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The wireless spectrum's increasing complexity poses challenges and opportunities, highlighting the necessity for real-time solutions and robust data processing capabilities. Digital Twin (DT), virtual replicas of physical systems, integrate real-time data to mirror their real-world counterparts, enabling precise monitoring and optimization. Incorporating DTs into wireless communication enhances predictive maintenance, resource allocation, and troubleshooting, thus bolstering network reliability. Our paper introduces TwiNet, enabling bidirectional, near-realtime links between real-world wireless spectrum scenarios and DT replicas. Utilizing the protocol, MQTT, we can achieve data transfer times with an average latency of 14 ms, suitable for real-time communication. This is confirmed by monitoring real-world traffic and mirroring it in real-time within the DT's wireless environment. We evaluate TwiNet's performance in two use cases: (i) assessing risky traffic configurations of UEs in a Safe Adaptive Data Rate (SADR) system, improving network performance by approximately 15% compared to original network selections; and (ii) deploying new CNNs in response to jammed pilots, achieving up to 97% accuracy training on artificial data and deploying a new model in as low as 2 minutes to counter persistent adversaries. TwiNet enables swift deployment and adaptation of DTs, addressing crucial challenges in modern wireless communication systems., Comment: 6 pages, 7 figures, conference paper

The Dice Similarity Coefficient (DSC) is the current de facto standard to determine agreement between a reference segmentation and one generated by manual / auto-contouring approaches. This metric is useful for non-spatially important images; however, radiation therapy requires consideration of nearby Organs-at-Risk (OARs) and their radiosensitivity which are currently unaccounted for with the traditional DSC. In this work, we introduce the OAR-DSC which accounts for nearby OARs and their radiosensitivity when computing the DSC. We illustrate the importance of this through cases where two proposed contours have similar DSC, but lower OAR-DSC when one contour expands closer to the surrounding OARs. This work is important because the OAR-DSC may be used by deep learning auto-contouring algorithms in a radiation therapy specific loss function, thereby progressing on the current disregard for the importance of these differences on the final radiation dose plan generation, delivery, and risks of patient toxicity., Comment: Proceedings of the XX-th international conference on the use of computers in radiation therapy (ICCR)

Listeners of long-form talk-audio content, such as podcast episodes, often find it challenging to understand the overall structure and locate relevant sections. A practical solution is to divide episodes into chapters--semantically coherent segments labeled with titles and timestamps. Since most episodes on our platform at Spotify currently lack creator-provided chapters, automating the creation of chapters is essential. Scaling the chapterization of podcast episodes presents unique challenges. First, episodes tend to be less structured than written texts, featuring spontaneous discussions with nuanced transitions. Second, the transcripts are usually lengthy, averaging about 16,000 tokens, which necessitates efficient processing that can preserve context. To address these challenges, we introduce PODTILE, a fine-tuned encoder-decoder transformer to segment conversational data. The model simultaneously generates chapter transitions and titles for the input transcript. To preserve context, each input text is augmented with global context, including the episode's title, description, and previous chapter titles. In our intrinsic evaluation, PODTILE achieved an 11% improvement in ROUGE score over the strongest baseline. Additionally, we provide insights into the practical benefits of auto-generated chapters for listeners navigating episode content. Our findings indicate that auto-generated chapters serve as a useful tool for engaging with less popular podcasts. Finally, we present empirical evidence that using chapter titles can enhance effectiveness of sparse retrieval in search tasks., Comment: 9 pages, 4 figures, CIKM industry track 2024

Scylla is a deep Hubble Space Telescope survey of the stellar populations, interstellar medium and star formation in the LMC and SMC. As a pure-parallel complement to the Ultraviolet Legacy Library of Young Stars as Essential Standards (ULLYSES) survey, Scylla obtained 342 orbits of ultraviolet (UV) through near-infrared (IR) imaging of the LMC and SMC with Wide Field Camera 3. In this paper, we describe the science objectives, observing strategy, data reduction procedure, and initial results from our photometric analysis of 96 observed fields. Although our observations were constrained by ULYSSES primary exposures, we imaged all fields in at least two filters (F475W and F814W), and 64% of fields in at least three and as many as seven WFC3 filters spanning the UV to IR. Overall, we reach average 50% completeness of $m_{\rm F225W}=26.0$, $m_{\rm F275W}=26.2$, $m_{\rm F336W}=26.9$, $m_{\rm F475W}=27.8$, $m_{\rm F814W}=25.5$, $m_{\rm F110W}=24.7$, and $m_{\rm F160W}=24.0$ Vega magnitudes in our photometric catalogs, which is faintward of the ancient main sequence turnoff in all filters. The primary science goals of Scylla include characterizing the structure and properties of dust in the MCs, as well as their spatially-resolved star formation and chemical enrichment histories. Our images and photometric catalogs, which represent the widest-area coverage of MCs with HST photometry to date, are available as a high-level science product at the Barbara A. Mikulski Archive for Space Telescopes., Comment: 25 pages, 16 figures, 8 tables. Accepted for publication in ApJS

We examine how large language models (LLMs) interpret historical stock returns and compare their forecasts with estimates from a crowd-sourced platform for ranking stocks. While stock returns exhibit short-term reversals, LLM forecasts over-extrapolate, placing excessive weight on recent performance similar to humans. LLM forecasts appear optimistic relative to historical and future realized returns. When prompted for 80% confidence interval predictions, LLM responses are better calibrated than survey evidence but are pessimistic about outliers, leading to skewed forecast distributions. The findings suggest LLMs manifest common behavioral biases when forecasting expected returns but are better at gauging risks than humans.

The main treatment modality for oropharyngeal cancer (OPC) is radiotherapy, where accurate segmentation of the primary gross tumor volume (GTVp) is essential. However, accurate GTVp segmentation is challenging due to significant interobserver variability and the time-consuming nature of manual annotation, while fully automated methods can occasionally fail. An interactive deep learning (DL) model offers the advantage of automatic high-performance segmentation with the flexibility for user correction when necessary. In this study, we examine interactive DL for GTVp segmentation in OPC. We implement state-of-the-art algorithms and propose a novel two-stage Interactive Click Refinement (2S-ICR) framework. Using the 2021 HEad and neCK TumOR (HECKTOR) dataset for development and an external dataset from The University of Texas MD Anderson Cancer Center for evaluation, the 2S-ICR framework achieves a Dice similarity coefficient of 0.713 $\pm$ 0.152 without user interaction and 0.824 $\pm$ 0.099 after five interactions, outperforming existing methods in both cases.

