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We update a previous N$^3$LL$^\prime$+${\cal O}(\alpha_s^3)$ determination of the strong coupling from a global fit to thrust data by including newly available perturbative ingredients, upgrading the renormalization scales to include a fully canonical scaling region, and implementing the log resummation in a way which ensures the integrated cross section is unaffected by the the leading $1/Q$ hadronization power corrections. Detailed discussions are provided concerning the stability of the results under variations of the fit range and the importance of summing up higher-order logarithmic terms for convergence and stability. We show that high-precision results can be achieved even when carrying out a more conservative fit by restricting the dataset to a region which is more clearly dominated by dijet events. This leads to $\alpha_s(m_Z) = 0.1136 \pm 0.0012$ with $\chi^2/{\rm dof}=0.86$, fully compatible with earlier results using a larger fit range. We also demonstrate that a number of additional effects associated to power corrections have a small impact on this fit result, including modifications to the renormalon substraction scheme for dijet power corrections and the inclusion of three-jet power correction models. The fit is also shown to provide very good agreement with data outside the fit range., Comment: 66 pages including appendices, 21 figures

Millimeter-wave (mmWave) is a key enabler for next-generation transportation systems. However, in an urban city scenario, mmWave is highly susceptible to blockages and shadowing. Therefore, base station (BS) placement is a crucial task in the infrastructure design where coverage requirements need to be met while simultaneously supporting localisation. This work assumes a pre-deployed BS and another BS is required to be added to support both localisation accuracy and coverage rate in an urban city scenario. To solve this complex multi-objective optimisation problem, we utilise deep reinforcement learning (DRL). Concretely, this work proposes: 1) a three-layered grid for state representation as the input of the DRL, which enables it to adapt to the changes in the wireless environment represented by changing the position of the pre-deployed BS, and 2) the design of a suitable reward function for the DRL agent to solve the multi-objective problem. Numerical analysis shows that the proposed deep Q-network (DQN) model can learn/adapt from the complex radio environment represented by the terrain map and provides the same/similar solution to the exhaustive search, which is used as a benchmark. In addition, we show that an exclusive optimisation of coverage rate does not result in improved localisation accuracy, and thus there is a trade-off between the two solutions., Comment: Accepted EuCNC 2024

Every ordered collection of sets in Euclidean space can be associated to a combinatorial code, which records the regions cut out by the sets in space. Given two ordered collections of sets, one can form a third collection in which the $i$-th set is the Cartesian product of the corresponding sets from the original collections. We prove a general "product theorem" which characterizes the code associated to the collection resulting from this operation, in terms of the codes associated to the original collections. We use this theorem to characterize the codes realizable by axis-parallel boxes, and exhibit differences between this class of codes and those realizable by convex open or closed sets. We also use our theorem to prove that a "monotonicity of open convexity" result of Cruz, Giusti, Itskov, and Kronholm holds for closed sets when some assumptions are slightly weakened., Comment: 15 pages, 6 figures