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The Equity Playbook Initiative Implementation in Kentucky underwent an efficacy study conducted by LXD Research during the 2022-2023 school year. The study aimed to assess the initiative's impact on student academic achievement and school climate. A total of 55 public schools participating in the Equity Playbook Initiative were compared with 240 statistically similar non-participating schools. The demographic breakdown of the sample included 65% economically disadvantaged students, with a significant representation of 30% African American students and 35% non-white students. The findings indicated that Equity Playbook schools significantly improved key academic outcomes, particularly among economically disadvantaged students. Notably, students attending Equity Playbook schools, especially those with a high percentage of economically disadvantaged students, showed significant improvement in testing on grade level in Science and Math compared to their counterparts in non-participating schools. Additionally, the study revealed a reduction in the Kentucky Summative Assessment (KSA) achievement gap for economically disadvantaged students among participating schools. Furthermore, the completion rates of advanced courses for African American and non-white students in Equity Playbook schools showed marked improvement compared to the schools that did not participate in the initiative. Qualitative interviews with state, district, and school-level educators and staff also provided positive feedback regarding the effects of the Equity Playbook Initiative. The findings suggest that the Equity Playbook Initiative holds promise in promoting student academic achievement and enhancing school climate. This study encourages further evaluation and broader adoption of the Equity Playbook Initiative in various districts and schools across Kentucky to leverage its potential benefits. [This report was prepared for engage2learn by LXD Research.]

LXD Research conducted a study to examine the relationship between investment in Zaner-Bloser Handwriting program and Grade 3 student proficiency in handwriting in Alabama. Data from 4,759 students across 54 schools were analyzed, with schools categorized into Low Zaner-Bloser Handwriting (>$1 and [less than or equal to]$5 per student per year), Moderate Zaner-Bloser Handwriting (>$5 and [less than or equal to]$10 per student per year), and High Zaner-Bloser Handwriting (>$10 per student per year) investment groups. The demographic profile of the sample included a diverse range of students, notably with a significant representation of low-income and minority groups. The study revealed a substantial positive correlation between the level of ZB-HW investment and handwriting proficiency. Notably, 91% of students in the High ZB-HW investment group achieved proficiency, compared to 82% in the Moderate group and 69% in the Low investment group. Additionally, each $1 increase in per-student investment was associated with an 18% increase in the likelihood of achieving proficiency. These findings highlight the effectiveness of Zaner-Bloser Handwriting in enhancing handwriting skills and underscore the importance of targeted investment in educational resources to support student outcomes. The findings and rigorous study design support Zaner-Bloser Handwriting as a comprehensive program that meets the criteria for ESSA Level 3. [This report was produced by Zaner-Bloser.]

Thanks to advancements in deep learning, speech generation systems now power a variety of real-world applications, such as text-to-speech for individuals with speech disorders, voice chatbots in call centers, cross-linguistic speech translation, etc. While these systems can autonomously generate human-like speech and replicate specific voices, they also pose risks when misused for malicious purposes. This motivates the research community to develop models for detecting synthesized speech (e.g., fake speech) generated by deep-learning-based models, referred to as the Deepfake Speech Detection task. As the Deepfake Speech Detection task has emerged in recent years, there are not many survey papers proposed for this task. Additionally, existing surveys for the Deepfake Speech Detection task tend to summarize techniques used to construct a Deepfake Speech Detection system rather than providing a thorough analysis. This gap motivated us to conduct a comprehensive survey, providing a critical analysis of the challenges and developments in Deepfake Speech Detection. Our survey is innovatively structured, offering an in-depth analysis of current challenge competitions, public datasets, and the deep-learning techniques that provide enhanced solutions to address existing challenges in the field. From our analysis, we propose hypotheses on leveraging and combining specific deep learning techniques to improve the effectiveness of Deepfake Speech Detection systems. Beyond conducting a survey, we perform extensive experiments to validate these hypotheses and propose a highly competitive model for the task of Deepfake Speech Detection. Given the analysis and the experimental results, we finally indicate potential and promising research directions for the Deepfake Speech Detection task., Comment: Journal preprint

We present measurements of $B \to K{}^{*}(892)\gamma$ decays using $365\,{\rm fb}^{-1}$ of data collected from 2019 to 2022 by the Belle~II experiment at the SuperKEKB asymmetric-energy $e^+e^-$ collider. The data sample contains $(387 \pm 6) \times 10^6$ $B\overline{B}$ events. We measure branching fractions ($\mathcal{B}$) and $C\!P$ asymmetries ($\mathcal{A}_{C\!P}$) for both $B^{0}\to K{}^{*0}\gamma$ and $B^{+}\to K{}^{*+}\gamma$ decays. The difference in $C\!P$ asymmetries ($\Delta \mathcal{A}_{C\!P}$) and the isospin asymmetry ($\Delta_{0+}$) between these neutral and charged channels are also measured. We obtain the following branching fractions and $C\!P$ asymmetries: $\mathcal{B} (B^{0} \to K{}^{*0}\gamma) = (4.14 \pm 0.10 \pm 0.11 ) \times 10^{-5}$, $\mathcal{B} (B^{+} \to K{}^{*+}\gamma) = (4.02 \pm 0.13 \pm 0.13 )\times 10^{-5}$, $\mathcal{A}_{C\!P} (B^{0} \to K{}^{*0}\gamma) = (-3.3 \pm 2.3 \pm 0.4 )\%$, and $\mathcal{A}_{C\!P} (B^{+} \to K{}^{*+}\gamma) = (-0.7 \pm 2.9 \pm 0.6 )\%$. The measured difference in $C\!P$ asymmetries is $\Delta \mathcal{A}_{C\!P} = (+2.6 \pm 3.8 \pm 0.7 )\%$, and the measured isospin asymmetry is $\Delta_{0+} = (+5.0 \pm 2.0 \pm 1.5 )\%$. The first uncertainties listed are statistical and the second are systematic. These results are consistent with world-average values and theory predictions.

