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Let $G$ be a group. The BCI problem asks whether two Haar graphs of $G$ are isomorphic if and only if they are isomorphic by an element of an explicit list of isomorphisms. We first generalize this problem in a natural way and give a theoretical way to solve the isomorphism problem for the natural generalization. We then restrict our attention to abelian groups and, with an exception, reduce the problem to the isomorphism problem for a related quotient, component, or corresponding Cayley digraph. For Haar graphs of an abelian group of odd order with connection sets $S$ those of Cayley graphs (i.e. $S = -S$), the exception does not exist. For Haar graphs of cyclic groups of odd order with connection sets those of a Cayley graph, among others, we solve the isomorphism problem.

Objective: To design and implement VIEWER, a versatile toolkit for visual analytics of clinical data, and to systematically evaluate its effectiveness across various clinical applications while gathering feedback for iterative improvements. Materials and Methods: VIEWER is an open-source and extensible toolkit that employs distributed natural language processing and interactive visualisation techniques to facilitate the rapid design, development, and deployment of clinical information retrieval, analysis, and visualisation at the point of care. Through an iterative and collaborative participatory design approach, VIEWER was designed and implemented in a large mental health institution, where its clinical utility and effectiveness were assessed using both quantitative and qualitative methods. Results: VIEWER provides interactive, problem-focused, and comprehensive views of longitudinal patient data from a combination of structured clinical data and unstructured clinical notes. Despite a relatively short adoption period and users' initial unfamiliarity, VIEWER significantly improved performance and task completion speed compared to the standard clinical information system. Users and stakeholders reported high satisfaction and expressed strong interest in incorporating VIEWER into their daily practice. Discussion: VIEWER provides a cost-effective enhancement to the functionalities of standard clinical information systems, with evaluation offering valuable feedback for future improvements. Conclusion: VIEWER was developed to improve data accessibility and representation across various aspects of healthcare delivery, including population health management and patient monitoring. The deployment of VIEWER highlights the benefits of collaborative refinement in optimizing health informatics solutions for enhanced patient care.

We study the connections between ordinary differential equations and optimization algorithms in a non-Euclidean setting. We propose a novel accelerated algorithm for minimising convex functions over a convex constrained set. This algorithm is a natural generalization of Nesterov's accelerated gradient descent method to the non-Euclidean setting and can be interpreted as an additive Runge-Kutta algorithm. The algorithm can also be derived as a numerical discretization of the ODE appearing in Krichene et al. (2015a). We use Lyapunov functions to establish convergence rates for the ODE and show that the discretizations considered achieve acceleration beyond the setting studied in Krichene et al. (2015a). Finally, we discuss how the proposed algorithm connects to various equations and algorithms in the literature., Comment: 25 pages, 5 figures

The XLZD collaboration is developing a two-phase xenon time projection chamber with an active mass of 60 to 80 t capable of probing the remaining WIMP-nucleon interaction parameter space down to the so-called neutrino fog. In this work we show that, based on the performance of currently operating detectors using the same technology and a realistic reduction of radioactivity in detector materials, such an experiment will also be able to competitively search for neutrinoless double beta decay in $^{136}$Xe using a natural-abundance xenon target. XLZD can reach a 3$\sigma$ discovery potential half-life of 5.7$\times$10$^{27}$ yr (and a 90% CL exclusion of 1.3$\times$10$^{28}$ yr) with 10 years of data taking, corresponding to a Majorana mass range of 7.3-31.3 meV (4.8-20.5 meV). XLZD will thus exclude the inverted neutrino mass ordering parameter space and will start to probe the normal ordering region for most of the nuclear matrix elements commonly considered by the community., Comment: 29 pages, 7 figures