Label scarcity problem is the main challenge that hinders the wide application of deep learning systems in automatic cardiovascular diseases (CVDs) detection using electrocardiography (ECG). Tuning pre-trained models alleviates this problem by transferring knowledge learned from large datasets to downstream small datasets. However, bottlenecks in computational efficiency and CVDs detection performance limit its clinical applications. It is difficult to improve the detection performance without significantly sacrificing model computational efficiency. Here, we propose a computation-efficient semi-supervised learning paradigm (FastECG) for robust and computation-efficient CVDs detection using ECG. It enables a robust adaptation of pre-trained models on downstream datasets with limited supervision and high computational efficiency. First, a random-deactivation technique is developed to achieve robust and fast low-rank adaptation of pre-trained weights. Subsequently, we propose a one-shot rank allocation module to determine the optimal ranks for the update matrices of the pre-trained weights. Finally, a lightweight semi-supervised learning pipeline is introduced to enhance model performance by leveraging labeled and unlabeled data with high computational efficiency. Extensive experiments on four downstream ECG datasets demonstrate that FastECG not only outperforms the state-of-the-art methods in multi-label CVDs detection but also consumes fewer GPU footprints, training time, and parameter storage space. As such, this paradigm provides an effective solution for achieving high computational efficiency and robust detection performance in the clinical applications of pre-trained models under limited supervision.

Variable stars in stellar clusters can offer key constraints on stellar evolution and pulsation models, utilising estimates of host cluster properties to constrain stellar physical parameters. We present a catalogue of 86 luminous (F814W<19) variable stars in M31 clusters identified by mining the archival Panchromatic Hubble Andromeda Treasury (PHAT) survey using a combination of statistical analysis of sparse PHAT light curves and difference imaging. We determine the evolutionary phases and initial masses of these variable stars by matching them with theoretical isochrones generated using host cluster properties from the literature. We calculate the probability of PHAT photometry being blended due to the highly crowded nature of cluster environments for each cluster-variable star, using these probabilities to inform our level of confidence in the derived properties of each star. Our 86 cluster-variable stars have initial masses between 0.8--67 $M_{\odot}$. Their evolutionary phases span the main sequence, more evolved hydrogen- and helium-burning phases, and the post-asymptotic giant branch. We identify numerous candidate variable star types: RV Tauri variables, red supergiants and slowly pulsating B-type supergiants, along with Wolf Rayet stars, $\alpha$ Cygni and Mira variables, a classical Cepheid and a possible super-asymptotic giant. We characterise 12 cluster-variable stars at higher confidence based on their difference image quality and lower blending probability. Ours is the first systematic study of variable stars in extragalactic stellar clusters leveraging the superior resolution of the Hubble Space Telescope and demonstrating the unique power of stellar clusters in constraining the fundamental properties of variable stars., Comment: 36 pages, 18 figures; accepted for publication in ApJ

Large language models (LLMs) are emerging as promising tools for mental health care, offering scalable support through their ability to generate human-like responses. However, the effectiveness of these models in clinical settings remains unclear. This scoping review aimed to assess the current generative applications of LLMs in mental health care, focusing on studies where these models were tested with human participants in real-world scenarios. A systematic search across APA PsycNet, Scopus, PubMed, and Web of Science identified 726 unique articles, of which 17 met the inclusion criteria. These studies encompassed applications such as clinical assistance, counseling, therapy, and emotional support. However, the evaluation methods were often non-standardized, with most studies relying on ad hoc scales that limit comparability and robustness. Privacy, safety, and fairness were also frequently underexplored. Moreover, reliance on proprietary models, such as OpenAI's GPT series, raises concerns about transparency and reproducibility. While LLMs show potential in expanding mental health care access, especially in underserved areas, the current evidence does not fully support their use as standalone interventions. More rigorous, standardized evaluations and ethical oversight are needed to ensure these tools can be safely and effectively integrated into clinical practice.

Babai and Frankl posed the ``odd cover problem" of finding the minimum cardinality of a collection of complete bipartite graphs such that every edge of the complete graph of order $n$ is covered an odd number of times. In a previous paper with O'Neill, some of the authors proved that this value is always $\lceil n / 2 \rceil$ or $\lceil n / 2 \rceil + 1$ and that it is the former whenever $n$ is a multiple of $8$. In this paper, we determine this value to be $\lceil n / 2 \rceil$ whenever $n$ is odd or equivalent to $18$ modulo $24$. We also further the study of odd covers of graphs which are not complete, wherein edges are covered an odd number of times and nonedges an even number of times by the complete bipartite graphs in the collection. Among various results on disjoint unions, we find the minimum cardinality of an odd cover of a union of odd cliques and of a union of cycles., Comment: 19 pages, 6 figures

In this paper we prove a novel result on two categories that appear in the local Langlands correspondence, for generalized Steinberg representations. Let $G$ be a semisimple reductive group split over a $p$-adic field $F$. The main result of this paper shows that category of modules over the extension algebra of generalized Steinberg representations of $G(F)$ appears as a full subcategory of equivariant perverse sheaves on the variety of Langlands parameters for these representations.

Utilizing large pre-trained models for specific tasks has yielded impressive results. However, fully fine-tuning these increasingly large models is becoming prohibitively resource-intensive. This has led to a focus on more parameter-efficient transfer learning, primarily within the same modality. But this approach has limitations, particularly in video understanding where suitable pre-trained models are less common. Addressing this, our study introduces a novel cross-modality transfer learning approach from images to videos, which we call parameter-efficient image-to-video transfer learning. We present the Facial-Emotion Adapter (FE-Adapter), designed for efficient fine-tuning in video tasks. This adapter allows pre-trained image models, which traditionally lack temporal processing capabilities, to analyze dynamic video content efficiently. Notably, it uses about 15 times fewer parameters than previous methods, while improving accuracy. Our experiments in video emotion recognition demonstrate that the FE-Adapter can match or even surpass existing fine-tuning and video emotion models in both performance and efficiency. This breakthrough highlights the potential for cross-modality approaches in enhancing the capabilities of AI models, particularly in fields like video emotion analysis where the demand for efficiency and accuracy is constantly rising.

