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This chartbook is the 14th version to be produced for the Appalachian Regional Commission (ARC) by the Population Reference Bureau (PRB). The Chartbook describes the diversity of the Appalachian Region on a host of demographic and economic measures and provides an important annual view of the area and its people. The data contained in the 2018-2022 Chartbook describe how residents in the Appalachian Region were faring before and during the COVID-19 pandemic that began in March 2020. Nearly half of the years during this time period were pre-pandemic and half were during the pandemic era. Thus, this Chartbook is a blend of these two eras. As future data releases reflect the post-pandemic era, data users will have additional insights on the long-term changes that the pandemic brought to Appalachia's social and economic dynamics. Most of the data shown here come from the 2018-2022 American Community Survey (ACS), a nationwide study collected continuously every year in every county in the United States by the U.S. Census Bureau. The ACS is designed to provide communities with reliable and timely demographic, social, economic, and housing data each year. To provide as much county-level data as possible, we use ACS 5-year data files which provide reliable estimates for geographic areas with fewer than 20,000 people. Since many counties in the Appalachian Region have fewer than 20,000 residents, these data permit comparable statistics for all 423 counties in the Region. The primary purpose of the ACS is to measure the changing characteristics of the U.S. population in a way that is continually updated. The estimates in this Chartbook, therefore, are data collected over the five-year (or 60-month) period from January 2018 through December 2022. These ACS estimates are not averages of monthly or annual values, but rather an aggregation of data collected continuously over that time period.

We consider the existence of suitable weak solutions to the Cahn-Hilliard equation with a non-constant (degenerate) mobility on a class of evolving surfaces. We also show weak-strong uniqueness for the case of a positive mobility function, and under some further assumptions on the initial data we show uniqueness for a class of strong solutions for a degenerate mobility function., Comment: 30 pages

Effective monitoring of manufacturing processes is crucial for maintaining product quality and operational efficiency. Modern manufacturing environments generate vast amounts of multimodal data, including visual imagery from various perspectives and resolutions, hyperspectral data, and machine health monitoring information such as actuator positions, accelerometer readings, and temperature measurements. However, interpreting this complex, high-dimensional data presents significant challenges, particularly when labeled datasets are unavailable. This paper presents a novel approach to multimodal sensor data fusion in manufacturing processes, inspired by the Contrastive Language-Image Pre-training (CLIP) model. We leverage contrastive learning techniques to correlate different data modalities without the need for labeled data, developing encoders for five distinct modalities: visual imagery, audio signals, laser position (x and y coordinates), and laser power measurements. By compressing these high-dimensional datasets into low-dimensional representational spaces, our approach facilitates downstream tasks such as process control, anomaly detection, and quality assurance. We evaluate the effectiveness of our approach through experiments, demonstrating its potential to enhance process monitoring capabilities in advanced manufacturing systems. This research contributes to smart manufacturing by providing a flexible, scalable framework for multimodal data fusion that can adapt to diverse manufacturing environments and sensor configurations.

The Lane-Emden inequality controls $\iint_{\mathbb{R}^{2d}}\rho(x)\rho(y)|x-y|^{-\lambda}\,dx\,dy$ in terms of the $L^1$ and $L^p$ norms of $\rho$. We provide a remainder estimate for this inequality in terms of a suitable distance of $\rho$ to the manifold of optimizers.

We consider the surface Stokes equation with Lagrange multiplier and approach it numerically. Using a Taylor-Hood surface finite element method, along with an appropriate estimation for the additional Lagrange multiplier, we establish optimal convergence results for the velocity in $H^1$ and $L^2$, and in $L^2$ for the two pressures. Furthermore, we present a new inf-sup condition to help with the stability and convergence results. This formulation offers the advantage of simplified implementation without approximating geometric quantities, although it requires a higher approximation of the parameterized surface. In addition, we provide numerical simulations that confirm the established error bounds and perform a comparative analysis against the penalty approach., Comment: 42 pages, 10 figures

A dedicated gamma-ray burst (GRB) afterglow observing program was performed between 2007 and 2016 with GROND, a seven-channel optical and near-infrared imager at the 2.2m telescope of the Max-Planck Society at ESO/La Silla. In this first of a series of papers, we describe the GRB observing plan, providing first readings of all so far unpublished GRB afterglow measurements and some observing statistics. In total, we observed 514 GRBs with GROND, including 434 Swift-detected GRBs, representing 81\% of the observable Swift sample. For GROND-observations within 30 min of the GRB trigger, the optical/NIR afterglow detection rate is 81\% for long- and 57\% for short-duration GRBs. We report the discovery of ten new GRB afterglows plus one candidate, along with redshift estimates (partly improved) for four GRBs and new host detections for seven GRBs. We identify the (already known) afterglow of GRB 140209A as the sixth GRB exhibiting a 2175 Angstroem dust feature. As a side result, we identified two blazars, with one at a redshift of z=3.8 (in the GRB 131209A field)., Comment: 20 pages, 31 figures, accepted for publication in Astronomy & Astrophysics

