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By computing a feedback control via the linear quadratic regulator (LQR) approach and simulating a non-linear non-autonomous closed-loop system using this feedback, we combine two numerically challenging tasks. For the first task, the computation of the feedback control, we use the non-autonomous generalized differential Riccati equation (DRE), whose solution determines the time-varying feedback gain matrix. Regarding the second task, we want to be able to simulate non-linear closed-loop systems for which it is known that the regulator is only valid for sufficiently small perturbations. Thus, one easily runs into numerical issues in the integrators when the closed-loop control varies greatly. For these systems, e.g., the A-stable implicit Euler methods fails.\newline On the one hand, we implement non-autonomous versions of splitting schemes and BDF methods for the solution of our non-autonomous DREs. These are well-established DRE solvers in the autonomous case. On the other hand, to tackle the numerical issues in the simulation of the non-linear closed-loop system, we apply a fractional-step-theta scheme with time-adaptivity tuned specifically to this kind of challenge. That is, we additionally base the time-adaptivity on the activity of the control. We compare this approach to the more classical error-based time-adaptivity.\newline We describe techniques to make these two tasks computable in a reasonable amount of time and are able to simulate closed-loop systems with strongly varying controls, while avoiding numerical issues. Our time-adaptivity approach requires fewer time steps than the error-based alternative and is more reliable.

The dependence of Natural Language Processing (NLP) intelligent software on Large Language Models (LLMs) is increasingly prominent, underscoring the necessity for robustness testing. Current testing methods focus solely on the robustness of LLM-based software to prompts. Given the complexity and diversity of real-world inputs, studying the robustness of LLMbased software in handling comprehensive inputs (including prompts and examples) is crucial for a thorough understanding of its performance. To this end, this paper introduces RITFIS, a Robust Input Testing Framework for LLM-based Intelligent Software. To our knowledge, RITFIS is the first framework designed to assess the robustness of LLM-based intelligent software against natural language inputs. This framework, based on given threat models and prompts, primarily defines the testing process as a combinatorial optimization problem. Successful test cases are determined by a goal function, creating a transformation space for the original examples through perturbation means, and employing a series of search methods to filter cases that meet both the testing objectives and language constraints. RITFIS, with its modular design, offers a comprehensive method for evaluating the robustness of LLMbased intelligent software. RITFIS adapts 17 automated testing methods, originally designed for Deep Neural Network (DNN)-based intelligent software, to the LLM-based software testing scenario. It demonstrates the effectiveness of RITFIS in evaluating LLM-based intelligent software through empirical validation. However, existing methods generally have limitations, especially when dealing with lengthy texts and structurally complex threat models. Therefore, we conducted a comprehensive analysis based on five metrics and provided insightful testing method optimization strategies, benefiting both researchers and everyday users.

A major challenge in computed tomography is reconstructing objects from incomplete data. An increasingly popular solution for these problems is to incorporate deep learning models into reconstruction algorithms. This study introduces a novel approach by integrating a Fourier neural operator (FNO) into the Filtered Backprojection (FBP) reconstruction method, yielding the FNO back projection (FNO-BP) network. We employ moment conditions for sinogram extrapolation to assist the model in mitigating artefacts from limited data. Notably, our deep learning architecture maintains a runtime comparable to classical filtered back projection (FBP) reconstructions, ensuring swift performance during both inference and training. We assess our reconstruction method in the context of the Helsinki Tomography Challenge 2022 and also compare it against regular FBP methods.

Social-ecological systems (SES) research aims to understand the nature of social-ecological phenomena, to find effective ways to foster or manage conditions under which desirable phenomena, such as sustainable resource use, occur or to change conditions or reduce the negative consequences of undesirable phenomena, such as poverty traps. Challenges such as these are often addressed using dynamical systems models (DSM) or agent-based models (ABM). Both modeling approaches have strengths and weaknesses. DSM are praised for their analytical tractability and efficient exploration of asymptotic dynamics and bifurcation, which are enabled by reduced number and heterogeneity of system components. ABM allows representing heterogeneity, agency, learning and interactions of diverse agents within SES, but this also comes at a price such as inefficiency to explore asymptotic dynamics or bifurcations. In this paper we combine DSM and ABM to leverage strengths of each modeling technique and gain deeper insights into dynamics of a system. We start with an ABM and research questions that the ABM was not able to answer. Using results of the ABM analysis as inputs for DSM, we create a DSM. Stability and bifurcation analysis of the DSM gives partial answers to the research questions and direct attention to where additional details are needed. This informs further ABM analysis, prevents burdening the ABM with less important details and reveals new insights about system dynamics. The iterative process and dialogue between the ABM and DSM leads to more complete answers to research questions and surpasses insights provided by each of the models separately. We illustrate the procedure with the example of the emergence of poverty traps in an agricultural system with endogenously driven innovation.