We introduce KANICE (Kolmogorov-Arnold Networks with Interactive Convolutional Elements), a novel neural architecture that combines Convolutional Neural Networks (CNNs) with Kolmogorov-Arnold Network (KAN) principles. KANICE integrates Interactive Convolutional Blocks (ICBs) and KAN linear layers into a CNN framework. This leverages KANs' universal approximation capabilities and ICBs' adaptive feature learning. KANICE captures complex, non-linear data relationships while enabling dynamic, context-dependent feature extraction based on the Kolmogorov-Arnold representation theorem. We evaluated KANICE on four datasets: MNIST, Fashion-MNIST, EMNIST, and SVHN, comparing it against standard CNNs, CNN-KAN hybrids, and ICB variants. KANICE consistently outperformed baseline models, achieving 99.35% accuracy on MNIST and 90.05% on the SVHN dataset. Furthermore, we introduce KANICE-mini, a compact variant designed for efficiency. A comprehensive ablation study demonstrates that KANICE-mini achieves comparable performance to KANICE with significantly fewer parameters. KANICE-mini reached 90.00% accuracy on SVHN with 2,337,828 parameters, compared to KANICE's 25,432,000. This study highlights the potential of KAN-based architectures in balancing performance and computational efficiency in image classification tasks. Our work contributes to research in adaptive neural networks, integrates mathematical theorems into deep learning architectures, and explores the trade-offs between model complexity and performance, advancing computer vision and pattern recognition. The source code for this paper is publicly accessible through our GitHub repository (https://github.com/m-ferdaus/kanice).

This report describes the experimental strategy and technologies for a next-generation xenon observatory sensitive to dark matter and neutrino physics. The detector will have an active liquid xenon target mass of 60-80 tonnes and is proposed by the XENON-LUX-ZEPLIN-DARWIN (XLZD) collaboration. The design is based on the mature liquid xenon time projection chamber technology of the current-generation experiments, LZ and XENONnT. A baseline design and opportunities for further optimization of the individual detector components are discussed. The experiment envisaged here has the capability to explore parameter space for Weakly Interacting Massive Particle (WIMP) dark matter down to the neutrino fog, with a 3$\sigma$ evidence potential for the spin-independent WIMP-nucleon cross sections as low as $3\times10^{-49}\rm cm^2$ (at 40 GeV/c$^2$ WIMP mass). The observatory is also projected to have a 3$\sigma$ observation potential of neutrinoless double-beta decay of $^{136}$Xe at a half-life of up to $5.7\times 10^{27}$ years. Additionally, it is sensitive to astrophysical neutrinos from the atmosphere, sun, and galactic supernovae., Comment: 32 pages, 14 figures

We report results of a search for nuclear recoils induced by weakly interacting massive particle (WIMP) dark matter using the LUX-ZEPLIN (LZ) two-phase xenon time projection chamber. This analysis uses a total exposure of $4.2\pm0.1$ tonne-years from 280 live days of LZ operation, of which $3.3\pm0.1$ tonne-years and 220 live days are new. A technique to actively tag background electronic recoils from $^{214}$Pb $\beta$ decays is featured for the first time. Enhanced electron-ion recombination is observed in two-neutrino double electron capture decays of $^{124}$Xe, representing a noteworthy new background. After removal of artificial signal-like events injected into the data set to mitigate analyzer bias, we find no evidence for an excess over expected backgrounds. World-leading constraints are placed on spin-independent (SI) and spin-dependent WIMP-nucleon cross sections for masses $\geq$9 GeV/$c^2$. The strongest SI exclusion set is $2.1\times10^{-48}$ cm$^{2}$ at the 90% confidence level at a mass of 36 GeV/$c^2$, and the best SI median sensitivity achieved is $5.0\times10^{-48}$ cm$^{2}$ for a mass of 40 GeV/$c^2$., Comment: 9 pages, 7 figures. See https://www.hepdata.net/record/155182 for a data release related to this paper

