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In this paper, we explore the integration of two revolutionary technologies, reconfigurable intelligent surfaces (RISs) and orthogonal time frequency space (OTFS) modulation, to enhance high-speed wireless communications. We introduce a novel phase shift design algorithm for RIS-assisted OTFS, optimizing energy reception and channel gain in dynamic environments. The study evaluates the proposed approach in a downlink scenario, demonstrating significant performance improvements compared to benchmark schemes in the literature, particularly in terms of bit error rate (BER). Our results showcase the potential of RIS to enhance the system's performance. Specifically, our proposed phase shift design technique outperforms the benchmark solutions by over 4 dB. Furthermore, even greater gains can be obtained as the number of RIS elements increases., Comment: 6 pages (double column), 5 figures, conference paper

Buchdahl star is the most compact object without an event horizon and is an excellent candidate for a black hole mimicker. Unlike black holes, rotating Buchdahl star can be over-extremal with respect to the black hole, sustaining a larger spin. We show that it can also develop an ergosphere above the threshold spin $\beta > 1/\sqrt{2}$, which allows extraction of its rotational energy. Electromagnetic field around Buchdahl star is also expected to differ from that of black hole in both strength and topology. In this paper, we explore the energetics of Buchdahl star focusing on the magnetic Penrose process in the two magnetic field configurations, i.e., uniform and dipole. Below the threshold spin, Buchdahl star is expected to be quiet, while above the threshold it can be much more efficient than the black hole if a dipolar magnetic field is developed on its surface., Comment: 11 pages, 4 captioned figures; discussions and references added

With Large Language Models (LLMs) being widely used across various tasks, detecting errors in their responses is increasingly crucial. However, little research has been conducted on error detection of LLM responses. Collecting error annotations on LLM responses is challenging due to the subjective nature of many NLP tasks, and thus previous research focuses on tasks of little practical value (e.g., word sorting) or limited error types (e.g., faithfulness in summarization). This work introduces ReaLMistake, the first error detection benchmark consisting of objective, realistic, and diverse errors made by LLMs. ReaLMistake contains three challenging and meaningful tasks that introduce objectively assessable errors in four categories (reasoning correctness, instruction-following, context-faithfulness, and parameterized knowledge), eliciting naturally observed and diverse errors in responses of GPT-4 and Llama 2 70B annotated by experts. We use ReaLMistake to evaluate error detectors based on 12 LLMs. Our findings show: 1) Top LLMs like GPT-4 and Claude 3 detect errors made by LLMs at very low recall, and all LLM-based error detectors perform much worse than humans. 2) Explanations by LLM-based error detectors lack reliability. 3) LLMs-based error detection is sensitive to small changes in prompts but remains challenging to improve. 4) Popular approaches to improving LLMs, including self-consistency and majority vote, do not improve the error detection performance. Our benchmark and code are provided at https://github.com/psunlpgroup/ReaLMistake., Comment: COLM 2024, 46 pages, Benchmark and code: https://github.com/psunlpgroup/ReaLMistake

Recently, large language models (LLMs) have evolved into interactive agents, proficient in planning, tool use, and task execution across a wide variety of tasks. However, without specific agent tuning, open-source models like LLaMA currently struggle to match the efficiency of GPT- 4, particularly given the scarcity of agent-tuning datasets for fine-tuning. In response, we introduce \textsc{Mimir}: a streamlined platform offering a customizable pipeline that enables users to leverage both private knowledge and publicly available, legally compliant datasets at scale for \textbf{personalized agent tuning}. Additionally, \textsc{Mimir} supports the generation of general instruction-tuning datasets from the same input. This dual capability ensures that language agents developed through the platform possess both specific agent abilities and general competencies. \textsc{Mimir} integrates these features into a cohesive end-to-end platform, facilitating everything from the uploading of personalized files to one-click agent fine-tuning.

