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We derive conditions for the existence of fixed points of cone mappings without assuming scalability of functions. Monotonicity and scalability are often inseparable in the literature in the context of searching for fixed points of interference mappings. In applications, such mappings are approximated by non-negative neural networks. It turns out, however, that the process of training non-negative networks requires imposing an artificial constraint on the weights of the model. However, in the case of specific non-negative data, it cannot be said that if the mapping is non-negative, it has only non-negative weights. Therefore, we considered the problem of the existence of fixed points for general neural networks, assuming the conditions of tangency conditions with respect to specific cones. This does not relax the physical assumptions, because even assuming that the input and output are to be non-negative, the weights can have (small, but) less than zero values. Such properties (often found in papers on the interpretability of weights of neural networks) lead to the weakening of the assumptions about the monotonicity or scalability of the mapping associated with the neural network. To the best of our knowledge, this paper is the first to study this phenomenon.

We quantify the elementary Borel-Cantelli Lemma by higher moments of the overlap count statistic in terms of the weighted summability of the probabilities. Applications include mean deviation frequencies in the Strong Law and the Law of the Iterated Logarithm.

In this work, we consider the task of improving the accuracy of dynamic models for model predictive control (MPC) in an online setting. Even though prediction models can be learned and applied to model-based controllers, these models are often learned offline. In this offline setting, training data is first collected and a prediction model is learned through an elaborated training procedure. After the model is trained to a desired accuracy, it is then deployed in a model predictive controller. However, since the model is learned offline, it does not adapt to disturbances or model errors observed during deployment. To improve the adaptiveness of the model and the controller, we propose an online dynamics learning framework that continually improves the accuracy of the dynamic model during deployment. We adopt knowledge-based neural ordinary differential equations (KNODE) as the dynamic models, and use techniques inspired by transfer learning to continually improve the model accuracy. We demonstrate the efficacy of our framework with a quadrotor robot, and verify the framework in both simulations and physical experiments. Results show that the proposed approach is able to account for disturbances that are possibly time-varying, while maintaining good trajectory tracking performance.

Passive acoustic monitoring is a promising method for surveying wildlife populations that are easier to detect acoustically than visually. When animal vocalisations can be uniquely identified on an array of several sensors, the potential exists to estimate population density through acoustic spatial capture-recapture (ASCR). Detections need to be correctly identified and associated across sensors so that capture histories can be built. However, sound classification is imperfect, and in some situations a high proportion of sounds detected on just a single sensor ("singletons") are not from the target species, i.e., are false positives. We present a case study of bowhead whale calls (Baleana mysticetus) collected in the Beaufort Sea in 2010. We propose a novel extension of ASCR that is robust to these false positives by conditioning on calls being detected by at least two sensors. We allow for individual-level detection heterogeneity through modelling a variable sound source level, we model an inhomogeneous call spatial density, and we include bearings with varying measurement error. We show via simulation based on the case study that the method produces near-unbiased estimates when correctly specified. Ignoring source level variation resulted in a strong negative bias, while ignoring inhomogeneous density resulted in severe positive bias. The case study analysis indicated a band of higher call density approximately 30km from shore; 60.7% of singletons were estimated to have been false positives.

Enhancing existing transmission lines is a useful tool to combat transmission congestion and guarantee transmission security with increasing demand and boosting the renewable energy source. This study concerns the selection of lines whose capacity should be expanded and by how much from the perspective of independent system operator (ISO) to minimize the system cost with the consideration of transmission line constraints and electricity generation and demand balance conditions, and incorporating ramp-up and startup ramp rates, shutdown ramp rates, ramp-down rate limits and minimum up and minimum down times. For that purpose, we develop the ISO unit commitment and economic dispatch model and show it as a right-hand side uncertainty multiple parametric analysis for the mixed integer linear programming (MILP) problem. We first relax the binary variable to continuous variables and employ the Lagrange method and Karush-Kuhn-Tucker conditions to obtain optimal solutions (optimal decision variables and objective function) and critical regions associated with active and inactive constraints. Further, we extend the traditional branch and bound method for the large-scale MILP problem by determining the upper bound of the problem at each node, then comparing the difference between the upper and lower bounds and reaching the approximate optimal solution within the decision makers' tolerated error range. In additional, the objective function's first derivative on the parameters of each line is used to inform the selection of lines to ease congestion and maximize social welfare. Finally, the amount of capacity upgrade will be chosen by balancing the cost-reduction rate of the objective function on parameters and the cost of the line upgrade. Our findings are supported by numerical simulation and provide transmission line planners with decision-making guidance.

