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We introduce the Granite Embedding models, a family of encoder-based embedding models designed for retrieval tasks, spanning dense-retrieval and sparse retrieval architectures, with both English and Multilingual capabilities. This report provides the technical details of training these highly effective 12 layer embedding models, along with their efficient 6 layer distilled counterparts. Extensive evaluations show that the models, developed with techniques like retrieval oriented pretraining, contrastive finetuning, knowledge distillation, and model merging significantly outperform publicly available models of similar sizes on both internal IBM retrieval and search tasks, and have equivalent performance on widely used information retrieval benchmarks, while being trained on high-quality data suitable for enterprise use. We publicly release all our Granite Embedding models under the Apache 2.0 license, allowing both research and commercial use at https://huggingface.co/collections/ibm-granite.

We present the results of a search for nonlinear gravitational wave memory in the NANOGrav 15-year data set. We find no significant evidence for memory signals in the dataset, with a maximum Bayes factor of 3.1 in favor of a model including memory. We therefore place upper limits on the strain of potential gravitational wave memory events as a function of sky location and observing epoch. We find upper limits that are not always more constraining than previous NANOGrav results. We show that it is likely due to the increase in common red noise between the 12.5-year and 15-year NANOGrav datasets.

We introduce Granite Vision, a lightweight large language model with vision capabilities, specifically designed to excel in enterprise use cases, particularly in visual document understanding. Our model is trained on a comprehensive instruction-following dataset, including document-related tasks, such as content extraction from tables, charts, diagrams, sketches, and infographics, as well as general image tasks. The architecture of Granite Vision is centered around visual modality alignment with a decoder-only, 2 billion parameter Granite large language model. Additionally, we introduce a dedicated safety classification approach in test-time that leverages a sparse set of attention vectors to identify potential harmful inputs. Despite its lightweight architecture, Granite Vision achieves strong results in standard benchmarks related to visual document understanding, as well as on the LiveXiv benchmark, which is designed to avoid test set contamination by using a constantly updated corpus of recently published Arxiv papers. We are releasing the model under the Apache-2 license, allowing for both research and commercial use, while offering complete visibility into the training data and other relevant details. See https://huggingface.co/ibm-granite/ for model weights.

We prove the Categorified Wrapping Number Conjecture for large classes of annular links, including alternating annular links and tangle closures exhibiting plumbed link phenomena. We do so by characterizing when a resolution is sufficient to produce a nonzero homology class in $k$-grading $\mathrm{wrap}(L)$ on its own. This characterization primarily concerns the type of crossing resolutions abutting trivial circles., Comment: 21 pages, 21 figures, comments welcome!

Autonomous robotic grasping of uncertain objects in uncertain environments is an impactful open challenge for the industries of the future. One such industry is the recycling of Waste Electrical and Electronic Equipment (WEEE) materials, in which electric devices are disassembled and readied for the recovery of raw materials. Since devices may contain hazardous materials and their disassembly involves heavy manual labor, robotic disassembly is a promising venue. However, since devices may be damaged, dirty and unidentified, robotic disassembly is challenging since object models are unavailable or cannot be relied upon. This case study explores grasping strategies for industrial robotic disassembly of WEEE devices with uncertain vision data. We propose three grippers and appropriate tactile strategies for force-based manipulation that improves grasping robustness. For each proposed gripper, we develop corresponding strategies that can perform effectively in different grasping tasks and leverage the grippers design and unique strengths. Through experiments conducted in lab and factory settings for four different WEEE devices, we demonstrate how object uncertainty may be overcome by tactile sensing and compliant techniques, significantly increasing grasping success rates.

This research investigates the performance of various machine learning algorithms (CNN, LSTM, VADER, and RoBERTa) for sentiment analysis of Twitter data related to imported food items in Trinidad and Tobago. The study addresses three primary research questions: the comparative accuracy and efficiency of the algorithms, the optimal configurations for each model, and the potential applications of the optimized models in a live system for monitoring public sentiment and its impact on the import bill. The dataset comprises tweets from 2018 to 2024, divided into imbalanced, balanced, and temporal subsets to assess the impact of data balancing and the COVID-19 pandemic on sentiment trends. Ten experiments were conducted to evaluate the models under various configurations. Results indicated that VADER outperformed the other models in both multi-class and binary sentiment classifications. The study highlights significant changes in sentiment trends pre- and post-COVID-19, with implications for import policies., Comment: 27 pages

