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The evaluation of text-generative vision-language models is a challenging yet crucial endeavor. By addressing the limitations of existing Visual Question Answering (VQA) benchmarks and proposing innovative evaluation methodologies, our research seeks to advance our understanding of these models' capabilities. We propose a novel VQA benchmark based on well-known visual classification datasets which allows a granular evaluation of text-generative vision-language models and their comparison with discriminative vision-language models. To improve the assessment of coarse answers on fine-grained classification tasks, we suggest using the semantic hierarchy of the label space to ask automatically generated follow-up questions about the ground-truth category. Finally, we compare traditional NLP and LLM-based metrics for the problem of evaluating model predictions given ground-truth answers. We perform a human evaluation study upon which we base our decision on the final metric. We apply our benchmark to a suite of vision-language models and show a detailed comparison of their abilities on object, action, and attribute classification. Our contributions aim to lay the foundation for more precise and meaningful assessments, facilitating targeted progress in the exciting field of vision-language modeling.

Multi-sequence magnetic resonance imaging (MRI) has found wide applications in both modern clinical studies and deep learning research. However, in clinical practice, it frequently occurs that one or more of the MRI sequences are missing due to different image acquisition protocols or contrast agent contraindications of patients, limiting the utilization of deep learning models trained on multi-sequence data. One promising approach is to leverage generative models to synthesize the missing sequences, which can serve as a surrogate acquisition. State-of-the-art methods tackling this problem are based on convolutional neural networks (CNN) which usually suffer from spectral biases, resulting in poor reconstruction of high-frequency fine details. In this paper, we propose Conditional Neural fields with Shift modulation (CoNeS), a model that takes voxel coordinates as input and learns a representation of the target images for multi-sequence MRI translation. The proposed model uses a multi-layer perceptron (MLP) instead of a CNN as the decoder for pixel-to-pixel mapping. Hence, each target image is represented as a neural field that is conditioned on the source image via shift modulation with a learned latent code. Experiments on BraTS 2018 and an in-house clinical dataset of vestibular schwannoma patients showed that the proposed method outperformed state-of-the-art methods for multi-sequence MRI translation both visually and quantitatively. Moreover, we conducted spectral analysis, showing that CoNeS was able to overcome the spectral bias issue common in conventional CNN models. To further evaluate the usage of synthesized images in clinical downstream tasks, we tested a segmentation network using the synthesized images at inference.

The Crank-Nicolson (CN) method is a well-known time integrator for evolutionary partial differential equations (PDEs) arising in many real-world applications. Since the solution at any time depends on the solution at previous time steps, the CN method is inherently difficult to parallelize. In this paper, we consider a parallel method for the solution of evolutionary PDEs with the CN scheme. Using an all-at-once approach, we can solve for all time steps simultaneously using a parallelizable over time preconditioner within a standard iterative method. Due to the diagonalization of the proposed preconditioner, we can prove that most eigenvalues of preconditioned matrices are equal to 1 and the others lie in the set: $\left\{z\in\mathbb{C}: 1/(1 + \alpha) < |z| < 1/(1 - \alpha)~{\rm and}~\Re{\rm e}(z) > 0\right\}$, where $0 < \alpha < 1$ is a free parameter. Besides, the efficient implementation of the proposed preconditioner is described. Given certain conditions, we prove that the preconditioned GMRES method exhibits a mesh-independent convergence rate. Finally, we will verify both theoretical findings and the efficacy of the proposed preconditioner via numerical experiments on financial option pricing PDEs.

We propose a hybrid iterative method based on MIONet for PDEs, which combines the traditional numerical iterative solver and the recent powerful machine learning method of neural operator, and further systematically analyze its theoretical properties, including the convergence condition, the spectral behavior, as well as the convergence rate, in terms of the errors of the discretization and the model inference. We show the theoretical results for the frequently-used smoothers, i.e. Richardson (damped Jacobi) and Gauss-Seidel. We give an upper bound of the convergence rate of the hybrid method w.r.t. the model correction period, which indicates a minimum point to make the hybrid iteration converge fastest. Several numerical examples including the hybrid Richardson (Gauss-Seidel) iteration for the 1-d (2-d) Poisson equation are presented to verify our theoretical results, and also reflect an excellent acceleration effect. As a meshless acceleration method, it is provided with enormous potentials for practice applications.