We utilize serendipitous observations from the Asteroid Terrestrial-impact Last Alert System (ATLAS) and the Zwicky Transient Facility (ZTF) in addition to targeted follow-up observations from the Las Cumbres Observatory (LCO) and Liverpool Telescope to analyze the first observed instance of cometary activity by the newly-discovered Jupiter-family comet C/2023 RN3 (ATLAS), whose orbital dynamics place it close to residing on a Centaur-like orbit. Across our 7-month baseline, we observe an epoch of cometary activity commencing in August 2023 with an increase in brightness of >5.4 mag. The lightcurve of 2023 RN3 indicates the presence of continuous cometary activity across our observations, suggesting the onset of a new period of sustained activity. We find no evidence of any outbursts on top of the observed brightening, nor do we find any significant color evolution across our observations. 2023 RN3 is visibly extended in LCO and Liverpool Telescope observations, indicating the presence of a spatially-extended coma. Numerical integration of 2023 RN3's orbit reveals the comet to have recently undergone a slight increase in semimajor axis due to a planetary encounter with Jupiter, however whether this orbital change could trigger 2023 RN3's cometary activity is unclear. Our estimate for the maximum dust production metric of Afrho ~400 cm is consistent with previous measurements for the Jupiter-family comet and Centaur populations., Comment: 20 pages, 9 figures

The 2023 Big ANN Challenge, held at NeurIPS 2023, focused on advancing the state-of-the-art in indexing data structures and search algorithms for practical variants of Approximate Nearest Neighbor (ANN) search that reflect the growing complexity and diversity of workloads. Unlike prior challenges that emphasized scaling up classical ANN search ~\cite{DBLP:conf/nips/SimhadriWADBBCH21}, this competition addressed filtered search, out-of-distribution data, sparse and streaming variants of ANNS. Participants developed and submitted innovative solutions that were evaluated on new standard datasets with constrained computational resources. The results showcased significant improvements in search accuracy and efficiency over industry-standard baselines, with notable contributions from both academic and industrial teams. This paper summarizes the competition tracks, datasets, evaluation metrics, and the innovative approaches of the top-performing submissions, providing insights into the current advancements and future directions in the field of approximate nearest neighbor search., Comment: Code: https://github.com/harsha-simhadri/big-ann-benchmarks/releases/tag/v0.3.0

Digital phenotyping offers a novel and cost-efficient approach for managing depression and anxiety. Previous studies, often limited to small-to-medium or specific populations, may lack generalizability. We conducted a cross-sectional analysis of data from 10,129 participants recruited from a UK-based general population between June 2020 and August 2022. Participants shared wearable (Fitbit) data and self-reported questionnaires on depression (PHQ-8), anxiety (GAD-7), and mood via a study app. We first examined the correlations between PHQ-8/GAD-7 scores and wearable-derived features, demographics, health data, and mood assessments. Subsequently, unsupervised clustering was used to identify behavioural patterns associated with depression or anxiety. Finally, we employed separate XGBoost models to predict depression and anxiety and compared the results using different subsets of features. We observed significant associations between the severity of depression and anxiety with several factors, including mood, age, gender, BMI, sleep patterns, physical activity, and heart rate. Clustering analysis revealed that participants simultaneously exhibiting lower physical activity levels and higher heart rates reported more severe symptoms. Prediction models incorporating all types of variables achieved the best performance ($R^2$=0.41, MAE=3.42 for depression; $R^2$=0.31, MAE=3.50 for anxiety) compared to those using subsets of variables. This study identified potential indicators for depression and anxiety, highlighting the utility of digital phenotyping and machine learning technologies for rapid screening of mental disorders in general populations. These findings provide robust real-world insights for future healthcare applications.