In the superparamagnetic regime, magnetic tunnel junctions switch between two resistance states due to random thermal fluctuations. The dwell time distribution in each state is exponential. We sample this distribution using a temporal encoding scheme, in which information is encoded in the time at which the device switches between its resistance states. We then develop a circuit element known as a probabilistic delay cell that applies an electrical current step to a superparamagnetic tunnel junction and a temporal measurement circuit that measures the timing of the first switching event. Repeated experiments confirm that these times are exponentially distributed. Temporal processing methods then allow us to digitally compute with these exponentially distributed probabilistic delay cells. We describe how to use these circuits in a Metropolis-Hastings stepper and in a weighted random sampler, both of which are computationally intensive applications that benefit from the efficient generation of exponentially distributed random numbers.

Pulse profile stability is a central assumption of standard pulsar timing methods. Thus, it is important for pulsar timing array experiments such as the North American Nanohertz Observatory for Gravitational Waves (NANOGrav) to account for any pulse profile variability present in their data sets. We show that in the NANOGrav 15-yr data set, the integrated pulse profile of PSR J1022+1001 as seen by the Arecibo radio telescope at 430, 1380, and 2030 MHz varies considerably in its shape from observation to observation. We investigate the possibility that this is due to the "ideal feed assumption" (IFA), on which NANOGrav's routine polarization calibration procedure relies. PSR J1022+1001 is $\sim 90\%$ polarized in one pulse profile component, and also has significant levels of circular polarization. Time-dependent deviations in the feed's polarimetric response (PR) could cause mixing between the intensity I and the other Stokes parameters, leading to the observed variability. We calibrate the PR using a mixture of Measurement Equation Modeling and Measurement Equation Template Matching techniques. The resulting profiles are no less variable than those calibrated using the IFA method, nor do they provide an improvement in the timing quality of this pulsar. We observe the pulse shape in 25-MHz bandwidths to vary consistently across the band, which cannot be explained by interstellar scintillation in combination with profile evolution with frequency. Instead, we favor phenomena intrinsic to the pulsar as the cause., Comment: 18 pages, 16 figures, 4 tables. Submitted to ApJ

Can computer vision help us explore the ocean? The ultimate challenge for computer vision is to recognize any visual phenomena, more than only the objects and animals humans encounter in their terrestrial lives. Previous datasets have explored everyday objects and fine-grained categories humans see frequently. We present the FathomVerse v0 detection dataset to push the limits of our field by exploring animals that rarely come in contact with people in the deep sea. These animals present a novel vision challenge. The FathomVerse v0 dataset consists of 3843 images with 8092 bounding boxes from 12 distinct morphological groups recorded at two locations on the deep seafloor that are new to computer vision. It features visually perplexing scenarios such as an octopus intertwined with a sea star, and confounding categories like vampire squids and sea spiders. This dataset can push forward research on topics like fine-grained transfer learning, novel category discovery, species distribution modeling, and carbon cycle analysis, all of which are important to the care and husbandry of our planet., Comment: 10 pages, 14 figures

Causal inference in the presence of intermediate variables is a challenging problem in many applications. Principal stratification (PS) provides a framework to estimate principal causal effects (PCE) in such settings. However, existing PS methods primarily focus on settings with binary intermediate variables. We propose a novel approach to estimate PCE with continuous intermediate variables in the context of stepped wedge cluster randomized trials (SW-CRTs). Our method leverages the time-varying treatment assignment in SW-CRTs to calibrate sensitivity parameters and identify the PCE under realistic assumptions. We demonstrate the application of our approach using data from a cohort SW-CRT evaluating the effect of a crowdsourcing intervention on HIV testing uptake among men who have sex with men in China, with social norms as a continuous intermediate variable. The proposed methodology expands the scope of PS to accommodate continuous variables and provides a practical tool for causal inference in SW-CRTs.