The Segment Anything Model (SAM) has achieved remarkable successes in the realm of natural image segmentation, but its deployment in the medical imaging sphere has encountered challenges. Specifically, the model struggles with medical images that feature low contrast, faint boundaries, intricate morphologies, and small-sized objects. To address these challenges and enhance SAM's performance in the medical domain, we introduce a comprehensive modification. Firstly, we incorporate a frozen Convolutional Neural Network (CNN) branch as an image encoder, which synergizes with SAM's original Vision Transformer (ViT) encoder through a novel variational attention fusion module. This integration bolsters the model's capability to capture local spatial information, which is often paramount in medical imagery. Moreover, to further optimize SAM for medical imaging, we introduce feature and position adapters within the ViT branch, refining the encoder's representations. We see that compared to current prompting strategies to fine-tune SAM for ultrasound medical segmentation, the use of text descriptions that serve as text prompts for SAM helps significantly improve the performance. Leveraging ChatGPT's natural language understanding capabilities, we generate prompts that offer contextual information and guidance to SAM, enabling it to better understand the nuances of ultrasound medical images and improve its segmentation accuracy. Our method, in its entirety, represents a significant stride towards making universal image segmentation models more adaptable and efficient in the medical domain., Comment: Accepted to ECCV 2024

Contemporary medical contrastive learning faces challenges from inconsistent semantics and sample pair morphology, leading to dispersed and converging semantic shifts. The variability in text reports, due to multiple authors, complicates semantic consistency. To tackle these issues, we propose a two-step approach. Initially, text reports are converted into a standardized triplet format, laying the groundwork for our novel concept of ``observations'' and ``verdicts''. This approach refines the {Entity, Position, Exist} triplet into binary questions, guiding towards a clear ``verdict''. We also innovate in visual pre-training with a Meijering-based masking, focusing on features representative of medical images' local context. By integrating this with our text conversion method, our model advances cross-modal representation in a multimodal contrastive learning framework, setting new benchmarks in medical image analysis., Comment: Accepted in MICCAI-24

Digital twin models are of high interest to Head and Neck Cancer (HNC) oncologists, who have to navigate a series of complex treatment decisions that weigh the efficacy of tumor control against toxicity and mortality risks. Evaluating individual risk profiles necessitates a deeper understanding of the interplay between different factors such as patient health, spatial tumor location and spread, and risk of subsequent toxicities that can not be adequately captured through simple heuristics. To support clinicians in better understanding tradeoffs when deciding on treatment courses, we developed DITTO, a digital-twin and visual computing system that allows clinicians to analyze detailed risk profiles for each patient, and decide on a treatment plan. DITTO relies on a sequential Deep Reinforcement Learning digital twin (DT) to deliver personalized risk of both long-term and short-term disease outcome and toxicity risk for HNC patients. Based on a participatory collaborative design alongside oncologists, we also implement several visual explainability methods to promote clinical trust and encourage healthy skepticism when using our system. We evaluate the efficacy of DITTO through quantitative evaluation of performance and case studies with qualitative feedback. Finally, we discuss design lessons for developing clinical visual XAI applications for clinical end users.

This paper introduces the Pandemic PACT Advanced Categorisation Engine (PPACE) along with its associated dataset. PPACE is a fine-tuned model developed to automatically classify research abstracts from funded biomedical projects according to WHO-aligned research priorities. This task is crucial for monitoring research trends and identifying gaps in global health preparedness and response. Our approach builds on human-annotated projects, which are allocated one or more categories from a predefined list. A large language model is then used to generate `rationales' explaining the reasoning behind these annotations. This augmented data, comprising expert annotations and rationales, is subsequently used to fine-tune a smaller, more efficient model. Developed as part of the Pandemic PACT project, which aims to track and analyse research funding and clinical evidence for a wide range of diseases with outbreak potential, PPACE supports informed decision-making by research funders, policymakers, and independent researchers. We introduce and release both the trained model and the instruction-based dataset used for its training. Our evaluation shows that PPACE significantly outperforms its baselines. The release of PPACE and its associated dataset offers valuable resources for researchers in multilabel biomedical document classification and supports advancements in aligning biomedical research with key global health priorities.

The recent advancements in large language models (LLMs) with billions of parameters have significantly boosted their performance across various real-world applications. However, the inference processes for these models require substantial energy and computational resources, presenting considerable deployment challenges. In contrast, human brains, which contain approximately 86 billion biological neurons, exhibit significantly greater energy efficiency compared to LLMs with a similar number of parameters. Inspired by this, we redesign 7 to 70 billion parameter LLMs using bio-plausible spiking mechanisms, emulating the efficient behavior of the human brain. We propose the first spiking large language model as recent LLMs termed SpikeLLM. Coupled with the proposed model, a novel spike-driven quantization framework named Optimal Brain Spiking is introduced to reduce the energy cost and accelerate inference speed via two essential approaches: first (second)-order differentiation-based salient channel detection, and per-channel salient outlier expansion with Generalized Integrate-and-Fire neurons. Our proposed spike-driven quantization can plug in main streams of quantization training methods. In the OmniQuant pipeline, SpikeLLM significantly reduces 25.51% WikiText2 perplexity and improves 3.08% average accuracy of 6 zero-shot datasets on a LLAMA2-7B 4A4W model. In the GPTQ pipeline, SpikeLLM realizes a sparse ternary quantization, which achieves additive in all linear layers. Compared with PB-LLM with similar operations, SpikeLLM also exceeds significantly. We will release our code on GitHub.

Generalization and robustness to input variation are core desiderata of machine learning research. Language varies along several axes, most importantly, language instance (e.g. French) and domain (e.g. news). While adapting NLP models to new languages within a single domain, or to new domains within a single language, is widely studied, research in joint adaptation is hampered by the lack of evaluation datasets. This prevents the transfer of NLP systems from well-resourced languages and domains to non-dominant language-domain combinations. To address this gap, we introduce M2QA, a multi-domain multilingual question answering benchmark. M2QA includes 13,500 SQuAD 2.0-style question-answer instances in German, Turkish, and Chinese for the domains of product reviews, news, and creative writing. We use M2QA to explore cross-lingual cross-domain performance of fine-tuned models and state-of-the-art LLMs and investigate modular approaches to domain and language adaptation. We witness 1) considerable performance variations across domain-language combinations within model classes and 2) considerable performance drops between source and target language-domain combinations across all model sizes. We demonstrate that M2QA is far from solved, and new methods to effectively transfer both linguistic and domain-specific information are necessary. We make M2QA publicly available at https://github.com/UKPLab/m2qa.

