Let $G=(V,E)$ be a countable graph. The Bunkbed graph of $G$ is the product graph $G \times K_2$, which has vertex set $V\times \{0,1\}$ with “horizontal” edges inherited from $G$ and additional “vertical” edges connecting $(w,0)$ and $(w,1)$ for each $w \in V$. Kasteleyn’s Bunkbed conjecture states that for each $u,v \in V$ and $p\in [0,1]$, the vertex $(u,0)$ is at least as likely to be connected to $(v,0)$ as to $(v,1)$ under Bernoulli-$p$ bond percolation on the bunkbed graph. We prove that the conjecture holds in the $p \uparrow 1$ limit in the sense that for each finite graph $G$ there exists $\varepsilon (G)\gt 0$ such that the bunkbed conjecture holds for $p \geqslant 1-\varepsilon (G)$.

Bringing together artistic and scientific modes of inquiry, Witness statements and the technologies of memory examines the impact that digital technologies have on the substance of truth and historical facts. Hosted as part of Heba Y. Amin and Anthony Downey's online symposium, which was held in conjunction with Amin's exhibition When I see the future, I close my eyes, Chapter I (curated by Downey for the Mosaic Rooms in 2020), the panel discussed the legacies of colonial power and command, regimes of memory, and the ex post facto constitution of evidence from online archives. Drawing upon the diverse backgrounds and experiences of the panellists, which included Helene Kazan (Oxford Brookes University), Naeem Mohaiemen (Columbia University), and Susan Schuppli (Goldsmiths, University of London), Heba Y. Amin (Staatliche Akademie der Bildenden Künste Stuttgart), and Anthony Downey (Birmingham City University), Witness statements and the technologies of memory sought to more fully understand the impact of digital archives on historical records and evidence-gathering. Against the backdrop of indiscriminate expurgations of online material, we observe how the evidentiary potential of digital archives is compromised by the commercial imperatives of social media networks, censorship, and state surveillance. Among the many questions that arise here, the extent to which personal recollections are often presented as virtual artefacts of memory – a technology of recall or a mnemo-technics in its own right – remains central to the debate about the future of memory in our post-digital age.

Reconstructing past climate events relies on the relevant proxies and how they are related. Depending only on such relationships, however, could not be robust because only few proxy observations are usually available at each age. A state-space model employs a prior to make the hidden past climate events correlated with one another so that extreme inferences are precluded. Here, we construct a Gaussian process state-space model for reconstructing past sea surface temperatures from the alkenone paleotemperature proxy and apply the model to nine sediment cores with three different calibration curves and compare the results.

This paper critically reviews literature about design framing to clarify an understanding of what is meant by the construct of a design frame. It describes the origins of the term design frame and characterises three distinct definitions that can be found within the literature. It reviews empirical studies of design framing to highlight definitional confusion between studies. It discusses the significance of Dorst’s propositional model of design frames and juxtaposes design frames with other related constructs. It clarifies ways that the resolution of nomenclature for describing design framing might lead to a more coherent body of empirical research into this topic. It suggests that there is value in developing a better cognitive model of design framing and outlines potential steps towards such a model.

Path planning is a key research issue in the field of unmanned aerial vehicle (UAV) applications. In practical applications, multi-objective path planning is usually required for multi-UAVs, so this paper proposes the improved balanced artificial bee colony (IB-ABC) algorithm to optimize multi-objective path planning. The algorithm adopts the ABC algorithm that emphasizes the global search capability, which is based on iterative feedback information. It uses single-element points, multi-element points, and iteration constraints to optimize the strategies of employed bees, follower bees, and scout bees, respectively. In terms of time and priority, simulation experiments prove that the IB-ABC algorithm can balance local and global search capabilities, accelerate the speed of convergence, and realize multi-UAV path planning in complex mountain environments.

Industrial robots are widely used in the painting industry, such as automobile manufacturing and solid wood furniture industry. An important problem is how to improve the efficiency of robot programming, especially in the current furniture industry with multiple products, small batches and increasingly high demand for customization. In this work, we propose an outer loop adaptive control scheme, which allow users to realize the practical application of the zero-moment lead-through teaching method based on dynamic model without opening the inner torque control interface of robots. In order to accurately estimate the influence of joint friction, a friction model is established based on static, Coulomb and viscous friction characteristics, and the Sigmoid function is used to represent the transition between motion states. An identification method is used to quickly identify the dynamic parameters of the robot. The joint position/speed command of the robot’s inner joint servo loop is dynamically generated based on the user-designed adaptive control law. In addition, the zero-moment lead-through teaching scheme based on the dynamic model is applied to a spray-painting robot with closed control system. In order to verify our method, CMA GR630ST is used to conduct experiments. We identified the parameters of the dynamic model and carried out the zero-moment lead-through teaching experiment to track the target trajectory. The results show that the proposed method can realize the application of modern control methods in industrial robot with closed control systems, and achieve a preliminary exploration to improve the application scenarios of spray-painting robots.

