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Topic detection is a complex process and depends on language because it somehow needs to analyze text. There have been few studies on topic detection in Persian, and the existing algorithms are not remarkable. Therefore, we aimed to study topic detection in Persian. The objectives of this study are: 1) to conduct an extensive study on the best algorithms for topic detection, 2) to identify necessary adaptations to make these algorithms suitable for the Persian language, and 3) to evaluate their performance on Persian social network texts. To achieve these objectives, we have formulated two research questions: First, considering the lack of research in Persian, what modifications should be made to existing frameworks, especially those developed in English, to make them compatible with Persian? Second, how do these algorithms perform, and which one is superior? There are various topic detection methods that can be categorized into different categories. Frequent pattern and clustering are selected for this research, and a hybrid of both is proposed as a new category. Then, ten methods from these three categories are selected. All of them are re-implemented from scratch, changed, and adapted with Persian. These ten methods encompass different types of topic detection methods and have shown good performance in English. The text of Persian social network posts is used as the dataset. Additionally, a new multiclass evaluation criterion, called FS, is used in this paper for the first time in the field of topic detection. Approximately 1.4 billion tokens are processed during experiments. The results indicate that if we are searching for keyword-topics that are easily understandable by humans, the hybrid category is better. However, if the aim is to cluster posts for further analysis, the frequent pattern category is more suitable.

This work presents an abstract framework for the design, implementation, and analysis of the multiscale spectral generalized finite element method (MS-GFEM), a particular numerical multiscale method originally proposed in [I. Babuska and R. Lipton, Multiscale Model.\;\,Simul., 9 (2011), pp.~373--406]. MS-GFEM is a partition of unity method employing optimal local approximation spaces constructed from local spectral problems. We establish a general local approximation theory demonstrating exponential convergence with respect to local degrees of freedom under certain assumptions, with explicit dependence on key problem parameters. Our framework applies to a broad class of multiscale PDEs with $L^{\infty}$-coefficients in both continuous and discrete, finite element settings, including highly indefinite problems (convection-dominated diffusion, as well as the high-frequency Helmholtz, Maxwell and elastic wave equations with impedance boundary conditions), and higher-order problems. Notably, we prove a local convergence rate of $O(e^{-cn^{1/d}})$ for MS-GFEM for all these problems, improving upon the $O(e^{-cn^{1/(d+1)}})$ rate shown by Babuska and Lipton. Moreover, based on the abstract local approximation theory for MS-GFEM, we establish a unified framework for showing low-rank approximations to multiscale PDEs. This framework applies to the aforementioned problems, proving that the associated Green's functions admit an $O(|\log\epsilon|^{d})$-term separable approximation on well-separated domains with error $\epsilon>0$. Our analysis improves and generalizes the result in [M. Bebendorf and W. Hackbusch, Numerische Mathematik, 95 (2003), pp.~1-28] where an $O(|\log\epsilon|^{d+1})$-term separable approximation was proved for Poisson-type problems.

The impact of using artificial intelligence (AI) to guide patient care or operational processes is an interplay of the AI model's output, the decision-making protocol based on that output, and the capacity of the stakeholders involved to take the necessary subsequent action. Estimating the effects of this interplay before deployment, and studying it in real time afterwards, are essential to bridge the chasm between AI model development and achievable benefit. To accomplish this, the Data Science team at Stanford Health Care has developed a Testing and Evaluation (T&E) mechanism to identify fair, useful and reliable AI models (FURM) by conducting an ethical review to identify potential value mismatches, simulations to estimate usefulness, financial projections to assess sustainability, as well as analyses to determine IT feasibility, design a deployment strategy, and recommend a prospective monitoring and evaluation plan. We report on FURM assessments done to evaluate six AI guided solutions for potential adoption, spanning clinical and operational settings, each with the potential to impact from several dozen to tens of thousands of patients each year. We describe the assessment process, summarize the six assessments, and share our framework to enable others to conduct similar assessments. Of the six solutions we assessed, two have moved into a planning and implementation phase. Our novel contributions - usefulness estimates by simulation, financial projections to quantify sustainability, and a process to do ethical assessments - as well as their underlying methods and open source tools, are available for other healthcare systems to conduct actionable evaluations of candidate AI solutions.

There is general agreement that some form of regulation is necessary both for AI creators to be incentivised to develop trustworthy systems, and for users to actually trust those systems. But there is much debate about what form these regulations should take and how they should be implemented. Most work in this area has been qualitative, and has not been able to make formal predictions. Here, we propose that evolutionary game theory can be used to quantitatively model the dilemmas faced by users, AI creators, and regulators, and provide insights into the possible effects of different regulatory regimes. We show that creating trustworthy AI and user trust requires regulators to be incentivised to regulate effectively. We demonstrate the effectiveness of two mechanisms that can achieve this. The first is where governments can recognise and reward regulators that do a good job. In that case, if the AI system is not too risky for users then some level of trustworthy development and user trust evolves. We then consider an alternative solution, where users can condition their trust decision on the effectiveness of the regulators. This leads to effective regulation, and consequently the development of trustworthy AI and user trust, provided that the cost of implementing regulations is not too high. Our findings highlight the importance of considering the effect of different regulatory regimes from an evolutionary game theoretic perspective.

We study general coordinate-wise MCMC schemes (such as Metropolis-within-Gibbs samplers), which are commonly used to fit Bayesian non-conjugate hierarchical models. We relate their convergence properties to the ones of the corresponding (potentially not implementable) Gibbs sampler through the notion of conditional conductance. This allows us to study the performances of popular Metropolis-within-Gibbs schemes for non-conjugate hierarchical models, in high-dimensional regimes where both number of datapoints and parameters increase. Given random data-generating assumptions, we establish dimension-free convergence results, which are in close accordance with numerical evidences. Applications to Bayesian models for binary regression with unknown hyperparameters and discretely observed diffusions are also discussed. Motivated by such statistical applications, auxiliary results of independent interest on approximate conductances and perturbation of Markov operators are provided.