We measure the high-mass stellar initial mass function (IMF) from resolved stars in M33 young stellar clusters. Leveraging \textit{Hubble Space Telescope's} high resolving power, we fully model the IMF probabilistically. We first model the optical CMD of each cluster to constrain its power-law slope $\Gamma$, marginalized over other cluster parameters in the fit (e.g., cluster age, mass, and radius). We then probabilistically model the distribution of MF slopes for a highly strict cluster sample of 9 clusters more massive than log(Mass/M$_{\odot}$)=3.6; above this mass, all clusters have well-populated main sequences of massive stars and should have accurate recovery of their MF slopes, based on extensive tests with artificial clusters. We find the ensemble IMF is best described by a mean high-mass slope of $\overline{\Gamma} = 1.49\pm0.18$, with an intrinsic scatter of $\sigma^{2}_{\Gamma} = 0.02^{+0.16}_{0.00}$, consistent with a universal IMF. We find no dependence of the IMF on environmental impacts such as the local star formation rate or galactocentric radius within M33, which serves as a proxy for metallicity. This $\overline{\Gamma}$ measurement is consistent with similar measurements in M31, despite M33 having a much higher star formation rate intensity. While this measurement is formally consistent with the canonical Kroupa ($\Gamma = 1.30$) IMF, as well as the Salpeter ($\Gamma = 1.35)$) value, it is the second Local Group cluster sample to show evidence for a somewhat steeper high-mass IMF slope. We explore the impacts a steeper IMF slope has on a number of astronomical sub-fields., Comment: Accepted for publication in ApJ. 9 Figures, 1 Table

We consider the emergence of large-scale cosmological expansion in scalar-tensor theories of gravity. This is achieved by modelling sub-horizon regions of space-time as weak-field expansions around Minkowski space, and then subsequently joining many such regions together to create a statistically homogeneous and isotropic cosmology. We find that when the scalar field can be treated perturbatively, the cosmological behaviour that emerges is well modelled by the Friedmann solutions of the theory. When non-perturbative screening mechanisms occur this result no longer holds, and in the case of scalar fields subject to the chameleon mechanism we find significant deviations from the expected Friedmann behaviour. In particular, the screened mass no longer contributes to the Klein-Gordon equation, suppressing deviations from general relativistic behaviour., Comment: 15 pages, 4 figures

While machine learning algorithms hold promise for personalised medicine, their clinical adoption remains limited. One critical factor contributing to this restraint is sample selection bias (SSB) which refers to the study population being less representative of the target population, leading to biased and potentially harmful decisions. Despite being well-known in the literature, SSB remains scarcely studied in machine learning for healthcare. Moreover, the existing techniques try to correct the bias by balancing distributions between the study and the target populations, which may result in a loss of predictive performance. To address these problems, our study illustrates the potential risks associated with SSB by examining SSB's impact on the performance of machine learning algorithms. Most importantly, we propose a new research direction for addressing SSB, based on the target population identification rather than the bias correction. Specifically, we propose two independent networks (T-Net) and a multitasking network (MT-Net) for addressing SSB, where one network/task identifies the target subpopulation which is representative of the study population and the second makes predictions for the identified subpopulation. Our empirical results with synthetic and semi-synthetic datasets highlight that SSB can lead to a large drop in the performance of an algorithm for the target population as compared with the study population, as well as a substantial difference in the performance for the target subpopulations that are representative of the selected and the non-selected patients from the study population. Furthermore, our proposed techniques demonstrate robustness across various settings, including different dataset sizes, event rates, and selection rates, outperforming the existing bias correction techniques., Comment: 20 pages and 11 figures (under review)

The adoption of large language models (LLMs) to assist clinicians has attracted remarkable attention. Existing works mainly adopt the close-ended question-answering (QA) task with answer options for evaluation. However, many clinical decisions involve answering open-ended questions without pre-set options. To better understand LLMs in the clinic, we construct a benchmark ClinicBench. We first collect eleven existing datasets covering diverse clinical language generation, understanding, and reasoning tasks. Furthermore, we construct six novel datasets and clinical tasks that are complex but common in real-world practice, e.g., open-ended decision-making, long document processing, and emerging drug analysis. We conduct an extensive evaluation of twenty-two LLMs under both zero-shot and few-shot settings. Finally, we invite medical experts to evaluate the clinical usefulness of LLMs. The benchmark data is available at https://github.com/AI-in-Health/ClinicBench., Comment: Accepted at EMNLP 2024 Main Conference

The Parameterised Post-Newtonian (PPN) approach is the default framework for performing precision tests of gravity in nearby astrophysical systems. In recent works we have extended this approach for cosmological applications, and in this paper we use observations of the anisotropies in the Cosmic Microwave Background to constrain the time variation of the PPN parameters $\alpha$ and $\gamma$ between last scattering and the present day. We find their time-averages over cosmological history should be within $\sim 20\%$ of their values in GR, with $\bar{\alpha}=0.89^{+0.08}_{-0.09}$ and $\bar{\gamma}=0.90^{+0.07}_{-0.08}$ at the $68\%$ confidence level. We also constrain the time derivatives of these parameters, and find that their present-day values should be within a factor of two of the best Solar System constraints. Many of these results have no counter-part from Solar System observations, and are entirely new constraints on the gravitational interaction. In all cases, we find that the data strongly prefer $\bar{\alpha}\simeq \bar{\gamma}$, meaning that observers would typically find local gravitational physics to be compatible with GR, despite considerable variation of $\alpha$ and $\gamma$ being allowed over cosmic history. This study lays the groundwork for future precision tests of gravity that combine observations made over all cosmological and astrophysical scales of length and time., Comment: Comments welcome

For a graph $G$ and a hereditary property $\mathcal{P}$, let $\text{ex}(G,\mathcal{P})$ denote the maximum number of edges of a subgraph of $G$ that belongs to $\mathcal{P}$. We prove that for every non-trivial hereditary property $\mathcal{P}$ such that $L \notin \mathcal{P}$ for some bipartite graph $L$ and for every fixed $p \in (0,1)$ we have \[\text{ex}(G(n,p),\mathcal{P}) \le n^{2-\varepsilon}\] with high probability, for some constant $\varepsilon = \varepsilon(\mathcal{P})>0$. This answers a question of Alon, Krivelevich and Samotij., Comment: 5 pages