The stylization of 3D scenes is an increasingly attractive topic in 3D vision. Although image style transfer has been extensively researched with promising results, directly applying 2D style transfer methods to 3D scenes often fails to preserve the structural and multi-view properties of 3D environments, resulting in unpleasant distortions in images from different viewpoints. To address these issues, we leverage the remarkable generative prior of diffusion-based models and propose a novel style transfer method, OSDiffST, based on a pre-trained one-step diffusion model (i.e., SD-Turbo) for rendering diverse styles in multi-view images of 3D scenes. To efficiently adapt the pre-trained model for multi-view style transfer on small datasets, we introduce a vision condition module to extract style information from the reference style image to serve as conditional input for the diffusion model and employ LoRA in diffusion model for adaptation. Additionally, we consider color distribution alignment and structural similarity between the stylized and content images using two specific loss functions. As a result, our method effectively preserves the structural information and multi-view consistency in stylized images without any 3D information. Experiments show that our method surpasses other promising style transfer methods in synthesizing various styles for multi-view images of 3D scenes. Stylized images from different viewpoints generated by our method achieve superior visual quality, with better structural integrity and less distortion. The source code is available at https://github.com/YushenZuo/OSDiffST., Comment: Accepted by ECCV 2024 AI for Visual Arts Workshop and Challenges, 18 pages, 7 figures

Hot Jupiters with close-by planetary companions are rare, with only a handful of them having been discovered so far. This could be due to their suggested dynamical histories, leading to the possible ejection of other planets. TOI-2109 b is special in this regard because it is the hot Jupiter with the closest relative separation from its host star, being separated by less than 2.3 stellar radii. Unexpectedly, transit timing measurements from recently obtained CHEOPS observations show low amplitude transit-timing variations (TTVs). We aim to search for signs of orbital decay and to characterise the apparent TTVs, trying to gain information about a possible companion. We fit the newly obtained CHEOPS light curves using TLCM and extract the resulting mid-transit timings. Successively, we use these measurements in combination with TESS and archival photometric data and radial velocity data to estimate the rate of tidal orbital decay of TOI-2109 b, as well as characterise the TTVs using the N-body code TRADES and the photodynamical approach of PyTTV. We find tentative evidence at $3\sigma$ for orbital decay in the TOI-2109 system, when we correct the mid-transit timings using the best-fitting sinusoidal model of the TTVs. We do not detect additional transits in the available photometric data, but find evidence towards the authenticity of the apparent TTVs, indicating a close-by, outer companion with $P_\mathrm{c} > 1.125\,$d. Due to the fast rotation of the star, the new planetary candidate cannot be detected in the available radial velocity (RV) measurements, and its parameters can only be loosely constrained by our joint TTV and RV modelling. TOI-2109 could join a small group of rare hot Jupiter systems that host close-by planetary companions, only one of which (WASP-47 b) has an outer companion. More high-precision photometric measurements are necessary to confirm the planetary companion., Comment: Accepted for publication in A&A. 21 pages, 21 figures

Many open-ended conversations (e.g., tutoring lessons or business meetings) revolve around pre-defined reference materials, like worksheets or meeting bullets. To provide a framework for studying such conversation structure, we introduce Problem-Oriented Segmentation & Retrieval (POSR), the task of jointly breaking down conversations into segments and linking each segment to the relevant reference item. As a case study, we apply POSR to education where effectively structuring lessons around problems is critical yet difficult. We present LessonLink, the first dataset of real-world tutoring lessons, featuring 3,500 segments, spanning 24,300 minutes of instruction and linked to 116 SAT math problems. We define and evaluate several joint and independent approaches for POSR, including segmentation (e.g., TextTiling), retrieval (e.g., ColBERT), and large language models (LLMs) methods. Our results highlight that modeling POSR as one joint task is essential: POSR methods outperform independent segmentation and retrieval pipelines by up to +76% on joint metrics and surpass traditional segmentation methods by up to +78% on segmentation metrics. We demonstrate POSR's practical impact on downstream education applications, deriving new insights on the language and time use in real-world lesson structures., Comment: EMNLP 2024 Findings. Our code and dataset are open-sourced at https://github.com/rosewang2008/posr

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

Large language models (LLMs) have achieved substantial progress in processing long contexts but still struggle with long-context reasoning. Existing approaches typically involve fine-tuning LLMs with synthetic data, which depends on annotations from human experts or advanced models like GPT-4, thus restricting further advancements. To address this issue, we investigate the potential for LLMs to self-improve in long-context reasoning and propose \ours, an approach specifically designed for this purpose. This approach is straightforward: we sample multiple outputs for each question, score them with Minimum Bayes Risk, and then apply supervised fine-tuning or preference optimization based on these outputs. Extensive experiments on several leading LLMs demonstrate the effectiveness of \ours, with an absolute improvement of $4.2$ points for Llama-3.1-8B-Instruct. Furthermore, \ours achieves superior performance compared to prior approaches that depend on data produced by human experts or advanced models. We anticipate that this work will open new avenues for self-improvement techniques in long-context scenarios, which are essential for the continual advancement of LLMs., Comment: Project Page: https://github.com/SihengLi99/SEALONG

Einstein's General Theory of Relativity predicts that accelerating mass distributions produce gravitational radiation, analogous to electromagnetic radiation from accelerating charges. These gravitational waves have not been directly detected to date, but are expected to open a new window to the Universe in the near future. Suitable telescopes are kilometre-scale laser interferometers measuring the distance between quasi free-falling mirrors. Recent advances in quantum metrology may now provide the required sensitivity boost. So-called squeezed light is able to quantum entangle the high-power laser fields in the interferometer arms, and could play a key role in the realization of gravitational wave astronomy., Comment: Review article about the development of squeezed light for gravitational wave detectors

3D part segmentation is a crucial and challenging task in 3D perception, playing a vital role in applications such as robotics, 3D generation, and 3D editing. Recent methods harness the powerful Vision Language Models (VLMs) for 2D-to-3D knowledge distillation, achieving zero-shot 3D part segmentation. However, these methods are limited by their reliance on text prompts, which restricts the scalability to large-scale unlabeled datasets and the flexibility in handling part ambiguities. In this work, we introduce SAMPart3D, a scalable zero-shot 3D part segmentation framework that segments any 3D object into semantic parts at multiple granularities, without requiring predefined part label sets as text prompts. For scalability, we use text-agnostic vision foundation models to distill a 3D feature extraction backbone, allowing scaling to large unlabeled 3D datasets to learn rich 3D priors. For flexibility, we distill scale-conditioned part-aware 3D features for 3D part segmentation at multiple granularities. Once the segmented parts are obtained from the scale-conditioned part-aware 3D features, we use VLMs to assign semantic labels to each part based on the multi-view renderings. Compared to previous methods, our SAMPart3D can scale to the recent large-scale 3D object dataset Objaverse and handle complex, non-ordinary objects. Additionally, we contribute a new 3D part segmentation benchmark to address the lack of diversity and complexity of objects and parts in existing benchmarks. Experiments show that our SAMPart3D significantly outperforms existing zero-shot 3D part segmentation methods, and can facilitate various applications such as part-level editing and interactive segmentation., Comment: Project Page: https://github.com/yhyang-myron/SAMPart3D-website

We introduce Edify Image, a family of diffusion models capable of generating photorealistic image content with pixel-perfect accuracy. Edify Image utilizes cascaded pixel-space diffusion models trained using a novel Laplacian diffusion process, in which image signals at different frequency bands are attenuated at varying rates. Edify Image supports a wide range of applications, including text-to-image synthesis, 4K upsampling, ControlNets, 360 HDR panorama generation, and finetuning for image customization.