In this paper, we propose an approach to tune optimal parameters of a robust PID controller by means of computed torque control (CTC) strategy for trajectory tracking of a Delta parallel robot, using a hybrid optimization algorithm of Particle Swarm Optimization (PSO) and differential evolution (DE). It differs from previous works that they propose robust PID controller parameters tuning based on conventional gradient-based optimization algorithms and apply them to process control. First, we reduce the tuning problem of a robust PID controller with CTC strategy satisfying requirements including robustness and disturbance attenuation to an optimization problem with nonlinear constraints by considering the nonlinear dynamic model of a Delta parallel robot. Second, we set up the design characteristics for the trajectory tracking of a Delta parallel robot. Then, we propose a robust PID controller in a way of obtaining the global optimization solution of the nonlinear optimization problem by running a PSO-DE hybrid optimization algorithm of finding the global optimal solution by maintaining the diversity of swarm during evolution based on the evolution of cognitive experience. Simulation and experimental results demonstrate that the proposed controller outperforms previous works with respect to robust performance and active disturbance attenuation when it is applied to tracking control of a Delta parallel robot.

An old conjecture of Erdős and McKay states that if all homogeneous sets in an $n$-vertex graph are of order $O(\!\log n)$ then the graph contains induced subgraphs of each size from $\{0,1,\ldots, \Omega \big(n^2\big)\}$. We prove a bipartite analogue of the conjecture: if all balanced homogeneous sets in an $n \times n$ bipartite graph are of order $O(\!\log n)$, then the graph contains induced subgraphs of each size from $\{0,1,\ldots, \Omega \big(n^2\big)\}$.

Gambling marketing is frequently visible in the United Kingdom, especially around the national sport, soccer. Previous research has documented the frequency with which gambling marketing logos can be seen in domestic club soccer, and also the frequency of television advertising around international tournaments. The present research investigates the frequency and content of television advertising during the men’s 2020 Euro soccer tournament, a high-profile tournament shown since the industry’s voluntary “whistle-to-whistle ban” on gambling advertising came into effect. Overall, 113 gambling adverts were recorded (4.5 adverts per relevant match). Financial inducements were the most frequently shown category (56.6%), followed by adverts raising awareness of a given operator’s brand (19.5%), adverts featuring the odds on specific complex bets (18.6%), and adverts promoting safer gambling (5.3%). Adverts featured a range of safer gambling messages, with the “when the fun stops, stop” message featuring in 56.6% of adverts. This research indicates that gambling advertising remains a frequent part of the experience of watching live televised soccer in the UK, and shows how the content of this advertising was comparable to what has been seen in the previous literature.

Given a graphon $W$ and a finite simple graph $H$, with vertex set $V(H)$, denote by $X_n(H, W)$ the number of copies of $H$ in a $W$-random graph on $n$ vertices. The asymptotic distribution of $X_n(H, W)$ was recently obtained by Hladký, Pelekis, and Šileikis [17] in the case where $H$ is a clique. In this paper, we extend this result to any fixed graph $H$. Towards this we introduce a notion of $H$-regularity of graphons and show that if the graphon $W$ is not $H$-regular, then $X_n(H, W)$ has Gaussian fluctuations with scaling $n^{|V(H)|-\frac{1}{2}}$. On the other hand, if $W$ is $H$-regular, then the fluctuations are of order $n^{|V(H)|-1}$ and the limiting distribution of $X_n(H, W)$ can have both Gaussian and non-Gaussian components, where the non-Gaussian component is a (possibly) infinite weighted sum of centred chi-squared random variables with the weights determined by the spectral properties of a graphon derived from $W$. Our proofs use the asymptotic theory of generalised $U$-statistics developed by Janson and Nowicki [22]. We also investigate the structure of $H$-regular graphons for which either the Gaussian or the non-Gaussian component of the limiting distribution (but not both) is degenerate. Interestingly, there are also $H$-regular graphons $W$ for which both the Gaussian or the non-Gaussian components are degenerate, that is, $X_n(H, W)$ has a degenerate limit even under the scaling $n^{|V(H)|-1}$. We give an example of this degeneracy with $H=K_{1, 3}$ (the 3-star) and also establish non-degeneracy in a few examples. This naturally leads to interesting open questions on higher order degeneracies.