The Gray-Scott model is a set of reaction-diffusion equations that describes chemical systems far from equilibrium. Interest in this model stems from its ability to generate spatio-temporal structures, including pulses, spots, stripes, and self-replicating patterns. We consider an extension of this model in which the spread of the different chemicals is assumed to be nonlocal, and can thus be represented by an integral operator. In particular, we focus on the case of strictly positive, symmetric, $L^1$ convolution kernels that have a finite second moment. Modeling the equations on a finite interval, we prove the existence of small-time weak solutions in the case of nonlocal Dirichlet and Neumann boundary constraints. We then use this result to develop a finite element numerical scheme that helps us explore the effects of nonlocal diffusion on the formation of pulse solutions.
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ACM/IEEE第23屆模型驅動工程語言和系統國際會議，是模型驅動軟件和系統工程的首要會議系列，由ACM-SIGSOFT和IEEE-TCSE支持組織。自1998年以來，模型涵蓋了建模的各個方面，從語言和方法到工具和應用程序。模特的參加者來自不同的背景，包括研究人員、學者、工程師和工業專業人士。MODELS 2019是一個論壇，參與者可以圍繞建模和模型驅動的軟件和系統交流前沿研究成果和創新實踐經驗。今年的版本將為建模社區提供進一步推進建模基礎的機會，并在網絡物理系統、嵌入式系統、社會技術系統、云計算、大數據、機器學習、安全、開源等新興領域提出建模的創新應用以及可持續性。
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Runtime analysis, as a branch of the theory of AI, studies how the number of iterations algorithms take before finding a solution (its runtime) depends on the design of the algorithm and the problem structure. Drift analysis is a state-of-the-art tool for estimating the runtime of randomised algorithms, such as evolutionary and bandit algorithms. Drift refers roughly to the expected progress towards the optimum per iteration. This paper considers the problem of deriving concentration tail-bounds on the runtime/regret of algorithms. It provides a novel drift theorem that gives precise exponential tail-bounds given positive, weak, zero and even negative drift. Previously, such exponential tail bounds were missing in the case of weak, zero, or negative drift. Our drift theorem can be used to prove a strong concentration of the runtime/regret of algorithms in AI. For example, we prove that the regret of the \rwab bandit algorithm is highly concentrated, while previous analyses only considered the expected regret. This means that the algorithm obtains the optimum within a given time frame with high probability, i.e. a form of algorithm reliability. Moreover, our theorem implies that the time needed by the co-evolutionary algorithm RLS-PD to obtain a Nash equilibrium in a \bilinear max-min-benchmark problem is highly concentrated. However, we also prove that the algorithm forgets the Nash equilibrium, and the time until this occurs is highly concentrated. This highlights a weakness in the RLS-PD which should be addressed by future work.
We propose Hyper-Dimensional Function Encoding (HDFE). Given samples of a continuous object (e.g. a function), HDFE produces an explicit vector representation of the given object, invariant to the sample distribution and density. Sample distribution and density invariance enables HDFE to consistently encode continuous objects regardless of their sampling, and therefore allows neural networks to receive continuous objects as inputs for machine learning tasks, such as classification and regression. Besides, HDFE does not require any training and is proved to map the object into an organized embedding space, which facilitates the training of the downstream tasks. In addition, the encoding is decodable, which enables neural networks to regress continuous objects by regressing their encodings. Therefore, HDFE serves as an interface for processing continuous objects. We apply HDFE to function-to-function mapping, where vanilla HDFE achieves competitive performance as the state-of-the-art algorithm. We apply HDFE to point cloud surface normal estimation, where a simple replacement from PointNet to HDFE leads to immediate 12% and 15% error reductions in two benchmarks. In addition, by integrating HDFE into the PointNet-based SOTA network, we improve the SOTA baseline by 2.5% and 1.7% in the same benchmarks.
Matrix-vector multiplication forms the basis of many iterative solution algorithms and as such is an important algorithm also for hierarchical matrices. However, due to its low computational intensity, its performance is typically limited by the available memory bandwidth. By optimizing the storage representation of the data within such matrices, this limitation can be lifted and the performance increased. This applies not only to hierarchical matrices but for also for other low-rank approximation schemes, e.g. block low-rank matrices.
Background:Technical systems are growing in complexity with more components and functions across various disciplines. Model-Driven Engineering (MDE) helps manage this complexity by using models as key artifacts. Domain-Specific Languages (DSL) supported by MDE facilitate modeling. As data generation in product development increases, there's a growing demand for AI algorithms, which can be challenging to implement. Integrating AI algorithms with DSL and MDE can streamline this process. Objective:This study aims to investigate the existing model-driven approaches relying on DSL in support of the engineering of AI software systems to sharpen future research further and define the current state of the art. Method:We conducted a Systemic Literature Review (SLR), collecting papers from five major databases resulting in 1335 candidate studies, eventually retaining 18 primary studies. Each primary study will be evaluated and discussed with respect to the adoption of MDE principles and practices and the phases of AI development support aligned with the stages of the CRISP-DM methodology. Results:The study's findings show that language workbenches are of paramount importance in dealing with all aspects of modeling language development and are leveraged to define DSL explicitly addressing AI concerns. The most prominent AI-related concerns are training and modeling of the AI algorithm, while minor emphasis is given to the time-consuming preparation of the data. Early project phases that support interdisciplinary communication of requirements, e.g., CRISP-DM Business Understanding phase, are rarely reflected. Conclusion:The study found that the use of MDE for AI is still in its early stages, and there is no single tool or method that is widely used. Additionally, current approaches tend to focus on specific stages of development rather than providing support for the entire development process.
