Research findings based on the data of current automatic identification systems (AISs) can only be applied to some parts of navigation research owing to their insufficient mining depth. Previously, route planning research has been based on the waypoint and corresponding optimised algorithm without considering the actual navigation situation and sailing habits. The planned route considerably differs from the actual sailing route, and the application result is undesirable. A novel solution to support the route planning problem has been introduced owing to the large accumulation of AIS big data. In this study, the ship navigable route framework (SNRF) which is reflected by real data via mining AIS big data serves as the basic network for the planned maritime route. This study uses the concept of manifold distance based on AIS big data to build a maritime SNRF through high-density searching. It can provide basic theoretical support for actual navigation distance calculation, route planning and route accessibility inspection in the future.

Let $h : \mathbb{R}^2 \to \mathbb{R}^2$ be an orientation preserving homeomorphism of the plane. For any bounded orbit $\mathcal{O}(x)=\{h^n(x):n\in\mathbb{Z}\}$ there exists a fixed point $p\in\mathbb{R}^2$ of h linked to $\mathcal{O}(x)$ in the sense of Gambaudo: one cannot find a Jordan curve $C\subseteq\mathbb{R}^2$ around $\mathcal{O}(x)$, separating it from p, that is isotopic to h(C) in $\mathbb{R}^2\setminus\left(\mathcal{O}(x)\cup\{p\}\right)$.

This study describes an optimal method for deploying rescue ships in response to marine accidents using dynamic programming and particle swarm optimisation in an archipelago. We solved the shortest distance problem from a rescue ship to a marine accident using dynamic programming, which avoids obstacles, such as land or aquacultures. The optimal location problem is NP-hard. However, the optimal locations were found to be efficient among the various candidate combinations using particle swarm optimisation. We compared two models based on the set covering location model (SCLM) and P-median model (PMM). The PMM outperformed the SCLM approach in the test. The findings of this study may be valuable for directing judgments regarding search and rescue (SAR) vessel placements to maximise resource utilisation efficiency and service quality. Furthermore, this process can flexibly arrange multiple rescue ships.

This paper is the first part in a series of three papers devoted to the study of enumerative invariants of abelian surfaces through the tropical approach. In this paper, we consider the enumeration of genus g curves of fixed degree passing through g points. We compute the tropical multiplicity provided by a correspondence theorem due to T. Nishinou and show that it is possible to refine this multiplicity in the style of the Block–Göttsche refined multiplicity to get tropical refined invariants.

Aiming at the error estimation problem of a radar detection system when the variation law of system error is unknown, an improved Gaussian mean-shift radar dynamic error registration algorithm (IGMSR) is proposed. The algorithm can effectively adapt to the variation of system error when the variation law of system error is unknown. The IGMSR algorithm uses the mean-shift method to contribute different characteristics to the estimation results of different sample points, and constructs weight coefficients according to the deviation of sample points from the mean and sampling time. The simulation results show that more than 90% of the constant system errors can be eliminated; for the systematic error with slow change, more than 80% of the bias can be eliminated in real time, while a previous method of Zhu and Wang (2018) can only eliminate 60% of the systematic error and require the change law to be known. This method overcomes the influence of random error and abnormal point, and the estimation results are more robust.

Identifying the absence of situation awareness (SA) in air traffic controllers is critical since it directly affects their hazard perception. This study aims to introduce and validate a multimodal methodology employing electroencephalogram (EEG) and eye-tracking to investigate SA variation within specific air traffic control contexts. Data from 28 participants executing the experiment involving three different SA-probe tests illustrated the conceptual relationship between EEG and eye-tracking indicators and SA variations, using behavioural data as a proxy. The results indicated that both EEG and eye-tracking metrics correlated positively with the SA levels required, that is, the frequency spectrum in the β (13–30 Hz) and γ (30–50 Hz) bands, alongside the fixation/saccade-based indicators and pupil dilation increased in response to higher SA levels. This research has substantial implications for investigating SA using a human-centric approach via psychophysiological indicators, revealing the intrinsic interactions between the human capability envelope and SA, contributing to the development of a real-time monitoring system of SA variations for air transportation safety research.

