亚洲男人的天堂2018av,欧美草比,久久久久久免费视频精选,国色天香在线看免费,久久久久亚洲av成人片仓井空

Causal representation learning algorithms discover lower-dimensional representations of data that admit a decipherable interpretation of cause and effect; as achieving such interpretable representations is challenging, many causal learning algorithms utilize elements indicating prior information, such as (linear) structural causal models, interventional data, or weak supervision. Unfortunately, in exploratory causal representation learning, such elements and prior information may not be available or warranted. Alternatively, scientific datasets often have multiple modalities or physics-based constraints, and the use of such scientific, multimodal data has been shown to improve disentanglement in fully unsupervised settings. Consequently, we introduce a causal representation learning algorithm (causalPIMA) that can use multimodal data and known physics to discover important features with causal relationships. Our innovative algorithm utilizes a new differentiable parametrization to learn a directed acyclic graph (DAG) together with a latent space of a variational autoencoder in an end-to-end differentiable framework via a single, tractable evidence lower bound loss function. We place a Gaussian mixture prior on the latent space and identify each of the mixtures with an outcome of the DAG nodes; this novel identification enables feature discovery with causal relationships. Tested against a synthetic and a scientific dataset, our results demonstrate the capability of learning an interpretable causal structure while simultaneously discovering key features in a fully unsupervised setting.

The accessibility of spatially distributed data, enabled by affordable sensors, field, and numerical experiments, has facilitated the development of data-driven solutions for scientific problems, including climate change, weather prediction, and urban planning. Neural Partial Differential Equations (Neural PDEs), which combine deep learning (DL) techniques with domain expertise (e.g., governing equations) for parameterization, have proven to be effective in capturing valuable correlations within spatiotemporal datasets. However, sparse and noisy measurements coupled with modeling approximation introduce aleatoric and epistemic uncertainties. Therefore, quantifying uncertainties propagated from model inputs to outputs remains a challenge and an essential goal for establishing the trustworthiness of Neural PDEs. This work evaluates various Uncertainty Quantification (UQ) approaches for both Forward and Inverse Problems in scientific applications. Specifically, we investigate the effectiveness of Bayesian methods, such as Hamiltonian Monte Carlo (HMC) and Monte-Carlo Dropout (MCD), and a more conventional approach, Deep Ensembles (DE). To illustrate their performance, we take two canonical PDEs: Burger's equation and the Navier-Stokes equation. Our results indicate that Neural PDEs can effectively reconstruct flow systems and predict the associated unknown parameters. However, it is noteworthy that the results derived from Bayesian methods, based on our observations, tend to display a higher degree of certainty in their predictions as compared to those obtained using the DE. This elevated certainty in predictions suggests that Bayesian techniques might underestimate the true underlying uncertainty, thereby appearing more confident in their predictions than the DE approach.

We combine Kronecker products, and quantitative information flow, to give a novel formal analysis for the fine-grained verification of utility in complex privacy pipelines. The combination explains a surprising anomaly in the behaviour of utility of privacy-preserving pipelines -- that sometimes a reduction in privacy results also in a decrease in utility. We use the standard measure of utility for Bayesian analysis, introduced by Ghosh at al., to produce tractable and rigorous proofs of the fine-grained statistical behaviour leading to the anomaly. More generally, we offer the prospect of formal-analysis tools for utility that complement extant formal analyses of privacy. We demonstrate our results on a number of common privacy-preserving designs.

Modern high-throughput sequencing assays efficiently capture not only gene expression and different levels of gene regulation but also a multitude of genome variants. Focused analysis of alternative alleles of variable sites at homologous chromosomes of the human genome reveals allele-specific gene expression and allele-specific gene regulation by assessing allelic imbalance of read counts at individual sites. Here we formally describe an advanced statistical framework for detecting the allelic imbalance in allelic read counts at single-nucleotide variants detected in diverse omics studies (ChIP-Seq, ATAC-Seq, DNase-Seq, CAGE-Seq, and others). MIXALIME accounts for copy-number variants and aneuploidy, reference read mapping bias, and provides several scoring models to balance between sensitivity and specificity when scoring data with varying levels of experimental noise-caused overdispersion.

While model architectures and training strategies have become more generic and flexible with respect to different data modalities over the past years, a persistent limitation lies in the assumption of fixed quantities and arrangements of input features. This limitation becomes particularly relevant in scenarios where the attributes captured during data acquisition vary across different samples. In this work, we aim at effectively leveraging data with varying features, without the need to constrain the input space to the intersection of potential feature sets or to expand it to their union. We propose a novel architecture that can directly process data without the necessity of aligned feature modalities by learning a general embedding space that captures the relationship between features across data samples with varying sets of features. This is achieved via a set-transformer architecture augmented by feature-encoder layers, thereby enabling the learning of a shared latent feature space from data originating from heterogeneous feature spaces. The advantages of the model are demonstrated for automatic cancer cell detection in acute myeloid leukemia in flow cytometry data, where the features measured during acquisition often vary between samples. Our proposed architecture's capacity to operate seamlessly across incongruent feature spaces is particularly relevant in this context, where data scarcity arises from the low prevalence of the disease. The code is available for research purposes at //github.com/lisaweijler/FATE.