Large Language Models (LLMs) store and retrieve vast amounts of factual knowledge acquired during pre-training. Prior research has localized and identified mechanisms behind knowledge recall; however, it has primarily focused on English monolingual models. The question of how these processes generalize to other languages and multilingual LLMs remains unexplored. In this paper, we address this gap by conducting a comprehensive analysis of two highly multilingual LLMs. We assess the extent to which previously identified components and mechanisms of factual recall in English apply to a multilingual context. Then, we examine when language plays a role in the recall process, uncovering evidence of language-independent and language-dependent mechanisms.

We study how features emerge, disappear, and persist across models fine-tuned on different domains of text. More specifically, we start from a base one-layer Transformer language model that is trained on a combination of the BabyLM corpus, and a collection of Python code from The Stack. This base model is adapted to two new domains of text: TinyStories, and the Lua programming language, respectively; and then these two models are merged using these two models using spherical linear interpolation. Our exploration aims to provide deeper insights into the stability and transformation of features across typical transfer-learning scenarios using small-scale models and sparse auto-encoders.

Despite extensive security research on various Android components, such as kernel or runtime, little attention has been paid to the proprietary vendor blobs within Android firmware. In this paper, we conduct a large-scale empirical study to understand the update patterns and assess the security implications of vendor blobs. We specifically focus on GPU blobs because they are loaded into every process for displaying graphics user interfaces and can affect the entire system's security. We examine over 13,000 Android firmware releases between January 2018 and April 2024. Our results reveal that device manufacturers often neglect vendor blob updates. About 82\% of firmware releases contain outdated GPU blobs (up to 1,281 days). A significant number of blobs also rely on obsolete LLVM core libraries released more than 15 years ago. To analyze their security implications, we develop a performant fuzzer that requires no physical access to mobile devices. We discover 289 security and behavioral bugs within the blobs. We also present a case study demonstrating how these vulnerabilities can be exploited via WebGL. This work underscores the critical security concerns associated with vulnerable vendor blobs and emphasizes the urgent need for timely updates from device manufacturers., Comment: The 30th International Conference on Parallel and Distributed Systems

We focus on the derivation and analysis of a model for multi-component phase separation occurring on biological membranes, inspired by observations of lipid raft formation. The model integrates local membrane composition with local membrane curvature, describing the membrane's geometry through a perturbation method represented as a graph over an undeformed Helfrich minimising surface, such as a sphere. The resulting energy consists of a small deformation functional coupled to a Cahn-Hilliard functional. By applying Onsager's variational principle, we obtain a multi-component Cahn-Hilliard equation for the vector $\boldsymbol\varphi$ of protein concentrations coupled to an evolution equation for the small deformation $u$ along the normal direction to the reference membrane. Then, in the case of a constant mobility matrix, we consider the Cauchy problem and we prove that it is (globally) well posed in a weak setting. We also demonstrate that any weak solution regularises in finite time and satisfies the so-called "strict separation property". This property allows usto show that any weak solution converges to a single stationary state by a suitable version of the Lojasiewicz-Simon inequality.

We present an investigation into the rotation and stellar activity of four fully convective M dwarf `twin' wide binaries. Components in each pair have (1) astrometry confirming they are common-proper-motion binaries, (2) Gaia $BP$, $RP$, and 2MASS $J$, $H$, and $K_s$ magnitudes matching within 0.10 mag, and (3) presumably the same age and composition. We report long-term photometry, rotation periods, multi-epoch H$\alpha$ equivalent widths, X-ray luminosities, time series radial velocities, and speckle observations for all components. Although it might be expected for the twin components to have matching magnetic attributes, this is not the case. Decade-long photometry of GJ 1183 AB indicates consistently higher spot activity on A than B, a trend matched by A appearing 58$\pm$9% stronger in $L_X$ and 26$\pm$9% stronger in H$\alpha$ on average -- this is despite similar rotation periods of A=0.86d and B=0.68d, thereby informing the range in activity for otherwise identical and similarly-rotating M dwarfs. The young $\beta$ Pic Moving Group member 2MA 0201+0117 AB displays a consistently more active B component that is 3.6$\pm$0.5 times stronger in $L_X$ and 52$\pm$19% stronger in H$\alpha$ on average, with distinct rotation at A=6.01d and B=3.30d. Finally, NLTT 44989 AB displays remarkable differences with implications for spindown evolution -- B has sustained H$\alpha$ emission while A shows absorption, and B is $\geq$39$\pm$4 times stronger in $L_X$, presumably stemming from the surprisingly different rotation periods of A=38d and B=6.55d. The last system, KX Com, has an unresolved radial velocity companion, and is therefore not a twin system., Comment: 40 pages, 17 figures, 6 tables, submitted to AJ on 2024-09-20