Cardiovascular disease (CVD) cohorts collect data longitudinally to study the association between CVD risk factors and event times. An important area of scientific research is to better understand what features of CVD risk factor trajectories are associated with the disease. We develop methods for feature selection in joint models where feature selection is viewed as a bi-level variable selection problem with multiple features nested within multiple longitudinal risk factors. We modify a previously proposed Bayesian sparse group selection (BSGS) prior, which has not been implemented in joint models until now, to better represent prior beliefs when selecting features both at the group level (longitudinal risk factor) and within group (features of a longitudinal risk factor). One of the advantages of our method over the BSGS method is the ability to account for correlation among the features within a risk factor. As a result, it selects important features similarly, but excludes the unimportant features within risk factors more efficiently than BSGS. We evaluate our prior via simulations and apply our method to data from the Atherosclerosis Risk in Communities (ARIC) study, a population-based, prospective cohort study consisting of over 15,000 men and women aged 45-64, measured at baseline and at six additional times. We evaluate which CVD risk factors and which characteristics of their trajectories (features) are associated with death from CVD. We find that systolic and diastolic blood pressure, glucose, and total cholesterol are important risk factors with different important features associated with CVD death in both men and women.

Causal mediation analysis of observational data is an important tool for investigating the potential causal effects of medications on disease-related risk factors, and on time-to-death (or disease progression) through these risk factors. However, when analyzing data from a cohort study, such analyses are complicated by the longitudinal structure of the risk factors and the presence of time-varying confounders. Leveraging data from the Atherosclerosis Risk in Communities (ARIC) cohort study, we develop a causal mediation approach, using (semi-parametric) Bayesian Additive Regression Tree (BART) models for the longitudinal and survival data. Our framework allows for time-varying exposures, confounders, and mediators, all of which can either be continuous or binary. We also identify and estimate direct and indirect causal effects in the presence of a competing event. We apply our methods to assess how medication, prescribed to target cardiovascular disease (CVD) risk factors, affects the time-to-CVD death.

Evidence has emerged for a stochastic signal correlated among 67 pulsars within the 15-year pulsar-timing data set compiled by the NANOGrav collaboration. Similar signals have been found in data from the European, Indian, Parkes, and Chinese PTAs. This signal has been interpreted as indicative of the presence of a nanohertz stochastic gravitational wave background. To explore the internal consistency of this result we investigate how the recovered signal strength changes as we remove the pulsars one by one from the data set. We calculate the signal strength using the (noise-marginalized) optimal statistic, a frequentist metric designed to measure correlated excess power in the residuals of the arrival times of the radio pulses. We identify several features emerging from this analysis that were initially unexpected. The significance of these features, however, can only be assessed by comparing the real data to synthetic data sets. After conducting identical analyses on simulated data sets, we do not find anything inconsistent with the presence of a stochastic gravitational wave background in the NANOGrav 15-year data. The methodologies developed here can offer additional tools for application to future, more sensitive data sets. While this analysis provides an internal consistency check of the NANOGrav results, it does not eliminate the necessity for additional investigations that could identify potential systematics or uncover unmodeled physical phenomena in the data., Comment: 21 pages, 11 figures, 2 tables

Machine Learning (ML) has offered innovative perspectives for accelerating the discovery of new functional materials, leveraging the increasing availability of material databases. Despite the promising advances, data-driven methods face constraints imposed by the quantity and quality of available data. Moreover, ML is often employed in tandem with simulated datasets originating from density functional theory (DFT), and assessed through in-sample evaluation schemes. This scenario raises questions about the practical utility of ML in uncovering new and significant material classes for industrial applications. Here, we propose a data-driven framework aimed at accelerating the discovery of new transparent conducting materials (TCMs), an important category of semiconductors with a wide range of applications. To mitigate the shortage of available data, we create and validate unique experimental databases, comprising several examples of existing TCMs. We assess state-of-the-art (SOTA) ML models for property prediction from the stoichiometry alone. We propose a bespoke evaluation scheme to provide empirical evidence on the ability of ML to uncover new, previously unseen materials of interest. We test our approach on a list of 55 compositions containing typical elements of known TCMs. Although our study indicates that ML tends to identify new TCMs compositionally similar to those in the training data, we empirically demonstrate that it can highlight material candidates that may have been previously overlooked, offering a systematic approach to identify materials that are likely to display TCMs characteristics.

