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A new approach to analyzing intrinsic properties of the Josephus function, $J_{_k}$, is presented in this paper. The linear structure between extreme points of $J_{_k}$ is fully revealed, leading to the design of an efficient algorithm for evaluating $J_{_k}(n)$. Algebraic expressions that describe how recursively compute extreme points, including fixed points, are derived. The existence of consecutive extreme and also fixed points for all $k\geq 2$ is proven as a consequence, which generalizes Knuth result for $k=2$. Moreover, an extensive comparative numerical experiment is conducted to illustrate the performance of the proposed algorithm for evaluating the Josephus function compared to established algorithms. The results show that the proposed scheme is highly effective in computing $J_{_k}(n)$ for large inputs.

Although deep learning models for abnormality classification can perform well in screening mammography, the demographic, imaging, and clinical characteristics associated with increased risk of model failure remain unclear. This retrospective study uses the Emory BrEast Imaging Dataset(EMBED) containing mammograms from 115931 patients imaged at Emory Healthcare between 2013-2020, with BI-RADS assessment, region of interest coordinates for abnormalities, imaging features, pathologic outcomes, and patient demographics. Multiple deep learning models were trained to distinguish between abnormal tissue patches and randomly selected normal tissue patches from screening mammograms. We assessed model performance by subgroups defined by age, race, pathologic outcome, tissue density, and imaging characteristics and investigated their associations with false negatives (FN) and false positives (FP). We also performed multivariate logistic regression to control for confounding between subgroups. The top-performing model, ResNet152V2, achieved accuracy of 92.6%(95%CI=92.0-93.2%), and AUC 0.975(95%CI=0.972-0.978). Before controlling for confounding, nearly all subgroups showed statistically significant differences in model performance. However, after controlling for confounding, we found lower FN risk associates with Other race(RR=0.828;p=.050), biopsy-proven benign lesions(RR=0.927;p=.011), and mass(RR=0.921;p=.010) or asymmetry(RR=0.854;p=.040); higher FN risk associates with architectural distortion (RR=1.037;p<.001). Higher FP risk associates to BI-RADS density C(RR=1.891;p<.001) and D(RR=2.486;p<.001). Our results demonstrate subgroup analysis is important in mammogram classifier performance evaluation, and controlling for confounding between subgroups elucidates the true associations between variables and model failure. These results can help guide developing future breast cancer detection models.

We develop a probabilistic graphical model (PGM) for artificially intelligent (AI) agents to infer human beliefs during a simulated urban search and rescue (USAR) scenario executed in a Minecraft environment with a team of three players. The PGM approach makes observable states and actions explicit, as well as beliefs and intentions grounded by evidence about what players see and do over time. This approach also supports inferring the effect of interventions, which are vital if AI agents are to assist human teams. The experiment incorporates manipulations of players' knowledge, and the virtual Minecraft-based testbed provides access to several streams of information, including the objects in the players' field of view. The participants are equipped with a set of marker blocks that can be placed near room entrances to signal the presence or absence of victims in the rooms to their teammates. In each team, one of the members is given a different legend for the markers than the other two, which may mislead them about the state of the rooms; that is, they will hold a false belief. We extend previous works in this field by introducing ToMCAT, an AI agent that can reason about individual and shared mental states. We find that the players' behaviors are affected by what they see in their in-game field of view, their beliefs about the meaning of the markers, and their beliefs about which meaning the team decided to adopt. In addition, we show that ToMCAT's beliefs are consistent with the players' actions and that it can infer false beliefs with accuracy significantly better than chance and comparable to inferences made by human observers.

Gibbs posteriors are proportional to a prior distribution multiplied by an exponentiated loss function, with a key tuning parameter weighting information in the loss relative to the prior and providing a control of posterior uncertainty. Gibbs posteriors provide a principled framework for likelihood-free Bayesian inference, but in many situations, including a single tuning parameter inevitably leads to poor uncertainty quantification. In particular, regardless of the value of the parameter, credible regions have far from the nominal frequentist coverage even in large samples. We propose a sequential extension to Gibbs posteriors to address this problem. We prove the proposed sequential posterior exhibits concentration and a Bernstein-von Mises theorem, which holds under easy to verify conditions in Euclidean space and on manifolds. As a byproduct, we obtain the first Bernstein-von Mises theorem for traditional likelihood-based Bayesian posteriors on manifolds. All methods are illustrated with an application to principal component analysis.

Pretrained language models are expected to effectively map input text to a set of vectors while preserving the inherent relationships within the text. Consequently, designing a white-box model to compute metrics that reflect the presence of specific internal relations in these vectors has become a common approach for post-hoc interpretability analysis of pretrained language models. However, achieving interpretability in white-box models and ensuring the rigor of metric computation becomes challenging when the source model lacks inherent interpretability. Therefore, in this paper, we discuss striking a balance in this trade-off and propose a novel line to constructing metrics for understanding the mechanisms of pretrained language models. We have specifically designed a family of metrics along this line of investigation, and the model used to compute these metrics is referred to as the tree topological probe. We conducted measurements on BERT-large by using these metrics. Based on the experimental results, we propose a speculation regarding the working mechanism of BERT-like pretrained language models, as well as a strategy for enhancing fine-tuning performance by leveraging the topological probe to improve specific submodules.