In this paper we describe ECG-SMART-NET for identification of occlusion myocardial infarction (OMI). OMI is a severe form of heart attack characterized by complete blockage of one or more coronary arteries requiring immediate referral for cardiac catheterization to restore blood flow to the heart. Two thirds of OMI cases are difficult to visually identify from a 12-lead electrocardiogram (ECG) and can be potentially fatal if not identified in a timely fashion. Previous works on this topic are scarce, and current state-of-the-art evidence suggests that both random forests with engineered features and convolutional neural networks (CNNs) are promising approaches to improve the ECG detection of OMI. While the ResNet architecture has been successfully adapted for use with ECG recordings, it is not ideally suited to capture informative temporal features within each lead and the spatial concordance or discordance across leads. We propose a clinically informed modification of the ResNet-18 architecture. The model first learns temporal features through temporal convolutional layers with 1xk kernels followed by a spatial convolutional layer, after the residual blocks, with 12x1 kernels to learn spatial features. The new ECG-SMART-NET was benchmarked against the original ResNet-18 and other state-of-the-art models on a multisite real-word clinical dataset that consists of 10,893 ECGs from 7,297 unique patients (rate of OMI = 6.5%). ECG-SMART-NET outperformed other models in the classification of OMI with a test AUC score of 0.889 +/- 0.027 and a test average precision score of 0.587 +/- 0.087., Comment: 7 pages, 7 figures, 5 tables

We study a two-player game played on undirected graphs called Trail Trap, which is a variant of a game known as Partizan Edge Geography. One player starts by choosing any edge and moving a token from one endpoint to the other; the other player then chooses a different edge and does the same. Alternating turns, each player moves their token along an unused edge from its current vertex to an adjacent vertex, until one player cannot move and loses. We present an algorithm to determine which player has a winning strategy when the graph is a tree, and partially characterize the trees on which a given player wins. Additionally, we show that Trail Trap is NP-hard, even for connected bipartite planar graphs with maximum degree $4$ as well as for disconnected graphs. We determine which player has a winning strategy for certain subclasses of complete bipartite graphs and grid graphs, and we propose several open problems for further study., Comment: 21 pages, 8 figures, 1 table

Recent years have witnessed the Open Radio Access Network (RAN) paradigm transforming the fundamental ways cellular systems are deployed, managed, and optimized. This shift is led by concepts such as openness, softwarization, programmability, interoperability, and intelligence of the network, all of which had never been applied to the cellular ecosystem before. The realization of the Open RAN vision into practical architectures, intelligent data-driven control loops, and efficient software implementations, however, is a multifaceted challenge, which requires (i) datasets to train Artificial Intelligence (AI) and Machine Learning (ML) models; (ii) facilities to test models without disrupting production networks; (iii) continuous and automated validation of the RAN software; and (iv) significant testing and integration efforts. This paper poses itself as a tutorial on how Colosseum - the world's largest wireless network emulator with hardware in the loop - can provide the research infrastructure and tools to fill the gap between the Open RAN vision, and the deployment and commercialization of open and programmable networks. We describe how Colosseum implements an Open RAN digital twin through a high-fidelity Radio Frequency (RF) channel emulator and end-to-end softwarized O-RAN and 5G-compliant protocol stacks, thus allowing users to reproduce and experiment upon topologies representative of real-world cellular deployments. Then, we detail the twinning infrastructure of Colosseum, as well as the automation pipelines for RF and protocol stack twinning. Finally, we showcase a broad range of Open RAN use cases implemented on Colosseum, including the real-time connection between the digital twin and real-world networks, and the development, prototyping, and testing of AI/ML solutions for Open RAN., Comment: 13 pages, 8 figures, 1 table, submitted to IEEE for publication

The Hubble tension has proven to be stubbornly persistent, despite widespread efforts to relax it. As a possible resolution of this problem we propose a radical alternative to the way in which cosmological models are viewed. Specifically, we consider building cosmological models from spaces that exhibit intrinsic symmetries, rather than as space-times with explicit symmetry. This change in perspective allows statistical homogeneity and isotropy to be maintained, while relaxing some strong mathematical constraints that the standard approach imposes. We show that a Hubble tension arises naturally in our new approach, and that (as a corollary) a prediction can be made for the radial component of the Baryon Acoustic Oscillations. Our prediction appears to be consistent with the DESI first-year data release, which has otherwise been interpreted as evidence for dynamical dark energy., Comment: 17 pages, 3 figures

If $\pi$ is a representation of a $p$-adic group $G(F)$, and $\phi$ is its Langlands parameter, can we use the moduli space of Langlands parameters to find a geometric property of $\phi$ that will detect when $\pi$ is generic? In this paper we show that if $G$ is classical or if we assume the Kazhdan-Lusztig hypothesis for $G$, then the answer is yes, and the property is that the orbit of $\phi$ is open. We also propose an adaptation of Shahidi's enhanced genericity conjecture to ABV-packets: for every Langlands parameter $\phi$ for a $p$-adic group $G(F)$, the ABV-packet $\Pi^{\mathrm{ABV}}_\phi(G(F))$ contains a generic representation if and only if the local adjoint L-function $L(s,\phi,\mathop{\text{Ad}})$ is regular at $s=1$, and show that this condition is equivalent to the "open parameter" condition above. We show that this genericity conjecture for ABV-packets follows from other standard conjectures and we verify its validity with the same conditions on $G$. We show that, in this case, the ABV-packet for $\phi$ coincides with its $L$-packet. Finally, we prove Vogan's conjecture on $A$-packets for tempered parameters.

Large AI models trained on audio data may have the potential to rapidly classify patients, enhancing medical decision-making and potentially improving outcomes through early detection. Existing technologies depend on limited datasets using expensive recording equipment in high-income, English-speaking countries. This challenges deployment in resource-constrained, high-volume settings where audio data may have a profound impact. This report introduces a novel data type and a corresponding collection system that captures health data through guided questions using only a mobile/web application. This application ultimately results in an audio electronic health record (voice EHR) which may contain complex biomarkers of health from conventional voice/respiratory features, speech patterns, and language with semantic meaning - compensating for the typical limitations of unimodal clinical datasets. This report introduces a consortium of partners for global work, presents the application used for data collection, and showcases the potential of informative voice EHR to advance the scalability and diversity of audio AI., Comment: 19 pages, 2 figures, 7 tables

Neutron reflectometry is a critical tool for investigating the structure of thin films and interfaces. However, the misapplication of the Born approximation to reflection geometry leads some to assume that the minimum thickness that may be probed by neutron reflectometry is limited by the Q-range of the measurement. In this study, we use model-dependent analysis, multiple isotopic contrasts, and magnetic spin states, to show that it is possible to resolve structures significantly smaller than this perceived limit. To quantify this "analytical resolution", we employ Bayesian model selection, offering a robust and quantifiable comparison between different analytical models. We believe that this work offers pivotal insights for the analysis of neutron reflectometry and hope that it will contribute to more accurate and information-rich analyses in the future., Comment: 21 pages, 7 figures