In a desired environmental protection system, groundwater may not be excluded. In addition to the problem of over-exploitation, in total disagreement with the concept of sustainable development, another not negligible issue concerns the groundwater contamination. Mainly, this aspect is due to intensive agricultural activities or industrialized areas. In literature, several papers have dealt with transport problem, especially for inverse problems in which the release history or the source location are identified. The innovative aim of the paper is to develop a data-driven model that is able to analyze multiple scenarios, even strongly non-linear, in order to solve forward and inverse transport problems, preserving the reliability of the results and reducing the uncertainty. Furthermore, this tool has the characteristic of providing extremely fast responses, essential to identify remediation strategies immediately. The advantages produced by the model were compared with literature studies. In this regard, a feedforward artificial neural network, which has been trained to handle different cases, represents the data-driven model. Firstly, to identify the concentration of the pollutant at specific observation points in the study area (forward problem); secondly, to deal with inverse problems identifying the release history at known source location; then, in case of one contaminant source, identifying the release history and, at the same time, the location of the source in a specific sub-domain of the investigated area. At last, the observation error is investigated and estimated. The results are satisfactorily achieved, highlighting the capability of the ANN to deal with multiple scenarios by approximating nonlinear functions without the physical point of view that describes the phenomenon, providing reliable results, with very low computational burden and uncertainty.

Near-term quantum systems tend to be noisy. Crosstalk noise has been recognized as one of several major types of noises in superconducting Noisy Intermediate-Scale Quantum (NISQ) devices. Crosstalk arises from the concurrent execution of two-qubit gates on nearby qubits, such as \texttt{CX}. It might significantly raise the error rate of gates in comparison to running them individually. Crosstalk can be mitigated through scheduling or hardware machine tuning. Prior scientific studies, however, manage crosstalk at a really late phase in the compilation process, usually after hardware mapping is done. It may miss great opportunities of optimizing algorithm logic, routing, and crosstalk at the same time. In this paper, we push the envelope by considering all these factors simultaneously at the very early compilation stage. We propose a crosstalk-aware quantum program compilation framework called CQC that can enhance crosstalk mitigation while achieving satisfactory circuit depth. Moreover, we identify opportunities for translation from intermediate representation to the circuit for application-specific crosstalk mitigation, for instance, the \texttt{CX} ladder construction in variational quantum eigensolvers (VQE). Evaluations through simulation and on real IBM-Q devices show that our framework can significantly reduce the error rate by up to 6$\times$, with only $\sim$60\% circuit depth compared to state-of-the-art gate scheduling approaches. In particular, for VQE, we demonstrate 49\% circuit depth reduction with 9.6\% fidelity improvement over prior art on the H4 molecule using IBMQ Guadalupe. Our CQC framework will be released on GitHub.

CyberPhysical systems (CPS) must be closely monitored to identify and potentially mitigate emergent problems that arise during their routine operations. However, the multivariate time-series data which they typically produce can be complex to understand and analyze. While formal product documentation often provides example data plots with diagnostic suggestions, the sheer diversity of attributes, critical thresholds, and data interactions can be overwhelming to non-experts who subsequently seek help from discussion forums to interpret their data logs. Deep learning models, such as Long Short-term memory (LSTM) networks can be used to automate these tasks and to provide clear explanations of diverse anomalies detected in real-time multivariate data-streams. In this paper we present RESAM, a requirements process that integrates knowledge from domain experts, discussion forums, and formal product documentation, to discover and specify requirements and design definitions in the form of time-series attributes that contribute to the construction of effective deep learning anomaly detectors. We present a case-study based on a flight control system for small Uncrewed Aerial Systems and demonstrate that its use guides the construction of effective anomaly detection models whilst also providing underlying support for explainability. RESAM is relevant to domains in which open or closed online forums provide discussion support for log analysis.

The existence of representative datasets is a prerequisite of many successful artificial intelligence and machine learning models. However, the subsequent application of these models often involves scenarios that are inadequately represented in the data used for training. The reasons for this are manifold and range from time and cost constraints to ethical considerations. As a consequence, the reliable use of these models, especially in safety-critical applications, is a huge challenge. Leveraging additional, already existing sources of knowledge is key to overcome the limitations of purely data-driven approaches, and eventually to increase the generalization capability of these models. Furthermore, predictions that conform with knowledge are crucial for making trustworthy and safe decisions even in underrepresented scenarios. This work provides an overview of existing techniques and methods in the literature that combine data-based models with existing knowledge. The identified approaches are structured according to the categories integration, extraction and conformity. Special attention is given to applications in the field of autonomous driving.

Artificial Intelligence (AI) is rapidly becoming integrated into military Command and Control (C2) systems as a strategic priority for many defence forces. The successful implementation of AI is promising to herald a significant leap in C2 agility through automation. However, realistic expectations need to be set on what AI can achieve in the foreseeable future. This paper will argue that AI could lead to a fragility trap, whereby the delegation of C2 functions to an AI could increase the fragility of C2, resulting in catastrophic strategic failures. This calls for a new framework for AI in C2 to avoid this trap. We will argue that antifragility along with agility should form the core design principles for AI-enabled C2 systems. This duality is termed Agile, Antifragile, AI-Enabled Command and Control (A3IC2). An A3IC2 system continuously improves its capacity to perform in the face of shocks and surprises through overcompensation from feedback during the C2 decision-making cycle. An A3IC2 system will not only be able to survive within a complex operational environment, it will also thrive, benefiting from the inevitable shocks and volatility of war.