量子计算有可能彻底改变和改变我们的生活和理解世界的方式。该审查旨在提供对量子计算的可访问介绍，重点是统计和数据分析中的应用。我们从介绍了了解量子计算所需的基本概念以及量子和经典计算之间的差异。我们描述了用作量子算法的构建块的核心量子子程序。然后，我们审查了一系列预期的量子算法，以便在统计和机器学习中提供计算优势。我们突出了将量子计算应用于统计问题的挑战和机遇，并讨论潜在的未来研究方向。

变异贝叶斯（VB）是机器学习和统计数据中的关键方法，是贝叶斯深度学习最近成功的基础。天然梯度是有效VB估计的重要组成部分，但在高维度上的计算量非常昂贵。我们提出了一种基于计算有效回归的自然梯度估计方法，并根据标准假设提供了收敛的保证。该方法使使用量子矩阵倒置可以进一步加速VB。我们证明问题设置满足了量子矩阵反转所需的条件以实现计算效率。该方法可与广泛的统计模型一起使用，不需要特殊用途或简化的变异分布。

Novel topological spin textures, such as magnetic skyrmions, benefit from their inherent stability, acting as the ground state in several magnetic systems. In the current study of atomic monolayer magnetic materials, reasonable initial guesses are still needed to search for those magnetic patterns. This situation underlines the need to develop a more effective way to identify the ground states. To solve this problem, in this work, we propose a genetic-tunneling-driven variance-controlled optimization approach, which combines a local energy minimizer back-end and a metaheuristic global searching front-end. This algorithm is an effective optimization solution for searching for magnetic ground states at extremely low temperatures and is also robust for finding low-energy degenerated states at finite temperatures. We demonstrate here the success of this method in searching for magnetic ground states of 2D monolayer systems with both artificial and calculated interactions from density functional theory. It is also worth noting that the inherent concurrent property of this algorithm can significantly decrease the execution time. In conclusion, our proposed method builds a useful tool for low-dimensional magnetic system energy optimization.

The release of ChatGPT, a language model capable of generating text that appears human-like and authentic, has gained significant attention beyond the research community. We expect that the convincing performance of ChatGPT incentivizes users to apply it to a variety of downstream tasks, including prompting the model to simplify their own medical reports. To investigate this phenomenon, we conducted an exploratory case study. In a questionnaire, we asked 15 radiologists to assess the quality of radiology reports simplified by ChatGPT. Most radiologists agreed that the simplified reports were factually correct, complete, and not potentially harmful to the patient. Nevertheless, instances of incorrect statements, missed key medical findings, and potentially harmful passages were reported. While further studies are needed, the initial insights of this study indicate a great potential in using large language models like ChatGPT to improve patient-centered care in radiology and other medical domains.

Efficient surrogate modelling is a key requirement for uncertainty quantification in data-driven scenarios. In this work, a novel approach of using Sparse Random Features for surrogate modelling in combination with self-supervised dimensionality reduction is described. The method is compared to other methods on synthetic and real data obtained from crashworthiness analyses. The results show a superiority of the here described approach over state of the art surrogate modelling techniques, Polynomial Chaos Expansions and Neural Networks.

Purpose: Tracking the 3D motion of the surgical tool and the patient anatomy is a fundamental requirement for computer-assisted skull-base surgery. The estimated motion can be used both for intra-operative guidance and for downstream skill analysis. Recovering such motion solely from surgical videos is desirable, as it is compliant with current clinical workflows and instrumentation. Methods: We present Tracker of Anatomy and Tool (TAToo). TAToo jointly tracks the rigid 3D motion of patient skull and surgical drill from stereo microscopic videos. TAToo estimates motion via an iterative optimization process in an end-to-end differentiable form. For robust tracking performance, TAToo adopts a probabilistic formulation and enforces geometric constraints on the object level. Results: We validate TAToo on both simulation data, where ground truth motion is available, as well as on anthropomorphic phantom data, where optical tracking provides a strong baseline. We report sub-millimeter and millimeter inter-frame tracking accuracy for skull and drill, respectively, with rotation errors below 1{\deg}. We further illustrate how TAToo may be used in a surgical navigation setting. Conclusion: We present TAToo, which simultaneously tracks the surgical tool and the patient anatomy in skull-base surgery. TAToo directly predicts the motion from surgical videos, without the need of any markers. Our results show that the performance of TAToo compares favorably to competing approaches. Future work will include fine-tuning of our depth network to reach a 1 mm clinical accuracy goal desired for surgical applications in the skull base.