Influence functions (IFs) elucidate how training data changes model behavior. However, the increasing size and non-convexity in large-scale models make IFs inaccurate. We suspect that the fragility comes from the first-order approximation which may cause nuisance changes in parameters irrelevant to the examined data. However, simply computing influence from the chosen parameters can be misleading, as it fails to nullify the hidden effects of unselected parameters on the analyzed data. Thus, our approach introduces generalized IFs, precisely estimating target parameters' influence while nullifying nuisance gradient changes on fixed parameters. We identify target update parameters closely associated with the input data by the output- and gradient-based parameter selection methods. We verify the generalized IFs with various alternatives of IFs on the class removal and label change tasks. The experiments align with the "less is more" philosophy, demonstrating that updating only 5\% of the model produces more accurate results than other influence functions across all tasks. We believe our proposal works as a foundational tool for optimizing models, conducting data analysis, and enhancing AI interpretability beyond the limitation of IFs. Codes are available at //github.com/hslyu/GIF.
Open Modification Search (OMS) is a promising algorithm for mass spectrometry analysis that enables the discovery of modified peptides. However, OMS encounters challenges as it exponentially extends the search scope. Existing OMS accelerators either have limited parallelism or struggle to scale effectively with growing data volumes. In this work, we introduce an OMS accelerator utilizing multi-level-cell (MLC) RRAM memory to enhance storage capacity by 3x. Through in-memory computing, we achieve up to 77x faster data processing with two to three orders of magnitude better energy efficiency. Testing was done on a fabricated MLC RRAM chip. We leverage hyperdimensional computing to tolerate up to 10% memory errors while delivering massive parallelism in hardware.
Graph Neural Networks (GNNs) are a large class of relational models for graph processing. Recent theoretical studies on the expressive power of GNNs have focused on two issues. On the one hand, it has been proven that GNNs are as powerful as the Weisfeiler-Lehman test (1-WL) in their ability to distinguish graphs. Moreover, it has been shown that the equivalence enforced by 1-WL equals unfolding equivalence. On the other hand, GNNs turned out to be universal approximators on graphs modulo the constraints enforced by 1-WL/unfolding equivalence. However, these results only apply to Static Attributed Undirected Homogeneous Graphs (SAUHG) with node attributes. In contrast, real-life applications often involve a much larger variety of graph types. In this paper, we conduct a theoretical analysis of the expressive power of GNNs for two other graph domains that are particularly interesting in practical applications, namely dynamic graphs and SAUGHs with edge attributes. Dynamic graphs are widely used in modern applications; hence, the study of the expressive capability of GNNs in this domain is essential for practical reasons and, in addition, it requires a new analyzing approach due to the difference in the architecture of dynamic GNNs compared to static ones. On the other hand, the examination of SAUHGs is of particular relevance since they act as a standard form for all graph types: it has been shown that all graph types can be transformed without loss of information to SAUHGs with both attributes on nodes and edges. This paper considers generic GNN models and appropriate 1-WL tests for those domains. Then, the known results on the expressive power of GNNs are extended to the mentioned domains: it is proven that GNNs have the same capability as the 1-WL test, the 1-WL equivalence equals unfolding equivalence and that GNNs are universal approximators modulo 1-WL/unfolding equivalence.
Quantum Hoare logic (QHL) is a formal verification tool specifically designed to ensure the correctness of quantum programs. There has been an ongoing challenge to achieve a relatively complete satisfaction-based QHL with while-loop since its inception in 2006. This paper presents a solution by proposing the first relatively complete satisfaction-based QHL with while-loop. The completeness is proved in two steps. First, we establish a semantics and proof system of Hoare triples with quantum programs and deterministic assertions. Then, by utilizing the weakest precondition of deterministic assertion, we construct the weakest preterm calculus of probabilistic expressions. The relative completeness of QHL is then obtained as a consequence of the weakest preterm calculus. Using our QHL, we formally verify the correctness of Deutsch's algorithm and quantum teleportation.
Reproducibility is a major concern across scientific fields. Human-Computer Interaction (HCI), in particular, is subject to diverse reproducibility challenges due to the wide range of research methodologies employed. In this article, we explore how the increasing adoption of Large Language Models (LLMs) across all user experience (UX) design and research activities impacts reproducibility in HCI. In particular, we review upcoming reproducibility challenges through the lenses of analogies from past to future (mis)practices like p-hacking and prompt-hacking, general bias, support in data analysis, documentation and education requirements, and possible pressure on the community. We discuss the risks and chances for each of these lenses with the expectation that a more comprehensive discussion will help shape best practices and contribute to valid and reproducible practices around using LLMs in HCI research.
In the context of the Internet of Things (IoT), reliable and energy-efficient provision of IoT applications has become critical. Equipping IoT systems with tools that enable a flexible, well-performing, and automated way of monitoring and managing IoT edge devices is an essential prerequisite. In current IoT systems, low-power edge appliances have been utilized in a way that can not be controlled and re-configured in a timely manner. Hence, conducting a trade-off solution between manageability, performance and design requirements are demanded. This paper introduces a novel approach for fine-grained monitoring and managing individual micro-services within low-power edge devices, which improves system reliability and energy efficiency. The proposed method enables operational flexibility for IoT edge devices by leveraging a modularization technique. Following a review of existing solutions for remote-managed IoT services, a detailed description of the suggested approach is presented. Also, to explore the essential design principles that must be considered in this approach, the suggested architecture is elaborated in detail. Finally, the advantages of the proposed solution to deal with disruptions are demonstrated in the proof of concept-based experiments.
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