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Quadratic quasinormal modes encode fundamental properties of black hole spacetimes. They are also one of the key ingredients of nonlinearities of General Relativity in the ringdown stage of binary black hole coalescence. In this work, we classify all possible quadratic coupling channels of quasinormal modes for a generic Kerr black hole, and use a frequency-domain pseudospectral code with hyperboloidal slicing to calculate these couplings. After accounting for all the channels in systems with reflection symmetry, our results become consistent with those extracted from numerical simulations and time-domain fits. We explore several observationally relevant quadratic modes and their detectability with third-generation ground-based detectors like Cosmic Explorer, as well as the space-borne detector LISA (Laser Interferometer Space Antenna). We find that several quadratic modes are detectable by both detectors. In addition, we make a theoretical prediction for how the signal-to-noise ratio of a quadratic quasinormal mode depends on the properties of progenitor binaries, offering insight into selecting golden events in future ringdown data analyses., Comment: 14 pages, 10 figures

Randomly sampling an acyclic orientation on the complete bipartite graph $K_{n,k}$ with parts of size $n$ and $k$, we investigate the length of the longest path. We provide a probability generating function for the distribution of the longest path length, and we use Analytic Combinatorics to perform asymptotic analysis of the probability distribution in the case of equal part sizes $n = k$ tending toward infinity. We show that the distribution is asymptotically Gaussian, and we obtain precise asymptotics for the mean and variance. These results address a question asked by Peter J. Cameron. Keywords: bipartite graph, directed graph, random graph, acyclic orientation, poly-Bernoulli numbers, lonesum matrices, generating function, analytic combinatorics, asymptotics., Comment: 24 pages

Since 2018, the potential for a high-energy neutrino telescope, named the Pacific Ocean Neutrino Experiment (P-ONE), has been thoroughly examined by two pathfinder missions, STRAW and STRAW-b, short for short for Strings for Absorption Length in Water. The P-ONE project seeks to install a neutrino detector with a one cubic kilometer volume in the Cascadia Basin's deep marine surroundings, situated near the western shores of Vancouver Island, Canada. To assess the environmental conditions and feasibility of constructing a neutrino detector of that scale, the pathfinder missions, STRAW and STRAW-b, have been deployed at a depth of 2.7 km within the designated site for P-ONE and were connected to the NEPTUNE observatory, operated by Ocean Networks Canada (ONC). While STRAW focused on analyzing the optical properties of water in the Cascadia Basin, \ac{strawb} employed cameras and spectrometers to investigate the characteristics of bioluminescence in the deep-sea environment. This report introduces the STRAW-b concept, covering its scientific objectives and the instrumentation used. Furthermore, it discusses the design considerations implemented to guarantee a secure and dependable deployment process of STRAW-b. Additionally, it showcases the data collected by battery-powered loggers, which monitored the mechanical stress on the equipment throughout the deployment. The report also offers an overview of STRAW-b's operation, with a specific emphasis on the notable advancements achieved in the data acquisition (DAQ) system and its successful integration with the server infrastructure of ONC., Comment: 20 pages, 11 figures, 2 tables

Classification models are expected to perform equally well for different classes, yet in practice, there are often large gaps in their performance. This issue of class bias is widely studied in cases of datasets with sample imbalance, but is relatively overlooked in balanced datasets. In this work, we introduce the concept of spectral imbalance in features as a potential source for class disparities and study the connections between spectral imbalance and class bias in both theory and practice. To build the connection between spectral imbalance and class gap, we develop a theoretical framework for studying class disparities and derive exact expressions for the per-class error in a high-dimensional mixture model setting. We then study this phenomenon in 11 different state-of-the-art pretrained encoders and show how our proposed framework can be used to compare the quality of encoders, as well as evaluate and combine data augmentation strategies to mitigate the issue. Our work sheds light on the class-dependent effects of learning, and provides new insights into how state-of-the-art pretrained features may have unknown biases that can be diagnosed through their spectra., Comment: 25 pages, 9 figures

Federated Learning (FL) is an emerging machine learning paradigm that enables the collaborative training of a shared global model across distributed clients while keeping the data decentralized. Recent works on designing systems for efficient FL have shown that utilizing serverless computing technologies, particularly Function-as-a-Service (FaaS) for FL, can enhance resource efficiency, reduce training costs, and alleviate the complex infrastructure management burden on data holders. However, existing serverless FL systems implicitly assume a uniform global model architecture across all participating clients during training. This assumption fails to address fundamental challenges in practical FL due to the resource and statistical data heterogeneity among FL clients. To address these challenges and enable heterogeneous client models in serverless FL, we utilize Knowledge Distillation (KD) in this paper. Towards this, we propose novel optimized serverless workflows for two popular conventional federated KD techniques, i.e., FedMD and FedDF. We implement these workflows by introducing several extensions to an open-source serverless FL system called FedLess. Moreover, we comprehensively evaluate the two strategies on multiple datasets across varying levels of client data heterogeneity using heterogeneous client models with respect to accuracy, fine-grained training times, and costs. Results from our experiments demonstrate that serverless FedDF is more robust to extreme non-IID data distributions, is faster, and leads to lower costs than serverless FedMD. In addition, compared to the original implementation, our optimizations for particular steps in FedMD and FedDF lead to an average speedup of 3.5x and 1.76x across all datasets., Comment: ACM/SIGAPP Symposium on Applied Computing 2024