Selecting the number of topics in LDA models is considered to be a difficult task, for which alternative approaches have been proposed. The performance of the recently developed singular Bayesian information criterion (sBIC) is evaluated and compared to the performance of alternative model selection criteria. The sBIC is a generalization of the standard BIC that can be implemented to singular statistical models. The comparison is based on Monte Carlo simulations and carried out for several alternative settings, varying with respect to the number of topics, the number of documents and the size of documents in the corpora. Performance is measured using different criteria which take into account the correct number of topics, but also whether the relevant topics from the DGPs are identified. Practical recommendations for LDA model selection in applications are derived.

Previous work has shown the potential of deep learning to predict renal obstruction using kidney ultrasound images. However, these image-based classifiers have been trained with the goal of single-visit inference in mind. We compare methods from video action recognition (i.e. convolutional pooling, LSTM, TSM) to adapt single-visit convolutional models to handle multiple visit inference. We demonstrate that incorporating images from a patient's past hospital visits provides only a small benefit for the prediction of obstructive hydronephrosis. Therefore, inclusion of prior ultrasounds is beneficial, but prediction based on the latest ultrasound is sufficient for patient risk stratification.

Prostate cancer is the most common cancer in men worldwide and the second leading cause of cancer death in the United States. One of the prognostic features in prostate cancer is the Gleason grading of histopathology images. The Gleason grade is assigned based on tumor architecture on Hematoxylin and Eosin (H&E) stained whole slide images (WSI) by the pathologists. This process is time-consuming and has known interobserver variability. In the past few years, deep learning algorithms have been used to analyze histopathology images, delivering promising results for grading prostate cancer. However, most of the algorithms rely on the fully annotated datasets which are expensive to generate. In this work, we proposed a novel weakly-supervised algorithm to classify prostate cancer grades. The proposed algorithm consists of three steps: (1) extracting discriminative areas in a histopathology image by employing the Multiple Instance Learning (MIL) algorithm based on Transformers, (2) representing the image by constructing a graph using the discriminative patches, and (3) classifying the image into its Gleason grades by developing a Graph Convolutional Neural Network (GCN) based on the gated attention mechanism. We evaluated our algorithm using publicly available datasets, including TCGAPRAD, PANDA, and Gleason 2019 challenge datasets. We also cross validated the algorithm on an independent dataset. Results show that the proposed model achieved state-of-the-art performance in the Gleason grading task in terms of accuracy, F1 score, and cohen-kappa. The code is available at https://github.com/NabaviLab/Prostate-Cancer.

Petrov-Galerkin formulations with optimal test functions allow for the stabilization of finite element simulations. In particular, given a discrete trial space, the optimal test space induces a numerical scheme delivering the best approximation in terms of a problem-dependent energy norm. This ideal approach has two shortcomings: first, we need to explicitly know the set of optimal test functions; and second, the optimal test functions may have large supports inducing expensive dense linear systems. Nevertheless, parametric families of PDEs are an example where it is worth investing some (offline) computational effort to obtain stabilized linear systems that can be solved efficiently, for a given set of parameters, in an online stage. Therefore, as a remedy for the first shortcoming, we explicitly compute (offline) a function mapping any PDE-parameter, to the matrix of coefficients of optimal test functions (in a basis expansion) associated with that PDE-parameter. Next, as a remedy for the second shortcoming, we use the low-rank approximation to hierarchically compress the (non-square) matrix of coefficients of optimal test functions. In order to accelerate this process, we train a neural network to learn a critical bottleneck of the compression algorithm (for a given set of PDE-parameters). When solving online the resulting (compressed) Petrov-Galerkin formulation, we employ a GMRES iterative solver with inexpensive matrix-vector multiplications thanks to the low-rank features of the compressed matrix. We perform experiments showing that the full online procedure as fast as the original (unstable) Galerkin approach. In other words, we get the stabilization with hierarchical matrices and neural networks practically for free. We illustrate our findings by means of 2D Eriksson-Johnson and Hemholtz model problems.