$^{76}$Ge can $\beta\beta$ decay into three possible excited states of $^{76}$Se, with the emission of two or, if the neutrino is Majorana, zero neutrinos. None of these six transitions have yet been observed. The MAJORANA DEMONSTRATOR was designed to study $\beta\beta$ decay of $^{76}$Ge using a low background array of high purity germanium detectors. With 98.2 kg-y of isotopic exposure, the DEMONSTRATOR sets the strongest half-life limits to date for all six transition modes. For $2\nu\beta\beta$ to the $0^+_1$ state of $^{76}$Se, this search has begun to probe for the first time half-life values predicted using modern many-body nuclear theory techniques, setting a limit of $T_{1/2}>1.5\times10^{24}$ y (90% CL)., Comment: 8 pages, 3 figures

Natural language processing (NLP) in the medical domain can underperform in real-world applications involving small datasets in a non-English language with few labeled samples and imbalanced classes. There is yet no consensus on how to approach this problem. We evaluated a set of NLP models including BERT-like transformers, few-shot learning with sentence transformers (SetFit), and prompted large language models (LLM), using three datasets of radiology reports on magnetic resonance images of epilepsy patients in Danish, a low-resource language. Our results indicate that BERT-like models pretrained in the target domain of radiology reports currently offer the optimal performances for this scenario. Notably, the SetFit and LLM models underperformed compared to BERT-like models, with LLM performing the worst. Importantly, none of the models investigated was sufficiently accurate to allow for text classification without any supervision. However, they show potential for data filtering, which could reduce the amount of manual labeling required.

Precise automated delineation of post-operative gross tumor volume in glioblastoma cases is challenging and time-consuming owing to the presence of edema and the deformed brain tissue resulting from the surgical tumor resection. To develop a model for automated delineation of post-operative gross tumor volumes in glioblastoma, we proposed a novel 3D double pocket U-Net architecture that has two parallel pocket U-Nets. Both U-Nets were trained simultaneously with two different subsets of MRI sequences and the output from the models was combined to do the final prediction. We strategically combined the MRI input sequences (T1, T2, T1C, FL) for model training to achieve improved segmentation accuracy. The dataset comprised 82 post-operative studies collected from 23 glioblastoma patients who underwent maximal safe tumor resection. All had gross tumor volume (GTV) segmentations performed by human experts, and these were used as a reference standard. The results of 3D double pocket U-Net were compared with baseline 3D pocket U-Net models and the ensemble of 3D pocket U-Net models. All the models were evaluated with fivefold cross-validation in terms of the Dice similarity coefficient and Hausdorff distance. Our proposed double U-Net model trained with input sequences [T1, T1C, FL + T2, T1C] achieved a better mean Dice score of 0.8585 and Hausdorff distance of 4.1942 compared to all the baseline models and ensemble models trained. The presence of infiltrating tumors and vasogenic edema in the post-operative MRI scans tends to reduce segmentation accuracy when considering the MRI sequences T1, T2, T1C, and FL together for model training. The double U-Net approach of combining subsets of the MRI sequences as distinct inputs for model training improves segmentation accuracy by 7% when compared with the conventional method of model training with all four sequences.

Multimodal vector search offers a new paradigm for information retrieval by exposing numerous pieces of functionality which are not possible in traditional lexical search engines. While multimodal vector search can be treated as a drop in replacement for these traditional systems, the experience can be significantly enhanced by leveraging the unique capabilities of multimodal search. Central to any information retrieval system is a user who expresses an information need, traditional user interfaces with a single search bar allow users to interact with lexical search systems effectively however are not necessarily optimal for multimodal vector search. In this paper we explore novel capabilities of multimodal vector search applications utilising CLIP models and present implementations and design patterns which better allow users to express their information needs and effectively interact with these systems in an information retrieval context., Comment: 12 pages, 8 figures, CIKM 2024 MMSR Workshop

A new proof following a suggestion of Kaplansky to use a result of Dixmier, and in this way avoid unbounded nets of operators, is given of the Kaplansky density theorem., Comment: 2 pages

Chiral crystals, like chiral molecules, cannot be superimposed onto their mirror images -- a fundamental property that has been linked to interesting physical behavior and exploited in functional devices. Among the simplest inorganic systems with crystallographic chirality, elemental tellurium adopts crystal structures with right- or left-handed chains. However, understanding the formation mechanisms of those structures has been difficult due to the rapid crystallization of Te, which reaches the spatial and temporal resolution limits of even the most advanced experiments. Here, we report ultra-large-scale, quantum-mechanically accurate simulations that reveal mechanisms of crystallization and the origin of crystallographic chirality in solid Te. We identify a characteristic, disordered cube-like structural motif -- a transient bonding environment with only nanosecond lifetime -- that enables both the rapid crystallization of Te and mediates chirality transfer. Based on the resulting microscopic understanding, we are able to explain the switching behavior of Te-based electrical devices.