Agents in mixed-motive coordination problems such as Chicken may fail to coordinate on a Pareto-efficient outcome. Safe Pareto improvements (SPIs) were originally proposed to mitigate miscoordination in cases where players lack probabilistic beliefs as to how their delegates will play a game; delegates are instructed to behave so as to guarantee a Pareto improvement on how they would play by default. More generally, SPIs may be defined as transformations of strategy profiles such that all players are necessarily better off under the transformed profile. In this work, we investigate the extent to which SPIs can reduce downsides of miscoordination between expected utility-maximizing agents. We consider games in which players submit computer programs that can condition their decisions on each other's code, and use this property to construct SPIs using programs capable of renegotiation. We first show that under mild conditions on players' beliefs, each player always prefers to use renegotiation. Next, we show that under similar assumptions, each player always prefers to be willing to renegotiate at least to the point at which they receive the lowest payoff they can attain in any efficient outcome. Thus subjectively optimal play guarantees players at least these payoffs, without the need for coordination on specific Pareto improvements. Lastly, we prove that renegotiation does not guarantee players any improvements on this bound., Comment: 20 pages, 4 figures

In this work, we study how far one can deviate from optimal behavior when embedding a planar graph. For a planar graph $G$, we say that a plane subgraph $H\subseteq G$ is a \textit{plane-saturated subgraph} if adding any edge (possibly with new vertices) to $H$ would either violate planarity or make the resulting graph no longer a subgraph of $G$. For a planar graph $G$, we define the \textit{plane-saturation ratio}, $\psr(G)$, as the minimum value of $\frac{e(H)}{e(G)}$ for a plane-saturated subgraph $H$ of $G$ and investigate how small $\psr(G)$ can be. While there exist planar graphs where $\psr(G)$ is arbitrarily close to $0$, we show that for all twin-free planar graphs, $\psr(G)>1/16$, and that there exist twin-free planar graphs where $\psr(G)$ is arbitrarily close to $1/16$. In fact, we study a broader category of planar graphs, focusing on classes characterized by a bounded number of degree $1$ and degree $2$ twin vertices. We offer solutions for some instances of bounds while positing conjectures for the remaining ones.

Large language models (LLMs), such as ChatGPT, have received substantial attention due to their capabilities for understanding and generating human language. While there has been a burgeoning trend in research focusing on the employment of LLMs in supporting different medical tasks (e.g., enhancing clinical diagnostics and providing medical education), a review of these efforts, particularly their development, practical applications, and outcomes in medicine, remains scarce. Therefore, this review aims to provide a detailed overview of the development and deployment of LLMs in medicine, including the challenges and opportunities they face. In terms of development, we provide a detailed introduction to the principles of existing medical LLMs, including their basic model structures, number of parameters, and sources and scales of data used for model development. It serves as a guide for practitioners in developing medical LLMs tailored to their specific needs. In terms of deployment, we offer a comparison of the performance of different LLMs across various medical tasks, and further compare them with state-of-the-art lightweight models, aiming to provide an understanding of the advantages and limitations of LLMs in medicine. Overall, in this review, we address the following questions: 1) What are the practices for developing medical LLMs 2) How to measure the medical task performance of LLMs in a medical setting? 3) How have medical LLMs been employed in real-world practice? 4) What challenges arise from the use of medical LLMs? and 5) How to more effectively develop and deploy medical LLMs? By answering these questions, this review aims to provide insights into the opportunities for LLMs in medicine and serve as a practical resource. We also maintain a regularly updated list of practical guides on medical LLMs at https://github.com/AI-in-Health/MedLLMsPracticalGuide, Comment: Preprint. Version 6. Update Figures 1-5; Tables 2-3; 31 pages

We consider the form of Hubble diagrams that would be constructed by observers in universes that are homogeneous but anisotropic, when averaged over suitably large length-scales. This is achieved by ray-tracing in different directions on the sky in families of exact inhomogeneous cosmological solutions of Einstein's equations, in order to determine the redshifts and luminosity distances that observers in these space-times would infer for distant astrophysical objects. We compare the results of this procedure to the Hubble diagrams that would be obtained by direct use of the large-scale-averaged anisotropic cosmological models, and find that observables calculated in the averaged model closely agree with those obtained from ray-tracing in all cases where a statistical homogeneity scale exists. In contrast, we find that in cosmologies with spaces that contain no statistical homogeneity scale that Hubble diagrams inferred from the averaged cosmological model can differ considerably from those that observers in the space-time would actually construct. We hope that these results will be of use for understanding and interpreting recent observations that suggest that large-scale anisotropy may have developed in the late Universe., Comment: 35 pages, 17 figures

The entry of large language models (LLMs) into research and commercial spaces has led to a trend of ever-larger models, with initial promises of generalisability, followed by a widespread desire to downsize and create specialised models without the need for complete fine-tuning, using Parameter Efficient Fine-tuning (PEFT) methods. We present an investigation into the suitability of different PEFT methods to clinical decision-making tasks, across a range of model sizes, including extremely small models with as few as $25$ million parameters. Our analysis shows that the performance of most PEFT approaches varies significantly from one task to another, with the exception of LoRA, which maintains relatively high performance across all model sizes and tasks, typically approaching or matching full fine-tuned performance. The effectiveness of PEFT methods in the clinical domain is evident, particularly for specialised models which can operate on low-cost, in-house computing infrastructure. The advantages of these models, in terms of speed and reduced training costs, dramatically outweighs any performance gain from large foundation LLMs. Furthermore, we highlight how domain-specific pre-training interacts with PEFT methods and model size, and discuss how these factors interplay to provide the best efficiency-performance trade-off. Full code available at: tbd.

We present NIRCam and NIRISS modules for DOLPHOT, a widely-used crowded field stellar photometry package. We describe details of the modules including pixel masking, astrometric alignment, star finding, photometry, catalog creation, and artificial star tests (ASTs). We tested these modules using NIRCam and NIRISS images of M92 (a Milky Way globular cluster), Draco II (an ultra-faint dwarf galaxy), and WLM (a star-forming dwarf galaxy). DOLPHOT's photometry is highly precise and the color-magnitude diagrams are deeper and have better definition than anticipated during original program design in 2017. The primary systematic uncertainties in DOLPHOT's photometry arise from mismatches in the model and observed point spread functions (PSFs) and aperture corrections, each contributing $\lesssim0.01$ mag to the photometric error budget. Version 1.2 of WebbPSF models, which include charge diffusion and interpixel capacitance effects, significantly reduced PSF-related uncertainties. We also observed minor ($\lesssim0.05$ mag) chip-to-chip variations in NIRCam's zero points, which will be addressed by the JWST flux calibration program. Globular cluster observations are crucial for photometric calibration. Temporal variations in the photometry are generally $\lesssim0.01$ mag, although rare large misalignment events can introduce errors up to 0.08 mag. We provide recommended DOLPHOT parameters, guidelines for photometric reduction, and advice for improved observing strategies. Our ERS DOLPHOT data products are available on MAST, complemented by comprehensive online documentation and tutorials for using DOLPHOT with JWST imaging data., Comment: 30 pages, 17 figures. Accepted to ApJS. Data products to be hosted on MAST. For DOLPHOT/JWST tutorials, see https://dolphot-jwst.readthedocs.io/en/latest/ . For more program and DOLPHOT info, see https://ers-stars.github.io