Generative Large Language Models (LLMs) hold significant promise in healthcare, demonstrating capabilities such as passing medical licensing exams and providing clinical knowledge. However, their current use as information retrieval tools is limited by challenges like data staleness, resource demands, and occasional generation of incorrect information. This study assessed the potential of LLMs to function as autonomous agents in a simulated tertiary care medical center, using real-world clinical cases across multiple specialties. Both proprietary and open-source LLMs were evaluated, with Retrieval Augmented Generation (RAG) enhancing contextual relevance. Proprietary models, particularly GPT-4, generally outperformed open-source models, showing improved guideline adherence and more accurate responses with RAG. The manual evaluation by expert clinicians was crucial in validating models' outputs, underscoring the importance of human oversight in LLM operation. Further, the study emphasizes Natural Language Programming (NLP) as the appropriate paradigm for modifying model behavior, allowing for precise adjustments through tailored prompts and real-world interactions. This approach highlights the potential of LLMs to significantly enhance and supplement clinical decision-making, while also emphasizing the value of continuous expert involvement and the flexibility of NLP to ensure their reliability and effectiveness in healthcare settings., Comment: Figures: 5, Tables: 3

In a companion paper we introduced the notion of asymptotically Minkowski spacetimes. These space-times are asymptotically flat at both null and spatial infinity, and furthermore there is a harmonious matching of limits of certain fields as one approaches $i^\circ$ in null and space-like directions. These matching conditions are quite weak but suffice to reduce the asymptotic symmetry group to a Poincar\'e group $\mathfrak{p}_{i^\circ}$. Restriction of $\mathfrak{p}_{i^\circ}$ to future null infinity $\mathscr{I}^{+}$ yields the canonical Poincar\'e subgroup $\mathfrak{p}^{\rm bms}_{i^\circ}$ of the BMS group $\mathfrak{B}$ selected in the companion paper and its restriction to spatial infinity $i^\circ$ gives the canonical subgroup $\mathfrak{p}^{\rm spi}_{i^\circ}$ of the Spi group $\mathfrak{S}$ there. As a result, one can meaningfully compare angular momentum that has been defined at $i^\circ$ using $\mathfrak{p}^{\rm spi}_{i^\circ}$ with that defined on $\mathscr{I}^{+}$ using $\mathfrak{p}^{\rm bms}_{i^\circ}$. We show that the angular momentum charge at $i^\circ$ equals the sum of the angular momentum charge at any 2-sphere cross-section $S$ of $\mathscr{I}^{+}$ and the total flux of angular momentum radiated across the portion of $\mathscr{I}^{+}$ to the past of $S$. In general the balance law holds only when angular momentum refers to ${\rm SO(3)}$ subgroups of the Poincar\'e group $\mathfrak{p}_{i^\circ}$., Comment: Version to appear in JHEP. Slightly edited to improve the presentation. Four references added. 30 pages, 1 figure

The Spi framework provides a 4-dimensional approach to investigate the asymptotic properties of gravitational fields as one recedes from isolated systems in any space-like direction, without reference to a Cauchy surface. It is well suited to unify descriptions at null and spatial infinity because $\mathscr{I}$ arises as the null cone of $i^\circ$. The goal of this work is to complete this task by introducing a natural extension of the asymptotic conditions at null and spatial infinity, by 'gluing' the two descriptions appropriately. Space-times satisfying these conditions are asymptotically flat in both regimes and thus represent isolated gravitating systems. They will be said to be Asymptotically Minkowskian at $i^\circ$. We show that in these space-times the Spi group $\mathfrak{S}$ as well as the BMS group $\mathcal{B}$ naturally reduce to a single Poincar\'e group, denoted by $\mathfrak{p}_{i^\circ}$ to highlight the fact that it arises from the gluing procedure at $i^\circ$. The asymptotic conditions are sufficiently weak to allow for the possibility that the Newman-Penrose component $\Psi^\circ_1$ diverges in the distant past along $\mathscr{I}^+$. This can occur in astrophysical sources that are not asymptotically stationary in the past, e.g. in scattering situations. Nonetheless, as we show in the companion paper, the energy momentum and angular momentum defined at $i^\circ$ equals the sum of that defined at a cross-section $S$ of $\mathscr{I}^+$ and corresponding flux across $\mathscr{I}^+$ to the past of $S$, when the quantities refer to the preferred Poincar\'e subgroup $\mathfrak{p}_{i^\circ}$., Comment: References and minor clarifications added. Version to appear in JHEP. 36 pages, 1 figure