By employing the closest point method, we extend the applicability of minimizing movements to the surface PDE setting. The corresponding approximation methods are created, and their convergence is observed. The numerical methods are then used to develop threshold dynamics algorithms for surface-constrained interfacial motions. In particular, show how the minimizing movements enable one to approximate multiphase, volume-preserving, curvature flows on surfaces via generalized MBO and HMBO algorithms., Comment: 54 pages

Building high-quality datasets for specialized tasks is a time-consuming and resource-intensive process that often requires specialized domain knowledge. We propose Corpus Retrieval and Augmentation for Fine-Tuning (CRAFT), a method for generating synthetic datasets, given a small number of user-written few-shots that demonstrate the task to be performed. Given the few-shot examples, we use large-scale public web-crawled corpora and similarity-based document retrieval to find other relevant human-written documents. Lastly, instruction-tuned large language models (LLMs) augment the retrieved documents into custom-formatted task samples, which then can be used for fine-tuning. We demonstrate that CRAFT can efficiently generate large-scale task-specific training datasets for four diverse tasks: biology question-answering (QA), medicine QA and commonsense QA as well as summarization. Our experiments show that CRAFT-based models outperform or achieve comparable performance to general LLMs for QA tasks, while CRAFT-based summarization models outperform models trained on human-curated data by 46 preference points.

To support and better understand how to scale effectively, in 2020, the Millions Learning project at the Center for Universal Education (CUE) at Brookings joined the Global Partnership for Education's (GPE) Knowledge and Innovation Exchange (KIX), a joint partnership between GPE and the International Development Research Centre (IDRC), to facilitate a cross-national, multiteam, design-based research and professional support initiative called Research on Scaling the Impact of Innovations in Education (ROSIE). Since 2021, ROSIE has brought together 15 researcher and practitioner teams working in 30 low- and middle-income countries to study the process of scaling education initiatives for impact. This brief reflects on the 15 KIX teams' experiences to shed light on the role of champions in the scaling process. The brief introduces a typology of champions and ways of working with them as it also shares examples of how scaling teams are identifying champions and managing common challenges to the engagement of champions (such as time constraints, personnel turnover, and cultural dynamics).

To support and better understand how to scale effectively, in 2020, the Millions Learning project at the Center for Universal Education (CUE) at Brookings joined the Global Partnership for Education's (GPE) Knowledge and Innovation Exchange (KIX), a joint partnership between GPE and the International Development Research Centre (IDRC), to facilitate a cross-national, multiteam, design-based research and professional support initiative called Research on Scaling the Impact of Innovations in Education (ROSIE). Since 2021, ROSIE has brought together 15 researcher and practitioner teams working in 30 low- and middle-income countries to study the process of scaling education initiatives for impact. This brief reflects on the 15 KIX teams' experiences to shed light on the role of research in the scaling process. The brief distinguishes between research for scaling and research about the scaling process itself, discusses different ways KIX-ROSIE teams are conducting and using research in their scaling work, and identifies some of the research challenges and solutions that emerged.

To support and better understand how to scale effectively, in 2020, the Millions Learning project at the Center for Universal Education (CUE) at Brookings joined the Global Partnership for Education's (GPE) Knowledge and Innovation Exchange (KIX), a joint partnership between GPE and the International Development Research Centre (IDRC), to facilitate a cross-national, multiteam, design-based research and professional support initiative called Research on Scaling the Impact of Innovations in Education (ROSIE). Since 2020, ROSIE has brought together 15 teams of researchers and practitioners working in 30 low-and middle-income countries to study the process of scaling education initiatives for impact. Equity-based scaling requires significant time, sensitivity, and resources and is not necessarily incentivized by wider forces and project parameters. Looking at how KIX-ROSIE teams pursued equity is the focus of this brief. Special attention is paid to four distinct ways equity was prioritized in their work. Additionally, this brief raises some conceptual complexities around equity in global education and offers reflections on equity challenges and opportunities.