The International Regulations for the Prevention of Collisions at Sea (IRPCS) provide a comprehensive set of instructions for watchkeeping officers to follow and prevent collisions at sea. This study compares how six newly qualified deck officers and six Master Mariners, who were all trained at the same college, applied the IRPCS. Individual, semi-structured interviews were used to uncover how the 12 participants applied and interpreted the rules for three authentic scenarios. Phenomenography was used to capture the qualitatively different means by which participants interpreted the IRPCS. For basic collision avoidance situations, the results indicated little difference between the cohorts' ability to interpret and apply the IRPCS. However, when the scenarios became more complicated, Master Mariners outperformed newly qualified deck officers. In these cases, Master Mariners displayed a greater capacity to assess the overall situation, whereas newly qualified deck officers tended to simplify by focusing on a single rule. These findings indicate that training needs to focus on developing situational awareness; and training scenarios need to incorporate multiple vessels in authentic scenarios to enhance newly qualified deck officers' capacities to interpret the IRPCS.

Wall-climbing robots work on large steel components with magnets, which limits the use of wireless sensors and magnetometers. This study aims to propose a novel autonomous localisation method (RGBD-IMU-AL) with an inertial measurement unit and a fixed RGB-D camera to improve the localisation performance of wall-climbing robots. The method contains five modules: calibration, tracking, three-dimensional (3D) reconstruction, location and attitude estimation. The calibration module is used to obtain the initial attitude angle. The tracking and 3D reconstruction module are used jointly to obtain the rough position and normal vector of the robot chassis. For the location module, a normal vector projection method is established to screen out the top point on the robot shell. An extended Kalman filter (EKF) is used to estimate the heading angle in the attitude estimation module. Experimental results show that the positioning error is within 0⋅02 m, and the positioning performance is better than that of the MS3D method. The heading angle error remains within 3⋅1°. The obtained results prove its applicability for the autonomous localisation in low-texture and magnetically disturbed environments.

We say that a graph H dominates another graph H′ if the number of homomorphisms from H′ to any graph G is dominated, in an appropriate sense, by the number of homomorphisms from H to G. We study the family of dominating graphs, those graphs with the property that they dominate all of their subgraphs. It has long been known that even-length paths are dominating in this sense and a result of Hatami implies that all weakly norming graphs are dominating. In a previous paper, we showed that every finite reflection group gives rise to a family of weakly norming, and hence dominating, graphs. Here we revisit this connection to show that there is a much broader class of dominating graphs.

In this paper, we establish some finiteness results about the multiplicative dependence of rational values modulo sets which are ‘close’ (with respect to the Weil height) to division groups of finitely generated multiplicative groups of a number field K. For example, we show that under some conditions on rational functions $f_1, \ldots, f_n\in K(X)$, there are only finitely many elements $\alpha \in K$ such that $f_1(\alpha),\ldots,f_n(\alpha)$ are multiplicatively dependent modulo such sets.

We show that if F is $\mathbb{Q}$ or a multiquadratic number field, $p\in\left\{{2,3,5}\right\}$, and $K/F$ is a Galois extension of degree a power of p, then for elliptic curves $E/\mathbb{Q}$ ordered by height, the average dimension of the p-Selmer groups of $E/K$ is bounded. In particular, this provides a bound for the average K-rank of elliptic curves $E/\mathbb{Q}$ for such K. Additionally, we give bounds for certain representation–theoretic invariants of Mordell–Weil groups over Galois extensions of such F.

The central result is that: for each finite Galois extension $K/F$ of number fields and prime number p, as $E/\mathbb{Q}$ varies, the difference in dimension between the Galois fixed space in the p-Selmer group of $E/K$ and the p-Selmer group of $E/F$ has bounded average.

In 2010, Turaev introduced knotoids as a variation on knots that replaces the embedding of a circle with the embedding of a closed interval with two endpoints which here we call poles. We define generalised knotoids to allow arbitrarily many poles, intervals and circles, each pole corresponding to any number of interval endpoints, including zero. This theory subsumes a variety of other related topological objects and introduces some particularly interesting new cases. We explore various analogs of knotoid invariants, including height, index polynomials, bracket polynomials and hyperbolicity. We further generalise to knotoidal graphs, which are a natural extension of spatial graphs that allow both poles and vertices.