This paper studies the convergence of a spatial semidiscretization of a three-dimensional stochastic Allen-Cahn equation with multiplicative noise. For non-smooth initial values, the regularity of the mild solution is investigated, and an error estimate is derived with the spatial $ L^2 $-norm. For smooth initial values, two error estimates with the general spatial $ L^q $-norms are established.

We prove explicit uniform two-sided bounds for the phase functions of Bessel functions and of their derivatives. As a consequence, we obtain new enclosures for the zeros of Bessel functions and their derivatives in terms of inverse values of some elementary functions. These bounds are valid, with a few exceptions, for all zeros and all Bessel functions with non-negative indices. We provide numerical evidence showing that our bounds either improve or closely match the best previously known ones.

In this study, we explore data assimilation for the Stochastic Camassa-Holm equation through the application of the particle filtering framework. Specifically, our approach integrates adaptive tempering, jittering, and nudging techniques to construct an advanced particle filtering system. All filtering processes are executed utilizing ensemble parallelism. We conduct extensive numerical experiments across various scenarios of the Stochastic Camassa-Holm model with transport noise and viscosity to examine the impact of different filtering procedures on the performance of the data assimilation process. Our analysis focuses on how observational data and the data assimilation step influence the accuracy and uncertainty of the obtained results.

When generating in-silico clinical electrophysiological outputs, such as electrocardiograms (ECGs) and body surface potential maps (BSPMs), mathematical models have relied on single physics, i.e. of the cardiac electrophysiology (EP), neglecting the role of the heart motion. Since the heart is the most powerful source of electrical activity in the human body, its motion dynamically shifts the position of the principal electrical sources in the torso, influencing electrical potential distribution and potentially altering the EP outputs. In this work, we propose a computational model for the simulation of ECGs and BSPMs by coupling a cardiac electromechanical model with a model that simulates the propagation of the EP signal in the torso, thanks to a flexible numerical approach, that simulates the torso domain deformation induced by the myocardial displacement. Our model accounts for the major mechano-electrical feedbacks, along with unidirectional displacement and potential couplings from the heart to the surrounding body. For the numerical discretization, we employ a versatile intergrid transfer operator that allows for the use of different Finite Element spaces to be used in the cardiac and torso domains. Our numerical results are obtained on a realistic 3D biventricular-torso geometry, and cover both cases of sinus rhythm and ventricular tachycardia (VT), solving both the electromechanical-torso model in dynamical domains, and the classical electrophysiology-torso model in static domains. By comparing standard 12-lead ECG and BSPMs, we highlight the non-negligible effects of the myocardial contraction on the EP-outputs, especially in pathological conditions, such as the VT.

We provide a new theoretical framework for the variable-step deferred correction (DC) methods based on the well-known BDF2 formula. By using the discrete orthogonal convolution kernels, some high-order BDF2-DC methods are proven to be stable on arbitrary time grids according to the recent definition of stability (SINUM, 60: 2253-2272). It significantly relaxes the existing step-ratio restrictions for the BDF2-DC methods (BIT, 62: 1789-1822). The associated sharp error estimates are established by taking the numerical effects of the starting approximations into account, and they suggest that the BDF2-DC methods have no aftereffect, that is, the lower-order starting scheme for the BDF2 scheme will not cause a loss in the accuracy of the high-order BDF2-DC methods. Extensive tests on the graded and random time meshes are presented to support the new theory.

We propose a generalization of nonlinear stability of numerical one-step integrators to Riemannian manifolds in the spirit of Butcher's notion of B-stability. Taking inspiration from Simpson-Porco and Bullo, we introduce non-expansive systems on such manifolds and define B-stability of integrators. In this first exposition, we provide concrete results for a geodesic version of the Implicit Euler (GIE) scheme. We prove that the GIE method is B-stable on Riemannian manifolds with non-positive sectional curvature. We show through numerical examples that the GIE method is expansive when applied to a certain non-expansive vector field on the 2-sphere, and that the GIE method does not necessarily possess a unique solution for large enough step sizes. Finally, we derive a new improved global error estimate for general Lie group integrators.