Computer-assisted systems are becoming broadly used in medicine. In endoscopy, most research focuses on the automatic detection of polyps or other pathologies, but localization and navigation of the endoscope are completely performed manually by physicians. To broaden this research and bring spatial Artificial Intelligence to endoscopies, data from complete procedures is needed. This paper introduces the Endomapper dataset, the first collection of complete endoscopy sequences acquired during regular medical practice, making secondary use of medical data. Its main purpose is to facilitate the development and evaluation of Visual Simultaneous Localization and Mapping (VSLAM) methods in real endoscopy data. The dataset contains more than 24 hours of video. It is the first endoscopic dataset that includes endoscope calibration as well as the original calibration videos. Meta-data and annotations associated with the dataset vary from the anatomical landmarks, procedure labeling, segmentations, reconstructions, simulated sequences with ground truth and same patient procedures. The software used in this paper is publicly available.
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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.
When modeling scientific and industrial problems, geometries are typically modeled by explicit boundary representations obtained from computer-aided design software. Unfitted (also known as embedded or immersed) finite element methods offer a significant advantage in dealing with complex geometries, eliminating the need for generating unstructured body-fitted meshes. However, current unfitted finite elements on nonlinear geometries are restricted to implicit (possibly high-order) level set geometries. In this work, we introduce a novel automatic computational pipeline to approximate solutions of partial differential equations on domains defined by explicit nonlinear boundary representations. For the geometrical discretization, we propose a novel algorithm to generate quadratures for the bulk and surface integration on nonlinear polytopes required to compute all the terms in unfitted finite element methods. The algorithm relies on a nonlinear triangulation of the boundary, a kd-tree refinement of the surface cells that simplify the nonlinear intersections of surface and background cells to simple cases that are diffeomorphically equivalent to linear intersections, robust polynomial root-finding algorithms and surface parameterization techniques. We prove the correctness of the proposed algorithm. We have successfully applied this algorithm to simulate partial differential equations with unfitted finite elements on nonlinear domains described by computer-aided design models, demonstrating the robustness of the geometric algorithm and showing high-order accuracy of the overall method.
Measures of association between cortical regions based on activity signals provide useful information for studying brain functional connectivity. Difficulties occur with signals of electric neuronal activity, where an observed signal is a mixture, i.e. an instantaneous weighted average of the true, unobserved signals from all regions, due to volume conduction and low spatial resolution. This is why measures of lagged association are of interest, since at least theoretically, "lagged association" is of physiological origin. In contrast, the actual physiological instantaneous zero-lag association is masked and confounded by the mixing artifact. A minimum requirement for a measure of lagged association is that it must not tend to zero with an increase of strength of true instantaneous physiological association. Such biased measures cannot tell apart if a change in its value is due to a change in lagged or a change in instantaneous association. An explicit testable definition for frequency domain lagged connectivity between two multivariate time series is proposed. It is endowed with two important properties: it is invariant to non-singular linear transformations of each vector time series separately, and it is invariant to instantaneous association. As a sanity check, in the case of two univariate time series, the new definition leads back to the bivariate lagged coherence of 2007 (eqs 25 and 26 in //doi.org/10.48550/arXiv.0706.1776).
Common regularization algorithms for linear regression, such as LASSO and Ridge regression, rely on a regularization hyperparameter that balances the tradeoff between minimizing the fitting error and the norm of the learned model coefficients. As this hyperparameter is scalar, it can be easily selected via random or grid search optimizing a cross-validation criterion. However, using a scalar hyperparameter limits the algorithm's flexibility and potential for better generalization. In this paper, we address the problem of linear regression with l2-regularization, where a different regularization hyperparameter is associated with each input variable. We optimize these hyperparameters using a gradient-based approach, wherein the gradient of a cross-validation criterion with respect to the regularization hyperparameters is computed analytically through matrix differential calculus. Additionally, we introduce two strategies tailored for sparse model learning problems aiming at reducing the risk of overfitting to the validation data. Numerical examples demonstrate that our multi-hyperparameter regularization approach outperforms LASSO, Ridge, and Elastic Net regression. Moreover, the analytical computation of the gradient proves to be more efficient in terms of computational time compared to automatic differentiation, especially when handling a large number of input variables. Application to the identification of over-parameterized Linear Parameter-Varying models is also presented.