Esophageal cancer is a major cause of cancer-related mortality internationally, with high recurrence rates and poor survival even among patients treated with curative-intent surgery. Investigating relevant prognostic factors and predicting prognosis can enhance post-operative clinical decision-making and potentially improve patients' outcomes. In this work, we assessed prognostic factor identification and discriminative performances of three models for Disease-Free Survival (DFS) and Overall Survival (OS) using a large multicenter international dataset from ENSURE study. We first employed Cox Proportional Hazards (CoxPH) model to assess the impact of each feature on outcomes. Subsequently, we utilised CoxPH and two deep neural network (DNN)-based models, DeepSurv and DeepHit, to predict DFS and OS. The significant prognostic factors identified by our models were consistent with clinical literature, with post-operative pathologic features showing higher significance than clinical stage features. DeepSurv and DeepHit demonstrated comparable discriminative accuracy to CoxPH, with DeepSurv slightly outperforming in both DFS and OS prediction tasks, achieving C-index of 0.735 and 0.74, respectively. While these results suggested the potential of DNNs as prognostic tools for improving predictive accuracy and providing personalised guidance with respect to risk stratification, CoxPH still remains an adequately good prediction model, with the data used in this study., Comment: 14 pages, 3 figures, 4 tables. To appear in CaPTion: MICCAI Workshop on Cancer Prevention, detection, and intervenTion, Sharib Ali et al., MICCAI 2024, Lecture Notes in Computer Science, Springer

Link Traversal queries face challenges in completeness and long execution time due to the size of the web. Reachability criteria define completeness by restricting the links followed by engines. However, the number of links to dereference remains the bottleneck of the approach. Web environments often have structures exploitable by query engines to prune irrelevant sources. Current criteria rely on using information from the query definition and predefined predicate. However, it is difficult to use them to traverse environments where logical expressions indicate the location of resources. We propose to use a rule-based reachability criterion that captures logical statements expressed in hypermedia descriptions within linked data documents to prune irrelevant sources. In this poster paper, we show how the Comunica link traversal engine is modified to take hints from a hypermedia control vocabulary, to prune irrelevant sources. Our preliminary findings show that by using this strategy, the query engine can significantly reduce the number of HTTP requests and the query execution time without sacrificing the completeness of results. Our work shows that the investigation of hypermedia controls in link pruning of traversal queries is a worthy effort for optimizing web queries of unindexed decentralized databases., Comment: 5 pages, 2 figures

Let $\Omega$ be a compact subset of $\mathbb{C}$ and let $A$ be a unital simple, separable $C^*$-algebra with stable rank one, real rank zero and strict comparison. We show that, given a Cu-morphism $\alpha:{\rm Cu}(C(\Omega))\to {\rm Cu}(A)$ with $\alpha(\langle \mathds{1}_{\Omega}\rangle)\leq \langle 1_A\rangle$, there exists a homomorphism $\phi: C(\Omega)\to A$ such that ${\rm Cu}(\phi)=\alpha$ and $\phi$ is unique up to approximate unitary equivalence. We also give classification results for maps from a large class of $C^*$-algebras to $A$ in terms of the Cuntz semigroup.

Over the last decade, experimental measurements of electrostatic screening lengths in concentrated electrolytes have exceeded theoretical predictions by orders of magnitude. This disagreement has led to a paradigm in which such screening lengths are referred to as 'anomalous underscreening', while others - predominantly those predicted by theory and molecular simulation - are referred to as 'normal underscreening'. Herein we use discrete Fourier analysis of the radial charge density obtained from molecular dynamics simulations to reveal the origin of anomalous underscreening in concentrated electrolytes. Normal underscreening above the Kirkwood point arises from low-frequency decay modes of the electrostatic potential, while anomalous underscreening arises from high-frequency decay modes that are observed only at high concentrations. The screening length associated with a particular decay mode is in turn determined by the degree of short-range interference between ion-ion correlation functions. The long-range decay associated with anomalous underscreening is thus ultimately determined by short range structure in the bulk electrolyte. These results reconcile the disagreement between experimental measurements and theoretical predictions of screening lengths in concentrated electrolytes., Comment: 16 pages, 3 figures

We take a first step towards developing a new language to describe causal structure, event horizons, and quantum extremal surfaces (QES) for the bulk description of holographic systems beyond the standard Einstein gravity regime. By considering the structure of boundary operator algebras, we introduce a stringy ``causal depth parameter'', which quantifies the depth of the emergent radial direction in the bulk, and a certain notion of ergodicity on the boundary. We define stringy event horizons in terms of the half-sided inclusion property, which is related to a stronger notion of boundary ergodic or quantum chaotic behavior. Using our definition, we argue that above the Hawking--Page temperature, there is an emergent sharp horizon structure in the large $N$ limit of $\mathcal{N}=4$ Super-Yang--Mills at finite nonzero 't Hooft coupling. In contrast, some previously considered toy models of black hole information loss do not have a stringy horizon. Our methods can also be used to probe violations of the equivalence principle for the bulk gravitational system, and to explore aspects of stringy nonlocality., Comment: 43 pages + appendices, 9 figures, 1 table

