{\rm L}^4$, compared to $\delta_{\rm L}^2$ of the linear velocity correlation function, and have the opposite sign. We present these terms up to $\delta_{\rm L}^4$ in real space based on the standard perturbation theory, and investigate the effect of non-linearity and the density-velocity contribution on the inferred growth rate $f\sigma_8$, using $N$-body simulations. We find that for a next-generation PV survey of volume $\sim {\cal O}(500 \, h^{-1} \, {\rm Mpc})^3$, these effects amount to a shift of $f\sigma_8$ by $\sim 10$ per cent and is comparable to the forecasted statistical error when the minimum scale used for parameter estimation is $r_{\rm min} = 20 \, h^{-1} \, {\rm Mpc}$., Comment: 17 pages, 6 figures. Minor corrections to non-linear calculation in section 2.2, conclusions unchanged. Accepted for publication in MNRAS

We describe the survey design and science goals for ODIN (One-hundred-deg^2 DECam Imaging in Narrowbands), a NOIRLab survey using the Dark Energy Camera (DECam) to obtain deep (AB~25.7) narrow-band images over an unprecedented area of sky. The three custom-built narrow-band filters, N419, N501, and N673, have central wavelengths of 419, 501, and 673 nm and respective full-widthat-half-maxima of 7.2, 7.4, and 9.8 nm, corresponding to Lya at z=2.4, 3.1, and 4.5 and cosmic times of 2.8, 2.1, and 1.4 Gyr, respectively. When combined with even deeper, public broad-band data from Hyper Suprime-Cam, DECam, and in the future, LSST, the ODIN narrow-band images will enable the selection of over 100,000 Lya-emitting (LAE) galaxies at these epochs. ODIN-selected LAEs will identify protoclusters as galaxy overdensities, and the deep narrow-band images enable detection of highly extended Lya blobs (LABs). Primary science goals include measuring the clustering strength and dark matter halo connection of LAEs, LABs, and protoclusters, and their respective relationship to filaments in the cosmic web. The three epochs allow the redshift evolution of these properties to be determined during the period known as Cosmic Noon, where star formation was at its peak. The two narrow-band filter wavelengths are designed to enable interloper rejection and further scientific studies by revealing [O II] and [O III] at z=0.34, Lya and He II 1640 at z=3.1, and Lyman continuum plus Lya at z=4.5. Ancillary science includes similar studies of the lower-redshift emission-line galaxy samples and investigations of nearby star-forming galaxies resolved into numerous [O III] and [S II] emitting regions., Comment: 21 pages, 8 figures, submitted to Astrophysical Journal

Dynamical cancellation frameworks present a potential means of mitigating the effect of a large vacuum energy, that would otherwise ruin the late-time, low energy dynamics of the Universe. Certain models in the literature, such as the Fab Four and Well Tempering, realize this idea by introducing some degeneracy in the dynamical equations. In this paper, we introduce a third potential route to self-tuning, and infer the existence of a new, exact Milne solution in the simplest tadpole plus cubic-Galileon scalar-tensor theory. We study the dynamics of the scalar field and metric in the vicinity of the Milne coordinate singularity, and find that the vacuum solution belongs to a more general family of Milne-like metrics. By numerically evolving the field equations for a range of initial conditions, we show that the Milne solution is not an attractor, and varying the initial scalar field data can lead to completely different asymptotic states; exponential growth of the scale factor, a static non-spatially flat metric or a severe finite-time instability in the scalar field and metric. We generalise the Milne solution to a class of FLRW spacetimes, finding that the tadpole-cubic Galileon model admits perfect-fluid-like solutions in the presence of matter. Finally, we present a second Horndeski model which also admits an exact Milne solution, hinting at the existence of a larger undiscovered model space containing vacuum-energy-screened solutions., Comment: 20 pages + refs, 4 figures, comments welcome

In this paper we characterise the Lp stability of perturbed linear Volterra integrodifferential convolution equations. Additionally we provide a framework which points to necessary and sufficient conditions on the forcing function that ensures the solution lies in a particular function space. We highlight how such a result is of interest when studying perturbed Stochastic Functional Differential Equations (SFDEs)., Comment: 6 pages

Spatial interpolation is a class of estimation problems where locations with known values are used to estimate values at other locations, with an emphasis on harnessing spatial locality and trends. Traditional Kriging methods have strong Gaussian assumptions, and as a result, often fail to capture complexities within the data. Inspired by the recent progress of graph neural networks, we introduce Kriging Convolutional Networks (KCN), a method of combining the advantages of Graph Convolutional Networks (GCN) and Kriging. Compared to standard GCNs, KCNs make direct use of neighboring observations when generating predictions. KCNs also contain the Kriging method as a specific configuration. We further improve the model's performance by adding attention. Empirically, we show that this model outperforms GCNs and Kriging in several applications. The implementation of KCN using PyTorch is publicized at the GitHub repository: https://github.com/tufts-ml/kcn-torch.

Automatic analysis of customer data for businesses is an area that is of interest to companies. Business to business data is studied rarely in academia due to the sensitive nature of such information. Applying natural language processing can speed up the analysis of prohibitively large sets of data. This paper addresses this subject and applies sentiment analysis, topic modelling and keyword extraction to a B2B data set. We show that accurate sentiment can be extracted from the notes automatically and the notes can be sorted by relevance into different topics. We see that without clear separation topics can lack relevance to a business context.

