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Partitioning for load balancing is a crucial first step to parallelize any type of computation. In this work, we propose SGORP, a new spatial partitioning method based on Subgradient Optimization, to solve the $d$-dimensional Rectilinear Partitioning Problem (RPP). Our proposed method allows the use of customizable objective functions as well as some user-specific constraints, such as symmetric partitioning on selected dimensions. Extensive experimental evaluation using over 600 test matrices shows that our algorithm achieves favorable performance against the state-of-the-art RPP and Symmetric RPP algorithms. Additionally, we show the effectiveness of our algorithm to do application-specific load balancing using two applications as motivation: Triangle Counting and Sparse Matrix Multiplication (SpGEMM), where we model their load-balancing problems as $3$-dimensional RPPs.

Cyber-Physical Systems (CPSs), e.g., elevator systems and autonomous driving systems, are progressively permeating our everyday lives. To ensure their safety, various analyses need to be conducted, such as anomaly detection and time-to-event analysis (the focus of this paper). Recently, it has been widely accepted that digital Twins (DTs) can serve as an efficient method to aid in the development, maintenance, and safe and secure operation of CPSs. However, CPSs frequently evolve, e.g., with new or updated functionalities, which demand their corresponding DTs be co-evolved, i.e., in synchronization with the CPSs. To that end, we propose a novel method, named PPT, utilizing an uncertainty-aware transfer learning for DT evolution. Specifically, we first pretrain PPT with a pretraining dataset to acquire generic knowledge about the CPSs, followed by adapting it to a specific CPS with the help of prompt tuning. Results highlight that PPT is effective in time-to-event analysis in both elevator and ADSs case studies, on average, outperforming a baseline method by 7.31 and 12.58 in terms of Huber loss, respectively. The experiment results also affirm the effectiveness of transfer learning, prompt tuning and uncertainty quantification in terms of reducing Huber loss by at least 21.32, 3.14 and 4.08, respectively, in both case studies.

MLIR has become popular since it was open sourced in 2019. A sub-project of LLVM, the flexibility provided by MLIR to represent Intermediate Representations (IR) as dialects at different abstraction levels, to mix these, and to leverage transformations between dialects provides opportunities for automated program optimisation and parallelisation. In addition to general purpose compilers built upon MLIR, domain specific abstractions have also been developed. In this paper we explore complimenting the Flang MLIR general purpose compiler by combining with the domain specific Open Earth Compiler's MLIR stencil dialect. Developing transformations to discover and extracts stencils from Fortran, this specialisation delivers between a 2 and 10 times performance improvement for our benchmarks on a Cray supercomputer compared to using Flang alone. Furthermore, by leveraging existing MLIR transformations we develop an auto-parallelisation approach targeting multi-threaded and distributed memory parallelism, and optimised execution on GPUs, without any modifications to the serial Fortran source code.

The video-language (VL) pretraining has achieved remarkable improvement in multiple downstream tasks. However, the current VL pretraining framework is hard to extend to multiple modalities (N modalities, N>=3) beyond vision and language. We thus propose LanguageBind, taking the language as the bind across different modalities because the language modality is well-explored and contains rich semantics. Specifically, we freeze the language encoder acquired by VL pretraining, then train encoders for other modalities with contrastive learning. As a result, all modalities are mapped to a shared feature space, implementing multi-modal semantic alignment. While LanguageBind ensures that we can extend VL modalities to N modalities, we also need a high-quality dataset with alignment data pairs centered on language. We thus propose VIDAL-10M with Video, Infrared, Depth, Audio and their corresponding Language, naming as VIDAL-10M. In our VIDAL-10M, all videos are from short video platforms with complete semantics rather than truncated segments from long videos, and all the video, depth, infrared, and audio modalities are aligned to their textual descriptions. After pretraining on VIDAL-10M, we outperform ImageBind by 1.2% R@1 on the MSR-VTT dataset with only 15% of the parameters in the zero-shot video-text retrieval, validating the high quality of our dataset. Beyond this, our LanguageBind has achieved great improvement in the zero-shot video, audio, depth, and infrared understanding tasks. For instance, on the LLVIP and NYU-D datasets, LanguageBind outperforms ImageBind-huge with 23.8% and 11.1% top-1 accuracy.