This study examines whether interviewer variances remain consistent across different modes in mixed-mode studies, using data from two distinct designs. In the first design, when interviewers are responsible for either face-to-face or telephone mode, we examine whether there are mode differences in interviewer variances for 1) sensitive political questions, 2) international items, 3) and item missing indicators on international items, using the Arab Barometer wave 6 Jordan data. In the second design, we draw on Health and Retirement Study (HRS) 2016 core survey data to examine the question on three topics when interviewers are responsible for both modes. The topics cover 1) the CESD depression scale, 2) interviewer observations, and 3) the physical activity scale. To account for the lack of interpenetrated designs in both data sources, we include respondent-level covariates in our models. We find significant differences in interviewer variances on one item (twelve items in total) in the Arab Barometer study; whereas for HRS, the results are three out of eighteen. Overall, we find the magnitude of the interviewer variances larger in FTF than TEL on sensitive items. We conduct simulations to understand the power to detect mode effects in the typically modest interviewer sample sizes.

Sublinearly Morse boundaries of proper geodesic spaces are introduced by Qing, Rafi and Tiozzo. Expanding on this work, Qing and Rafi recently developed the quasi-redirecting boundary, denoted $\partial G$, to include all directions of metric spaces at infinity. Both boundaries are topological spaces that consist of equivalence classes of quasi-geodesic rays and are quasi-isometrically invariant. In this paper, we study these boundaries when the space is equipped with a geometric group action. In particular, we show that $G$ acts minimally on $\partial_\kappa G$ and that contracting elements of G induces a weak north-south dynamic on $\partial_\kappa G$. We also prove, when $\partial G$ exists and $|\partial_\kappa G|\geq3$, $G$ acts minimally on $\partial G$ and $\partial G$ is a second countable topological space. The last section concerns the restriction to proper CAT(0) spaces and finite dimensional \CAT cube complexes. We show that when $G$ acts geometrically on a finite dimensional CAT(0) cube complex (whose QR boundary is assumed to exist), then a nontrivial QR boundary implies the existence of a Morse element in $G$. Lastly, we show that if $X$ is a proper cocompact CAT(0) space, then $\partial G$ is a visibility space., Comment: 27 pages, 11 figures

The background index is an important quantity which is used in projecting and calculating the half-life sensitivity of neutrinoless double-beta decay ($0\nu\beta\beta$) experiments. A novel analysis framework is presented to calculate the background index using the specific activities, masses and simulated efficiencies of an experiment's components as distributions. This Bayesian framework includes a unified approach to combine specific activities from assay. Monte Carlo uncertainty propagation is used to build a background index distribution from the specific activity, mass and efficiency distributions. This analysis method is applied to the MAJORANA DEMONSTRATOR, which deployed arrays of high-purity Ge detectors enriched in $^{76}$Ge to search for $0\nu\beta\beta$. The framework projects a mean background index of $\left[8.95 \pm 0.36\right] \times 10^{-4}$cts/(keV kg yr) from $^{232}$Th and $^{238}$U in the DEMONSTRATOR's components., Comment: 9 pages, 3 figures

HiCCL (Hierarchical Collective Communication Library) addresses the growing complexity and diversity in high-performance network architectures. As GPU systems have envolved into networks of GPUs with different multilevel communication hierarchies, optimizing each collective function for a specific system has become a challenging task. Consequently, many collective libraries struggle to adapt to different hardware and software, especially across systems from different vendors. HiCCL's library design decouples the collective communication logic from network-specific optimizations through a compositional API. The communication logic is composed using multicast, reduction, and fence primitives, which are then factorized for a specified network hieararchy using only point-to-point operations within a level. Finally, striping and pipelining optimizations applied as specified for streamlining the execution. Performance evaluation of HiCCL across four different machines$\unicode{x2014}$two with Nvidia GPUs, one with AMD GPUs, and one with Intel GPUs$\unicode{x2014}$demonstrates an average 17$\times$ higher throughput than the collectives of highly specialized GPU-aware MPI implementations, and competitive throughput with those of vendor-specific libraries (NCCL, RCCL, and OneCCL), while providing portability across all four machines.