Let $H_n$ be the minimal number such that any $n$-dimensional convex body can be covered by $H_n$ translates of interior of that body. Similarly $H_n^s$ is the corresponding quantity for symmetric bodies. It is possible to define $H_n$ and $H_n^s$ in terms of illumination of the boundary of the body using external light sources, and the famous Hadwiger's covering conjecture (illumination conjecture) states that $H_n=H_{n}^s=2^n$. In this note we obtain new upper bounds on $H_n$ and $H_{n}^s$ for small dimensions $n$. Our main idea is to cover the body by translates of John's ellipsoid (the inscribed ellipsoid of the largest volume). Using specific lattice coverings, estimates of quermassintegrals for convex bodies in John's position, and calculations of mean widths of regular simplexes, we prove the following new upper bounds on $H_n$ and $H_n^s$: $H_5\le 933$, $H_6\le 6137$, $H_7\le 41377$, $H_8\le 284096$, $H_4^s\le 72$, $H_5^s\le 305$, and $H_6^s\le 1292$. For larger $n$, we describe how the general asymptotic bounds $H_n\le \binom{2n}{n}n(\ln n+\ln\ln n+5)$ and $H_n^s\le 2^n n(\ln n+\ln\ln n+5)$ due to Rogers and Shephard can be improved for specific values of $n$., Comment: 12 pages

We search for super-imposed oscillations linearly or logarithmically spaced in Fourier wavenumbers in Planck and South Pole Telescope (SPT-3G) 2018 temperature and polarization data. The SPT-3G temperature and polarization data provide a new window to test these oscillations at high multipoles beyond the Planck angular resolution and sensitivity. We consider both models with a constant and a Gaussian modulated amplitude, which correspond to three and four additional parameters beyond power-law primordial power spectrum for the templates considered, respectively. We find that each of the four models considered can provide an improved fit to Planck data, consistently with previous findings, and to SPT-3G data, always compared to $\Lambda$CDM. For a constant amplitude of the superimposed oscillations, we find tighter constraints on the amplitude of the oscillations from the combined Planck/SPT-3G data set than in each individual data sets. When the ranges of parameters which provide a better fit to Planck and SPT-3G data overlap, as in the case of Gaussian modulated oscillations, we find a larger $\Delta \chi^2$ - $- 17 \, (-16)$ for logarithmic (linear) oscillations - in a combined Planck/SPT-3G data set than in each individual data sets. These findings will be further tested with upcoming CMB temperature and polarization measurements at high multipoles provided by ongoing ground experiments., Comment: 10 pages, 9 figures, 2 tables

The percent-level precision attained by modern cosmic ray (CR) observations motivates reaching a comparable or better control of theoretical uncertainties. Here we focus on energy-loss processes affecting low-energy CR protons ($\sim 0.1-5$ GeV), where the experimental errors are small and collisional effects play a comparatively larger role with respect to collisionless transport ones. We study three aspects of the problem: i) We quantitatively assess the role of the nuclear elastic cross-section, for the first time, providing analytical formulae for the stopping power and inelasticity. ii) We discuss the error arising from treating both elastic and pion production inelastic interactions as continuous energy loss processes, as opposed to catastrophic ones. The former is the approximation used in virtually all modern numerical calculations. iii) We consider sub-leading effects such as relativistic corrections, radiative and medium processes in ionization energy-losses. Our analysis reveals that neglecting i) leads to errors close to 1%, notably around and below 1 GeV; neglecting ii) leads to errors reaching about 3% within the considered energy range; iii) contributes to a minor effect, gauged at the level of 0.1%. Consequently, while iii) can currently be neglected, ii) warrants consideration, and we also recommend incorporating i) into computations. We conclude with some perspectives on further steps to be taken towards a high-precision goal of theoretical CR predictions regarding the treatment of energy-losses., Comment: v1: 14 pages, 11 figures