Recent advances in whole-slide image (WSI) scanners and computational capabilities have significantly propelled the application of artificial intelligence in histopathology slide analysis. While these strides are promising, current supervised learning approaches for WSI analysis come with the challenge of exhaustively labeling high-resolution slides - a process that is both labor-intensive and time-consuming. In contrast, self-supervised learning (SSL) pretraining strategies are emerging as a viable alternative, given that they don't rely on explicit data annotations. These SSL strategies are quickly bridging the performance disparity with their supervised counterparts. In this context, we introduce an SSL framework. This framework aims for transferable representation learning and semantically meaningful clustering by synergizing invariance loss and clustering loss in WSI analysis. Notably, our approach outperforms common SSL methods in downstream classification and clustering tasks, as evidenced by tests on the Camelyon16 and a pancreatic cancer dataset. The code and additional details are accessible at: //github.com/wwyi1828/CluSiam.

Explainable recommender systems (RS) have traditionally followed a one-size-fits-all approach, delivering the same explanation level of detail to each user, without considering their individual needs and goals. Further, explanations in RS have so far been presented mostly in a static and non-interactive manner. To fill these research gaps, we aim in this paper to adopt a user-centered, interactive explanation model that provides explanations with different levels of detail and empowers users to interact with, control, and personalize the explanations based on their needs and preferences. We followed a user-centered approach to design interactive explanations with three levels of detail (basic, intermediate, and advanced) and implemented them in the transparent Recommendation and Interest Modeling Application (RIMA). We conducted a qualitative user study (N=14) to investigate the impact of providing interactive explanations with varying level of details on the users' perception of the explainable RS. Our study showed qualitative evidence that fostering interaction and giving users control in deciding which explanation they would like to see can meet the demands of users with different needs, preferences, and goals, and consequently can have positive effects on different crucial aspects in explainable recommendation, including transparency, trust, satisfaction, and user experience.

Trendy suggestions for learning-based elastic warps enable the deep image stitchings to align images exposed to large parallax errors. Despite the remarkable alignments, the methods struggle with occasional holes or discontinuity between overlapping and non-overlapping regions of a target image as the applied training strategy mostly focuses on overlap region alignment. As a result, they require additional modules such as seam finder and image inpainting for hiding discontinuity and filling holes, respectively. In this work, we suggest Recurrent Elastic Warps (REwarp) that address the problem with Dirichlet boundary condition and boost performances by residual learning for recurrent misalign correction. Specifically, REwarp predicts a homography and a Thin-plate Spline (TPS) under the boundary constraint for discontinuity and hole-free image stitching. Our experiments show the favorable aligns and the competitive computational costs of REwarp compared to the existing stitching methods. Our source code is available at //github.com/minshu-kim/REwarp.

Named entity recognition (NER) is the task to identify text spans that mention named entities, and to classify them into predefined categories such as person, location, organization etc. NER serves as the basis for a variety of natural language applications such as question answering, text summarization, and machine translation. Although early NER systems are successful in producing decent recognition accuracy, they often require much human effort in carefully designing rules or features. In recent years, deep learning, empowered by continuous real-valued vector representations and semantic composition through nonlinear processing, has been employed in NER systems, yielding stat-of-the-art performance. In this paper, we provide a comprehensive review on existing deep learning techniques for NER. We first introduce NER resources, including tagged NER corpora and off-the-shelf NER tools. Then, we systematically categorize existing works based on a taxonomy along three axes: distributed representations for input, context encoder, and tag decoder. Next, we survey the most representative methods for recent applied techniques of deep learning in new NER problem settings and applications. Finally, we present readers with the challenges faced by NER systems and outline future directions in this area.

Image segmentation is an important component of many image understanding systems. It aims to group pixels in a spatially and perceptually coherent manner. Typically, these algorithms have a collection of parameters that control the degree of over-segmentation produced. It still remains a challenge to properly select such parameters for human-like perceptual grouping. In this work, we exploit the diversity of segments produced by different choices of parameters. We scan the segmentation parameter space and generate a collection of image segmentation hypotheses (from highly over-segmented to under-segmented). These are fed into a cost minimization framework that produces the final segmentation by selecting segments that: (1) better describe the natural contours of the image, and (2) are more stable and persistent among all the segmentation hypotheses. We compare our algorithm's performance with state-of-the-art algorithms, showing that we can achieve improved results. We also show that our framework is robust to the choice of segmentation kernel that produces the initial set of hypotheses.