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A general a posteriori error analysis applies to five lowest-order finite element methods for two fourth-order semi-linear problems with trilinear non-linearity and a general source. A quasi-optimal smoother extends the source term to the discrete trial space, and more importantly, modifies the trilinear term in the stream-function vorticity formulation of the incompressible 2D Navier-Stokes and the von K\'{a}rm\'{a}n equations. This enables the first efficient and reliable a posteriori error estimates for the 2D Navier-Stokes equations in the stream-function vorticity formulation for Morley, two discontinuous Galerkin, $C^0$ interior penalty, and WOPSIP discretizations with piecewise quadratic polynomials.

In indoor scenes, reverberation is a crucial factor in degrading the perceived quality and intelligibility of speech. In this work, we propose a generative dereverberation method. Our approach is based on a probabilistic model utilizing a recurrent variational auto-encoder (RVAE) network and the convolutive transfer function (CTF) approximation. Different from most previous approaches, the output of our RVAE serves as the prior of the clean speech. And our target is the maximum a posteriori (MAP) estimation of clean speech, which is achieved iteratively through the expectation maximization (EM) algorithm. The proposed method integrates the capabilities of network-based speech prior modelling and CTF-based observation modelling. Experiments on single-channel speech dereverberation show that the proposed generative method noticeably outperforms the advanced discriminative networks.

Current physics-informed (standard or operator) neural networks still rely on accurately learning the initial conditions of the system they are solving. In contrast, standard numerical methods evolve such initial conditions without needing to learn these. In this study, we propose to improve current physics-informed deep learning strategies such that initial conditions do not need to be learned and are represented exactly in the predicted solution. Moreover, this method guarantees that when a DeepONet is applied multiple times to time step a solution, the resulting function is continuous.

Telemanipulation has become a promising technology that combines human intelligence with robotic capabilities to perform tasks remotely. However, it faces several challenges such as insufficient transparency, low immersion, and limited feedback to the human operator. Moreover, the high cost of haptic interfaces is a major limitation for the application of telemanipulation in various fields, including elder care, where our research is focused. To address these challenges, this paper proposes the usage of nonlinear model predictive control for telemanipulation using low-cost virtual reality controllers, including multiple control goals in the objective function. The framework utilizes models for human input prediction and taskrelated models of the robot and the environment. The proposed framework is validated on an UR5e robot arm in the scenario of handling liquid without spilling. Further extensions of the framework such as pouring assistance and collision avoidance can easily be included.

In recent years, cross-modal reasoning (CMR), the process of understanding and reasoning across different modalities, has emerged as a pivotal area with applications spanning from multimedia analysis to healthcare diagnostics. As the deployment of AI systems becomes more ubiquitous, the demand for transparency and comprehensibility in these systems' decision-making processes has intensified. This survey delves into the realm of interpretable cross-modal reasoning (I-CMR), where the objective is not only to achieve high predictive performance but also to provide human-understandable explanations for the results. This survey presents a comprehensive overview of the typical methods with a three-level taxonomy for I-CMR. Furthermore, this survey reviews the existing CMR datasets with annotations for explanations. Finally, this survey summarizes the challenges for I-CMR and discusses potential future directions. In conclusion, this survey aims to catalyze the progress of this emerging research area by providing researchers with a panoramic and comprehensive perspective, illuminating the state of the art and discerning the opportunities. The summarized methods, datasets, and other resources are available at //github.com/ZuyiZhou/Awesome-Interpretable-Cross-modal-Reasoning.

Automated Audio Captioning (AAC) systems attempt to generate a natural language sentence, a caption, that describes the content of an audio recording, in terms of sound events. Existing datasets provide audio-caption pairs, with captions written in English only. In this work, we explore multilingual AAC, using machine translated captions. We translated automatically two prominent AAC datasets, AudioCaps and Clotho, from English to French, German and Spanish. We trained and evaluated monolingual systems in the four languages, on AudioCaps and Clotho. In all cases, the models achieved similar performance, about 75% CIDEr on AudioCaps and 43% on Clotho. In French, we acquired manual captions of the AudioCaps eval subset. The French system, trained on the machine translated version of AudioCaps, achieved significantly better results on the manual eval subset, compared to the English system for which we automatically translated the outputs to French. This advocates in favor of building systems in a target language instead of simply translating to a target language the English captions from the English system. Finally, we built a multilingual model, which achieved results in each language comparable to each monolingual system, while using much less parameters than using a collection of monolingual systems.