This technical report presents our initial attempt to build a spoken large language model (LLM) for Taiwanese Mandarin, specifically tailored to enable real-time, speech-to-speech interaction in multi-turn conversations. Our end-to-end model incorporates a decoder-only transformer architecture and aims to achieve seamless interaction while preserving the conversational flow, including full-duplex capabilities allowing simultaneous speaking and listening. The paper also details the training process, including data preparation with synthesized dialogues and adjustments for real-time interaction. We also developed a platform to evaluate conversational fluency and response coherence in multi-turn dialogues. We hope the release of the report can contribute to the future development of spoken LLMs in Taiwanese Mandarin., Comment: Work in progress

The detection of a stochastic gravitational wave background by pulsar timing arrays suggests the presence of a supermassive black hole binary population. Although the observed spectrum generally aligns with predictions from orbital evolution driven by gravitational wave emission in circular orbits, there is a discernible preference for a turnover at the lowest observed frequencies. This turnover could indicate a significant hardening phase, transitioning from early environmental influences to later stages predominantly influenced by gravitational wave emission. In the vicinity of these binaries, the ejection of stars or dark matter particles through gravitational three-body slingshots efficiently extracts orbital energy, leading to a low-frequency turnover in the spectrum. By analyzing the NANOGrav 15-year data, we assess how the gravitational wave spectrum depends on the initial inner galactic profile prior to disruption by binary ejections, accounting for a range of initial binary eccentricities. Our findings suggest a parsec-scale galactic center density around $10^6\,M_\odot/\textrm{pc}^3$ across most of the parameter space, offering insights into the environmental effects on black hole evolution and combined matter density near galaxy centers., Comment: 15 pages, 5 figures

The accurate alignment of 3D woodblock geometrical models with 2D orthographic projection images presents a significant challenge in the digital preservation of Vietnamese cultural heritage. This paper proposes a unified image processing algorithm to address this issue, enhancing the registration quality between 3D woodblock models and their 2D representations. The method includes determining the plane of the 3D character model, establishing a transformation matrix to align this plane with the 2D printed image plane, and creating a parallel-projected depth map for precise alignment. This process minimizes disocclusions and ensures that character shapes and strokes are correctly positioned. Experimental results highlight the importance of structure-based comparisons to optimize alignment for large-scale Han-Nom character datasets. The proposed approach, combining density-based and structure-based methods, demonstrates improved registration performance, offering an effective normalization scheme for digital heritage preservation.

We first present a simple recursive algorithm that generates cyclic rotation Gray codes for stamp foldings and semi-meanders, where consecutive strings differ by a stamp rotation. These are the first known Gray codes for stamp foldings and semi-meanders, and we thus solve an open problem posted by Sawada and Li in [Electron. J. Comb. 19(2), 2012]. We then introduce an iterative algorithm that generates the same rotation Gray codes for stamp foldings and semi-meanders. Both the recursive and iterative algorithms generate stamp foldings and semi-meanders in constant amortized time and $O(n)$-amortized time per string respectively, using a linear amount of memory.

This paper reports on the shared tasks organized by the 21st IWSLT Conference. The shared tasks address 7 scientific challenges in spoken language translation: simultaneous and offline translation, automatic subtitling and dubbing, speech-to-speech translation, dialect and low-resource speech translation, and Indic languages. The shared tasks attracted 18 teams whose submissions are documented in 26 system papers. The growing interest towards spoken language translation is also witnessed by the constantly increasing number of shared task organizers and contributors to the overview paper, almost evenly distributed across industry and academia., Comment: IWSLT 2024; 59 pages

We consider the problem of stragglers in distributed computing systems. Stragglers, which are compute nodes that unpredictably slow down, often increase the completion times of tasks. One common approach to mitigating stragglers is work replication, where only the first completion among replicated tasks is accepted, discarding the others. However, discarding work leads to resource wastage. In this paper, we propose a method for exploiting the work completed by stragglers rather than discarding it. The idea is to increase the granularity of the assigned work, and to increase the frequency of worker updates. We show that the proposed method reduces the completion time of tasks via experiments performed on a simulated cluster as well as on Amazon EC2 with Apache Hadoop., Comment: This paper has been accepted for publication in IEEE Transactions on Services Computing. The initial results presented in this paper appeared in the proceedings of the Allerton Conference on Communication, Control, and Computing in 2023

Both detailed and rapid population studies alike predict that binary black hole (BHBH) formation is orders of magnitude more efficient at low metallicity than high metallicity, while binary neutron star (NSNS) formation remains mostly flat with metallicity, and black hole-neutron star (BHNS) mergers show intermediate behavior. This finding is a key input to employ double compact objects as tracers of low-metallicity star formation, as spectral sirens, and for merger rate calculations. Yet, the literature offers various (sometimes contradicting) explanations for these trends. We investigate the dominant cause for the metallicity dependence of double compact object formation. We find that the BHBH formation efficiency at low metallicity is set by initial condition distributions, and conventional simulations suggest that about one in eight interacting binary systems with sufficient mass to form black holes will lead to a merging BHBH. We further find that the significance of metallicities in double compact object formation is a question of formation channel. The stable mass transfer and chemically homogeneous evolution channels mainly diminish at high metallicities due to changes in stellar radii, while the common envelope channel is primarily impacted by the combined effects of stellar winds and mass-scaled natal kicks. Outdated giant wind prescriptions exacerbate the latter effect, suggesting BHBH formation may be much less metallicity dependent than previously assumed. NSNS formation efficiency remains metallicity independent as they form exclusively through the common envelope channel, with natal kicks that are uncorrelated with mass. Forthcoming GW observations will provide valuable constraints on these findings, Comment: 14 pages, 8 Figures, Submitted to ApJ, Scripts and data to reproduce this work are at https://github.com/LiekeVanSon/ZdependentFormEff , and https://zenodo.org/records/13999532

Data sharing is a prerequisite for collaborative innovation, enabling organizations to leverage diverse datasets for deeper insights. In real-world applications like FinTech and Smart Manufacturing, transactional data, often in tabular form, are generated and analyzed for insight generation. However, such datasets typically contain sensitive personal/business information, raising privacy concerns and regulatory risks. Data synthesis tackles this by generating artificial datasets that preserve the statistical characteristics of real data, removing direct links to individuals. However, attackers can still infer sensitive information using background knowledge. Differential privacy offers a solution by providing provable and quantifiable privacy protection. Consequently, differentially private data synthesis has emerged as a promising approach to privacy-aware data sharing. This paper provides a comprehensive overview of existing differentially private tabular data synthesis methods, highlighting the unique challenges of each generation model for generating tabular data under differential privacy constraints. We classify the methods into statistical and deep learning-based approaches based on their generation models, discussing them in both centralized and distributed environments. We evaluate and compare those methods within each category, highlighting their strengths and weaknesses in terms of utility, privacy, and computational complexity. Additionally, we present and discuss various evaluation methods for assessing the quality of the synthesized data, identify research gaps in the field and directions for future research.