In this paper, the limitations of YOLOv5s model on small target detection task are deeply studied and improved. The performance of the model is successfully enhanced by introducing GhostNet-based convolutional module, RepGFPN-based Neck module optimization, CA and Transformer's attention mechanism, and loss function improvement using NWD. The experimental results validate the positive impact of these improvement strategies on model precision, recall and mAP. In particular, the improved model shows significant superiority in dealing with complex backgrounds and tiny targets in real-world application tests. This study provides an effective optimization strategy for the YOLOv5s model on small target detection, and lays a solid foundation for future related research and applications.

For the first time, the concept of CHTW-systems as a multidimensional representation of Petri nets, based on the assumption of the spatial distribution of tokens (resources) in positions (branes) and, accordingly, the spatial representation of transitions and arcs is proposed. The theoretical constructs are based on the concept of hybrid functional Petri nets [10]. The introduced concepts of branes and carriers are distant analogies of the corresponding concepts in superstring theory, but the theory of CHTW-systems is neither part of superstring theory nor its development. The description of CHTW-system as a dynamic system for stationary and non-stationary cases is considered. The initial classification of CHTW systems is provided enabling understanding of further research directions.

In this paper, we present a new computational framework using coupled and decoupled approximations for a Cahn-Hilliard-Navier-Stokes model with variable densities and degenerate mobility. In this sense, the coupled approximation is shown to conserve the mass of the fluid, preserve the point-wise bounds of the density and decrease an energy functional. In contrast, the decoupled scheme is presented as a more computationally efficient alternative but the discrete energy-decreasing property can not be assured. Both schemes are based on a finite element approximation for the Navier-Stokes fluid flow with discontinuous pressure and an upwind discontinuous Galerkin scheme for the Cahn-Hilliard part. Finally, several numerical experiments contrasting both approaches are conducted. In particular, results for a convergence test, a simple qualitative comparison and some well-known benchmark problems are shown.

It is well known since 1960s that by exploring the tensor product structure of the discrete Laplacian on Cartesian meshes, one can develop a simple direct Poisson solver with an $\mathcal O(N^{\frac{d+1}d})$ complexity in $d$-dimension. The GPU acceleration of numerically solving PDEs has been explored successfully around fifteen years ago and become more and more popular in the past decade, driven by significant advancement in both hardware and software technologies, especially in the recent few years. We present in this paper a simple but extremely fast MATLAB implementation on a modern GPU, which can be easily reproduced, for solving 3D Poisson type equations using a spectral-element method. In particular, it costs less than one second on a Nvidia A100 for solving a Poisson equation with one billion degree of freedoms.

Graph convolution networks (GCN) are increasingly popular in many applications, yet remain notoriously hard to train over large graph datasets. They need to compute node representations recursively from their neighbors. Current GCN training algorithms suffer from either high computational costs that grow exponentially with the number of layers, or high memory usage for loading the entire graph and node embeddings. In this paper, we propose a novel efficient layer-wise training framework for GCN (L-GCN), that disentangles feature aggregation and feature transformation during training, hence greatly reducing time and memory complexities. We present theoretical analysis for L-GCN under the graph isomorphism framework, that L-GCN leads to as powerful GCNs as the more costly conventional training algorithm does, under mild conditions. We further propose L^2-GCN, which learns a controller for each layer that can automatically adjust the training epochs per layer in L-GCN. Experiments show that L-GCN is faster than state-of-the-arts by at least an order of magnitude, with a consistent of memory usage not dependent on dataset size, while maintaining comparable prediction performance. With the learned controller, L^2-GCN can further cut the training time in half. Our codes are available at //github.com/Shen-Lab/L2-GCN.