Free electrons in the interstellar medium refract and diffract radio waves along multiple paths, resulting in angular and temporal broadening of radio pulses that limits pulsar timing precision. We determine multifrequency, multi-epoch scattering times for the large dispersion measure millisecond pulsar J1903+0327 by developing a three component model for the emitted pulse shape that is convolved with a best fit pulse broadening function (PBF) identified from a family of thin-screen and extended-media PBFs. We show that the scattering time, $\tau$, at a fiducial frequency of 1500 MHz changes by approximately 10% over a 5.5yr span with a characteristic timescale of approximately 100 days. We also constrain the spectral index and inner scale of the wavenumber spectrum of electron density variations along this line of sight. We find that the scaling law for $\tau$ vs. radio frequency is strongly affected by any mismatch between the true and assumed PBF or between the true and assumed intrinsic pulse shape. We show using simulations that refraction is a plausible cause of the epoch dependence of $\tau$, manifesting as changes in the PBF shape and $1/e$ time scale. Finally, we discuss the implications of our scattering results on pulsar timing including time of arrival delays and dispersion measure misestimation., Comment: 16 pages, 14 figures, submitted to ApJ

Neutrinoless double beta decay {($0\nu\beta\beta$)} provides a way to probe physics beyond the Standard Model of particle physics. The upcoming nEXO experiment will search for $0\nu\beta\beta$ decay in $^{136}$Xe with a projected half-life sensitivity exceeding $10^{28}$ years at the 90\% confidence level using a liquid xenon (LXe) Time Projection Chamber (TPC) filled with 5 tonnes of Xe enriched to $\sim$90\% in the {$\beta \beta$}-decaying isotope $^{136}$Xe. In parallel, a potential future upgrade to nEXO is being investigated with the aim to further suppress radioactive backgrounds and to confirm $\beta \beta$-decay events. This technique, known as Ba-tagging, comprises extracting and identifying the $\beta \beta$-decay daughter $^{136}$Ba ion. One tagging approach being pursued involves extracting a small volume of LXe in the vicinity of a potential $\beta \beta$-decay using a capillary tube and facilitating a liquid-to-gas phase transition by heating the capillary exit. The Ba ion is then separated from the accompanying Xe gas using a radio-frequency (RF) carpet and RF funnel, conclusively identifying the ion as $^{136}$Ba via laser-fluorescence spectroscopy and mass spectrometry. Simultaneously, an accelerator-driven Ba ion source is being developed to validate and optimize this technique. The motivation for the project, the development of the different aspects, along with the current status and results, are discussed here., Comment: 23 pages, 15 figures

Naturally occurring materials are often disordered, with their bulk properties being challenging to predict from the structure, due to the lack of underlying crystalline axes. In this paper, we develop a digital pipeline from algorithmically-created configurations with tunable disorder to 3D printed materials, as a tool to aid in the study of such materials, using electrical resistance as a test case. The designed material begins with a random point cloud that is iteratively evolved using Lloyd's algorithm to approach uniformity, with the points being connected via a Delaunay triangulation to form a disordered network metamaterial. Utilizing laser powder bed fusion additive manufacturing with stainless steel 17-4 PH and titanium alloy Ti-6Al-4V, we are able to experimentally measure the bulk electrical resistivity of the disordered network. We found that the graph Laplacian accurately predicts the effective resistance of the structure, but is highly sensitive to anisotropy and global network topology, preventing a single network statistic or disorder characterization from predicting global resistivity., Comment: 9 pages, 8 figures

Graph Neural Networks (GNNs) have become an essential tool for analyzing graph-structured data, leveraging their ability to capture complex relational information. While the expressivity of GNNs, particularly their equivalence to the Weisfeiler-Leman (1-WL) isomorphism test, has been well-documented, understanding their generalization capabilities remains critical. This paper focuses on the generalization of GNNs by investigating their Vapnik-Chervonenkis (VC) dimension. We extend previous results to demonstrate that 1-dimensional GNNs with a single parameter have an infinite VC dimension for unbounded graphs. Furthermore, we show that this also holds for GNNs using analytic non-polynomial activation functions, including the 1-dimensional GNNs that were recently shown to be as expressive as the 1-WL test. These results suggest inherent limitations in the generalization ability of even the most simple GNNs, when viewed from the VC dimension perspective., Comment: 10 pages