Inspired by the traditional partial differential equation (PDE) approach for image denoising, we propose a novel neural network architecture, referred as NODE-ImgNet, that combines neural ordinary differential equations (NODEs) with convolutional neural network (CNN) blocks. NODE-ImgNet is intrinsically a PDE model, where the dynamic system is learned implicitly without the explicit specification of the PDE. This naturally circumvents the typical issues associated with introducing artifacts during the learning process. By invoking such a NODE structure, which can also be viewed as a continuous variant of a residual network (ResNet) and inherits its advantage in image denoising, our model achieves enhanced accuracy and parameter efficiency. In particular, our model exhibits consistent effectiveness in different scenarios, including denoising gray and color images perturbed by Gaussian noise, as well as real-noisy images, and demonstrates superiority in learning from small image datasets.

Stress prediction in porous materials and structures is challenging due to the high computational cost associated with direct numerical simulations. Convolutional Neural Network (CNN) based architectures have recently been proposed as surrogates to approximate and extrapolate the solution of such multiscale simulations. These methodologies are usually limited to 2D problems due to the high computational cost of 3D voxel based CNNs. We propose a novel geometric learning approach based on a Graph Neural Network (GNN) that efficiently deals with three-dimensional problems by performing convolutions over 2D surfaces only. Following our previous developments using pixel-based CNN, we train the GNN to automatically add local fine-scale stress corrections to an inexpensively computed coarse stress prediction in the porous structure of interest. Our method is Bayesian and generates densities of stress fields, from which credible intervals may be extracted. As a second scientific contribution, we propose to improve the extrapolation ability of our network by deploying a strategy of online physics-based corrections. Specifically, we condition the posterior predictions of our probabilistic predictions to satisfy partial equilibrium at the microscale, at the inference stage. This is done using an Ensemble Kalman algorithm, to ensure tractability of the Bayesian conditioning operation. We show that this innovative methodology allows us to alleviate the effect of undesirable biases observed in the outputs of the uncorrected GNN, and improves the accuracy of the predictions in general.

We survey recent contributions to finite element exterior calculus over manifolds and surfaces within a comprehensive formalism for the error analysis of vector-valued partial differential equations over manifolds. Our primary focus is on uniformly bounded commuting projections over manifolds: these projections map from Sobolev de Rham complexes onto finite element de Rham complexes, commute with the differential operators, and satisfy uniform bounds in Lebesgue norms. They enable the Galerkin theory of Hilbert complexes for a large range of intrinsic finite element methods over manifolds. However, these intrinsic finite element methods are generally not computable and thus primarily of theoretical interest. This leads to our second point: estimating the geometric variational crime incurred by transitioning to computable approximate problems. Lastly, our third point addresses how to estimate the approximation error of the intrinsic finite element method in terms of the mesh size. If the solution is not continuous, then such an estimate is achieved via modified Cl\'ement or Scott-Zhang interpolants that facilitate a broken Bramble--Hilbert lemma.

We numerically investigate the generalized Steklov problem for the modified Helmholtz equation and focus on the relation between its spectrum and the geometric structure of the domain. We address three distinct aspects: (i) the asymptotic behavior of eigenvalues for polygonal domains; (ii) the dependence of the integrals of eigenfunctions on the domain symmetries; and (iii) the localization and exponential decay of Steklov eigenfunctions away from the boundary for smooth shapes and in the presence of corners. For this purpose, we implemented two complementary numerical methods to compute the eigenvalues and eigenfunctions of the associated Dirichlet-to-Neumann operator for various simply-connected planar domains. We also discuss applications of the obtained results in the theory of diffusion-controlled reactions and formulate several conjectures with relevance in spectral geometry.

Assessing the environmental impact of the mineral extraction industry plays a critical role in understanding and mitigating the ecological consequences of extractive activities. This paper presents MineSegSAT, a model that presents a novel approach to predicting environmentally impacted areas of mineral extraction sites using the SegFormer deep learning segmentation architecture trained on Sentinel-2 data. The data was collected from non-overlapping regions over Western Canada in 2021 containing areas of land that have been environmentally impacted by mining activities that were identified from high-resolution satellite imagery in 2021. The SegFormer architecture, a state-of-the-art semantic segmentation framework, is employed to leverage its advanced spatial understanding capabilities for accurate land cover classification. We investigate the efficacy of loss functions including Dice, Tversky, and Lovasz loss respectively. The trained model was utilized for inference over the test region in the ensuing year to identify potential areas of expansion or contraction over these same periods. The Sentinel-2 data is made available on Amazon Web Services through a collaboration with Earth Daily Analytics which provides corrected and tiled analytics-ready data on the AWS platform. The model and ongoing API to access the data on AWS allow the creation of an automated tool to monitor the extent of disturbed areas surrounding known mining sites to ensure compliance with their environmental impact goals.