We consider a setting in which $N$ agents aim to speedup a common Stochastic Approximation (SA) problem by acting in parallel and communicating with a central server. We assume that the up-link transmissions to the server are subject to asynchronous and potentially unbounded time-varying delays. To mitigate the effect of delays and stragglers while reaping the benefits of distributed computation, we propose \texttt{DASA}, a Delay-Adaptive algorithm for multi-agent Stochastic Approximation. We provide a finite-time analysis of \texttt{DASA} assuming that the agents' stochastic observation processes are independent Markov chains. Significantly advancing existing results, \texttt{DASA} is the first algorithm whose convergence rate depends only on the mixing time $\tau_{mix}$ and on the average delay $\tau_{avg}$ while jointly achieving an $N$-fold convergence speedup under Markovian sampling. Our work is relevant for various SA applications, including multi-agent and distributed temporal difference (TD) learning, Q-learning and stochastic optimization with correlated data.

The effectiveness of Deep Neural Networks (DNNs) heavily relies on the abundance and accuracy of available training data. However, collecting and annotating data on a large scale is often both costly and time-intensive, particularly in medical cases where practitioners are already occupied with their duties. Moreover, ensuring that the model remains robust across various scenarios of image capture is crucial in medical domains, especially when dealing with ultrasound images that vary based on the settings of different devices and the manual operation of the transducer. To address this challenge, we introduce a novel pipeline called MEDDAP, which leverages Stable Diffusion (SD) models to augment existing small datasets by automatically generating new informative labeled samples. Pretrained checkpoints for SD are typically based on natural images, and training them for medical images requires significant GPU resources due to their heavy parameters. To overcome this challenge, we introduce USLoRA (Ultrasound Low-Rank Adaptation), a novel fine-tuning method tailored specifically for ultrasound applications. USLoRA allows for selective fine-tuning of weights within SD, requiring fewer than 0.1\% of parameters compared to fully fine-tuning only the UNet portion of SD. To enhance dataset diversity, we incorporate different adjectives into the generation process prompts, thereby desensitizing the classifiers to intensity changes across different images. This approach is inspired by clinicians' decision-making processes regarding breast tumors, where tumor shape often plays a more crucial role than intensity. In conclusion, our pipeline not only outperforms classifiers trained on the original dataset but also demonstrates superior performance when encountering unseen datasets. The source code is available at https://github.com/yasamin-med/MEDDAP., Comment: submitted to miccai 2024 submitted to miccai 2024 Submitted to MICCAI-2024

Modern Language Models (LMs) are capable of following long and complex instructions that enable a large and diverse set of user requests. While Information Retrieval (IR) models use these LMs as the backbone of their architectures, virtually none of them allow users to provide detailed instructions alongside queries, thus limiting their ability to satisfy complex information needs. In this work, we study the use of instructions in IR systems. First, we introduce our dataset FollowIR, which contains a rigorous instruction evaluation benchmark as well as a training set for helping IR models learn to better follow real-world instructions. FollowIR repurposes detailed instructions -- also known as narratives -- developed for professional assessors to evaluate retrieval systems. In particular, we build our benchmark from three collections curated for shared tasks at the Text REtrieval Conference (TREC). These collections contains hundreds to thousands of labeled documents per query, making them suitable for our exploration. Through this process, we can measure how well IR models follow instructions, through a new pairwise evaluation framework. Our results indicate that existing retrieval models fail to correctly use instructions, using them for basic keywords and struggling to understand long-form information. However, we show that it is possible for IR models to learn to follow complex instructions: our new FollowIR-7B model has significant improvements after fine-tuning on our training set.

