Let $S_g$ denote the genus g closed orientable surface. A coherent filling pair of simple closed curves, $(\alpha,\beta)$ in $S_g$, is a filling pair that has its geometric intersection number equal to the absolute value of its algebraic intersection number. A minimally intersecting filling pair, $(\alpha,\beta)$ in $S_g$, is one whose intersection number is the minimal among all filling pairs of $S_g$. In this paper, we give a simple geometric procedure for constructing minimally intersecting coherent filling pairs on $S_g, \ g \geq 3,$ from the starting point of a coherent filling pair of curves on a torus. Coherent filling pairs have a natural correspondence to square-tiled surfaces, or origamis, and we discuss the origami obtained from the construction.

Maritime safety faces growing challenges due to an expanding global fleet, tighter schedules, and increasingly complex stakeholder interactions. This study integrates multiple data sources to determine a more accurate representation of major marine accident causative factors in the United Kingdom. Logistic regression and data modelling are applied to Automatic Identification System data (2011–2017) and reported accidents from the Marine Accident Investigation Branch (2013–2019). Results show that larger vessels, daytime transits, service ships, winter conditions, and confined high-density areas such as ports impact accident likelihood. Interviews validate the data and emphasize the influence of port geometry and channel complexity. Among major UK ports, London, Plymouth and Milford Haven exhibit the highest accident-to-traffic densities. While maritime regulations and safety management systems in ports and vessels are seen as adequate by industry professionals, human factors require the greatest attention to improve maritime safety.

Let $M^{({k})}_{d}(n)$ be the manifold of n-tuples $(x_1,\ldots,x_n)\in(\mathbb{R}^d)^n$ having non-k-equal coordinates. We show that, for $d\geq2$, $M^{({3})}_{d}(n)$ is rationally formal if and only if $n\leq6$. This stands in sharp contrast with the fact that all classical configuration spaces $M^{({2})}_d(n)=\text{Conf}(\mathbb{R}^d,n)$ are rationally formal, just as are all complements of arrangements of arbitrary complex subspaces with geometric lattice of intersections. The rational non-formality of $M^{({3})}_{d}(n)$ for $n \gt 6$ is established via detection of non-trivial triple Massey products, which are assessed geometrically through Poincaré duality.

The paper explores the accuracy of WiFi-Round Trip Timing (RTT) positioning in indoor environments. Filtering techniques are applied to WiFi-RTT positioning in indoor environments, enhanced by Residual Signal Strength Indicator (RSSI)-based outlier detection. A Genetic and Grid filter are compared with a Particle filter and single-epoch least-squares across a range of test scenarios. In static scenarios, 67% of trials had sub-metre accuracy and 90.5% had a root mean square error (RMSE) below 2 m. In Non-Line-of-Sight (NLOS) conditions, 38% of trials had sub-metre accuracy, whereas for environments with full Line-of-Sight (LOS) conditions, 95.2% of trials had sub-metre accuracy. In scenarios with motion, 22.2% of trials had sub-metre accuracy. RSSI-based outlier detection in NLOS conditions, provided an average improvement of 41.3% over no outlier detection across all algorithms in the static and 14% in the dynamic tests. The Genetic filter achieved a mean improvement of 49.2% in the static and 47% in the dynamic tests compared with least squares.

Let G and H be finite-dimensional vector spaces over $\mathbb{F}_p$. A subset $A \subseteq G \times H$ is said to be transverse if all of its rows $\{x \in G \colon (x,y) \in A\}$, $y \in H$, are subspaces of G and all of its columns $\{y \in H \colon (x,y) \in A\}$, $x \in G$, are subspaces of H. As a corollary of a bilinear version of the Bogolyubov argument, Gowers and the author proved that dense transverse sets contain bilinear varieties of bounded codimension. In this paper, we provide a direct combinatorial proof of this fact. In particular, we improve the bounds and evade the use of Fourier analysis and Freiman’s theorem and its variants.