We examine bicoset digraphs and their natural properties from the point of view of symmetry. We then consider connected bicoset digraphs that are $X$-joins with collections of empty graphs, and show that their automorphism groups can be obtained from their natural irreducible quotients. We then show that such digraphs can be recognized from their connection sets., Comment: The work of the second author is supported in part by the Slovenian Research Agency (research program P1-0285 and research projects N1-0140, N1-0160, J1-2451, N1-0208, J1-3001, J1-3003, J1-4008, and J1-50000), while the work of the third author is supported in part by the Slovenian Research Agency (research program P1-0285 and Young Researchers Grant)

We consider the dispersion (van der Waals, vdW) interaction among N parallel elongated objects such as DNA/RNA strands or metallic nanotubes, which are polarizable primarily along the long axis. Within a quasi-one-dimensional model, we prove that the irreducible N -object vdW energy contribution is negative (attractive) for even N and positive (repulsive) for odd N. We confirm these results up to $N=4$ via a 3-dimensional plasma cylinder model. This suggests a preference for even-N clustering of elongated structures in nanoscience and biology. This work could have implications e.g. for nanotube bundle formation and for the clustering of long-chain biomolecules at separations exceeding chemical bond lengths., Comment: 15 pages, 3 figures

The broad physics reach of the LUX-ZEPLIN (LZ) experiment covers rare phenomena beyond the direct detection of dark matter. We report precise measurements of the extremely rare decay of $^{124}$Xe through the process of two-neutrino double electron capture (2$\nu$2EC), utilizing a $1.39\,\mathrm{kg} \times \mathrm{yr}$ isotopic exposure from the first LZ science run. A half-life of $T_{1/2}^{2\nu2\mathrm{EC}} = (1.09 \pm 0.14_{\text{stat}} \pm 0.05_{\text{sys}}) \times 10^{22}\,\mathrm{yr}$ is observed with a statistical significance of $8.3\,\sigma$, in agreement with literature. First empirical measurements of the KK capture fraction relative to other K-shell modes were conducted, and demonstrate consistency with respect to recent signal models at the $1.4\,\sigma$ level., Comment: 15 pages, 3 figures

Electronic Health Records are large repositories of valuable clinical data, with a significant portion stored in unstructured text format. This textual data includes clinical events (e.g., disorders, symptoms, findings, medications and procedures) in context that if extracted accurately at scale can unlock valuable downstream applications such as disease prediction. Using an existing Named Entity Recognition and Linking methodology, MedCAT, these identified concepts need to be further classified (contextualised) for their relevance to the patient, and their temporal and negated status for example, to be useful downstream. This study performs a comparative analysis of various natural language models for medical text classification. Extensive experimentation reveals the effectiveness of transformer-based language models, particularly BERT. When combined with class imbalance mitigation techniques, BERT outperforms Bi-LSTM models by up to 28% and the baseline BERT model by up to 16% for recall of the minority classes. The method has been implemented as part of CogStack/MedCAT framework and made available to the community for further research.

The Boulby UnderGround Screening (BUGS) facility, located at the Boulby Underground Laboratory, has significantly advanced its material screening capabilities by installing two XIA UltraLo-1800 alpha particle detectors. This study presents a comprehensive evaluation of one of these detectors, operated 1,100 meters underground at the Boulby Underground Laboratory, which provides significant shielding from cosmic radiation and maintains a low ambient radon activity of 2.30 $\pm$ 0.03 Bq/m$^3$. Our evaluation focuses on energy reconstruction accuracy, background radiation rates, and operational stability. The XIA UltraLo-1800 detector demonstrates remarkable stability in energy reconstruction, with less than 0.1 MeV variation over four years. Moreover, the implementation of a graphite-filled PTFE liner in the sample tray resulted in a significant reduction in background radiation levels compared to measurements with the original stainless steel tray, achieving an average activity of 0.15 $\pm$ 0.01 $\alpha$/cm$^2$/khr. Copper sample assays, performed before and after radon exposure, demonstrated the detector's ability to accurately identify and quantify $^{210}$Po contamination. By implementing the robust cleanliness procedures and protocols described in this article, we observed a reduction in $^{210}$Po activity from 0.504 $\pm$ 0.022 mBq to 0.336 $\pm$ 0.013 mBq, highlighting the crucial role of refined cleaning methods in minimizing background for sensitive experiments. Additionally, observations of elevated background activity levels post-high-activity sample measurements illustrate the need for careful management of assay conditions and environment to maintain low background levels. These results highlight the potential of the XIA UltraLo-1800 in enhancing the precision of material assays essential for reducing background interference in rare event experiments.