Spectrum has become an extremely scarce and congested resource. As a consequence, spectrum sensing enables the coexistence of different wireless technologies in shared spectrum bands. Most existing work requires spectrograms to classify signals. Ultimately, this implies that images need to be continuously created from I/Q samples, thus creating unacceptable latency for real-time operations. In addition, spectrogram-based approaches do not achieve sufficient granularity level as they are based on object detection performed on pixels and are based on rectangular bounding boxes. For this reason, we propose a completely novel approach based on semantic spectrum segmentation, where multiple signals are simultaneously classified and localized in both time and frequency at the I/Q level. Conversely from the state-of-the-art computer vision algorithm, we add non-local blocks to combine the spatial features of signals, and thus achieve better performance. In addition, we propose a novel data generation approach where a limited set of easy-to-collect real-world wireless signals are ``stitched together'' to generate large-scale, wideband, and diverse datasets. Experimental results obtained on multiple testbeds (including the Arena testbed) using multiple antennas, multiple sampling frequencies, and multiple radios over the course of 3 days show that our approach classifies and localizes signals with a mean intersection over union (IOU) of 96.70% across 5 wireless protocols while performing in real-time with a latency of 2.6 ms. Moreover, we demonstrate that our approach based on non-local blocks achieves 7% more accuracy when segmenting the most challenging signals with respect to the state-of-the-art U-Net algorithm. We will release our 17 GB dataset and code.

Spectrum sensing is an essential component of modern wireless networks as it offers a tool to characterize spectrum usage and better utilize it. Deep Learning (DL) has become one of the most used techniques to perform spectrum sensing as they are capable of delivering high accuracy and reliability. However, current techniques suffer from ad-hoc implementations and high complexity, which makes them unsuited for practical deployment on wireless systems where flexibility and fast inference time are necessary to support real-time spectrum sensing. In this paper, we introduce DeepSweep, a novel DL-based transceiver design that allows scalable, accurate, and fast spectrum sensing while maintaining a high level of customizability to adapt its design to a broad range of application scenarios and use cases. DeepSweep is designed to be seamlessly integrated with well-established transceiver designs and leverages shallow convolutional neural network (CNN) to "sweep" the spectrum and process captured IQ samples fast and reliably without interrupting ongoing demodulation and decoding operations. DeepSweep reduces training and inference times by more than 2 times and 10 times respectively, achieves up to 98 percent accuracy in locating spectrum activity, and produces outputs in less than 1 ms, thus showing that DeepSweep can be used for a broad range of spectrum sensing applications and scenarios., Comment: 6 pages, 9 figures, IEEE ICMLCN 2024 - IEEE International Conference on Machine Learning for Communication and Networking, Stockholm, Sweden, 2024

Large Language Models (LLMs), particularly those similar to ChatGPT, have significantly influenced the field of Natural Language Processing (NLP). While these models excel in general language tasks, their performance in domain-specific downstream tasks such as biomedical and clinical Named Entity Recognition (NER), Relation Extraction (RE), and Medical Natural Language Inference (NLI) is still evolving. In this context, our study investigates the potential of instruction tuning for biomedical language processing, applying this technique to two general LLMs of substantial scale. We present a comprehensive, instruction-based model trained on a dataset that consists of approximately $200,000$ instruction-focused samples. This dataset represents a carefully curated compilation of existing data, meticulously adapted and reformatted to align with the specific requirements of our instruction-based tasks. This initiative represents an important step in utilising such models to achieve results on par with specialised encoder-only models like BioBERT and BioClinicalBERT for various classical biomedical NLP tasks. Our work includes an analysis of the dataset's composition and its impact on model performance, providing insights into the intricacies of instruction tuning. By sharing our codes, models, and the distinctively assembled instruction-based dataset, we seek to encourage ongoing research and development in this area.

Young stellar objects (YSOs) are the gold standard for tracing star formation in galaxies but have been unobservable beyond the Milky Way and Magellanic Clouds. But that all changed when the James Webb Space Telescope was launched, which we use to identify YSOs in the Local Group galaxy M33, marking the first time that individual YSOs have been identified at these large distances. We present MIRI imaging mosaics at 5.6 and 21 microns that cover a significant portion of one of M33's spiral arms that has existing panchromatic imaging from the Hubble Space Telescope and deep ALMA CO measurements. Using these MIRI and Hubble Space Telescope images, we identify point sources using the new DOLPHOT MIRI module. We identify 793 candidate YSOs from cuts based on colour, proximity to giant molecular clouds (GMCs), and visual inspection. Similar to Milky Way GMCs, we find that higher mass GMCs contain more YSOs and YSO emission, which further shows YSOs identify star formation better than most tracers that cannot capture this relationship at cloud scales. We find evidence of enhanced star formation efficiency in the southern spiral arm by comparing the YSOs to the molecular gas mass., Comment: 12 pages, 10 figures, 1 tables, accepted for publication at MNRAS

We introduce Adapters, an open-source library that unifies parameter-efficient and modular transfer learning in large language models. By integrating 10 diverse adapter methods into a unified interface, Adapters offers ease of use and flexible configuration. Our library allows researchers and practitioners to leverage adapter modularity through composition blocks, enabling the design of complex adapter setups. We demonstrate the library's efficacy by evaluating its performance against full fine-tuning on various NLP tasks. Adapters provides a powerful tool for addressing the challenges of conventional fine-tuning paradigms and promoting more efficient and modular transfer learning. The library is available via https://adapterhub.ml/adapters., Comment: EMNLP 2023: Systems Demonstrations

