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Postoperative infection diagnosis is a common and serious complication that generally poses a high diagnostic challenge. This study focuses on PJI, a type of postoperative infection. X-ray examination is an imaging examination for suspected PJI patients that can evaluate joint prostheses and adjacent tissues, and detect the cause of pain. Laboratory examination data has high sensitivity and specificity and has significant potential in PJI diagnosis. In this study, we proposed a self-supervised masked autoencoder pre-training strategy and a multimodal fusion diagnostic network MED-NVC, which effectively implements the interaction between two modal features through the feature fusion network of CrossAttention. We tested our proposed method on our collected PJI dataset and evaluated its performance and feasibility through comparison and ablation experiments. The results showed that our method achieved an ACC of 94.71% and an AUC of 98.22%, which is better than the latest method and also reduces the number of parameters. Our proposed method has the potential to provide clinicians with a powerful tool for enhancing accuracy and efficiency.

The (modern) arbitrary derivative (ADER) approach is a popular technique for the numerical solution of differential problems based on iteratively solving an implicit discretization of their weak formulation. In this work, focusing on an ODE context, we investigate several strategies to improve this approach. Our initial emphasis is on the order of accuracy of the method in connection with the polynomial discretization of the weak formulation. We demonstrate that precise choices lead to higher-order convergences in comparison to the existing literature. Then, we put ADER methods into a Deferred Correction (DeC) formalism. This allows to determine the optimal number of iterations, which is equal to the formal order of accuracy of the method, and to introduce efficient $p$-adaptive modifications. These are defined by matching the order of accuracy achieved and the degree of the polynomial reconstruction at each iteration. We provide analytical and numerical results, including the stability analysis of the new modified methods, the investigation of the computational efficiency, an application to adaptivity and an application to hyperbolic PDEs with a Spectral Difference (SD) space discretization.

A new multivariate density estimator for stationary sequences is obtained by Fourier inversion of the thresholded empirical characteristic function. This estimator does not depend on the choice of parameters related to the smoothness of the density; it is directly adaptive. We establish oracle inequalities valid for independent, $\alpha$-mixing and $\tau$-mixing sequences, which allows us to derive optimal convergence rates, up to a logarithmic loss. On general anisotropic Sobolev classes, the estimator adapts to the regularity of the unknown density but also achieves directional adaptivity. In particular, if A is an invertible matrix, if the observations are drawn from X $\in$ R^d , d $\ge$ 1, it achieves the rate implied by the regularity of AX, which may be more regular than X. The estimator is easy to implement and numerically efficient. It depends on the calibration of a parameter for which we propose an innovative numerical selection procedure, using the Euler characteristic of the thresholded areas.

We deal with the reduced four-equation model for dynamics of the heterogeneous compressible binary mixtures with the stiffened gas equations of state. We study its further reduced form, with the excluded volume concentrations and a quadratic equation for the common pressure of the components, that can be called a quasi-homogeneous form. We prove new properties of this equation, derive a simple formula for the squared speed of sound, give an alternative proof for a formula that relates it to the squared Wood speed of sound, and a short derivation of the pressure balance equation. For the first time, we introduce regularizations of the heterogeneous model (in the quasi-homogeneous form). In the 1D case, we construct the corresponding explicit two-level in time and symmetric three-point in space finite-difference schemes without limiters and present numerical results for various flows with shock waves.

The Stable Diffusion model is a prominent text-to-image generation model that relies on a text prompt as its input, which is encoded using the Contrastive Language-Image Pre-Training (CLIP). However, text prompts have limitations when it comes to incorporating implicit information from reference images. Existing methods have attempted to address this limitation by employing expensive training procedures involving millions of training samples for image-to-image generation. In contrast, this paper demonstrates that the CLIP model, as utilized in Stable Diffusion, inherently possesses the ability to instantaneously convert images into text prompts. Such an image-to-prompt conversion can be achieved by utilizing a linear projection matrix that is calculated in a closed form. Moreover, the paper showcases that this capability can be further enhanced by either utilizing a small amount of similar-domain training data (approximately 100 images) or incorporating several online training steps (around 30 iterations) on the reference images. By leveraging these approaches, the proposed method offers a simple and flexible solution to bridge the gap between images and text prompts. This methodology can be applied to various tasks such as image variation and image editing, facilitating more effective and seamless interaction between images and textual prompts.

Atmospheric aerosols influence the Earth's climate, primarily by affecting cloud formation and scattering visible radiation. However, aerosol-related physical processes in climate simulations are highly uncertain. Constraining these processes could help improve model-based climate predictions. We propose a scalable statistical framework for constraining parameters in expensive climate models by comparing model outputs with observations. Using the C3.ai Suite, a cloud computing platform, we use a perturbed parameter ensemble of the UKESM1 climate model to efficiently train a surrogate model. A method for estimating a data-driven model discrepancy term is described. The strict bounds method is applied to quantify parametric uncertainty in a principled way. We demonstrate the scalability of this framework with two weeks' worth of simulated aerosol optical depth data over the South Atlantic and Central African region, written from the model every three hours and matched in time to twice-daily MODIS satellite observations. When constraining the model using real satellite observations, we establish constraints on combinations of two model parameters using much higher time-resolution outputs from the climate model than previous studies. This result suggests that, within the limits imposed by an imperfect climate model, potentially very powerful constraints may be achieved when our framework is scaled to the analysis of more observations and for longer time periods.