When there is a fault, the protection system automatically removes one or more transmission lines on a fast time scale of less than one minute. The outaged lines form a pattern in the transmission network. We extract these patterns from utility outage data, determine some key statistics of these patterns, and then show how to generate new patterns consistent with these statistics. The generated patterns provide a new and easily feasible way to model the overall effect of the protection system at the scale of a large transmission system. This new generative modeling of protection is expected to contribute to simulations of disturbances in large grids so that they can better quantify the risk of blackouts. Analysis of the pattern sizes suggests an index that describes how much outages spread in the transmission network at the fast timescale.

Centaurs are small Solar System objects on chaotic orbits in the giant planet region, forming an evolutionary continuum with the Kuiper belt objects and Jupiter-family comets. Some Centaurs are known to exhibit cometary activity, though unlike comets this activity tends not to correlate with heliocentric distance and the mechanism behind it is currently poorly understood. We utilize serendipitous observations from the Asteroid Terrestrial-impact Last Alert System (ATLAS), Zwicky Transient Facility (ZTF), Panoramic Survey Telescope and Rapid Response System (Pan-STARRS), Dark Energy Survey (DES), and Gaia in addition to targeted follow-up observations from the Las Cumbres Observatory, TRAnsiting Planets and PlanetesImals Small Telescope South (TRAPPIST-South), and Gemini North telescope to analyze an unexpected brightening exhibited by the known active Centaur (2060) Chiron in 2021. This is highly indicative of a cometary outburst. As of 2023 February, Chiron has still not returned to its pre-brightening magnitude. We find Chiron's rotational lightcurve, phase curve effects, and possible high-albedo surface features to be unlikely causes of this observed brightening. We consider the most likely cause to be an epoch of either new or increased cometary activity, though we cannot rule out a possible contribution from Chiron's reported ring system, such as a collision of as-yet unseen satellites shepherding the rings. We find no evidence for coma in our Gemini or TRAPPIST-South observations, though this does not preclude the possibility that Chiron is exhibiting a coma that is too faint for observation or constrained to the immediate vicinity of the nucleus., Comment: 39 pages, 14 figures, 14 tables. Has been accepted for publication in PSJ

We focus on large blackouts in electric distribution systems caused by extreme winds. Such events have a large cost and impact on customers. To quantify resilience to these events, we formulate large event risk and show how to calculate it from the historical outage data routinely collected by utilities' outage management systems. Risk is defined using an event cost exceedance curve. The tail of this curve and the large event risk is described by the probability of a large cost event and the slope magnitude of the tail on a log-log plot. Resilience can be improved by planned investments to upgrade system components or speed up restoration. The benefits that these investments would have had if they had been made in the past can be quantified by "rerunning history" with the effects of the investment included, and then recalculating the large event risk to find the improvement in resilience. An example using utility data shows a 12% and 22% reduction in the probability of a large cost event due to 10% wind hardening and 10% faster restoration respectively. This new data-driven approach to quantify resilience and resilience investments is realistic and much easier to apply than complicated approaches based on modeling all the phases of resilience. Moreover, an appeal to improvements to past lived experience may well be persuasive to customers and regulators in making the case for resilience investments.