Despite much attention, the comparison of reduced-dimension representations of high-dimensional data remains a challenging problem in multiple fields, especially when representations remain high-dimensional compared to sample size. We offer a framework for evaluating the topological similarity of high-dimensional representations of very high-dimensional data, a regime where topological structure is more likely captured in the distribution of topological "noise" than a few prominent generators. Treating each representational map as a metric embedding, we compute the Vietoris-Rips persistence of its image. We then use the topological bootstrap to analyze the re-sampling stability of each representation, assigning a "prevalence score" for each nontrivial basis element of its persistence module. Finally, we compare the persistent homology of representations using a prevalence-weighted variant of the Wasserstein distance. Notably, our method is able to compare representations derived from different samples of the same distribution and, in particular, is not restricted to comparisons of graphs on the same vertex set. In addition, representations need not lie in the same metric space. We apply this analysis to a cross-sectional sample of representations of functional neuroimaging data in a large cohort and hierarchically cluster under the prevalence-weighted Wasserstein. We find that the ambient dimension of a representation is a stronger predictor of the number and stability of topological features than its decomposition rank. Our findings suggest that important topological information lies in repeatable, low-persistence homology generators, whose distributions capture important and interpretable differences between high-dimensional data representations.
Improving the resolution of fluorescence microscopy beyond the diffraction limit can be achievedby acquiring and processing multiple images of the sample under different illumination conditions.One of the simplest techniques, Random Illumination Microscopy (RIM), forms the super-resolvedimage from the variance of images obtained with random speckled illuminations. However, thevalidity of this process has not been fully theorized. In this work, we characterize mathematicallythe sample information contained in the variance of diffraction-limited speckled images as a functionof the statistical properties of the illuminations. We show that an unambiguous two-fold resolutiongain is obtained when the speckle correlation length coincides with the width of the observationpoint spread function. Last, we analyze the difference between the variance-based techniques usingrandom speckled illuminations (as in RIM) and those obtained using random fluorophore activation(as in Super-resolution Optical Fluctuation Imaging, SOFI).
End-to-end relation extraction (E2ERE) is an important and realistic application of natural language processing (NLP) in biomedicine. In this paper, we aim to compare three prevailing paradigms for E2ERE using a complex dataset focused on rare diseases involving discontinuous and nested entities. We use the RareDis information extraction dataset to evaluate three competing approaches (for E2ERE): NER $\rightarrow$ RE pipelines, joint sequence to sequence models, and generative pre-trained transformer (GPT) models. We use comparable state-of-the-art models and best practices for each of these approaches and conduct error analyses to assess their failure modes. Our findings reveal that pipeline models are still the best, while sequence-to-sequence models are not far behind; GPT models with eight times as many parameters are worse than even sequence-to-sequence models and lose to pipeline models by over 10 F1 points. Partial matches and discontinuous entities caused many NER errors contributing to lower overall E2E performances. We also verify these findings on a second E2ERE dataset for chemical-protein interactions. Although generative LM-based methods are more suitable for zero-shot settings, when training data is available, our results show that it is better to work with more conventional models trained and tailored for E2ERE. More innovative methods are needed to marry the best of the both worlds from smaller encoder-decoder pipeline models and the larger GPT models to improve E2ERE. As of now, we see that well designed pipeline models offer substantial performance gains at a lower cost and carbon footprint for E2ERE. Our contribution is also the first to conduct E2ERE for the RareDis dataset.
We consider the task of estimating functions belonging to a specific class of nonsmooth functions, namely so-called tame functions. These functions appear in a wide range of applications: training deep learning, value functions of mixed-integer programs, or wave functions of small molecules. We show that tame functions are approximable by piecewise polynomials on any full-dimensional cube. We then present the first ever mixed-integer programming formulation of piecewise polynomial regression. Together, these can be used to estimate tame functions. We demonstrate promising computational results.
The simulation of geological facies in an unobservable volume is essential in various geoscience applications. Given the complexity of the problem, deep generative learning is a promising approach to overcome the limitations of traditional geostatistical simulation models, in particular their lack of physical realism. This research aims to investigate the application of generative adversarial networks and deep variational inference for conditionally simulating meandering channels in underground volumes. In this paper, we review the generative deep learning approaches, in particular the adversarial ones and the stabilization techniques that aim to facilitate their training. The proposed approach is tested on 2D and 3D simulations generated by the stochastic process-based model Flumy. Morphological metrics are utilized to compare our proposed method with earlier iterations of generative adversarial networks. The results indicate that by utilizing recent stabilization techniques, generative adversarial networks can efficiently sample from target data distributions. Moreover, we demonstrate the ability to simulate conditioned simulations through the latent variable model property of the proposed approach.
This article proposes a highly accurate and conservative method for hyperbolic systems using the finite volume approach. This innovative scheme constructs the intermediate states at the interfaces of the control volumes using the method of characteristics. The approach is simple to implement, generates entropic solutions, and avoids solving Riemann problems. A diffusion control parameter is introduced to increase the accuracy of the scheme. Numerical examples are presented for the Euler equation for an ideal gas. The results demonstrate the method's ability to capture contact discontinuity and shock wave profiles with high accuracy and low cost as well as its robustness.
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