Robotic surgery has reached a high level of maturity and has become an integral part of standard surgical care. However, existing surgeon consoles are bulky, take up valuable space in the operating room, make surgical team coordination challenging, and their proprietary nature makes it difficult to take advantage of recent technological advances, especially in virtual and augmented reality. One potential area for further improvement is the integration of modern sensory gloves into robotic platforms, allowing surgeons to control robotic arms intuitively with their hand movements. We propose one such system that combines an HTC Vive tracker, a Manus Meta Prime 3 XR sensory glove, and SCOPEYE wireless smart glasses. The system controls one arm of a da Vinci surgical robot. In addition to moving the arm, the surgeon can use fingers to control the end-effector of the surgical instrument. Hand gestures are used to implement clutching and similar functions. In particular, we introduce clutching of the instrument orientation, a functionality unavailable in the da Vinci system. The vibrotactile elements of the glove are used to provide feedback to the user when gesture commands are invoked. A qualitative and quantitative evaluation has been conducted that compares the current device with the dVRK console. The system is shown to have excellent tracking accuracy, and the new interface allows surgeons to perform common surgical training tasks with minimal practice efficiently., Comment: 6 pages, 4 figures, 7 tables, submitted to International Conference on Robotics and Automation (ICRA) 2025

Since 1772, when Euler first described two methods of obtaining two pairs of biquadrates with equal sums, several methods of solving the diophantine equation $x^4+y^4=z^4+w^4$ have been published. All these methods yield parametric solutions in terms of homogeneous bivariate polynomials of odd degrees. In this paper we describe a method that yields three parametric solutions of the aforesaid diophantine equation in terms of homogeneous bivariate polynomials of even degrees, namely degrees~$74$, $88$ and $132$ respectively., Comment: 8 pages

We present BEHAVIOR-1K, a comprehensive simulation benchmark for human-centered robotics. BEHAVIOR-1K includes two components, guided and motivated by the results of an extensive survey on "what do you want robots to do for you?". The first is the definition of 1,000 everyday activities, grounded in 50 scenes (houses, gardens, restaurants, offices, etc.) with more than 9,000 objects annotated with rich physical and semantic properties. The second is OMNIGIBSON, a novel simulation environment that supports these activities via realistic physics simulation and rendering of rigid bodies, deformable bodies, and liquids. Our experiments indicate that the activities in BEHAVIOR-1K are long-horizon and dependent on complex manipulation skills, both of which remain a challenge for even state-of-the-art robot learning solutions. To calibrate the simulation-to-reality gap of BEHAVIOR-1K, we provide an initial study on transferring solutions learned with a mobile manipulator in a simulated apartment to its real-world counterpart. We hope that BEHAVIOR-1K's human-grounded nature, diversity, and realism make it valuable for embodied AI and robot learning research. Project website: https://behavior.stanford.edu., Comment: A preliminary version was published at 6th Conference on Robot Learning (CoRL 2022)

Automated slice classification is clinically relevant since it can be incorporated into medical image segmentation workflows as a preprocessing step that would flag slices with a higher probability of containing tumors, thereby directing physicians attention to the important slices. In this work, we train a ResNet-18 network to classify axial slices of lymphoma PET/CT images (collected from two institutions) depending on whether the slice intercepted a tumor (positive slice) in the 3D image or if the slice did not (negative slice). Various instances of the network were trained on 2D axial datasets created in different ways: (i) slice-level split and (ii) patient-level split; inputs of different types were used: (i) only PET slices and (ii) concatenated PET and CT slices; and different training strategies were employed: (i) center-aware (CAW) and (ii) center-agnostic (CAG). Model performances were compared using the area under the receiver operating characteristic curve (AUROC) and the area under the precision-recall curve (AUPRC), and various binary classification metrics. We observe and describe a performance overestimation in the case of slice-level split as compared to the patient-level split training. The model trained using patient-level split data with the network input containing only PET slices in the CAG training regime was the best performing/generalizing model on a majority of metrics. Our models were additionally more closely compared using the sensitivity metric on the positive slices from their respective test sets., Comment: 10 pages, 6 figures, 2 tables

