The study of associations between an individual's age and imaging and non-imaging data is an active research area that attempts to aid understanding of the effects and patterns of aging. In this work we have conducted a supervoxel-wise association study between both volumetric and tissue density features in coronary computed tomography angiograms and the chronological age of a subject, to understand the localized changes in morphology and tissue density with age. To enable a supervoxel-wise study of volume and tissue density, we developed a novel method based on image segmentation, inter-subject image registration, and robust supervoxel-based correlation analysis, to achieve a statistical association study between the images and age. We evaluate the registration methodology in terms of the Dice coefficient for the heart chambers and myocardium, and the inverse consistency of the transformations, showing that the method works well in most cases with high overlap and inverse consistency. In a sex-stratified study conducted on a subset of $n=1388$ images from the SCAPIS study, the supervoxel-wise analysis was able to find localized associations with age outside of the commonly segmented and analyzed sub-regions, and several substantial differences between the sexes in the association of age and volume.
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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.
Understanding the global organization of complicated and high dimensional data is of primary interest for many branches of applied sciences. It is typically achieved by applying dimensionality reduction techniques mapping the considered data into lower dimensional space. This family of methods, while preserving local structures and features, often misses the global structure of the dataset. Clustering techniques are another class of methods operating on the data in the ambient space. They group together points that are similar according to a fixed similarity criteria, however unlike dimensionality reduction techniques, they do not provide information about the global organization of the data. Leveraging ideas from Topological Data Analysis, in this paper we provide an additional layer on the output of any clustering algorithm. Such data structure, ClusterGraph, provides information about the global layout of clusters, obtained from the considered clustering algorithm. Appropriate measures are provided to assess the quality and usefulness of the obtained representation. Subsequently the ClusterGraph, possibly with an appropriate structure--preserving simplification, can be visualized and used in synergy with state of the art exploratory data analysis techniques.
The unpredictability of random numbers is fundamental to both digital security and applications that fairly distribute resources. However, existing random number generators have limitations-the generation processes cannot be fully traced, audited, and certified to be unpredictable. The algorithmic steps used in pseudorandom number generators are auditable, but they cannot guarantee that their outputs were a priori unpredictable given knowledge of the initial seed. Device-independent quantum random number generators can ensure that the source of randomness was unknown beforehand, but the steps used to extract the randomness are vulnerable to tampering. Here, for the first time, we demonstrate a fully traceable random number generation protocol based on device-independent techniques. Our protocol extracts randomness from unpredictable non-local quantum correlations, and uses distributed intertwined hash chains to cryptographically trace and verify the extraction process. This protocol is at the heart of a public traceable and certifiable quantum randomness beacon that we have launched. Over the first 40 days of operation, we completed the protocol 7434 out of 7454 attempts -- a success rate of 99.7%. Each time the protocol succeeded, the beacon emitted a pulse of 512 bits of traceable randomness. The bits are certified to be uniform with error times actual success probability bounded by $2^{-64}$. The generation of certifiable and traceable randomness represents one of the first public services that operates with an entanglement-derived advantage over comparable classical approaches.
Sequential neural posterior estimation (SNPE) techniques have been recently proposed for dealing with simulation-based models with intractable likelihoods. Unlike approximate Bayesian computation, SNPE techniques learn the posterior from sequential simulation using neural network-based conditional density estimators by minimizing a specific loss function. The SNPE method proposed by Lueckmann et al. (2017) used a calibration kernel to boost the sample weights around the observed data, resulting in a concentrated loss function. However, the use of calibration kernels may increase the variances of both the empirical loss and its gradient, making the training inefficient. To improve the stability of SNPE, this paper proposes to use an adaptive calibration kernel and several variance reduction techniques. The proposed method greatly speeds up the process of training and provides a better approximation of the posterior than the original SNPE method and some existing competitors as confirmed by numerical experiments. We also manage to demonstrate the superiority of the proposed method for a high-dimensional model with real-world dataset.
Determining the difficulty of a text involves assessing various textual features that may impact the reader's text comprehension, yet current research in Vietnamese has only focused on statistical features. This paper introduces a new approach that integrates statistical and semantic approaches to assessing text readability. Our research utilized three distinct datasets: the Vietnamese Text Readability Dataset (ViRead), OneStopEnglish, and RACE, with the latter two translated into Vietnamese. Advanced semantic analysis methods were employed for the semantic aspect using state-of-the-art language models such as PhoBERT, ViDeBERTa, and ViBERT. In addition, statistical methods were incorporated to extract syntactic and lexical features of the text. We conducted experiments using various machine learning models, including Support Vector Machine (SVM), Random Forest, and Extra Trees and evaluated their performance using accuracy and F1 score metrics. Our results indicate that a joint approach that combines semantic and statistical features significantly enhances the accuracy of readability classification compared to using each method in isolation. The current study emphasizes the importance of considering both statistical and semantic aspects for a more accurate assessment of text difficulty in Vietnamese. This contribution to the field provides insights into the adaptability of advanced language models in the context of Vietnamese text readability. It lays the groundwork for future research in this area.