We extract the galaxy density and momentum power spectra from a subset of early-type galaxies in the SDSS DR7 main galaxy catalog. Using galaxy distance information inferred from the improved fundamental plane described in \citet{Yoon_2020}, we reconstruct the peculiar velocities of the galaxies and generate number density and density-weighted velocity fields, from which we extract the galaxy density and momentum power spectra. We compare the measured values to the theoretical expectation of the same statistics, assuming an input $\Lambda$CDM model and using a third-order perturbative expansion. After validating our analysis pipeline with a series of mock data sets, we apply our methodology to the SDSS data and arrive at constraints $f\sigma_{8} = 0.471_{-0.080}^{+0.077}$ and $b_{1}\sigma_{8} = 0.920_{-0.070}^{+0.070}$ at a mean redshift $\bar{z} = 0.04$. Our result is consistent with the Planck cosmological best fit parameters for the $\Lambda$CDM model. The momentum power spectrum is found to be strongly contaminated by small scale velocity dispersion, which suppresses power by $\sim {\cal O}(30\%)$ on intermediate scales $k \sim 0.05 \, h \, {\rm Mpc}^{-1}$., Comment: 15 figures, 4 tables, accepted for ApJ

The apparent shape of galaxy clustering depends on the adopted cosmology used to convert observed redshift to comoving distance, the $r(z)$ relation, as it changes the line elements along and across the line of sight differently. The Alcock-Paczy\'nski (AP) test exploits this property to constrain the expansion history of the universe. We present an extensive review of past studies on the AP test. We adopt an extended AP test method introduced by Park et al. (2019), which uses the full shape of redshift-space two-point correlation function (CF) as the standard shape, and apply it to the SDSS DR7, BOSS, and eBOSS LRG samples covering the redshift range up to $z=0.8$.We calibrate the test against the nonlinear cosmology-dependent systematic evolution of the CF shape using the Multiverse simulations. We focus on examining whether or not the flat $\Lambda$CDM `concordance' model is consistent with observation. We constrain the flat $w$CDM model to have $w=-0.892_{-0.050}^{+0.045}$ and $\Omega_m=0.282_{-0.023}^{+0.024}$ from our AP test alone, which is significantly tighter than the constraints from the BAO or SNe I$a$ methods by a factor of 3 - 6. When the AP test result is combined with the recent BAO and SNe I$a$ results, we obtain $w=-0.903_{-0.023}^{+0.023}$ and $\Omega_m=0.285_{-0.009}^{+0.014}$. This puts a strong tension with the flat $\Lambda$CDM model with $w=-1$ at $4.2\sigma$ level. Consistency with $w=-1$ is obtained only when the Planck CMB observation is combined. It remains to see if this tension between observations of galaxy distribution at low redshifts and CMB anisotropy at the decoupling epoch becomes greater in the future studies and leads us to a new paradigm of cosmology., Comment: 21 pages, 11 figures, accepted by ApJ

In this paper we investigate the mean square asymptotic stability of a perturbed scalar linear stochastic functional differential equation. Specifically, we are able to give necessary and sufficient conditions on the forcing terms for convergence of the mean square, exponential convergence of the mean square, and integrability of the mean square of solutions. It is also essential that the underlying unperturbed SFDE is mean square asymptotically stable for these results to hold., Comment: 36 pages, to appear in Applied Numerical Mathematics as part of the conference proceedings for FAATNA (Functional Analysis, Approximation Theory and Numerical Analysis), Matera Italy, July 2022

This study presents insights from interviews with nineteen Knowledge Graph (KG) practitioners who work in both enterprise and academic settings on a wide variety of use cases. Through this study, we identify critical challenges experienced by KG practitioners when creating, exploring, and analyzing KGs that could be alleviated through visualization design. Our findings reveal three major personas among KG practitioners - KG Builders, Analysts, and Consumers - each of whom have their own distinct expertise and needs. We discover that KG Builders would benefit from schema enforcers, while KG Analysts need customizable query builders that provide interim query results. For KG Consumers, we identify a lack of efficacy for node-link diagrams, and the need for tailored domain-specific visualizations to promote KG adoption and comprehension. Lastly, we find that implementing KGs effectively in practice requires both technical and social solutions that are not addressed with current tools, technologies, and collaborative workflows. From the analysis of our interviews, we distill several visualization research directions to improve KG usability, including knowledge cards that balance digestibility and discoverability, timeline views to track temporal changes, interfaces that support organic discovery, and semantic explanations for AI and machine learning predictions.

Purpose: Thoracic radiographs are commonly used to evaluate patients with confirmed or suspected thoracic pathology. Proper patient positioning is more challenging in canine and feline radiography than in humans due to less patient cooperation and body shape variation. Improper patient positioning during radiograph acquisition has the potential to lead to a misdiagnosis. Asymmetrical hemithoraces are one of the indications of obliquity for which we propose an automatic classification method. Approach: We propose a hemithoraces segmentation method based on Convolutional Neural Networks (CNNs) and active contours. We utilized the U-Net model to segment the ribs and spine and then utilized active contours to find left and right hemithoraces. We then extracted features from the left and right hemithoraces to train an ensemble classifier which includes Support Vector Machine, Gradient Boosting and Multi-Layer Perceptron. Five-fold cross-validation was used, thorax segmentation was evaluated by Intersection over Union (IoU), and symmetry classification was evaluated using Precision, Recall, Area under Curve and F1 score. Results: Classification of symmetry for 900 radiographs reported an F1 score of 82.8% . To test the robustness of the proposed thorax segmentation method to underexposure and overexposure, we synthetically corrupted properly exposed radiographs and evaluated results using IoU. The results showed that the models IoU for underexposure and overexposure dropped by 2.1% and 1.2%, respectively. Conclusions: Our results indicate that the proposed thorax segmentation method is robust to poor exposure radiographs. The proposed thorax segmentation method can be applied to human radiography with minimal changes., Comment: Submitted to SPIE Journal of Medical Imaging