Accurate detection and segmentation of diffuse large B-cell lymphoma (DLBCL) from PET images has important implications for estimation of total metabolic tumor volume, radiomics analysis, surgical intervention and radiotherapy. Manual segmentation of tumors in whole-body PET images is time-consuming, labor-intensive and operator-dependent. In this work, we develop and validate a fast and efficient three-step cascaded deep learning model for automated detection and segmentation of DLBCL tumors from PET images. As compared to a single end-to-end network for segmentation of tumors in whole-body PET images, our three-step model is more effective (improves 3D Dice score from 58.9% to 78.1%) since each of its specialized modules, namely the slice classifier, the tumor detector and the tumor segmentor, can be trained independently to a high degree of skill to carry out a specific task, rather than a single network with suboptimal performance on overall segmentation., Comment: 8 pages, 3 figures, 3 tables

Text summarization and simplification are among the most widely used applications of AI. However, models developed for such tasks are often prone to hallucination, which can result from training on unaligned data. One efficient approach to address this issue is Loss Truncation (LT) (Kang and Hashimoto, 2020), an approach to modify the standard log loss to adaptively remove noisy examples during training. However, we find that LT alone yields a considerable number of hallucinated entities on various datasets. We study the behavior of the underlying losses between factual and non-factual examples, to understand and refine the performance of LT. We demonstrate that LT's performance is limited when the underlying assumption that noisy targets have higher NLL loss is not satisfied, and find that word-level NLL among entities provides better signal for distinguishing factuality. We then leverage this to propose a fine-grained NLL loss and fine-grained data cleaning strategies, and observe improvements in hallucination reduction across some datasets. Our work is available at https://https://github.com/yale-nlp/fine-grained-lt., Comment: EACL 2024

Today's virtual reality (VR) systems provide immersive interactions that seamlessly connect users with online services and one another. However, these immersive interfaces also introduce new vulnerabilities, making it easier for users to fall prey to new attacks. In this work, we introduce the immersive hijacking attack, where a remote attacker takes control of a user's interaction with their VR system, by trapping them inside a malicious app that masquerades as the full VR interface. Once trapped, all of the user's interactions with apps, services and other users can be recorded and modified without their knowledge. This not only allows traditional privacy attacks but also introduces new interaction attacks, where two VR users encounter vastly different immersive experiences during their interaction. We present our implementation of the immersive hijacking attack on Meta Quest headsets and conduct IRB-approved user studies that validate its efficacy and stealthiness. Finally, we examine effectiveness and tradeoffs of various potential defenses, and propose a multifaceted defense pipeline., Comment: 13 pages

This paper proposes a high-performance and energy-efficient optical near-sensor accelerator for vision applications, called Lightator. Harnessing the promising efficiency offered by photonic devices, Lightator features innovative compressive acquisition of input frames and fine-grained convolution operations for low-power and versatile image processing at the edge for the first time. This will substantially diminish the energy consumption and latency of conversion, transmission, and processing within the established cloud-centric architecture as well as recently designed edge accelerators. Our device-to-architecture simulation results show that with favorable accuracy, Lightator achieves 84.4 Kilo FPS/W and reduces power consumption by a factor of ~24x and 73x on average compared with existing photonic accelerators and GPU baseline., Comment: 6 pages, 10 figures

While large language models have achieved remarkable performance on various code generation benchmarks, there have been growing concerns regarding potential contamination of these benchmarks as they may be leaked into pretraining and finetuning data. While recent work has investigated contamination in natural language generation and understanding tasks, there has been less extensive research into how data contamination impacts the evaluation of code generation, which is critical for understanding the robustness and reliability of LLMs in programming contexts. In this work, we perform a comprehensive study of data contamination of popular code generation benchmarks, and precisely quantify their overlap with pretraining corpus through both surface-level and semantic-level matching. In our experiments, we show that there are substantial overlap between popular code generation benchmarks and open training corpus, and models perform significantly better on the subset of the benchmarks where similar solutions are seen during training. We also conduct extensive analysis on the factors that affects model memorization and generalization, such as model size, problem difficulty, and question length. We release all resulting files from our matching pipeline for future research.