We introduce a novel classification framework for time-series imputation using deep learning, with a particular focus on clinical data. By identifying conceptual gaps in the literature and existing reviews, we devise a taxonomy grounded on the inductive bias of neural imputation frameworks, resulting in a classification of existing deep imputation strategies based on their suitability for specific imputation scenarios and data-specific properties. Our review further examines the existing methodologies employed to benchmark deep imputation models, evaluating their effectiveness in capturing the missingness scenarios found in clinical data and emphasising the importance of reconciling mathematical abstraction with clinical insights. Our classification aims to serve as a guide for researchers to facilitate the selection of appropriate deep learning imputation techniques tailored to their specific clinical data. Our novel perspective also highlights the significance of bridging the gap between computational methodologies and medical insights to achieve clinically sound imputation models.

It has long been known that a vertex-transitive graph $\Gamma$ is isomorphic to a double coset graph $\text{Cos}(G,H,S)$ of a transitive group $G\le\text{Aut}(\Gamma)$, a vertex stabilizer $H\le G$, and some subset $S\subseteq G$. We show that the automorphism group of the Cayley graph $\text{Cay}(G,S)$ with connection set $S$ can be obtained from the automorphism group of $\text{Cos}(G,H,S)$ and vice versa. We also show that the isomorphism problem for double coset graphs is equivalent to the isomorphism problem for Cayley graphs provided one knows all groups $G$ for which a fixed Cayley graph is a Cayley graph of $G$. Our main tool is a "recognition theorem", which recognizes when a Cayley graph of a group $G$ is a wreath product of two graphs based upon its connection set., Comment: This work is supported in part by the Slovenian Research Agency (research program P1-0285 and research projects N1-0140, N1-0160, J1-2451, N1-0208, J1-3001, J1-3003, J1-4008, and J1-50000)

Speech and language biomarkers have the potential to be regular, objective assessments of symptom severity in several health conditions, both in-clinic and remotely using mobile devices. However, the complex nature of speech and often subtle changes associated with health mean that findings are highly dependent on methodological and cohort choices. These are often not reported adequately in studies investigating speech-based health assessment, hindering the progress of methodological speech research. Our objectives were to) facilitate replicable speech research by presenting an adaptable speech collection and analytical method and design checklist for other researchers to adapt for their own experiments and develop an exemplar protocol that reduces and controls for confounding factors in repeated recordings of speech, including device choice, speech elicitation task and non-pathological variability. The presented protocol comprises the elicitation of read speech, held vowels and a picture description collected with a freestanding condenser microphone, 3 smartphones and a headset. We extracted a set of 14 exemplar speech features. We collected healthy speech from 28 individuals 3 times in 1 day, repeated at the same times 8-11 weeks later, and from 25 individuals on 3 days in 1 week at fixed times. Participant characteristics collected included sex, age, native language status and voice use habits. Before each recording, we collected information on recent voice use, food and drink intake, and emotional state. The extracted features are presented providing a resource of normative values. Speech data collection, processing, analysis and reporting towards clinical research and practice varies widely. Greater harmonisation of study protocols and consistent reporting are urgently required to translate speech processing into clinical research and practice., Comment: Main manuscript: 49 pages double spaced. 3 figures, 6 tables. Submitted to BMC Methods. Replacement with substantially revised version

Weakly interacting massive particles (WIMPs) may interact with a virtual pion that is exchanged between nucleons. This interaction channel is important to consider in models where the spin-independent isoscalar channel is suppressed. Using data from the first science run of the LUX-ZEPLIN dark matter experiment, containing 60 live days of data in a 5.5~tonne fiducial mass of liquid xenon, we report the results on a search for WIMP-pion interactions. We observe no significant excess and set an upper limit of $1.5\times10^{-46}$~cm$^2$ at a 90\% confidence level for a WIMP mass of 33~GeV/c$^2$ for this interaction.