When faced with a new customer, many factors contribute to an insurance firm's decision of what offer to make to that customer. In addition to the expected cost of providing the insurance, the firm must consider the other offers likely to be made to the customer, and how sensitive the customer is to differences in price. Moreover, firms often target a specific portfolio of customers that could depend on, e.g., age, location, and occupation. Given such a target portfolio, firms may choose to modulate an individual customer's offer based on whether the firm desires the customer within their portfolio. We term the problem of modulating offers to achieve a desired target portfolio the portfolio pursuit problem. Having formulated the portfolio pursuit problem as a sequential decision making problem, we devise a novel reinforcement learning algorithm for its solution. We test our method on a complex synthetic market environment, and demonstrate that it outperforms a baseline method which mimics current industry approaches to portfolio pursuit., Comment: 16 pages, 1 figure

We study the Factorization Paradox from the bottom up by adapting methods from perturbative renormalization. Just as quantum field theories are plagued with loop divergences that need to be cancelled systematically by introducing counterterms, gravitational path integrals are plagued by wormhole contributions that spoil the factorization of the holographic dual. These wormholes must be cancelled by some stringy effects in a UV complete, holographic theory of quantum gravity. In a simple model of two-dimensional topological gravity, we outline a gravitational analog of the recursive BPHZ procedure in order to systematically introduce ``counter-wormholes" which parametrize the unknown stringy effects that lead to factorization. Underlying this procedure is a Hopf algebra of symmetries which is analogous to the Connes--Kreimer Hopf algebra underlying perturbative renormalization. The group dual to this Hopf algebra acts to reorganize contributions from spacetimes with distinct topology, and can be seen as a gauge group relating various equivalent ways of constructing a factorizing gravitational path integral., Comment: 35 pages + appendix, 11 figures, 1 table

This monograph elucidates and extends many theorems and conjectures in analytic number theory and algebraic asymptotic analysis via the natural notions of degree and logexponential degree. The Riemann hypothesis, for example, is equivalent to the statement that the degree of the function $\pi(x)- \operatorname{li}(x)$ is $1/2$, where $\pi(x)$ is the prime counting function and $\operatorname{li}(x)$ is the logarithmic integral function. Part 1 of the text is a survey of analytic number theory, Part 2 introduces the notion of logexponential degree and uses it to extend results in algebraic asymptotic analysis, and Part 3 applies the results of Part 2 to the various functions that figure most prominently in analytic number theory. Central to the notion of logexponential degree are Hardy's logarithmico-exponential functions, which are real functions defined in a neighborhood of $\infty$ that can be built from $\operatorname{id}$, $\exp$, and $\log$ using the operations $+$, $\cdot$, $/$, and $\circ$. Such functions are natural benchmarks for the orders of growth of functions in analytic number theory. The main goal of Part 3 is to express the logexponential degree of various functions in analytic number theory in terms of as few "logexponential primitives" as possible. The logexponential degree of the function $e^\gamma \prod_{p\leq x}(1-1/p) -1/\log x$, for example, can be expressed in terms of that of $\pi(x)- \operatorname{li}(x)$ and vice versa (where $\gamma \approx 0.5772$ is the Euler-Mascheroni constant), despite the fact that very little is known about the logexponential degree of either function separately, even on condition of the Riemann hypothesis., Comment: 517 pages. This monograph is an unedited version of a monograph that is to be published in World Scientific's Monographs in Number Theory Series: see https://www.worldscientific.com/worldscibooks/10.1142/13521#/t=aboutBook. World Scientific has graciously agreed to allow this upload to ArXiv

We derive various novel free boundary problems as limits of a coupled bulk-surface reaction-diffusion system modelling ligand-receptor dynamics on evolving domains. These limiting free boundary problems may be formulated as Stefan-type problems on an evolving hypersurface. Our results are new even in the setting where there is no domain evolution. The models are of particular relevance to a number of applications in cell biology. The analysis utilises $L^\infty$-estimates in the manner of De Giorgi iterations and other technical tools, all in an evolving setting. We also report on numerical simulations.

We develop a theory of nonlinear low-magnetic-field magnetotransport on a helical edge of a quantum spin Hall insulator due to the edge state coupling to bulk midgap states. We focus on the part of the nonlinear I-V characteristic that is odd in the applied magnetic field, and quadratic in the applied bias voltage. This part of the I-V characteristic corresponds to the resistance of the sample being dependent on the relative orientation of the current and an external magnetic field, hence represents a type of edge magnetochiral anisotropy. We identify two mechanisms of the magnetochiral anisotropy. One is related to the Hubbard interaction on the midgap state, which leads to the dependence of the scattering characteristics on the current flowing on the edge, which results in bias-voltage-dependent resistance, or equivalently conductance, hence a nonlinear I-V. The other is related to the modification of the edge dispersion by a magnetic field, and requires nonlinearity in the edge dispersion. We compare the developed theory to the experiments on monolayer $\mathrm{WTe}_{2}$, and find good agreement with the developed theory., Comment: 5 pages, 16 pages of supplemental material

