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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.