The Data Acquisition System (DAQ) for the LUX-ZEPLIN (LZ) dark matter detector is described. The signals from 745 PMTs, distributed across three subsystems, are sampled with 100-MHz 32-channel digitizers (DDC-32s). A basic waveform analysis is carried out on the on-board Field Programmable Gate Arrays (FPGAs) to extract information about the observed scintillation and electroluminescence signals. This information is used to determine if the digitized waveforms should be preserved for offline analysis. The system is designed around the Kintex-7 FPGA. In addition to digitizing the PMT signals and providing basic event selection in real time, the flexibility provided by the use of FPGAs allows us to monitor the performance of the detector and the DAQ in parallel to normal data acquisition. The hardware and software/firmware of this FPGA-based Architecture for Data acquisition and Realtime monitoring (FADR) are discussed and performance measurements are described., Comment: 18 pages, 24 figures

LUX-ZEPLIN (LZ) is a tonne-scale experiment searching for direct dark matter interactions and other rare events. It is located at the Sanford Underground Research Facility (SURF) in Lead, South Dakota, USA. The core of the LZ detector is a dual-phase xenon time projection chamber (TPC), designed with the primary goal of detecting Weakly Interacting Massive Particles (WIMPs) via their induced low energy nuclear recoils. Surrounding the TPC, two veto detectors immersed in an ultra-pure water tank enable reducing background events to enhance the discovery potential. Intricate calibration systems are purposely designed to precisely understand the responses of these three detector volumes to various types of particle interactions and to demonstrate LZ's ability to discriminate between signals and backgrounds. In this paper, we present a comprehensive discussion of the key features, requirements, and performance of the LZ calibration systems, which play a crucial role in enabling LZ's WIMP-search and its broad science program. The thorough description of these calibration systems, with an emphasis on their novel aspects, is valuable for future calibration efforts in direct dark matter and other rare-event search experiments.

The first science run of the LUX-ZEPLIN (LZ) experiment, a dual-phase xenon time project chamber operating in the Sanford Underground Research Facility in South Dakota, USA, has reported leading limits on spin-independent WIMP-nucleon interactions and interactions described from a non-relativistic effective field theory (NREFT). Using the same 5.5~t fiducial mass and 60 live days of exposure we report on the results of a relativistic extension to the NREFT. We present constraints on couplings from covariant interactions arising from the coupling of vector, axial currents, and electric dipole moments of the nucleon to the magnetic and electric dipole moments of the WIMP which cannot be described by recasting previous results described by an NREFT. Using a profile-likelihood ratio analysis, in an energy region between 0~keV$_\text{nr}$ to 270~keV$_\text{nr}$, we report 90% confidence level exclusion limits on the coupling strength of five interactions in both the isoscalar and isovector bases., Comment: 7 pages, 4 figures

Let $k$ be odd, and $n$ an odd multiple of $3$. We prove that $C_k \rtimes C_8$ and $(C_n \times C_3)\rtimes C_8$ do not have the Directed Cayley Isomorphism (DCI) property. When $k$ is also prime, $C_k \rtimes C_8$ had previously been proved to have the Cayley Isomorphism (CI) property. To the best of our knowledge, the groups $C_p \rtimes C_8$ (where $p$ is an odd prime) are only the second known infinite family of groups that have the CI property but do not have the DCI property. This also shows that no group with an element of order $8$ has the DCI property., Comment: 4 pages

Prior research has shown that changes in seasons and weather can have a significant impact on depression severity. However, findings are inconsistent across populations, and the interplay between weather, behavior, and depression has not been fully quantified. This study analyzed real-world data from 428 participants (a subset; 68.7% of the cohort) in the RADAR-MDD longitudinal mobile health study to investigate seasonal variations in depression (measured through a remote validated assessment - PHQ-8) and examine the potential interplay between dynamic weather changes, physical activity (monitored via wearables), and depression severity. The clustering of PHQ-8 scores identified four distinct seasonal variations in depression severity: one stable trend and three varying patterns where depression peaks in different seasons. Among these patterns, participants within the stable trend had the oldest average age (p=0.002) and the lowest baseline PHQ-8 score (p=0.003). Mediation analysis assessing the indirect effect of weather on physical activity and depression showed significant differences among participants with different affective responses to weather. These findings illustrate the heterogeneity in individuals' seasonal depression variations and responses to weather, underscoring the necessity for personalized approaches to help understand the impact of environmental factors on the real-world effectiveness of behavioral treatments.