The future detection of quasi-normal modes (QNMs) from black hole ringdown will allow for consistency and independent tests of general relativity (GR) in the strong-field regime. In this paper, we perform a ringdown Fisher forecast when including the dominant quadratic QNM (QQNM) expected in nearly equal-mass quasi-circular binary black holes (BBHs) observed by next-generation ground-based detectors, Einstein Telescope (ET) and Cosmic Explorer (CE). We consider a ringdown model with a total of four modes: three linear QNMs labeled by $(\ell m n)=(220), (330), (440)$ and one QQNM coming from the self-interaction of the dominant linear (220) QNM. We perform a forecast in two scenarios, when the QQNM parameters are considered to be: (a) independent of the linear QNMs; (b) dependent on the (220) QNM parameters, according to GR. In Scenario (a) we find the QQNM to generally be measured with better precision than the (440) mode but worse than the (330) mode. As shown in the past, high-spin BBHs tend to have higher relative QQNMs. Even in such cases, we only expect to confidently detect and resolve these four independent QNMs for nearby events, below redshift $z\sim 0.5$ in ET and CE for intermediate-mass BHs. In Scenario (b) we find the QQNM to be extremely useful for improving the precision on the (440) parameters, with negligible improvements on the (220) parameters. In this case, the (440) parameters are expected to be measured even better than those of the (330) QNM. As a result, we expect to confidently detect and resolve the three independent linear QNMs for events even at high redshifts, up to $z\sim 35$ in ET and CE for intermediate-mass BHs. Therefore, thanks to the inclusion of the QQNM, virtually all second-generation BBH events will provide excellent consistency tests of GR.

We present a novel algorithm for real-time planar semantic mapping tailored for humanoid robots navigating complex terrains such as staircases. Our method is adaptable to any odometry input and leverages GPU-accelerated processes for planar extraction, enabling the rapid generation of globally consistent semantic maps. We utilize an anisotropic diffusion filter on depth images to effectively minimize noise from gradient jumps while preserving essential edge details, enhancing normal vector images' accuracy and smoothness. Both the anisotropic diffusion and the RANSAC-based plane extraction processes are optimized for parallel processing on GPUs, significantly enhancing computational efficiency. Our approach achieves real-time performance, processing single frames at rates exceeding $30~Hz$, which facilitates detailed plane extraction and map management swiftly and efficiently. Extensive testing underscores the algorithm's capabilities in real-time scenarios and demonstrates its practical application in humanoid robot gait planning, significantly improving its ability to navigate dynamic environments., Comment: Accepted by The 2024 IEEE-RAS International Conference on Humanoid Robots. The code: https://github.com/BTFrontier/polygon_mapping

In a standard navigation pipeline, a robot localizes at every time step to lower navigational errors. However, in some scenarios, a robot needs to selectively localize when it is expensive to obtain observations. For example, an underwater robot surfacing to localize too often hinders it from searching for critical items underwater, such as black boxes from crashed aircraft. On the other hand, if the robot never localizes, poor state estimates cause failure to find the items due to inadvertently leaving the search area or entering hazardous, restricted areas. Motivated by these scenarios, we investigate approaches to help a robot determine "when to localize?" We formulate this as a bi-criteria optimization problem: minimize the number of localization actions while ensuring the probability of failure (due to collision or not reaching a desired goal) remains bounded. In recent work, we showed how to formulate this active localization problem as a constrained Partially Observable Markov Decision Process (POMDP), which was solved using an online POMDP solver. However, this approach is too slow and requires full knowledge of the robot transition and observation models. In this paper, we present RiskRL, a constrained Reinforcement Learning (RL) framework that overcomes these limitations. RiskRL uses particle filtering and recurrent Soft Actor-Critic network to learn a policy that minimizes the number of localizations while ensuring the probability of failure constraint is met. Our numerical experiments show that RiskRL learns a robust policy that outperforms the baseline by at least 13% while also generalizing to unseen environments.

Cost Adaptive Multi-queue eviction Policy (CAMP) is an algorithm for a general purpose key-value store (KVS) that manages key-value pairs computed by applications with different access patterns, key-value sizes, and varying costs for each key-value pair. CAMP is an approximation of the Greedy Dual Size (GDS) algorithm that can be implemented as efficiently as LRU. In particular, CAMP's eviction policies are as effective as those of GDS but require only a small fraction of the updates to an internal data structure in order to make those decisions. Similar to an implementation of LRU using queues, it adapts to changing workload patterns based on the history of requests for different key-value pairs. It is superior to LRU because it considers both the size and cost of key-value pairs to maximize the utility of the available memory across competing applications. We compare CAMP with both LRU and an alternative that requires human intervention to partition memory into pools and assign grouping of key-value pairs to different pools. The results demonstrate CAMP is as fast as LRU while outperforming both LRU and the pooled alternative. We also present results from an implementation of CAMP using Twitter's version of memcached., Comment: A shorter version of CAMP appeared in the Proceedings of the ACM/IFIP/USENIX Middleware Conference, Bordeaux, France, December 2014. See https://github.com/scdblab/CAMP for an implementation

As current training data for Large Language Models (LLMs) are dominated by English corpus, they are English-centric and they present impressive performance on English reasoning tasks.\footnote{This paper primarily studies English-centric models, but our method could be universal by using the centric language in the dictionary for non-English-centric LLMs.} Yet, they usually suffer from lower performance in other languages. There are about 7,000 languages over the world, and many are low-resourced on English-centric LLMs. For the sake of people who primarily speak these languages, it is especially urgent to enable our LLMs in those languages. Model training is usually effective, but computationally expensive and requires experienced NLP practitioners. This paper presents a novel and simple yet effective method called \textbf{D}ictionary \textbf{I}nsertion \textbf{P}rompting (\textbf{DIP}). When providing a non-English prompt, DIP looks up a word dictionary and inserts words' English counterparts into the prompt for LLMs. It then enables better translation into English and better English model thinking steps which leads to obviously better results. We experiment with about 200 languages from FLORES-200. Since there are no adequate datasets, we use the NLLB translator to create synthetic multilingual benchmarks from the existing 4 English reasoning benchmarks such as GSM8K and AQuA. Despite the simplicity and computationally lightweight, we surprisingly found the effectiveness of DIP on math and commonsense reasoning tasks on multiple open-source and close-source LLMs.\footnote{Our dictionaries, code, and synthetic benchmarks will be open-sourced to facilitate future research.}