This contribution presents the recent research developments within the Cosmic Ray Extremely Distributed Observatory (CREDO) in the search for resolution of various scientific puzzles, ranging from fundamental physical questions to applications like the determination of earthquake precursors. The state-of-the art theoretical, numerical and computational aspects of these phenomena are addressed, as well as recent experimental developments for detection., Comment: 9 pages, 7 figures. Based on the contribution to the XVIII Mexican Workshop on Particles and Fields in Puebla, Mexico, November 2022. M\'exico

We investigate the transport properties of massive Dirac fermions subjected to uncorrelated scalar potential disorder, and mass disorder. Using a finite difference method, the conductance is calculated for a wide variety of combinations of these two disorder strengths. By calculating the scaling of conductivity with system size we find that, depending on the combination, the system can have an insulating, scale invariant, and metallic behavior. We identify the critical values of these disorder strengths where the phase transitions occur. We study both the zero and nonzero average mass cases to examine the effect of scalar potential disorder on band gap. Our results suggest a suppression of the band gap by the scalar potential disorder., Comment: 9 pages, 9 figures

Dynamic digital timing analysis is a less accurate but fast alternative to highly accurate but slow analog simulations of digital circuits. It relies on gate delay models, which allow the determination of input-to-output delays of a gate on a per-transition basis. Accurate delay models not only consider the effect of preceding output transitions here but also delay variations induced by multi-input switching (MIS) effects in the case of multi-input gates. Starting out from a first-order hybrid delay model for CMOS two-input NOR gates, we develop a hybrid delay model for Muller C gates and show how to augment these models and their analytic delay formulas by a first-order interconnect. Moreover, we conduct a systematic evaluation of the resulting modeling accuracy: Using SPICE simulations, we quantify the MIS effects on the gate delays under various wire lengths, load capacitances, and input strengths for two different CMOS technologies, comparing these results to the predictions of appropriately parameterized versions of our new gate delay models. Overall, our experimental results reveal that they capture all MIS effects with a surprisingly good accuracy despite being first-order only.

Thresholded hybrid systems are restricted dynamical systems, where the current mode, and hence the ODE system describing its behavior, is solely determined by externally supplied digital input signals and where the only output signals are digital ones generated by comparing an internal state variable to a threshold value. An attractive feature of such systems is easy composition, which is facilitated by their purely digital interface. A particularly promising application domain of thresholded hybrid systems is digital integrated circuits: Modern digital circuit design considers them as a composition of Millions and even Billions of elementary logic gates, like inverters, GOR and Gand. Since every such logic gate is eventually implemented as an electronic circuit, however, which exhibits a behavior that is governed by some ODE system, thresholded hybrid systems are ideally suited for making the transition from the analog to the digital world rigorous. In this paper, we prove that the mapping from digital input signals to digital output signals is continuous for a large class of thresholded hybrid systems. Moreover, we show that, under some mild conditions regarding causality, this continuity also continues to hold for arbitrary compositions, which in turn guarantees that the composition faithfully captures the analog reality. By applying our generic results to some recently developed thresholded hybrid gate models, both for single-input single-output gates like inverters and for a two-input CMOS NOR gate, we show that they are continuous. Moreover, we provide a novel thresholded hybrid model for the two-input NOR gate, which is not only continuous but also, unlike the existing one, faithfully models all multi-input switching effects., Comment: There was a missing author from the last submission. arXiv admin note: substantial text overlap with arXiv:2303.14048