Next Point-of-Interest (POI) recommendation is a critical task in location-based services that aim to provide personalized suggestions for the user's next destination. Previous works on POI recommendation have laid focused on modeling the user's spatial preference. However, existing works that leverage spatial information are only based on the aggregation of users' previous visited positions, which discourages the model from recommending POIs in novel areas. This trait of position-based methods will harm the model's performance in many situations. Additionally, incorporating sequential information into the user's spatial preference remains a challenge. In this paper, we propose Diff-POI: a Diffusion-based model that samples the user's spatial preference for the next POI recommendation. Inspired by the wide application of diffusion algorithm in sampling from distributions, Diff-POI encodes the user's visiting sequence and spatial character with two tailor-designed graph encoding modules, followed by a diffusion-based sampling strategy to explore the user's spatial visiting trends. We leverage the diffusion process and its reversed form to sample from the posterior distribution and optimized the corresponding score function. We design a joint training and inference framework to optimize and evaluate the proposed Diff-POI. Extensive experiments on four real-world POI recommendation datasets demonstrate the superiority of our Diff-POI over state-of-the-art baseline methods. Further ablation and parameter studies on Diff-POI reveal the functionality and effectiveness of the proposed diffusion-based sampling strategy for addressing the limitations of existing methods.

The autologistic actor attribute model, or ALAAM, is the social influence counterpart of the better-known exponential-family random graph model (ERGM) for social selection. Extensive experience with ERGMs has shown that the problem of near-degeneracy which often occurs with simple models can be overcome by using "geometrically weighted" or "alternating" statistics. In the much more limited empirical applications of ALAAMs to date, the problem of near-degeneracy, although theoretically expected, appears to have been less of an issue. In this work I present a comprehensive survey of ALAAM applications, showing that this model has to date only been used with relatively small networks, in which near-degeneracy does not appear to be a problem. I show near-degeneracy does occur in simple ALAAM models of larger empirical networks, define some geometrically weighted ALAAM statistics analogous to those for ERGM, and demonstrate that models with these statistics do not suffer from near-degeneracy and hence can be estimated where they could not be with the simple statistics.

We study a finite volume scheme approximating a parabolic-elliptic Keller-Segel system with power law diffusion with exponent $\gamma \in [1,3]$ and periodic boundary conditions. We derive conditional a posteriori bounds for the error measured in the $L^\infty(0,T;H^1(\Omega))$ norm for the chemoattractant and by a quasi-norm-like quantity for the density. These results are based on stability estimates and suitable conforming reconstructions of the numerical solution. We perform numerical experiments showing that our error bounds are linear in mesh width and elucidating the behaviour of the error estimator under changes of $\gamma$.

Graph Convolution Networks (GCNs) manifest great potential in recommendation. This is attributed to their capability on learning good user and item embeddings by exploiting the collaborative signals from the high-order neighbors. Like other GCN models, the GCN based recommendation models also suffer from the notorious over-smoothing problem - when stacking more layers, node embeddings become more similar and eventually indistinguishable, resulted in performance degradation. The recently proposed LightGCN and LR-GCN alleviate this problem to some extent, however, we argue that they overlook an important factor for the over-smoothing problem in recommendation, that is, high-order neighboring users with no common interests of a user can be also involved in the user's embedding learning in the graph convolution operation. As a result, the multi-layer graph convolution will make users with dissimilar interests have similar embeddings. In this paper, we propose a novel Interest-aware Message-Passing GCN (IMP-GCN) recommendation model, which performs high-order graph convolution inside subgraphs. The subgraph consists of users with similar interests and their interacted items. To form the subgraphs, we design an unsupervised subgraph generation module, which can effectively identify users with common interests by exploiting both user feature and graph structure. To this end, our model can avoid propagating negative information from high-order neighbors into embedding learning. Experimental results on three large-scale benchmark datasets show that our model can gain performance improvement by stacking more layers and outperform the state-of-the-art GCN-based recommendation models significantly.