In time-series analysis, many recent works seek to provide a unified view and representation for time-series across multiple domains, leading to the development of foundation models for time-series data. Despite diverse modeling techniques, existing models are black boxes and fail to provide insights and explanations about their representations. In this paper, we present VQShape, a pre-trained, generalizable, and interpretable model for time-series representation learning and classification. By introducing a novel representation for time-series data, we forge a connection between the latent space of VQShape and shape-level features. Using vector quantization, we show that time-series from different domains can be described using a unified set of low-dimensional codes, where each code can be represented as an abstracted shape in the time domain. On classification tasks, we show that the representations of VQShape can be utilized to build interpretable classifiers, achieving comparable performance to specialist models. Additionally, in zero-shot learning, VQShape and its codebook can generalize to previously unseen datasets and domains that are not included in the pre-training process. The code and pre-trained weights are available at https://github.com/YunshiWen/VQShape., Comment: Accepted by Neural Information Processing Systems (NeurIPS) 2024

Purpose: ECG and respiratory-gated preclinical cardiac CEST-MRI acquisitions are difficult due to variable saturation recovery with T1, RF interference in the ECG signal, and offset-to-offset variation in Z-magnetization and cardiac phase introduced by changes in cardiac frequency and trigger delays. Methods: The proposed method consists of segmented saturation modules with radial FLASH readouts and golden angle progression. The segmented saturation blocks drive the system to steady-state, and because center k-space is sampled repeatedly, steady-state saturation dominates contrast during gridding and reconstruction. Ten complete Z-spectra were acquired in healthy mice using both ECG and respiratory-gated, and ungated methods. Z-spectra were also acquired at multiple saturation B1 values to optimize for amide and creatine contrasts. Results: There was no significant difference between CEST contrasts (amide, creatine, MT) calculated from images acquired using ECG and respiratory-gated and ungated methods (p = 0.27, 0.11, 0.47). A saturation power of 1.8$\mu$T provides optimal contrast amplitudes for both amide and total creatine contrast without significantly complicating CEST contrast quantification due to water direct saturation, magnetization transfer, and RF spillover between amide and creatine pools. Further, variability in CEST contrast measurements was significantly reduced using the ungated radial FLASH acquisition (p = 0.002, 0.006 for amide and creatine respectively). Conclusion: This method enables CEST mapping in the murine myocardium without the need for cardiac or respiratory gating. Quantitative CEST contrasts are consistent with those obtained using gated sequences, and per-contrast variance is significantly reduced. This approach makes preclinical cardiac CEST-MRI easily accessible, even for investigators without prior experience in cardiac imaging.

In June 2022, the Gaia mission released a catalog of astrometric orbital solutions for 168,065 binary systems, by far the largest such catalog to date. Unlike previous binary stars catalogs, which were heterogeneous collections of orbits from different surveys and instruments, these orbits were derived using Gaia data alone. Despite this homogeneity, the selection function is difficult to characterize because of choices made in the construction of the catalog. Understanding the catalog's selection function is required to model and interpret its contents. We use a combination of analytic and empirical prescriptions to construct a function that computes the probability that a binary with a given set of properties would have been published in the Gaia Data Release 3 astrometric orbit catalog. We also construct a binary population synthesis model based on Moe & Di Stefano (2017) to validate our characterization of the selection function, finding good agreement with the actual Gaia NSS catalog, with the exception of the orbital eccentricity distribution. The NSS catalog suggests high-eccentricity orbits are relatively uncommon at intermediate periods $100 \lesssim P_{orb} \lesssim 1000$ days. As an example application of the selection function, we estimate the Gaia DR3 detection probabilities of the star + BH binaries Gaia BH1, BH2, and BH3. We also estimate the population of Sun-like star + BH binaries in the Galaxy to be $\sim 5000$ for $100 < P_{orb} < 400$ day, $\lesssim 2,000$ for $400 < P_{orb} < 1000$ day, and $ \lesssim 20,000$ for $1000 < P_{orb} < 2000$ days., Comment: 24 pages, 14 figures, 2 appendices. Submitted to ApJ, comments welcome. Selection function code will be available here: https://github.com/caseylam/dr3_nss_ast_orbits_selection

We measure the time-integrated CP asymmetry in $D^{0} \rightarrow K^{0}_{S}K^{0}_{S}$ decays reconstructed in $e^{+}e^{-} \rightarrow c\overline{c}$ events collected by the Belle and Belle II experiments. The corresponding data samples have integrated luminosities of 980 fb$^{-1}$ and 428 fb$^{-1}$, respectively. The $D^{0}$ decays are required to originate from the $D^{*+} \rightarrow D^{0}\pi^{+}$ decay, which determines the charm flavor at production time. A control sample of $D^{0} \rightarrow K^{+}K^{-}$ decays is used to correct for production and detection asymmetries. The result, $(-1.4\pm1.3{\rm(stat)}\pm0.1{\rm (syst)})\%$, is consistent with previous determinations and with CP symmetry., Comment: 10 pages, 3 figures. arXiv admin note: text overlap with arXiv:2410.22961

Despite the versatility of pre-trained language models (PLMs) across domains, their large memory footprints pose significant challenges in federated learning (FL), where the training model has to be distributed between a server and clients. One potential solution to bypass such constraints might be the use of parameter-efficient fine-tuning (PEFT) in the context of FL. However, we have observed that typical PEFT tends to severely suffer from heterogeneity among clients in FL scenarios, resulting in unstable and slow convergence. In this paper, we propose Client-Customized Adaptation (C2A), a novel hypernetwork-based FL framework that generates client-specific adapters by conditioning the client information. With the effectiveness of the hypernetworks in generating customized weights through learning to adopt the different characteristics of inputs, C2A can maximize the utility of shared model parameters while minimizing the divergence caused by client heterogeneity. To verify the efficacy of C2A, we perform extensive evaluations on FL scenarios involving heterogeneity in label and language distributions. Comprehensive evaluation results clearly support the superiority of C2A in terms of both efficiency and effectiveness in FL scenarios., Comment: Published at Findings of ACL 2023