The isometric mapping method employs the shortest path algorithm to estimate the Euclidean distance between points on High dimensional (HD) manifolds. This may not be sufficient for weakly uniformed HD data as it could lead to overestimating distances between far neighboring points, resulting in inconsistencies between the intrinsic (local) and extrinsic (global) distances during the projection. To address this issue, we modify the shortest path algorithm by adding a novel constraint inspired by the Parzen-Rosenblatt (PR) window, which helps to maintain the uniformity of the constructed shortest-path graph in Isomap. Multiple imaging datasets overall of 72,236 cases, 70,000 MINST data, 1596 from multiple Chest-XRay pneumonia datasets, and three NSCLC CT/PET datasets with a total of 640 lung cancer patients, were used to benchmark and validate PR-Isomap. 431 imaging biomarkers were extracted from each modality. Our results indicate that PR-Isomap projects HD attributes into a lower-dimensional (LD) space while preserving information, visualized by the MNIST dataset indicating the maintaining local and global distances. PR-Isomap achieved the highest comparative accuracies of 80.9% (STD:5.8) for pneumonia and 78.5% (STD:4.4), 88.4% (STD:1.4), and 61.4% (STD:11.4) for three NSCLC datasets, with a confidence interval of 95% for outcome prediction. Similarly, the multivariate Cox model showed higher overall survival, measured with c-statistics and log-likelihood test, of PR-Isomap compared to other dimensionality reduction methods. Kaplan Meier survival curve also signifies the notable ability of PR-Isomap to distinguish between high-risk and low-risk patients using multimodal imaging biomarkers preserving HD imaging characteristics for precision medicine., Comment: This is the author's version

Randomized controlled trials (RCTs) with binary primary endpoints introduce novel challenges for inferring the causal effects of treatments. The most significant challenge is non-collapsibility, in which the conditional odds ratio estimand under covariate adjustment differs from the unconditional estimand in the logistic regression analysis of RCT data. This issue gives rise to apparent paradoxes, such as the variance of the estimator for the conditional odds ratio from a covariate-adjusted model being greater than the variance of the estimator from the unadjusted model. We address this challenge in the context of adjustment based on predictions of control outcomes from generative artificial intelligence (AI) algorithms, which are referred to as prognostic scores. We demonstrate that prognostic score adjustment in logistic regression increases the power of the Wald test for the conditional odds ratio under a fixed sample size, or alternatively reduces the necessary sample size to achieve a desired power, compared to the unadjusted analysis. We derive formulae for prospective calculations of the power gain and sample size reduction that can result from adjustment for the prognostic score. Furthermore, we utilize g-computation to expand the scope of prognostic score adjustment to inferences on the marginal risk difference, relative risk, and odds ratio estimands. We demonstrate the validity of our formulae via extensive simulation studies that encompass different types of logistic regression model specifications. Our simulation studies also indicate how prognostic score adjustment can reduce the variance of g-computation estimators for the marginal estimands while maintaining frequentist properties such as asymptotic unbiasedness and Type I error rate control. Our methodology can ultimately enable more definitive and conclusive analyses for RCTs with binary primary endpoints., Comment: 27 pages, 1 figure, 9 tables

We study the non-equilibrium dynamics of a quantum spin 1/2 XXZ model confined in a two-dimensional bi-layer system, with couplings mediated by inverse power-law interactions, falling off with distance $r$ as $1/r^{\alpha}$, and spatio-temporal control of the spins enabled via local fields. An initial state of spins with opposite magnetization in the two layers is dynamically unstable resulting in exponential generation of correlated pairs of excitations. We find that scalable generation of entanglement in the form of two-mode squeezing between the layers can generically be achieved in powerlaw models. We further demonstrate that spatially-temporally engineered interactions allow to significantly increase the generated entanglement and in fact achieve Heisenberg limited scaling. This work is relevant to a wide variety of experimental atomic, molecular, and optical platforms, which realize powerlaw spin models, and demonstrates the advantage of spatio-temporal control to maximize the generation of metrologically useful entanglement, with potential applications in quantum-enhanced sensing., Comment: Main text (7 pages, 4 figures), Supplementary Material (4 pages, 9 figures)

