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This study focuses on the use of model and data fusion for improving the Spalart-Allmaras (SA) closure model for Reynolds-averaged Navier-Stokes solutions of separated flows. In particular, our goal is to develop of models that not-only assimilate sparse experimental data to improve performance in computational models, but also generalize to unseen cases by recovering classical SA behavior. We achieve our goals using data assimilation, namely the Ensemble Kalman Filtering approach (EnKF), to calibrate the coefficients of the SA model for separated flows. A holistic calibration strategy is implemented via a parameterization of the production, diffusion, and destruction terms. This calibration relies on the assimilation of experimental data collected velocity profiles, skin friction, and pressure coefficients for separated flows. Despite using of observational data from a single flow condition around a backward-facing step (BFS), the recalibrated SA model demonstrates generalization to other separated flows, including cases such as the 2D-bump and modified BFS. Significant improvement is observed in the quantities of interest, i.e., skin friction coefficient ($C_f$) and pressure coefficient ($C_p$) for each flow tested. Finally, it is also demonstrated that the newly proposed model recovers SA proficiency for external, unseparated flows, such as flow around a NACA-0012 airfoil without any danger of extrapolation, and that the individually calibrated terms in the SA model are targeted towards specific flow-physics wherein the calibrated production term improves the re-circulation zone while destruction improves the recovery zone.

Multicast enables efficient one-to-many communications. Several applications benefit from its scalability properties, e.g., live-streaming and large-scale software updates. Historically, multicast applications have used specialized transport protocols. The flexibility of the recently standardized QUIC protocol opens the possibility of providing both unicast and multicast services to applications with a single transport protocol. We present MCQUIC, an extended version of the QUIC protocol that supports multicast communications. We show how QUIC features and built-in security can be leveraged for multicast transport. We present the design of MCQUIC and implement it in Cloudflare quiche. We assess its performance through benchmarks and in emulated networks under realistic scenarios. We also demonstrate MCQUIC in a campus network. By coupling QUIC with our multicast extension, applications can rely on multicast for efficiency with the possibility to fall back on unicast in case of incompatible network conditions.

High-order structures have been recognised as suitable models for systems going beyond the binary relationships for which graph models are appropriate. Despite their importance and surge in research on these structures, their random cases have been only recently become subjects of interest. One of these high-order structures is the oriented hypergraph, which relates couples of subsets of an arbitrary number of vertices. Here we develop the Erd\H{o}s-R\'enyi model for oriented hypergraphs, which corresponds to the random realisation of oriented hyperedges of the complete oriented hypergraph. A particular feature of random oriented hypergraphs is that the ratio between their expected number of oriented hyperedges and their expected degree or size is 3/2 for large number of vertices. We highlight the suitability of oriented hypergraphs for modelling large collections of chemical reactions and the importance of random oriented hypergraphs to analyse the unfolding of chemistry.

Diffusion models (DMs) demonstrate potent image generation capabilities in various generative modeling tasks. Nevertheless, their primary limitation lies in slow sampling speed, requiring hundreds or thousands of sequential function evaluations through large neural networks to generate high-quality images. Sampling from DMs can be seen as solving corresponding stochastic differential equations (SDEs) or ordinary differential equations (ODEs). In this work, we formulate the sampling process as an extended reverse-time SDE (ER SDE), unifying prior explorations into ODEs and SDEs. Leveraging the semi-linear structure of ER SDE solutions, we offer exact solutions and arbitrarily high-order approximate solutions for VP SDE and VE SDE, respectively. Based on the solution space of the ER SDE, we yield mathematical insights elucidating the superior performance of ODE solvers over SDE solvers in terms of fast sampling. Additionally, we unveil that VP SDE solvers stand on par with their VE SDE counterparts. Finally, we devise fast and training-free samplers, ER-SDE Solvers, elevating the efficiency of stochastic samplers to unprecedented levels. Experimental results demonstrate achieving 3.45 FID in 20 function evaluations and 2.24 FID in 50 function evaluations on the ImageNet 64$\times$64 dataset.

