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Kernel techniques are among the most influential approaches in data science and statistics. Under mild conditions, the reproducing kernel Hilbert space associated to a kernel is capable of encoding the independence of $M\ge 2$ random variables. Probably the most widespread independence measure relying on kernels is the so-called Hilbert-Schmidt independence criterion (HSIC; also referred to as distance covariance in the statistics literature). Despite various existing HSIC estimators designed since its introduction close to two decades ago, the fundamental question of the rate at which HSIC can be estimated is still open. In this work, we prove that the minimax optimal rate of HSIC estimation on $\mathbb R^d$ for Borel measures containing the Gaussians with continuous bounded translation-invariant characteristic kernels is $\mathcal O\!\left(n^{-1/2}\right)$. Specifically, our result implies the optimality in the minimax sense of many of the most-frequently used estimators (including the U-statistic, the V-statistic, and the Nystr\"om-based one) on $\mathbb R^d$.

The Yang and Prentice (YP) regression models have garnered interest from the scientific community due to their ability to analyze data whose survival curves exhibit intersection. These models include proportional hazards (PH) and proportional odds (PO) models as specific cases. However, they encounter limitations when dealing with multivariate survival data due to potential dependencies between the times-to-event. A solution is introducing a frailty term into the hazard functions, making it possible for the times-to-event to be considered independent, given the frailty term. In this study, we propose a new class of YP models that incorporate frailty. We use the exponential distribution, the piecewise exponential distribution (PE), and Bernstein polynomials (BP) as baseline functions. Our approach adopts a Bayesian methodology. The proposed models are evaluated through a simulation study, which shows that the YP frailty models with BP and PE baselines perform similarly to the generator parametric model of the data. We apply the models in two real data sets.

Multi-view depth estimation has achieved impressive performance over various benchmarks. However, almost all current multi-view systems rely on given ideal camera poses, which are unavailable in many real-world scenarios, such as autonomous driving. In this work, we propose a new robustness benchmark to evaluate the depth estimation system under various noisy pose settings. Surprisingly, we find current multi-view depth estimation methods or single-view and multi-view fusion methods will fail when given noisy pose settings. To address this challenge, we propose a single-view and multi-view fused depth estimation system, which adaptively integrates high-confident multi-view and single-view results for both robust and accurate depth estimations. The adaptive fusion module performs fusion by dynamically selecting high-confidence regions between two branches based on a wrapping confidence map. Thus, the system tends to choose the more reliable branch when facing textureless scenes, inaccurate calibration, dynamic objects, and other degradation or challenging conditions. Our method outperforms state-of-the-art multi-view and fusion methods under robustness testing. Furthermore, we achieve state-of-the-art performance on challenging benchmarks (KITTI and DDAD) when given accurate pose estimations. Project website: //github.com/Junda24/AFNet/.

Reconfigurable intelligent surface (RIS) is a novel meta-material which can form a smart radio environment by dynamically altering reflection directions of the impinging electromagnetic waves. In the prior literature, the inter-RIS links which also contribute to the performance of the whole system are usually neglected when multiple RISs are deployed. In this paper we investigate a general double-RIS assisted multiple-input multiple-output (MIMO) wireless communication system under spatially correlated non line-of-sight propagation channels, where the cooperation of the double RISs is also considered. The design objective is to maximize the achievable ergodic rate based on full statistical channel state information (CSI). Specifically, we firstly present a closed-form asymptotic expression for the achievable ergodic rate by utilizing replica method from statistical physics. Then a full statistical CSI-enabled optimal design is proposed which avoids high pilot training overhead compared to instantaneous CSI-enabled design. To further reduce the signal processing overhead and lower the complexity for practical realization, a common-phase scheme is proposed to design the double RISs. Simulation results show that the derived asymptotic ergodic rate is quite accurate even for small-sized antenna arrays. And the proposed optimization algorithm can achieve substantial gain at the expense of a low overhead and complexity. Furthermore, the cooperative double-RIS assisted MIMO framework is proven to achieve superior ergodic rate performance and high communication reliability under harsh propagation environment.

Recently it was shown that the response time of First-Come-First-Served (FCFS) scheduling can be stochastically and asymptotically improved upon by the {\it Nudge} scheduling algorithm in case of light-tailed job size distributions. Such improvements are feasible even when the jobs are partitioned into two types and the scheduler only has information about the type of incoming jobs (but not their size). In this paper we introduce Nudge-$M$ scheduling, where basically any incoming type-1 job is allowed to pass any type-2 job that is still waiting in the queue given that it arrived as one of the last $M$ jobs. We prove that Nudge-$M$ has an asymptotically optimal response time within a large family of Nudge scheduling algorithms when job sizes are light-tailed. Simple explicit results for the asymptotic tail improvement ratio (ATIR) of Nudge-$M$ over FCFS are derived as well as explicit results for the optimal parameter $M$. An expression for the ATIR that only depends on the type-1 ad type-2 mean job sizes and the fraction of type-1 jobs is presented in the heavy traffic setting. The paper further presents a numerical method to compute the response time distribution and mean response time of Nudge-$M$ scheduling provided that the job size distribution of both job types follows a phase-type distribution (by making use of the framework of Markov modulated fluid queues with jumps).