Magnetic fields surrounding black holes are responsible for various astrophysical phenomena related to accretion processes and relativistic jets. Depending on the source, the configuration of the field lines may differ significantly, affecting the trajectories of charged particles and the corresponding observables. Usually, the magnetic fields around black holes are modeled within a single source or current generating the field. However, magnetic fields can have more than a single origin, being a combination of different fields, such as, e.g., that of an accretion disk and external large-scale or Galactic ones. In this paper, we propose a combined magnetic field solution given by the superposition of the uniform and Blandford-Znajek split-monopole magnetic fields in a strong gravity regime of the Schwarzschild black hole. We show that when the combined magnetic field components are aligned, the resulting field is of a paraboloidal jetlike shape. Such a configuration is supported by relativistic jet observations and is often utilized in general relativistic magnetohydrodynamical simulations. In the opposite orientation of the two field components, we observe looplike field structures magnetically connecting the black hole with an accretion disk and the magnetic null points, which can be related to the regions of magnetic reconnection. In the combined magnetic field configurations, we analyze the dynamics of charged particles, study their stability conditions, and find the locations of stable off-equatorial structures close to the symmetry axis. We consider an ionization of Keplerian accretion disk as a particular scenario of particle scattering. From the numerical experiments, we conclude that charged particles in the jetlike combination show a strong tendency to escape from the black hole. In contrast, the looplike combination supports accretion of charged particles into the black hole., Comment: 18 pages, 13 figures, accepted to Phys. Rev. D

It is well known that supermassive black holes in the centers of galaxies are capable of accelerating charged particles to very high energies. In many cases, the particle acceleration by black holes occurs electromagnetically through an electric field induced by the source. In such scenarios, the accelerated particles radiate electromagnetic waves, leading to the appearance of the backreaction force, which can considerably change the dynamics, especially, if the particles are relativistic. The effect of the radiation reaction force due to accelerating electric field of the central body in curved spacetime has not been considered previously. We study the dynamics of radiating charged particles in the field of the Schwarzschild black hole in the presence of an electric field associated with a small central charge of negligible gravitational influence. We start from the flat spacetime description, solving the Lorentz-Dirac equation reduced to the Landau-Lifshitz form. In curved spacetime, we use the DeWitt-Brehme equation and discuss the effect of the self-force, also known as the tail term, within the given approach. We also study the pure effect of the self-force to calculate the radiative deceleration of radially moving charged particles. In the case of bounded orbits, we find that the radiation reaction force can stabilize and circularize the orbits of oscillating charged particles by suppressing the oscillations or causing the particles to spiral down into the black hole depending on the sign of the electrostatic interaction. In all cases, we calculate the energy losses and exact trajectories of charged particles for different values and signs of electric charge.

Motivated by applications in large-scale and multi-agent reinforcement learning, we study the non-asymptotic performance of stochastic approximation (SA) schemes with delayed updates under Markovian sampling. While the effect of delays has been extensively studied for optimization, the manner in which they interact with the underlying Markov process to shape the finite-time performance of SA remains poorly understood. In this context, our first main contribution is to show that under time-varying bounded delays, the delayed SA update rule guarantees exponentially fast convergence of the \emph{last iterate} to a ball around the SA operator's fixed point. Notably, our bound is \emph{tight} in its dependence on both the maximum delay $\tau_{max}$, and the mixing time $\tau_{mix}$. To achieve this tight bound, we develop a novel inductive proof technique that, unlike various existing delayed-optimization analyses, relies on establishing uniform boundedness of the iterates. As such, our proof may be of independent interest. Next, to mitigate the impact of the maximum delay on the convergence rate, we provide the first finite-time analysis of a delay-adaptive SA scheme under Markovian sampling. In particular, we show that the exponent of convergence of this scheme gets scaled down by $\tau_{avg}$, as opposed to $\tau_{max}$ for the vanilla delayed SA rule; here, $\tau_{avg}$ denotes the average delay across all iterations. Moreover, the adaptive scheme requires no prior knowledge of the delay sequence for step-size tuning. Our theoretical findings shed light on the finite-time effects of delays for a broad class of algorithms, including TD learning, Q-learning, and stochastic gradient descent under Markovian sampling., Comment: Accepted to the 27th International Conference on Artificial Intelligence and Statistics (AISTATS) 2024!