When estimating quantities and fields that are difficult to measure directly, such as the fluidity of ice, from point data sources, such as satellite altimetry, it is important to solve a numerical inverse problem that is formulated with Bayesian consistency. Otherwise, the resultant probability density function for the difficult to measure quantity or field will not be appropriately clustered around the truth. In particular, the inverse problem should be formulated by evaluating the numerical solution at the true point locations for direct comparison with the point data source. If the data are first fitted to a gridded or meshed field on the computational grid or mesh, and the inverse problem formulated by comparing the numerical solution to the fitted field, the benefits of additional point data values below the grid density will be lost. We demonstrate, with examples in the fields of groundwater hydrology and glaciology, that a consistent formulation can increase the accuracy of results and aid discourse between modellers and observationalists. To do this, we bring point data into the finite element method ecosystem as discontinuous fields on meshes of disconnected vertices. Point evaluation can then be formulated as a finite element interpolation operation (dual-evaluation). This new abstraction is well-suited to automation, including automatic differentiation. We demonstrate this through implementation in Firedrake, which generates highly optimised code for solving Partial Differential Equations (PDEs) with the finite element method. Our solution integrates with dolfin-adjoint/pyadjoint, allowing PDE-constrained optimisation problems, such as data assimilation, to be solved through forward and adjoint mode automatic differentiation.

Generalized Additive Models (GAMs) have recently experienced a resurgence in popularity due to their interpretability, which arises from expressing the target value as a sum of non-linear transformations of the features. Despite the current enthusiasm for GAMs, their susceptibility to concurvity - i.e., (possibly non-linear) dependencies between the features - has hitherto been largely overlooked. Here, we demonstrate how concurvity can severly impair the interpretability of GAMs and propose a remedy: a conceptually simple, yet effective regularizer which penalizes pairwise correlations of the non-linearly transformed feature variables. This procedure is applicable to any differentiable additive model, such as Neural Additive Models or NeuralProphet, and enhances interpretability by eliminating ambiguities due to self-canceling feature contributions. We validate the effectiveness of our regularizer in experiments on synthetic as well as real-world datasets for time-series and tabular data. Our experiments show that concurvity in GAMs can be reduced without significantly compromising prediction quality, improving interpretability and reducing variance in the feature importances.

We propose a set of goodness-of-fit tests for the semiparametric accelerated failure time (AFT) model, including an omnibus test, a link function test, and a functional form test. This set of tests is derived from a multi-parameter cumulative sum process shown to follow asymptotically a zero-mean Gaussian process. Its evaluation is based on the asymptotically equivalent perturbed version, which enables both graphical and numerical evaluations of the assumed AFT model. Empirical p-values are obtained using the Kolmogorov-type supremum test, which provides a reliable approach for estimating the significance of both proposed un-standardized and standardized test statistics. The proposed procedure is illustrated using the induced smoothed rank-based estimator but is directly applicable to other popular estimators such as non-smooth rank-based estimator or least-squares estimator.Our proposed methods are rigorously evaluated using extensive simulation experiments that demonstrate their effectiveness in maintaining a Type I error rate and detecting departures from the assumed AFT model in practical sample sizes and censoring rates. Furthermore, the proposed approach is applied to the analysis of the Primary Biliary Cirrhosis data, a widely studied dataset in survival analysis, providing further evidence of the practical usefulness of the proposed methods in real-world scenarios. To make the proposed methods more accessible to researchers, we have implemented them in the R package afttest, which is publicly available on the Comprehensive R Archieve Network.

With the rapid increase of large-scale, real-world datasets, it becomes critical to address the problem of long-tailed data distribution (i.e., a few classes account for most of the data, while most classes are under-represented). Existing solutions typically adopt class re-balancing strategies such as re-sampling and re-weighting based on the number of observations for each class. In this work, we argue that as the number of samples increases, the additional benefit of a newly added data point will diminish. We introduce a novel theoretical framework to measure data overlap by associating with each sample a small neighboring region rather than a single point. The effective number of samples is defined as the volume of samples and can be calculated by a simple formula $(1-\beta^{n})/(1-\beta)$, where $n$ is the number of samples and $\beta \in [0,1)$ is a hyperparameter. We design a re-weighting scheme that uses the effective number of samples for each class to re-balance the loss, thereby yielding a class-balanced loss. Comprehensive experiments are conducted on artificially induced long-tailed CIFAR datasets and large-scale datasets including ImageNet and iNaturalist. Our results show that when trained with the proposed class-balanced loss, the network is able to achieve significant performance gains on long-tailed datasets.