We generalize K\"ahler information manifolds of complex-valued signal processing filters by introducing weighted Hardy spaces and smooth transformations of transfer functions. We prove that the Riemannian geometry of a linear filter induced from weighted Hardy norms for the smooth transformations of its transfer function is a K\"ahler manifold. Additionally, the K\"ahler potential of the linear system geometry corresponds to the square of the weighted Hardy norms of its composite transfer functions. Based on properties of K\"ahler manifolds, geometric objects on the manifolds of the linear systems in weighted Hardy spaces are computed in much simpler ways. Moreover, K\"ahler information manifolds of signal filters in weighted Hardy spaces incorporate various well-known information manifolds under the unified framework. We also cover several examples from time series models of which metric tensor, Levi-Civita connection, and K\"ahler potentials are represented with polylogarithms of poles and zeros from the transfer functions with weight vectors in exponential forms.

With the increasing availability of large scale datasets, computational power and tools like automatic differentiation and expressive neural network architectures, sequential data are now often treated in a data-driven way, with a dynamical model trained from the observation data. While neural networks are often seen as uninterpretable black-box architectures, they can still benefit from physical priors on the data and from mathematical knowledge. In this paper, we use a neural network architecture which leverages the long-known Koopman operator theory to embed dynamical systems in latent spaces where their dynamics can be described linearly, enabling a number of appealing features. We introduce methods that enable to train such a model for long-term continuous reconstruction, even in difficult contexts where the data comes in irregularly-sampled time series. The potential for self-supervised learning is also demonstrated, as we show the promising use of trained dynamical models as priors for variational data assimilation techniques, with applications to e.g. time series interpolation and forecasting.

Multi-sensor modal fusion has demonstrated strong advantages in 3D object detection tasks. However, existing methods that fuse multi-modal features through a simple channel concatenation require transformation features into bird's eye view space and may lose the information on Z-axis thus leads to inferior performance. To this end, we propose FusionFormer, an end-to-end multi-modal fusion framework that leverages transformers to fuse multi-modal features and obtain fused BEV features. And based on the flexible adaptability of FusionFormer to the input modality representation, we propose a depth prediction branch that can be added to the framework to improve detection performance in camera-based detection tasks. In addition, we propose a plug-and-play temporal fusion module based on transformers that can fuse historical frame BEV features for more stable and reliable detection results. We evaluate our method on the nuScenes dataset and achieve 72.6% mAP and 75.1% NDS for 3D object detection tasks, outperforming state-of-the-art methods.

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.

Recently, deep learning-based methods achieved promising performance in nuclei detection and classification applications. However, training deep learning-based methods requires a large amount of pixel-wise annotated data, which is time-consuming and labor-intensive, especially in 3D images. An alternative approach is to adapt weak-annotation methods, such as labeling each nucleus with a point, but this method does not extend from 2D histopathology images (for which it was originally developed) to 3D immunofluorescent images. The reason is that 3D images contain multiple channels (z-axis) for nuclei and different markers separately, which makes training using point annotations difficult. To address this challenge, we propose the Label-efficient Contrastive learning-based (LECL) model to detect and classify various types of nuclei in 3D immunofluorescent images. Previous methods use Maximum Intensity Projection (MIP) to convert immunofluorescent images with multiple slices to 2D images, which can cause signals from different z-stacks to falsely appear associated with each other. To overcome this, we devised an Extended Maximum Intensity Projection (EMIP) approach that addresses issues using MIP. Furthermore, we performed a Supervised Contrastive Learning (SCL) approach for weakly supervised settings. We conducted experiments on cardiovascular datasets and found that our proposed framework is effective and efficient in detecting and classifying various types of nuclei in 3D immunofluorescent images.

Knowledge graph reasoning (KGR), aiming to deduce new facts from existing facts based on mined logic rules underlying knowledge graphs (KGs), has become a fast-growing research direction. It has been proven to significantly benefit the usage of KGs in many AI applications, such as question answering and recommendation systems, etc. According to the graph types, the existing KGR models can be roughly divided into three categories, \textit{i.e.,} static models, temporal models, and multi-modal models. The early works in this domain mainly focus on static KGR and tend to directly apply general knowledge graph embedding models to the reasoning task. However, these models are not suitable for more complex but practical tasks, such as inductive static KGR, temporal KGR, and multi-modal KGR. To this end, multiple works have been developed recently, but no survey papers and open-source repositories comprehensively summarize and discuss models in this important direction. To fill the gap, we conduct a survey for knowledge graph reasoning tracing from static to temporal and then to multi-modal KGs. Concretely, the preliminaries, summaries of KGR models, and typical datasets are introduced and discussed consequently. Moreover, we discuss the challenges and potential opportunities. The corresponding open-source repository is shared on GitHub: //github.com/LIANGKE23/Awesome-Knowledge-Graph-Reasoning.