Content creators increasingly utilize generative artificial intelligence (Gen-AI) on platforms such as YouTube, TikTok, Instagram, and various blogging sites to produce imaginative images, AI-generated videos, and articles using Large Language Models (LLMs). Despite its growing popularity, there remains an underexplored area concerning the specific domains where AI-generated content is being applied, and the methodologies content creators employ with Gen-AI tools during the creation process. This study initially explores this emerging area through a qualitative analysis of 68 YouTube videos demonstrating Gen-AI usage. Our research focuses on identifying the content domains, the variety of tools used, the activities performed, and the nature of the final products generated by Gen-AI in the context of user-generated content.

Prognostics and Health Management (PHM) is a discipline focused on predicting the point at which systems or components will cease to perform as intended, typically measured as Remaining Useful Life (RUL). RUL serves as a vital decision-making tool for contingency planning, guiding the timing and nature of system maintenance. Historically, PHM has primarily been applied to hardware systems, with its application to software only recently explored. In a recent study we introduced a methodology and demonstrated how changes in software can impact the RUL of software. However, in practical software development, real-time performance is also influenced by various environmental attributes, including operating systems, clock speed, processor performance, RAM, machine core count and others. This research extends the analysis to assess how changes in environmental attributes, such as operating system and clock speed, affect RUL estimation in software. Findings are rigorously validated using real performance data from controlled test beds and compared with predictive model-generated data. Statistical validation, including regression analysis, supports the credibility of the results. The controlled test bed environment replicates and validates faults from real applications, ensuring a standardized assessment platform. This exploration yields actionable knowledge for software maintenance and optimization strategies, addressing a significant gap in the field of software health management.

Batch Normalization's (BN) unique property of depending on other samples in a batch is known to cause problems in several tasks, including sequence modeling. Yet, BN-related issues are hardly studied for long video understanding, despite the ubiquitous use of BN in CNNs (Convolutional Neural Networks) for feature extraction. Especially in surgical workflow analysis, where the lack of pretrained feature extractors has led to complex, multi-stage training pipelines, limited awareness of BN issues may have hidden the benefits of training CNNs and temporal models end to end. In this paper, we analyze pitfalls of BN in video learning, including issues specific to online tasks such as a 'cheating' effect in anticipation. We observe that BN's properties create major obstacles for end-to-end learning. However, using BN-free backbones, even simple CNN-LSTMs beat the state of the art {\color{\colorrevtwo}on three surgical workflow benchmarks} by utilizing adequate end-to-end training strategies which maximize temporal context. We conclude that awareness of BN's pitfalls is crucial for effective end-to-end learning in surgical tasks. By reproducing results on natural-video datasets, we hope our insights will benefit other areas of video learning as well. Code is available at: \url{//gitlab.com/nct_tso_public/pitfalls_bn}

The moving discontinuous Galerkin method with interface condition enforcement (MDG-ICE) is a high-order, r-adaptive method that treats the grid as a variable and weakly enforces the conservation law, constitutive law, and corresponding interface conditions in order to implicitly fit high-gradient flow features. In this paper, we develop an optimization solver based on the Levenberg-Marquardt algorithm that features an anisotropic, locally adaptive penalty method to enhance robustness and prevent cell degeneration in the computation of hypersonic, viscous flows. Specifically, we incorporate an anisotropic grid regularization based on the mesh-implied metric that inhibits grid motion in directions with small element length scales, an element shape regularization that inhibits nonlinear deformations of the high-order elements, and a penalty regularization that penalizes degenerate elements. Additionally, we introduce a procedure for locally scaling the regularization operators in an adaptive, elementwise manner in order to maintain grid validity. We apply the proposed MDG-ICE formulation to two- and three-dimensional test cases involving viscous shocks and/or boundary layers, including Mach 17.6 hypersonic viscous flow over a circular cylinder and Mach 5 hypersonic viscous flow over a sphere, which are very challenging test cases for conventional numerical schemes on simplicial grids. Even without artificial dissipation, the computed solutions are free from spurious oscillations and yield highly symmetric surface heat-flux profiles.

National Security Letters (NSLs) are similar to administrative subpoenas and can be issued directly by elements of the executive branch without requiring prior approval from a court or grand jury. Importantly, NSLs authorize the imposition of nondisclosure orders (aka "gag orders") on the receiving party. Controversy about potential abuses of this authority has driven a range of legal and policy discussions. To address these concerns, both the public sector and the private sector have sought to document the usage of NSLs in aggregated form. However, each data source is limited in scope, time, and kind. In this paper, we consolidate the available data around NSLs and answer two questions: (1) what can the public effectively learn from the reported data and does this information suffice to assess the NSL usage? (2) how accessible is this data collection? We show that longitudinal trends in the usage of NSLs can be observed. For instance, we find a significant increase in NSL requests for non-US persons and that the policy reforms to decrease the mandated nondisclosure period appear to be effective. The observed trends suggest that the current transparency mechanisms are viable safeguards against the excessive use of NSLs. However, aggregating and normalizing the data requires manual reviewing, parsing, and validating. We even find inconsistencies within and across official data sources. Overall, the laborious data collection process hinders external and internal auditing efforts and demonstrates the need for a unified and more usable dataset for NSLs.