We consider extremal problems related to decks and multidecks of rooted binary trees (a.k.a. rooted phylogenetic tree shapes). Here, the deck (resp. multideck) of a tree $T$ refers to the set (resp. multiset) of leaf induced binary subtrees of $T$. On the one hand, we consider the reconstruction of trees from their (multi)decks. We give lower and upper bounds on the minimum (multi)deck size required to uniquely encode a rooted binary tree on $n$ leaves. On the other hand, we consider problems related to deck cardinalities. In particular, we characterize trees with minimum-size as well as maximum-size decks. Finally, we present some exhaustive computations for $k$-universal trees, i.e., rooted binary trees that contain all $k$-leaf rooted binary trees as induced subtrees., Comment: 18 pages, 14 figures

Deep learning has significantly advanced the potential for automated contouring in radiotherapy planning. In this manuscript, guided by contemporary literature, we underscore three key insights: (1) High-quality training data is essential for auto-contouring algorithms; (2) Auto-contouring models demonstrate commendable performance even with limited medical image data; (3) The quantitative performance of auto-contouring is reaching a plateau. Given these insights, we emphasize the need for the radiotherapy research community to embrace data-centric approaches to further foster clinical adoption of auto-contouring technologies., Comment: 13 pages, 4 figures

The growing capabilities and increasingly widespread deployment of AI systems necessitate robust benchmarks for measuring their cooperative capabilities. Unfortunately, most multi-agent benchmarks are either zero-sum or purely cooperative, providing limited opportunities for such measurements. We introduce a general-sum variant of the zero-sum board game Diplomacy -- called Welfare Diplomacy -- in which players must balance investing in military conquest and domestic welfare. We argue that Welfare Diplomacy facilitates both a clearer assessment of and stronger training incentives for cooperative capabilities. Our contributions are: (1) proposing the Welfare Diplomacy rules and implementing them via an open-source Diplomacy engine; (2) constructing baseline agents using zero-shot prompted language models; and (3) conducting experiments where we find that baselines using state-of-the-art models attain high social welfare but are exploitable. Our work aims to promote societal safety by aiding researchers in developing and assessing multi-agent AI systems. Code to evaluate Welfare Diplomacy and reproduce our experiments is available at https://github.com/mukobi/welfare-diplomacy.

Backdoor attacks pose a serious security threat for training neural networks as they surreptitiously introduce hidden functionalities into a model. Such backdoors remain silent during inference on clean inputs, evading detection due to inconspicuous behavior. However, once a specific trigger pattern appears in the input data, the backdoor activates, causing the model to execute its concealed function. Detecting such poisoned samples within vast datasets is virtually impossible through manual inspection. To address this challenge, we propose a novel approach that enables model training on potentially poisoned datasets by utilizing the power of recent diffusion models. Specifically, we create synthetic variations of all training samples, leveraging the inherent resilience of diffusion models to potential trigger patterns in the data. By combining this generative approach with knowledge distillation, we produce student models that maintain their general performance on the task while exhibiting robust resistance to backdoor triggers., Comment: Published at NeurIPS 2023 Workshop on Backdoors in Deep Learning: The Good, the Bad, and the Ugly

Text-to-image generation (TTI) refers to the usage of models that could process text input and generate high fidelity images based on text descriptions. Text-to-image generation using neural networks could be traced back to the emergence of Generative Adversial Network (GAN), followed by the autoregressive Transformer. Diffusion models are one prominent type of generative model used for the generation of images through the systematic introduction of noises with repeating steps. As an effect of the impressive results of diffusion models on image synthesis, it has been cemented as the major image decoder used by text-to-image models and brought text-to-image generation to the forefront of machine-learning (ML) research. In the era of large models, scaling up model size and the integration with large language models have further improved the performance of TTI models, resulting the generation result nearly indistinguishable from real-world images, revolutionizing the way we retrieval images. Our explorative study has incentivised us to think that there are further ways of scaling text-to-image models with the combination of innovative model architectures and prediction enhancement techniques. We have divided the work of this survey into five main sections wherein we detail the frameworks of major literature in order to delve into the different types of text-to-image generation methods. Following this we provide a detailed comparison and critique of these methods and offer possible pathways of improvement for future work. In the future work, we argue that TTI development could yield impressive productivity improvements for creation, particularly in the context of the AIGC era, and could be extended to more complex tasks such as video generation and 3D generation.

The Gravity Spy project aims to uncover the origins of glitches, transient bursts of noise that hamper analysis of gravitational-wave data. By using both the work of citizen-science volunteers and machine-learning algorithms, the Gravity Spy project enables reliable classification of glitches. Citizen science and machine learning are intrinsically coupled within the Gravity Spy framework, with machine-learning classifications providing a rapid first-pass classification of the dataset and enabling tiered volunteer training, and volunteer-based classifications verifying the machine classifications, bolstering the machine-learning training set and identifying new morphological classes of glitches. These classifications are now routinely used in studies characterizing the performance of the LIGO gravitational-wave detectors. Providing the volunteers with a training framework that teaches them to classify a wide range of glitches, as well as additional tools to aid their investigations of interesting glitches, empowers them to make discoveries of new classes of glitches. This demonstrates that, when giving suitable support, volunteers can go beyond simple classification tasks to identify new features in data at a level comparable to domain experts. The Gravity Spy project is now providing volunteers with more complicated data that includes auxiliary monitors of the detector to identify the root cause of glitches., Comment: 33 pages, 5 figures, published in European Physical Journal Plus for focus issue on "Citizen science for physics: From Education and Outreach to Crowdsourcing fundamental research"

We provide an $\Omega(n\log n) $ lower bound and an $O(n^2)$ upper bound for the smallest size of rooted binary trees (a.k.a. phylogenetic tree shapes), which are universal for rooted binary trees with $n$ leaves, i.e., contain all of them as induced binary subtrees. We explicitly compute the smallest universal trees for $n\leq 11$. We also provide an $\Omega(n^2) $ lower bound and an $O(n^4)$ upper bound for the smallest size of tanglegrams, which are universal for size $n$ tanglegrams, i.e., which contain all of them as induced subtanglegrams. Some of our results generalize to rooted $d$-ary trees and to $d$-ary tanglegrams., Comment: 18 pages, 14 figures

Motivated by classical work of Alon and F\"uredi, we introduce and address the following problem: determine the minimum number of affine hyperplanes in $\mathbb{R}^d$ needed to cover every point of the triangular grid $T_d(n) := \{(x_1,\dots,x_d)\in\mathbb{Z}_{\ge 0}^d\mid x_1+\dots+x_d\le n-1\}$ at least $k$ times. For $d = 2$, we solve the problem exactly for $k \leq 4$, and obtain a partial solution for $k > 4$. We also obtain an asymptotic formula (in $n$) for all $d \geq k - 2$. The proofs rely on combinatorial arguments and linear programming., Comment: 23 pages, 3 figures