Segmentation of brain structures on MRI is the primary step for further quantitative analysis of brain diseases. Manual segmentation is still considered the gold standard in terms of accuracy; however, such data is extremely time-consuming to generate. This paper presents a deep learning-based segmentation approach for 12 deep-brain structures, utilizing multiple region-based U-Nets. The brain is divided into three focal regions of interest that encompass the brainstem, the ventricular system, and the striatum. Next, three region-based U-nets are run in parallel to parcellate these larger structures into their respective four substructures. This approach not only greatly reduces the training and processing times but also significantly enhances the segmentation accuracy, compared to segmenting the entire MRI image at once. Our approach achieves remarkable accuracy with an average Dice Similarity Coefficient (DSC) of 0.901 and 95% Hausdorff Distance (HD95) of 1.155 mm. The method was compared with state-of-the-art segmentation approaches, demonstrating a high level of accuracy and robustness of the proposed method.

With an aim to analyse the performance of Markov chain Monte Carlo (MCMC) methods, in our recent work we derive a large deviation principle (LDP) for the empirical measures of Metropolis-Hastings (MH) chains on a continuous state space. One of the (sufficient) assumptions for the LDP involves the existence of a particular type of Lyapunov function, and it was left as an open question whether or not such a function exists for specific choices of MH samplers. In this paper we analyse the properties of such Lyapunov functions and investigate their existence for some of the most popular choices of MCMC samplers built on MH dynamics: Independent Metropolis Hastings, Random Walk Metropolis, and the Metropolis-adjusted Langevin algorithm. We establish under what conditions such a Lyapunov function exists, and from this obtain LDPs for some instances of the MCMC algorithms under consideration. To the best of our knowledge, these are the first large deviation results for empirical measures associated with Metropolis-Hastings chains for specific choices of proposal and target distributions.

We propose an implicit Discontinuous Galerkin (DG) discretization for incompressible two-phase flows using an artificial compressibility formulation. The conservative level set (CLS) method is employed in combination with a reinitialization procedure to capture the moving interface. A projection method based on the L-stable TR-BDF2 method is adopted for the time discretization of the Navier-Stokes equations and of the level set method. Adaptive Mesh Refinement (AMR) is employed to enhance the resolution in correspondence of the interface between the two fluids. The effectiveness of the proposed approach is shown in a number of classical benchmarks. A specific analysis on the influence of different choices of the mixture viscosity is also carried out.

We propose an operator learning approach to accelerate geometric Markov chain Monte Carlo (MCMC) for solving infinite-dimensional nonlinear Bayesian inverse problems. While geometric MCMC employs high-quality proposals that adapt to posterior local geometry, it requires computing local gradient and Hessian information of the log-likelihood, incurring a high cost when the parameter-to-observable (PtO) map is defined through expensive model simulations. We consider a delayed-acceptance geometric MCMC method driven by a neural operator surrogate of the PtO map, where the proposal is designed to exploit fast surrogate approximations of the log-likelihood and, simultaneously, its gradient and Hessian. To achieve a substantial speedup, the surrogate needs to be accurate in predicting both the observable and its parametric derivative (the derivative of the observable with respect to the parameter). Training such a surrogate via conventional operator learning using input--output samples often demands a prohibitively large number of model simulations. In this work, we present an extension of derivative-informed operator learning [O'Leary-Roseberry et al., J. Comput. Phys., 496 (2024)] using input--output--derivative training samples. Such a learning method leads to derivative-informed neural operator (DINO) surrogates that accurately predict the observable and its parametric derivative at a significantly lower training cost than the conventional method. Cost and error analysis for reduced basis DINO surrogates are provided. Numerical studies on PDE-constrained Bayesian inversion demonstrate that DINO-driven MCMC generates effective posterior samples 3--9 times faster than geometric MCMC and 60--97 times faster than prior geometry-based MCMC. Furthermore, the training cost of DINO surrogates breaks even after collecting merely 10--25 effective posterior samples compared to geometric MCMC.

Recent advances in 3D fully convolutional networks (FCN) have made it feasible to produce dense voxel-wise predictions of volumetric images. In this work, we show that a multi-class 3D FCN trained on manually labeled CT scans of several anatomical structures (ranging from the large organs to thin vessels) can achieve competitive segmentation results, while avoiding the need for handcrafting features or training class-specific models. To this end, we propose a two-stage, coarse-to-fine approach that will first use a 3D FCN to roughly define a candidate region, which will then be used as input to a second 3D FCN. This reduces the number of voxels the second FCN has to classify to ~10% and allows it to focus on more detailed segmentation of the organs and vessels. We utilize training and validation sets consisting of 331 clinical CT images and test our models on a completely unseen data collection acquired at a different hospital that includes 150 CT scans, targeting three anatomical organs (liver, spleen, and pancreas). In challenging organs such as the pancreas, our cascaded approach improves the mean Dice score from 68.5 to 82.2%, achieving the highest reported average score on this dataset. We compare with a 2D FCN method on a separate dataset of 240 CT scans with 18 classes and achieve a significantly higher performance in small organs and vessels. Furthermore, we explore fine-tuning our models to different datasets. Our experiments illustrate the promise and robustness of current 3D FCN based semantic segmentation of medical images, achieving state-of-the-art results. Our code and trained models are available for download: //github.com/holgerroth/3Dunet_abdomen_cascade.