A survey was conducted from February 2022 to May 2022 on the usage of antibiotics at a poultry farm in different areas of Multan, Punjab Pakistan. A well-organized questionnaire was used for the collection of data. Sixty poultry farms were surveyed randomly in the Multan district. All of these Farms were using antibiotics. Antibiotics are commonly used for the treatment of diseases. Some are used as preventive medicine and a few are used as growth promotors. neomycin, erythromycin, oxytetracycline, streptomycin, and colistin are the broad-spectrum antibiotics that are being used commercially. Enrofloxacin and Furazolidone are the common antibiotics that are being used in Studies these days. The class of Fluoroquinolones is commonly used in poultry farms. Thirty-three patterns of antibiotic usage were observed at poultry farms. multi-drug practices were also observed on various farms. In this study, 25% of antibiotics are prescribed by the veterans while more than 90 % were acquired from the veterinary store. This study provides information about the antibiotics which are commonly being used in the study location district Multan. It is expected that the finding of this survey will be helpful in the development of new strategies against the misuse of antibiotics on farms.

In the rapidly evolving landscape of modern healthcare, the integration of wearable & portable technology provides a unique opportunity for personalized health monitoring in the community. Devices like the Apple Watch, FitBit, and AliveCor KardiaMobile have revolutionized the acquisition and processing of intricate health data streams. Amidst the variety of data collected by these gadgets, single-lead electrocardiogram (ECG) recordings have emerged as a crucial source of information for monitoring cardiovascular health. There has been significant advances in artificial intelligence capable of interpreting these 1-lead ECGs, facilitating clinical diagnosis as well as the detection of rare cardiac disorders. This design study describes the development of an innovative multiplatform system aimed at the rapid deployment of AI-based ECG solutions for clinical investigation & care delivery. The study examines design considerations, aligning them with specific applications, develops data flows to maximize efficiency for research & clinical use. This process encompasses the reception of single-lead ECGs from diverse wearable devices, channeling this data into a centralized data lake & facilitating real-time inference through AI models for ECG interpretation. An evaluation of the platform demonstrates a mean duration from acquisition to reporting of results of 33.0 to 35.7 seconds, after a standard 30 second acquisition. There were no substantial differences in acquisition to reporting across two commercially available devices (Apple Watch and KardiaMobile). These results demonstrate the succcessful translation of design principles into a fully integrated & efficient strategy for leveraging 1-lead ECGs across platforms & interpretation by AI-ECG algorithms. Such a platform is critical to translating AI discoveries for wearable and portable ECG devices to clinical impact through rapid deployment.

The gravitational waves emitted by a perturbed black hole ringing down are well described by damped sinusoids, whose frequencies are those of quasinormal modes. Typically, first-order black hole perturbation theory is used to calculate these frequencies. Recently, it was shown that second-order effects are necessary in binary black hole merger simulations to model the gravitational-wave signal observed by a distant observer. Here, we show that the horizon of a newly formed black hole after the head-on collision of two black holes also shows evidence of non-linear modes. Specifically, we identify one quadratic mode for the $l=2$ shear data, and two quadratic ones for the $l=4,6$ data in simulations with varying mass ratio and boost parameter. The quadratic mode amplitudes display a quadratic relationship with the amplitudes of the linear modes that generate them., Comment: Version appeared in PRL. 14 pages, 15 figures

In this work we study the acyclic orientations of complete multipartite graphs. We obtain an encoding of the acyclic orientations of the complete $p$-partite graph with size of its parts $n:=n_1,n_2,\ldots,n_p$ via a vector with $p$ symbols and length $n_1+n_2+\ldots+n_p$ when the parts are fixed but not the vertices in each part. We also give a recursive way to construct all acyclic orientations of a complete multipartite graph, this construction can be done by computer easily in order $\mathcal{O}(n)$. Besides, obtained codification of the acyclic orientations allows us to count the number of non-isomorphic acyclic orientations of the complete multipartite graphs. Furthermore, we obtain a closed formula for non-isomorphic acyclic orientations of the complete multipartite graphs with a directed spanning tree. In addition, we obtain a closed formula for the ordinary generating functions for the number of strings in the alphabet $\{s_1,s_2,\ldots,s_p\}$ with $k_1$ characters $s_1$, $k_2$ characters $s_2$, and so on with $k_p$ characters $s_p$ such that no two consecutive characters are the same. Finally, we obtain a closed formula for the number of acyclic orientation of a complete multipartite graph $K_{n_1,\ldots,n_p}$ with labelled vertices., Comment: 15 pages, 3 figures and 3 tables