Cavitation is a process where bubbles form and collapse within a fluid with dynamic, spatially varying pressure. This phenomenon can concentrate energy density by 12 orders of magnitude, creating light-emitting plasma or damaging nearby surfaces. A key question in cavitation theory and experiments is: what are the upper limits of energy density achievable through this spontaneous multiscale process? Among the many physical processes at play, we focus on fluid compressibility, modeled using the Tait-Murnaghan equation of state for a homentropic Euler fluid. We examine spherical cavities corresponding to experimentally realizable sonoluminescing bubbles, whose radius changes by a factor of over 100. These bubbles reach velocities exceeding the speed of sound of the surrounding fluid. However, all-Mach hydrodynamic solvers, such as those implemented using the Basilisk software, can exhibit unphysical behavior even at early times when motion is nearly incompressible. To accurately capture high Mach number motion and resolve dynamics in the sonoluminescence regime, we introduced a uniform bubble approximation for the ideal gas inside the bubble. This leading-order approximation clarifies the significant effects of compressibility. Our results reproduce the equation-of-state-dependent asymptotic power-law region predicted by analytic calculations. This confirms our method's ability to capture high Mach number motion and suggests that the asymptotic regime could be experimentally observed. Convergence of this method is demonstrated for bubbles in both water and liquid lithium, showing that compressibility slows collapse. Additionally, an outgoing shock wave in the compressible fluid is resolved., Comment: 19 pages, 9 figures

Multiple measures assessment (MMA) is an alternative placement system that involves the consideration of alternative measures of students' performance--such as high school grades or GPA--in addition to or in place of standardized test scores to better place students. While the evidence for MMA is strong, placement reform has yet to spread to many colleges and states. Moreover, despite growing support for MMA, many colleges may not be implementing the most promising MMA systems, and some may shift back to standardized testing in the post-pandemic environment. CAPR has sought to assist colleges and states nationwide with the adoption and implementation of MMA practices that place more students--and allow more students to be successful--in college-level courses. As part of these efforts, CAPR worked with colleges in Arkansas and Texas to adopt and expand MMA. The findings in this report are derived from interviews with personnel from 12 two- and four-year public colleges in those states that went through considerable effort to improve their placement systems and to make them sustainable on a large scale. The study focused on three questions: What was the design of the MMA system at each college? How were colleges adopting MMA practices and what were key facilitators and hindrances? And what was the average cost of implementation? The authors found that adoption of MMA at each study college required collaboration among institutional leaders, administrators, faculty members, and advisors. The report highlights the roles of key actors in the adoption of MMA and the important role that state context and policies played in implementation. It also describes challenges that colleges had to overcome during implementation, such as obtaining staff buy-in, managing student data, and ensuring sufficient staffing.

To help the nation respond to the pandemic, Congress injected about $4.6 trillion into the U.S. economy through the Coronavirus Aid, Relief, and Economic Security (CARES) Act and subsequent legislation. Of this amount, over $75 billion was directed to institutions of higher education through the Higher Education Emergency Relief (HEER) Fund, including nearly $25 billion to community colleges. Using data from the U.S. Department of Education's Education Stabilization Fund Transparency Portal and the Integrated Postsecondary Education Data System, this ARCC Network report examines how HEER funds were distributed to community colleges and the extent to which the colleges spent those funds. It also explores how HEER funding and spending patterns differed by institutional and student characteristics. HEER funding was based mostly on particular kinds of enrollments: States and community colleges with higher enrollments received more funds, and those with higher percentages of Pell recipients and full-time students tended to receive larger awards. The majority of HEER funds were intended to aid in the transition to distance learning, support faculty and staff training, and maintain core instruction and services at colleges. A substantial portion of HEER funding also went to students in the form of emergency aid, and some colleges received "other" HEER funding based on institutional characteristics to address additional unmet needs. Community colleges spent nearly all the HEER funding they received: Collectively, 976 community colleges spent 95% of funds, and nearly half the colleges (484) spent virtually all of their HEER funds. Colleges that spent less of their HEER funding tended to have received larger per-student awards. [This report was written with the Accelerating Recovery in Community Colleges (ARCC) Network.]