Prompt engineering for large language models (LLMs) is often a manual time-intensive process that involves generating, evaluating, and refining prompts iteratively to ensure high-quality outputs. While there has been work on automating prompt engineering, the solutions generally are either tuned to specific tasks with given answers or are quite costly. We introduce GRAD-SUM, a scalable and flexible method for automatic prompt engineering that builds on gradient-based optimization techniques. Our approach incorporates user-defined task descriptions and evaluation criteria, and features a novel gradient summarization module to generalize feedback effectively. Our results demonstrate that GRAD-SUM consistently outperforms existing methods across various benchmarks, highlighting its versatility and effectiveness in automatic prompt optimization., Comment: 15 pages, 2 figures

Data on the web is naturally unindexed and decentralized. Centralizing web data, especially personal data, raises ethical and legal concerns. Yet, compared to centralized query approaches, decentralization-friendly alternatives such as Link Traversal Query Processing (LTQP) are significantly less performant and understood. The two main difficulties of LTQP are the lack of apriori information about data sources and the high number of HTTP requests. Exploring decentralized-friendly ways to document unindexed networks of data sources could lead to solutions to alleviate those difficulties. RDF data shapes are widely used to validate linked data documents, therefore, it is worthwhile to investigate their potential for LTQP optimization. In our work, we built an early version of a source selection algorithm for LTQP using RDF data shape mappings with linked data documents and measured its performance in a realistic setup. In this article, we present our algorithm and early results, thus, opening opportunities for further research for shape-based optimization of link traversal queries. Our initial experiments show that with little maintenance and work from the server, our method can reduce up to 80% the execution time and 97% the number of links traversed during realistic queries. Given our early results and the descriptive power of RDF data shapes it would be worthwhile to investigate non-heuristic-based query planning using RDF shapes., Comment: 6 pages, 2 figures

We consider the momentum formulation of the two-dimensional surface quasi-geostrophic equations forced by random noise, of both additive and linear multiplicative types. For any prescribed deterministic function under some conditions, we construct solutions to each system whose energy is the fixed function. Consequently, we prove non-uniqueness of almost sure Markov selections of suitable class of weak solutions associated to the momentum surface quasi-geostrophic equations in both cases of noise.

Some worry that advanced artificial agents may resist being shut down. The Incomplete Preferences Proposal (IPP) is an idea for ensuring that doesn't happen. A key part of the IPP is using a novel 'Discounted REward for Same-Length Trajectories (DREST)' reward function to train agents to (1) pursue goals effectively conditional on each trajectory-length (be 'USEFUL'), and (2) choose stochastically between different trajectory-lengths (be 'NEUTRAL' about trajectory-lengths). In this paper, we propose evaluation metrics for USEFULNESS and NEUTRALITY. We use a DREST reward function to train simple agents to navigate gridworlds, and we find that these agents learn to be USEFUL and NEUTRAL. Our results thus suggest that DREST reward functions could also train advanced agents to be USEFUL and NEUTRAL, and thereby make these advanced agents useful and shutdownable.

There is an increasing trend towards evaluating NLP models with LLM-generated judgments instead of human judgments. In the absence of a comparison against human data, this raises concerns about the validity of these evaluations; in case they are conducted with proprietary models, this also raises concerns over reproducibility. We provide JUDGE-BENCH, a collection of 20 NLP datasets with human annotations, and comprehensively evaluate 11 current LLMs, covering both open-weight and proprietary models, for their ability to replicate the annotations. Our evaluations show that each LLM exhibits a large variance across datasets in its correlation to human judgments. We conclude that LLMs are not yet ready to systematically replace human judges in NLP.

The neural moving horizon estimator (NMHE) is a relatively new and powerful state estimator that combines the strengths of neural networks (NNs) and model-based state estimation techniques. Various approaches exist for constructing NMHEs, each with its unique advantages and limitations. However, a comprehensive literature review that consolidates existing knowledge, outlines design guidelines and highlights future research directions is currently lacking. This systematic literature review synthesizes the existing knowledge on NMHE, addressing the above knowledge gap. The paper (1) explains the fundamental principles of NMHE, (2) explores different NMHE architectures, discussing the pros and cons of each, (3) investigates the NN architectures used in NMHE, providing insights for future designs, (4) examines the real-time implementability of current approaches, offering recommendations for practical applications, and (5) discusses the current limitations of NMHE approaches and outlines directions for future research. These insights can significantly improve the design and application of NMHE, which is critical for enhancing state estimation in complex systems.