Quasi-phase matching (QPM) is a technique extensively utilized in nonlinear optics for enhancing the efficiency and stability of frequency conversion processes. However, the conventional QPM relies on periodically poled ferroelectric crystals, which are limited in availability. The 3R phase of molybdenum disulfide (3R-MoS2), a transition metal dichalcogenide (TMDc) with the broken inversion symmetry, stands out as a promising candidate for QPM, enabling efficient nonlinear process. Here, we experimentally demonstrate the QPM at nanoscale, utilizing van der Waals stacking of 3R-MoS2 layers with specific orientation to realize second harmonic generation (SHG) enhancement beyond the non QPM limit. We have also demonstrated enhanced spontaneous parametric down-conversion (SPDC) via QPM of 3R-MoS2 homo-structure, enabling more efficient generation of entangled photon pairs. The tunable capacity of 3R-MoS2 van der Waals stacking provides a platform for tuning phase-matching condition. This technique opens interesting possibilities for potential applications in nonlinear process and quantum technology.

Astrometry from Gaia DR3 has produced a sample of $\sim$170,000 Keplerian orbital solutions, with many more anticipated in the next few years. These data have enormous potential to constrain the population of binary stars, giant planets, and compact objects in the Solar neighborhood. But in order to use the published orbit catalogs for statistical inference, it is necessary to understand their selection function: what is the probability that a binary with a given set of properties ends up in a catalog? We show that such a selection function for the Gaia DR3 astrometric binary catalog can be forward-modeled from the Gaia scanning law, including individual 1D astrometric measurements, the fitting of a cascade of astrometric models, and quality cuts applied in post-processing. We populate a synthetic Milky Way model with binary stars and generate a mock catalog of astrometric orbits. The mock catalog is quite similar to the DR3 astrometric binary sample, suggesting that our selection function is a sensible approximation of reality. Our fitting also produces a sample of spurious astrometric orbits similar to those found in DR3; these are mainly the result of scan angle-dependent astrometric biases in marginally resolved wide binaries. We show that Gaia's sensitivity to astrometric binaries falls off rapidly at high eccentricities, but only weakly at high inclinations. We predict that DR4 will yield $\sim 1$ million astrometric orbits, mostly for bright ($G \lesssim 15$) systems with long periods ($P_{\rm orb} \gtrsim 1000$ d). We provide code to simulate and fit realistic Gaia epoch astrometry for any data release and determine whether any hypothetical binary would receive a cataloged orbital solution., Comment: 22 pages, 17 figures, accepted to OJAp. Code at https://github.com/kareemelbadry/gaiamock

Patient experience and care quality are crucial for a hospital's sustainability and reputation. The analysis of patient feedback offers valuable insight into patient satisfaction and outcomes. However, the unstructured nature of these comments poses challenges for traditional machine learning methods following a supervised learning paradigm. This is due to the unavailability of labeled data and the nuances these texts encompass. This research explores leveraging Large Language Models (LLMs) in conducting Multi-label Text Classification (MLTC) of inpatient comments shared after a stay in the hospital. GPT-4 Turbo was leveraged to conduct the classification. However, given the sensitive nature of patients' comments, a security layer is introduced before feeding the data to the LLM through a Protected Health Information (PHI) detection framework, which ensures patients' de-identification. Additionally, using the prompt engineering framework, zero-shot learning, in-context learning, and chain-of-thought prompting were experimented with. Results demonstrate that GPT-4 Turbo, whether following a zero-shot or few-shot setting, outperforms traditional methods and Pre-trained Language Models (PLMs) and achieves the highest overall performance with an F1-score of 76.12% and a weighted F1-score of 73.61% followed closely by the few-shot learning results. Subsequently, the results' association with other patient experience structured variables (e.g., rating) was conducted. The study enhances MLTC through the application of LLMs, offering healthcare practitioners an efficient method to gain deeper insights into patient feedback and deliver prompt, appropriate responses.

We perform a model-independent measurement of the $D^0$-$\overline{D}{}^0$ mixing parameters using samples of $e^+e^-$-collision data collected by the Belle and Belle II experiments that have integrated luminosities of $951\ \text{fb}^{-1}$ and $408\ \text{fb}^{-1}$, respectively. Approximately $2.05\times10^6$ neutral $D$ mesons are reconstructed in the $D^0\rightarrow K^0_{S}\pi^+\pi^-$ channel, with the neutral $D$ flavor tagged by the charge of the pion in the $D^{*+}\rightarrow D^0\pi^+$ decay. Assuming charge-parity symmetry, the mixing parameters are measured to be $ x = (4.0\pm1.7\pm0.4)\times 10^{-3} $ and $ y = (2.9\pm1.4\pm0.3)\times 10^{-3}$, where the first uncertainties are statistical and the second systematic. The results are consistent with previous determinations.

Accurate damage prediction is crucial for disaster preparedness and response strategies, particularly given the frequent earthquakes in Turkey. Utilizing datasets on earthquake data, infrastructural quality metrics, and contemporary socioeconomic factors, we tested various machine-learning architectures to forecast death tolls and fatalities per affected population. Our findings indicate that the Random Forest model provides the most reliable predictions. The model highlights earthquake magnitude and building stability as the primary determinants of damage. This research contributes to the reduction of fatalities in future seismic events in Turkey.

Pulmonary embolism (PE) is a leading cause of preventable in-hospital mortality. Advances in diagnosis, risk stratification, and prevention can improve outcomes. There are few large publicly available datasets that contain PE labels for research. Using the MIMIC-IV database, we extracted all available radiology reports of computed tomography pulmonary angiography (CTPA) scans and two physicians manually labeled the results as PE positive (acute PE) or PE negative. We then applied a previously finetuned Bio_ClinicalBERT transformer language model, VTE-BERT, to extract labels automatically. We verified VTE-BERT's reliability by measuring its performance against manual adjudication. We also compared the performance of VTE-BERT to diagnosis codes. We found that VTE-BERT has a sensitivity of 92.4% and positive predictive value (PPV) of 87.8% on all 19,942 patients with CTPA radiology reports from the emergency room and/or hospital admission. In contrast, diagnosis codes have a sensitivity of 95.4% and PPV of 83.8% on the subset of 11,990 hospitalized patients with discharge diagnosis codes. We successfully add nearly 20,000 labels to CTPAs in a publicly available dataset and demonstrate the external validity of a semi-supervised language model in accelerating hematologic research.