Volatile memristors have recently gained popularity as promising devices for neuromorphic circuits, capable of mimicking the leaky function of neurons and offering advantages over capacitor-based circuits in terms of power dissipation and area. Additionally, volatile memristors are useful as selector devices and for hardware security circuits such as physical unclonable functions. To facilitate the design and simulation of circuits, a compact behavioral model is essential. This paper proposes V-VTEAM, a compact, simple, general, and flexible behavioral model for volatile memristors, inspired by the VTEAM nonvolatile memristor model and developed in MATLAB. The validity of the model is demonstrated by fitting it to an ion drift/diffusion-based Ag/SiOx/C/W volatile memristor, achieving a relative root mean error square of 4.5%., Comment: 4 pages, 4 figures, 1 table, to be published in proceedings of 2024 International Flexible Electronics Technology Conference (IFETC 2024)

This work presents a simple and robust method to construct a B-spline based Everett map, for application in the Preisach model of hysteresis, to predict static hysteresis behavior. Its strength comes from the ability to directly capture the Everett map as a well-founded closed-form B-spline surface expression, while also eliminating model artifacts that plague Everett map based Preisach models. Contrary to other works, that applied numerical descriptions for the Everett map, the presented approach is of completely analytic nature. In this work the B-spline surface fitting procedure and the necessary set of constraints are explained. Furthermore, the B-spline based Everett map is validated by ensuring that model artifacts were properly eliminated. Additionally, the model was compared with four benchmark excitations. Namely, a degaussing signal, a set of first-order reversal curves, an arbitrary excitation with high-order reversal curves, and a PWM like signal. The model was able to reproduce all benchmarks with high accuracy., Comment: 6 pages, 3 figures

The Big Data explosion has necessitated the development of search algorithms that scale sub-linearly in time and memory. While compression algorithms and search algorithms do exist independently, few algorithms offer both, and those which do are domain-specific. We present panCAKES, a novel approach to compressive search, i.e., a way to perform $k$-NN and $\rho$-NN search on compressed data while only decompressing a small, relevant, portion of the data. panCAKES assumes the manifold hypothesis and leverages the low-dimensional structure of the data to compress and search it efficiently. panCAKES is generic over any distance function for which the distance between two points is proportional to the memory cost of storing an encoding of one in terms of the other. This property holds for many widely-used distance functions, e.g. string edit distances (Levenshtein, Needleman-Wunsch, etc.) and set dissimilarity measures (Jaccard, Dice, etc.). We benchmark panCAKES on a variety of datasets, including genomic, proteomic, and set data. We compare compression ratios to gzip, and search performance between the compressed and uncompressed versions of the same dataset. panCAKES achieves compression ratios close to those of gzip, while offering sub-linear time performance for $k$-NN and $\rho$-NN search. We conclude that panCAKES is an efficient, general-purpose algorithm for exact compressive search on large datasets that obey the manifold hypothesis. We provide an open-source implementation of panCAKES in the Rust programming language.

The bulk behaviour of granular materials is tied to its mesoscale and particle-scale features: strength properties arise from the buildup of various anisotropic structures at the particle-scale induced by grain connectivity (fabric), force transmission, and frictional mobilization. More fundamentally, these anisotropic structures work collectively to define features like the bulk friction coefficient and the stress tensor at the macroscale and can be explained by the Stress-Force-Fabric (SFF) relationship stemming from the microscale. Although the SFF relation has been extensively verified by discrete numerical simulations, a laboratory realization has remained elusive due to the challenge of measuring both normal and frictional contact forces. In this study, we analyze experiments performed on a photoelastic granular system under four different loading conditions: uniaxial compression, isotropic compression, pure shear, and annular shear. During these experiments, we record particle locations, contacts, and normal and frictional forces vectors to measure the particle-scale response to progressing strain. We track microscale measures like the packing fraction, average coordination number and average normal force along with anisotropic distributions of contacts and forces. We match the particle-scale anisotropy to the bulk using the SFF relation, which is founded on two key principles, a Stress Rule to describe the stress tensor and a Sum Rule to describe the bulk friction coefficient; we find that the Sum and Stress Rules accurately describe bulk measurements. Additionally, we test the assumption that fabric and forces transmit load equally through our granular packings and show that this assumption is sufficient at large strain values, and can be applied to areas like rock mechanics, soft colloids, or cellular tissue where force information is inaccessible., Comment: 10 pages, 5 figures, 5 pages supplemental with 6 figures