Statistical learning under distribution shift is challenging when neither prior knowledge nor fully accessible data from the target distribution is available. Distributionally robust learning (DRL) aims to control the worst-case statistical performance within an uncertainty set of candidate distributions, but how to properly specify the set remains challenging. To enable distributional robustness without being overly conservative, in this paper, we propose a shape-constrained approach to DRL, which incorporates prior information about the way in which the unknown target distribution differs from its estimate. More specifically, we assume the unknown density ratio between the target distribution and its estimate is isotonic with respect to some partial order. At the population level, we provide a solution to the shape-constrained optimization problem that does not involve the isotonic constraint. At the sample level, we provide consistency results for an empirical estimator of the target in a range of different settings. Empirical studies on both synthetic and real data examples demonstrate the improved accuracy of the proposed shape-constrained approach.
Hematoxylin and Eosin (H&E) staining of whole slide images (WSIs) is considered the gold standard for pathologists and medical practitioners for tumor diagnosis, surgical planning, and post-operative assessment. With the rapid advancement of deep learning technologies, the development of numerous models based on convolutional neural networks and transformer-based models has been applied to the precise segmentation of WSIs. However, due to privacy regulations and the need to protect patient confidentiality, centralized storage and processing of image data are impractical. Training a centralized model directly is challenging to implement in medical settings due to these privacy concerns.This paper addresses the dispersed nature and privacy sensitivity of medical image data by employing a federated learning framework, allowing medical institutions to collaboratively learn while protecting patient privacy. Additionally, to address the issue of original data reconstruction through gradient inversion during the federated learning training process, differential privacy introduces noise into the model updates, preventing attackers from inferring the contributions of individual samples, thereby protecting the privacy of the training data.Experimental results show that the proposed method, FedDP, minimally impacts model accuracy while effectively safeguarding the privacy of cancer pathology image data, with only a slight decrease in Dice, Jaccard, and Acc indices by 0.55%, 0.63%, and 0.42%, respectively. This approach facilitates cross-institutional collaboration and knowledge sharing while protecting sensitive data privacy, providing a viable solution for further research and application in the medical field.
In the present work, strong approximation errors are analyzed for both the spatial semi-discretization and the spatio-temporal fully discretization of stochastic wave equations (SWEs) with cubic polynomial nonlinearities and additive noises. The fully discretization is achieved by the standard Galerkin ffnite element method in space and a novel exponential time integrator combined with the averaged vector ffeld approach. The newly proposed scheme is proved to exactly satisfy a trace formula based on an energy functional. Recovering the convergence rates of the scheme, however, meets essential difffculties, due to the lack of the global monotonicity condition. To overcome this issue, we derive the exponential integrability property of the considered numerical approximations, by the energy functional. Armed with these properties, we obtain the strong convergence rates of the approximations in both spatial and temporal direction. Finally, numerical results are presented to verify the previously theoretical findings.
The gradient bounds of generalized barycentric coordinates play an essential role in the $H^1$ norm approximation error estimate of generalized barycentric interpolations. Similarly, the $H^k$ norm, $k>1$, estimate needs upper bounds of high-order derivatives, which are not available in the literature. In this paper, we derive such upper bounds for the Wachspress generalized barycentric coordinates on simple convex $d$-dimensional polytopes, $d\ge 1$. The result can be used to prove optimal convergence for Wachspress-based polytopal finite element approximation of, for example, fourth-order elliptic equations. Another contribution of this paper is to compare various shape-regularity conditions for simple convex polytopes, and to clarify their relations using knowledge from convex geometry.
Graph representation learning for hypergraphs can be used to extract patterns among higher-order interactions that are critically important in many real world problems. Current approaches designed for hypergraphs, however, are unable to handle different types of hypergraphs and are typically not generic for various learning tasks. Indeed, models that can predict variable-sized heterogeneous hyperedges have not been available. Here we develop a new self-attention based graph neural network called Hyper-SAGNN applicable to homogeneous and heterogeneous hypergraphs with variable hyperedge sizes. We perform extensive evaluations on multiple datasets, including four benchmark network datasets and two single-cell Hi-C datasets in genomics. We demonstrate that Hyper-SAGNN significantly outperforms the state-of-the-art methods on traditional tasks while also achieving great performance on a new task called outsider identification. Hyper-SAGNN will be useful for graph representation learning to uncover complex higher-order interactions in different applications.
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