Machine learning (ML) for text classification has been widely used in various domains, such as toxicity detection, chatbot consulting, and review analysis. These applications can significantly impact ethics, economics, and human behavior, raising serious concerns about trusting ML decisions. Several studies indicate that traditional metrics, such as model confidence and accuracy, are insufficient to build human trust in ML models. These models often learn spurious correlations during training and predict based on them during inference. In the real world, where such correlations are absent, their performance can deteriorate significantly. To avoid this, a common practice is to test whether predictions are reasonable. Along with this, a challenge known as the trustworthiness oracle problem has been introduced. Due to the lack of automated trustworthiness oracles, the assessment requires manual validation of the decision process disclosed by explanation methods, which is time-consuming and not scalable. We propose TOKI, the first automated trustworthiness oracle generation method for text classifiers, which automatically checks whether the prediction-contributing words are related to the predicted class using explanation methods and word embeddings. To demonstrate its practical usefulness, we introduce a novel adversarial attack method targeting trustworthiness issues identified by TOKI. We compare TOKI with a naive baseline based solely on model confidence using human-created ground truths of 6,000 predictions. We also compare TOKI-guided adversarial attack method with A2T, a SOTA adversarial attack method. Results show that relying on prediction uncertainty cannot distinguish between trustworthy and untrustworthy predictions, TOKI achieves 142% higher accuracy than the naive baseline, and TOKI-guided adversarial attack method is more effective with fewer perturbations than A2T.

Alternative data provides valuable insights for lenders to evaluate a borrower's creditworthiness, which could help expand credit access to underserved groups and lower costs for borrowers. But some forms of alternative data have historically been excluded from credit underwriting because it could act as an illegal proxy for a protected class like race or gender, causing redlining. We propose a method for applying causal inference to a supervised machine learning model to debias alternative data so that it might be used for credit underwriting. We demonstrate how our algorithm can be used against a public credit dataset to improve model accuracy across different racial groups, while providing theoretically robust nondiscrimination guarantees.

This paper aims at developing novel shuffling gradient-based methods for tackling two classes of minimax problems: nonconvex-linear and nonconvex-strongly concave settings. The first algorithm addresses the nonconvex-linear minimax model and achieves the state-of-the-art oracle complexity typically observed in nonconvex optimization. It also employs a new shuffling estimator for the "hyper-gradient", departing from standard shuffling techniques in optimization. The second method consists of two variants: semi-shuffling and full-shuffling schemes. These variants tackle the nonconvex-strongly concave minimax setting. We establish their oracle complexity bounds under standard assumptions, which, to our best knowledge, are the best-known for this specific setting. Numerical examples demonstrate the performance of our algorithms and compare them with two other methods. Our results show that the new methods achieve comparable performance with SGD, supporting the potential of incorporating shuffling strategies into minimax algorithms., Comment: 45 pages, 5 figures (38th Conference on Neural Information Processing Systems (NeurIPS 2024))

Radio pulsars allow the study of the ionised interstellar medium and its dispersive effects, a major noise source in gravitational wave searches using pulsars. In this paper, we compare the functionality and reliability of three commonly used schemes to measure temporal variations in interstellar propagation effects in pulsar-timing data. We carry out extensive simulations at low observing frequencies (100-200 MHz) by injecting long-term correlated noise processes with power-law spectra and white noise, to evaluate the robustness, accuracy and precision of the following three mitigation methods: epoch-wise (EW) measurements of interstellar dispersion; the DMX method of simultaneous, piece-wise fits to interstellar dispersion; and DMGP, which models dispersion variations through Gaussian processes using a Bayesian analysis method. We then evaluate how reliably the input signals are reconstructed and how the various methods react to the presence of achromatic long-period noise. All the methods perform well, provided the achromatic long-period noise is modeled for DMX and DMGP. The most precise method is DMGP, followed by DMX and EW, while the most accurate is EW, followed by DMX and DMGP. We also test different scenarios including simulations of L-band ToAs and realistic DM injection, with no significant variation in the obtained results. Given the nature of our simulations and our scope, we deem that EW is the most reliable method to study the Galactic ionized media. Future works should be conducted to confirm this result via more realistic simulations. We note that DM GP and DMX seem to be the most performing techniques in removing long-term correlated noise, and hence for gravitational wave studies. However, full simulations of pulsar timing array experiments are needed to support this interpretation.

We analyze the error rates of the Hamiltonian Monte Carlo algorithm with leapfrog integrator for Bayesian neural network inference. We show that due to the non-differentiability of activation functions in the ReLU family, leapfrog HMC for networks with these activation functions has a large local error rate of $\Omega(\epsilon)$ rather than the classical error rate of $O(\epsilon^3)$. This leads to a higher rejection rate of the proposals, making the method inefficient. We then verify our theoretical findings through empirical simulations as well as experiments on a real-world dataset that highlight the inefficiency of HMC inference on ReLU-based neural networks compared to analytical networks., Comment: Paper published at NeurIPS 2024

Dissipationless localized bound states of open quantum systems are significantly robust to decoherence and have potential applications in quantum technologies. In this work, the decoherence dynamics and dissipationless localized bound states of a two-mode open quantum system are investigated. The conditions for the emergence of dissipationless localized bound states are analytically solved, and the corresponding critical system-environment couplings under different values of the inter-mode coupling and the detuning are determined. The decoherence dynamics of the system under such conditions are analyzed and dissipationless coherence between the different localized bound states against decoherence is clearly shown. This may provide a new avenue to develop dissipationless quantum technology for quantum operations., Comment: 10 pages, 6 figures

We investigate the realizability of balanced functions on tropical curves, establishing new sufficient criteria for superabundant functions on genus two curves, analogous to the well-spacedness condition in genus one. We find that realizability is sensitive to the precise locations of conjugate and Weierstrass points on the tropical curve. The key input is a combinatorial comparison of semistable limit theorems for maps of curves. Amini-Baker-Brugall\'e-Rabinoff previously showed that realizability of functions is equivalent to ``modifiability'' to a tropical admissible cover. The resulting criteria are typically inexplicit; we develop combinatorial techniques to derive explicit, verifiable criteria from these. We then develop a dimensional reduction technique to deduce statements about maps to $\mathbb{R}^r$ from ones about maps to $\mathbb{R}$. By proving directly that modifiability and well-spacedness are equivalent in genus one, we obtain a new proof that well-spaced maps are realizable. Along the way, we explain how the modifiability criterion can be viewed as a comparison result for properness statements for moduli of relative maps and admissible covers., Comment: 38 pages, 16 figures

We define and study the dual mixed volume rational function of a sequence of polytopes, a dual version of the mixed volume polynomial. This concept has direct relations to the adjoint polynomials and the canonical forms of polytopes. We show that dual mixed volume is additive under mixed subdivisions, and is related by a change of variables to the dual volume of the Cayley polytope. We study dual mixed volume of zonotopes, generalized permutohedra, and associahedra. The latter reproduces the planar $\phi^3$-scalar amplitude at tree level.