Let $E/\mathbb{Q}$ be an elliptic curve. We say that $E$ has a near coincidence of level $(n,m)$ if $m \mid n$ and $\mathbb{Q}(E[n]) = \mathbb{Q}(E[m],\zeta_{n})$. In the present paper we classify near coincidences of prime power level. We use this result to give a classification of values of $n$ for which ${\rm Gal}(\mathbb{Q}(E[n])/\mathbb{Q})$ is a nilpotent group. In particular, if we assume that there are no non-CM rational points on the modular curves $X_{ns}^{+}(p)$ for primes $p > 11$, then ${\rm Gal}(\mathbb{Q}(E[n])/\mathbb{Q})$ nilpotent implies that $n$ is a power of $2$ or $n \in \{ 3, 5, 6, 7, 15, 21 \}$., Comment: 26 pages

The NANOGrav 15-year data provides compelling evidence for a stochastic gravitational-wave (GW) background at nanohertz frequencies. The simplest model-independent approach to characterizing the frequency spectrum of this signal consists in a simple power-law fit involving two parameters: an amplitude A and a spectral index \gamma. In this paper, we consider the next logical step beyond this minimal spectral model, allowing for a running (i.e., logarithmic frequency dependence) of the spectral index, \gamma_run(f) = \gamma + \beta \ln(f/f_ref). We fit this running-power-law (RPL) model to the NANOGrav 15-year data and perform a Bayesian model comparison with the minimal constant-power-law (CPL) model, which results in a 95% credible interval for the parameter \beta consistent with no running, \beta \in [-0.80,2.96], and an inconclusive Bayes factor, B(RPL vs. CPL) = 0.69 +- 0.01. We thus conclude that, at present, the minimal CPL model still suffices to adequately describe the NANOGrav signal; however, future data sets may well lead to a measurement of nonzero \beta. Finally, we interpret the RPL model as a description of primordial GWs generated during cosmic inflation, which allows us to combine our results with upper limits from big-bang nucleosynthesis, the cosmic microwave background, and LIGO-Virgo-KAGRA., Comment: 18 pages, 4 figures, 2 tables. v2: matches version published in ApJ Letters

Conceptual Engineers want to make words better. However, they often underestimate how varied our usage of words is. In this paper, we take the first steps in exploring the contextual nuances of words by creating conceptual landscapes -- 2D surfaces representing the pragmatic usage of words -- that conceptual engineers can use to inform their projects. We use the spoken component of the British National Corpus and BERT to create contextualised word embeddings, and use Gaussian Mixture Models, a selection of metrics, and qualitative analysis to visualise and numerically represent lexical landscapes. Such an approach has not yet been used in the conceptual engineering literature and provides a detailed examination of how different words manifest in various contexts that is potentially useful to conceptual engineering projects. Our findings highlight the inherent complexity of conceptual engineering, revealing that each word exhibits a unique and intricate landscape. Conceptual Engineers cannot, therefore, use a one-size-fits-all approach when improving words -- a task that may be practically intractable at scale.

Recent advancements in sensors have led to high resolution and high data throughput at the pixel level. Simultaneously, the adoption of increasingly large (deep) neural networks (NNs) has lead to significant progress in computer vision. Currently, visual intelligence comes at increasingly high computational complexity, energy, and latency. We study a data-driven system that combines dynamic sensing at the pixel level with computer vision analytics at the video level and propose a feedback control loop to minimize data movement between the sensor front-end and computational back-end without compromising detection and tracking precision. Our contributions are threefold: (1) We introduce anticipatory attention and show that it leads to high precision prediction with sparse activation of pixels; (2) Leveraging the feedback control, we show that the dimensionality of learned feature vectors can be significantly reduced with increased sparsity; and (3) We emulate analog design choices (such as varying RGB or Bayer pixel format and analog noise) and study their impact on the key metrics of the data-driven system. Comparative analysis with traditional pixel and deep learning models shows significant performance enhancements. Our system achieves a 10X reduction in bandwidth and a 15-30X improvement in Energy-Delay Product (EDP) when activating only 30% of pixels, with a minor reduction in object detection and tracking precision. Based on analog emulation, our system can achieve a throughput of 205 megapixels/sec (MP/s) with a power consumption of only 110 mW per MP, i.e., a theoretical improvement of ~30X in EDP., Comment: Accepted to the Conference on Dynamic Data-Driven Applications Systems (DDDAS2024)