Solid-state cooling devices offer compact, quiet, reliable and environmentally friendly solutions that currently rely primarily on the thermoelectric (TE) effect. Despite more than two centuries of research, classical thermoelectric coolers suffer from low efficiency which hampers wider application. In this study, the less researched Anomalous Ettingshausen effect (AEE), a transverse thermoelectric phenomenon, is presented as a new approach for on-chip cooling. This effect can be boosted in materials with non-trivial band topologies as demonstrated in the Heusler alloy $\text{Co}_2\text{MnGa}$. Enabled by the high quality of our material, in situ scanning thermal microscopy experiments reveal a record-breaking anomalous Ettingshausen coefficient of $-2.1$~mV in $\mu$m-sized on-chip cooling devices at room temperature. A significant 44\% of the effect is contributed by the intrinsic topological properties, in particular the Berry curvature of $\text{Co}_2\text{MnGa}$, emphasising the unique potential of magnetic Weyl semimetals for high-performance spot cooling in nanostructures.

Searches for dark matter with liquid xenon time projection chamber experiments have traditionally focused on the region of the parameter space that is characteristic of weakly interacting massive particles, ranging from a few GeV/$c^2$ to a few TeV/$c^2$. Models of dark matter with a mass much heavier than this are well motivated by early production mechanisms different from the standard thermal freeze-out, but they have generally been less explored experimentally. In this work, we present a re-analysis of the first science run (SR1) of the LZ experiment, with an exposure of $0.9$ tonne$\times$year, to search for ultraheavy particle dark matter. The signal topology consists of multiple energy deposits in the active region of the detector forming a straight line, from which the velocity of the incoming particle can be reconstructed on an event-by-event basis. Zero events with this topology were observed after applying the data selection calibrated on a simulated sample of signal-like events. New experimental constraints are derived, which rule out previously unexplored regions of the dark matter parameter space of spin-independent interactions beyond a mass of 10$^{17}$ GeV/$c^2$., Comment: 9 pages, 7 figures

Let $E$ and $E'$ be 2-isogenous elliptic curves over $\Q$. Following \cite{ck}, we call a good prime $p$ \emph{anomalous} if $E(\F_p) \simeq E'(\F_p)$ but $E(\F_{p^2}) \not \simeq E'(\F_{p^2})$. Our main result is an explicit formula for the proportion of anomalous primes for any such pair of elliptic curves. We consider both the CM case and the non-CM case., Comment: 29 pages

Missingness is ubiquitous in multivariate time series and poses an obstacle to reliable downstream analysis. Although recurrent network imputation achieved the SOTA, existing models do not scale to deep architectures that can potentially alleviate issues arising in complex data. Moreover, imputation carries the risk of biased estimations of the ground truth. Yet, confidence in the imputed values is always unmeasured or computed post hoc from model output. We propose DEep Attention Recurrent Imputation (DEARI), which jointly estimates missing values and their associated uncertainty in heterogeneous multivariate time series. By jointly representing feature-wise correlations and temporal dynamics, we adopt a self attention mechanism, along with an effective residual component, to achieve a deep recurrent neural network with good imputation performance and stable convergence. We also leverage self-supervised metric learning to boost performance by optimizing sample similarity. Finally, we transform DEARI into a Bayesian neural network through a novel Bayesian marginalization strategy to produce stochastic DEARI, which outperforms its deterministic equivalent. Experiments show that DEARI surpasses the SOTA in diverse imputation tasks using real-world datasets, namely air quality control, healthcare and traffic.