We establish a general scale-dependent Poincar\'{e}-Hardy type identity involving a vector field on the hyperbolic space. By choosing suitable parameter, potential and vector field in this identity, we can recover, as well as derive new versions of several Poincar\'{e} type, Hardy type and Poincar\'{e}-Hardy type inequalities in the literature. We also investigate weighted Poincar\'{e} inequalities on hyperbolic space, where the weight functions depend on a scaling parameter. This leads to a new family of scale-dependent Poincar\'{e} inequalities with Gaussian type measure on the hyperbolic space which is of independent interest. As a result, we derive both scale-dependent and scale-invariant $L^{2}$-stability results for the Heisenberg uncertainty principle in this setting.

Massive Multiple-Input Multiple-Output (massive MIMO) technology stands as a cornerstone in 5G and beyonds. Despite the remarkable advancements offered by massive MIMO technology, the extreme number of antennas introduces challenges during the channel estimation (CE) phase. In this paper, we propose a single-step Deep Neural Network (DNN) for CE, termed Iterative Sequential DNN (ISDNN), inspired by recent developments in data detection algorithms. ISDNN is a DNN based on the projected gradient descent algorithm for CE problems, with the iterative iterations transforming into a DNN using the deep unfolding method. Furthermore, we introduce the structured channel ISDNN (S-ISDNN), extending ISDNN to incorporate side information such as directions of signals and antenna array configurations for enhanced CE. Simulation results highlight that ISDNN significantly outperforms another DNN-based CE (DetNet), in terms of training time (13%), running time (4.6%), and accuracy (0.43 dB). Furthermore, the S-ISDNN demonstrates even faster than ISDNN in terms of training time, though its overall performance still requires further improvement.

Large language models (LLMs) have achieved a degree of success in generating coherent and contextually relevant text, yet they remain prone to a significant challenge known as hallucination: producing information that is not substantiated by the input or external knowledge. Previous efforts to mitigate hallucinations have focused on techniques such as fine-tuning models on high-quality datasets, incorporating fact-checking mechanisms, and developing adversarial training methods. While these approaches have shown some promise, they often address the issue at the level of individual model outputs, leaving unexplored the effects of inter-model interactions on hallucination. This study investigates the phenomenon of hallucination in LLMs through a novel experimental framework where multiple instances of GPT-4o-Mini models engage in a debate-like interaction prompted with questions from the TruthfulQA dataset. One model is deliberately instructed to generate plausible but false answers while the other models are asked to respond truthfully. The experiment is designed to assess whether the introduction of misinformation by one model can challenge the truthful majority to better justify their reasoning, improving performance on the TruthfulQA benchmark. The findings suggest that inter-model interactions can offer valuable insights into improving the accuracy and robustness of LLM outputs, complementing existing mitigation strategies.

We establish a new family of the critical higher order Sobolev interpolation inequalities for radial functions as well as for non-radial functions. These Sobolev interpolation inequalities are sharp in the sense that they use the optimal quadratic forms of the sharp Hardy-Rellich inequalities and cover the Sobolev critical exponents. Our results extend those studied by Dietze and Nam in [15] for the first order derivative case to higher order setting. The well-known P\'{o}lya-Szeg\"{o} symmetrization principle and the nonlinear ground state representation play an important role in the work of [15]. To overcome the absence of the P\'{o}lya-Szeg\"{o} principle and the nonlinear ground state representation in the higher order case, our proofs rely on the Fourier analysis and a higher order verion of the Talenti comparison principle. We also study a new version of the critical Hardy-Sobolev interpolation inequality involving the critical quadratic form of the Hardy inequality and Lorentz norms. Our critical Hardy-Sobolev interpolation inequality complements the result of Dietze and Nam in [15].

We present new observations from CHEOPS and TESS to clarify the architecture of the planetary system hosted by the old Galactic thick disk star TOI-561. Our global analysis, which also includes previously published photometric and radial velocity data, incontrovertibly proves that TOI-561 is hosting at least four transiting planets with periods of 0.44 days (TOI-561 b), 10.8 days (TOI-561 c), 25.7 days (TOI-561 d), and 77.1 days (TOI-561 e) and a fifth non-transiting candidate, TOI-561f with a period of 433 days. The precise characterisation of TOI-561's orbital architecture is interesting since old and metal-poor thick disk stars are less likely to host ultra-short period Super-Earths like TOI-561 b. The new period of planet -e is consistent with the value obtained using radial velocity alone and is now known to be $77.14399\pm0.00025$ days, thanks to the new CHEOPS and TESS transits. The new data allowed us to improve its radius ($R_p = 2.517 \pm 0.045 R_{\oplus}$ from 5$\%$ to 2$\%$ precision) and mass ($M_p = 12.4 \pm 1.4 M_{\oplus}$) estimates, implying a density of $\rho_p = 0.778 \pm 0.097 \rho_{\oplus}$. Thanks to recent TESS observations and the focused CHEOPS visit of the transit of TOI-561 e, a good candidate for exomoon searches, the planet's period is finally constrained, allowing us to predict transit times through 2030 with 20-minute accuracy. We present an updated version of the internal structure of the four transiting planets. We finally performed a detailed stability analysis, which confirmed the long-term stability of the outer planet TOI-561 f., Comment: 13 pages, 10 Figures. Accepted on MNRAS. Updated the author list

The proliferation of machine learning models in diverse clinical applications has led to a growing need for high-fidelity, medical image training data. Such data is often scarce due to cost constraints and privacy concerns. Alleviating this burden, medical image synthesis via generative adversarial networks (GANs) emerged as a powerful method for synthetically generating photo-realistic images based on existing sets of real medical images. However, the exact image set size required to efficiently train such a GAN is unclear. In this work, we experimentally establish benchmarks that measure the relationship between a sample dataset size and the fidelity of the generated images, given the dataset's distribution of image complexities. We analyze statistical metrics based on delentropy, an image complexity measure rooted in Shannon's entropy in information theory. For our pipeline, we conduct experiments with two state-of-the-art GANs, StyleGAN 3 and SPADE-GAN, trained on multiple medical imaging datasets with variable sample sizes. Across both GANs, general performance improved with increasing training set size but suffered with increasing complexity., Comment: Accepted to ACCV, Workshop on Generative AI for Synthetic Medical Data