Local variable selection aims to discover localized effects by assessing the impact of covariates on outcomes within specific regions defined by other covariates. We outline some challenges of local variable selection in the presence of non-linear relationships and model misspecification. Specifically, we highlight a potential drawback of common semi-parametric methods: even slight model misspecification can result in a high rate of false positives. To address these shortcomings, we propose a methodology based on orthogonal cut splines that achieves consistent local variable selection in high-dimensional scenarios. Our approach offers simplicity, handles both continuous and discrete covariates, and provides theory for high-dimensional covariates and model misspecification. We discuss settings with either independent or dependent data. Our proposal allows including adjustment covariates that do not undergo selection, enhancing flexibility in modeling complex scenarios. We illustrate its application in simulation studies with both independent and functional data, as well as with two real datasets. One dataset evaluates salary gaps associated with discrimination factors at different ages, while the other examines the effects of covariates on brain activation over time. The approach is implemented in the R package mombf.

Fourth-order variational inequalities are encountered in various scientific and engineering disciplines, including elliptic optimal control problems and plate obstacle problems. In this paper, we consider additive Schwarz methods for solving fourth-order variational inequalities. Based on a unified framework of various finite element methods for fourth-order variational inequalities, we develop one- and two-level additive Schwarz methods. We prove that the two-level method is scalable in the sense that the convergence rate of the method depends on $H/h$ and $H/\delta$ only, where $h$ and $H$ are the typical diameters of an element and a subdomain, respectively, and $\delta$ measures the overlap among the subdomains. This proof relies on a new nonlinear positivity-preserving coarse interpolation operator, the construction of which was previously unknown. To the best of our knowledge, this analysis represents the first investigation into the scalability of the two-level additive Schwarz method for fourth-order variational inequalities. Our theoretical results are verified by numerical experiments.

Complex interval arithmetic is a powerful tool for the analysis of computational errors. The naturally arising rectangular, polar, and circular (together called primitive) interval types are not closed under simple arithmetic operations, and their use yields overly relaxed bounds. The later introduced polygonal type, on the other hand, allows for arbitrarily precise representation of the above operations for a higher computational cost. We propose the polyarcular interval type as an effective extension of the previous types. The polyarcular interval can represent all primitive intervals and most of their arithmetic combinations precisely and has an approximation capability competing with that of the polygonal interval. In particular, in antenna tolerance analysis it can achieve perfect accuracy for lower computational cost then the polygonal type, which we show in a relevant case study. In this paper, we present a rigorous analysis of the arithmetic properties of all five interval types, involving a new algebro-geometric method of boundary analysis.

The spread of the Internet of Things (IoT) is demanding new, powerful architectures for handling the huge amounts of data produced by the IoT devices. In many scenarios, many existing isolated solutions applied to IoT devices use a set of rules to detect, report and mitigate malware activities or threats. This paper describes a development environment that allows the programming and debugging of such rule-based multi-agent solutions. The solution consists of the integration of a rule engine into the agent, the use of a specialized, wrapping agent class with a graphical user interface for programming and testing purposes, and a mechanism for the incremental composition of behaviors. Finally, a set of examples and a comparative study were accomplished to test the suitability and validity of the approach. The JADE multi-agent middleware has been used for the practical implementation of the approach.

Graph representation learning for hypergraphs can be used to extract patterns among higher-order interactions that are critically important in many real world problems. Current approaches designed for hypergraphs, however, are unable to handle different types of hypergraphs and are typically not generic for various learning tasks. Indeed, models that can predict variable-sized heterogeneous hyperedges have not been available. Here we develop a new self-attention based graph neural network called Hyper-SAGNN applicable to homogeneous and heterogeneous hypergraphs with variable hyperedge sizes. We perform extensive evaluations on multiple datasets, including four benchmark network datasets and two single-cell Hi-C datasets in genomics. We demonstrate that Hyper-SAGNN significantly outperforms the state-of-the-art methods on traditional tasks while also achieving great performance on a new task called outsider identification. Hyper-SAGNN will be useful for graph representation learning to uncover complex higher-order interactions in different applications.