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An infinite game on the set of real numbers appeared in Matthew Baker's work [Math. Mag. 80 (2007), no. 5, pp. 377--380] in which he asks whether it can help characterize countable subsets of the reals. This question is in a similar spirit to how the Banach-Mazur Game characterizes meager sets in an arbitrary topological space. In a recent paper, Will Brian and Steven Clontz prove that in Baker's game, Player II has a winning strategy if and only if the payoff set is countable. They also asked if it is possible, in general linear orders, for Player II to have a winning strategy on some uncountable set. To this we give a positive answer and moreover construct, for every infinite cardinal $\kappa$, a dense linear order of size $\kappa$ on which Player II has a winning strategy on all payoff sets. We finish with some future research questions, further underlining the difficulty in generalizing the characterization of Brian and Clontz to linear orders.

Hydrogen has emerged as a promising option for promoting decarbonization in various sectors by serving as a replacement for natural gas while retaining the combustion-based conversion system. However, its higher reactivity compared to natural gas introduces a significant risk of flashback. This study investigates the impact of operating and geometry parameters on flashback phenomena in multi-slit burners fed with hydrogen-methane-air mixtures. For this purpose, transient numerical simulations, which take into account conjugate heat transfer between the fluid and the solid walls, are coupled with stochastic sensitivity analysis based on Generalized Polynomial Chaos. This allows deriving comprehensive maps of flashback velocities and burner temperatures within the parameter space of hydrogen content, equivalence ratio, and slit width, using a limited number of numerical simulations. Moreover, we assess the influence of different parameters and their interactions on flashback propensity. The ranges we investigate encompass highly H2-enriched lean mixtures, ranging from 80% to 100% H2 by volume, with equivalence ratios ranging from 0.5 to 1.0. We also consider slit widths that are typically encountered in burners for end-user devices, ranging from 0.5 mm to 1.2 mm. The study highlights the dominant role of preferential diffusion in affecting flashback physics and propensity as parameters vary, including significant enrichment close to the burner plate due to the Soret effect. These findings hold promise for driving the design and optimization of perforated burners, enabling their safe and efficient operation in practical end-user applications.

The potential for data-driven applications to scale-resolving simulations of turbulent flows is assessed herein. Multigrid sequential data assimilation algorithms have been used to calibrate solvers for Large Eddy Simulation for the analysis of the high-Reynolds-number flow around a rectangular cylinder of aspect ratio 5:1. This test case has been chosen because of a number of physical complexities which elude accurate representation using reduced-order numerical simulation. The results for the statistical moments of the velocity and pressure flow field show that the data-driven techniques employed, which are based on the Ensemble Kalman Filter, are able to significantly improve the predictive features of the solver for reduced grid resolution. In addition, it was observed that, despite the sparse and asymmetric distribution of observation in the data-driven process, the data augmented results exhibit perfectly symmetric statistics and a significantly improved accuracy also far from the sensor location.

The game of Jenga represents an inspiring benchmark for developing innovative manipulation solutions for complex tasks. Indeed, it encouraged the study of novel robotics methods to successfully extract blocks from the tower. A Jenga game round undoubtedly embeds many traits of complex industrial or surgical manipulation tasks, requiring a multi-step strategy, the combination of visual and tactile data, and the highly precise motion of the robotic arm to perform a single block extraction. In this work, we propose a novel, cost-effective architecture for playing Jenga with e.Do, a 6-DOF anthropomorphic manipulator manufactured by Comau, a standard depth camera, and an inexpensive monodirectional force sensor. Our solution focuses on a visual-based control strategy to accurately align the end-effector with the desired block, enabling block extraction by pushing. To this aim, we train an instance segmentation deep learning model on a synthetic custom dataset to segment each piece of the Jenga tower, allowing visual tracking of the desired block's pose during the motion of the manipulator. We integrate the visual-based strategy with a 1D force sensor to detect whether the block can be safely removed by identifying a force threshold value. Our experimentation shows that our low-cost solution allows e.DO to precisely reach removable blocks and perform up to 14 consecutive extractions in a row.

Precise and accurate localization in outdoor and indoor environments is a challenging problem that currently constitutes a significant limitation for several practical applications. Ultra-wideband (UWB) localization technology represents a valuable low-cost solution to the problem. However, non-line-of-sight (NLOS) conditions and complexity of the specific radio environment can easily introduce a positive bias in the ranging measurement, resulting in highly inaccurate and unsatisfactory position estimation. In the light of this, we leverage the latest advancement in deep neural network optimization techniques and their implementation on ultra-low-power microcontrollers to introduce an effective range error mitigation solution that provides corrections in either NLOS or LOS conditions with a few mW of power. Our extensive experimentation endorses the advantages and improvements of our low-cost and power-efficient methodology.

Single-Image Super-Resolution can support robotic tasks in environments where a reliable visual stream is required to monitor the mission, handle teleoperation or study relevant visual details. In this work, we propose an efficient Generative Adversarial Network model for real-time Super-Resolution, called EdgeSRGAN (code available at https://github.com/PIC4SeR/EdgeSRGAN). We adopt a tailored architecture of the original SRGAN and model quantization to boost the execution on CPU and Edge TPU devices, achieving up to 200 fps inference. We further optimize our model by distilling its knowledge to a smaller version of the network and obtain remarkable improvements compared to the standard training approach. Our experiments show that our fast and lightweight model preserves considerably satisfying image quality compared to heavier state-of-the-art models. Finally, we conduct experiments on image transmission with bandwidth degradation to highlight the advantages of the proposed system for mobile robotic applications.

Domain Generalization (DG) studies the capability of a deep learning model to generalize to out-of-training distributions. In the last decade, literature has been massively filled with training methodologies that claim to obtain more abstract and robust data representations to tackle domain shifts. Recent research has provided a reproducible benchmark for DG, pointing out the effectiveness of naive empirical risk minimization (ERM) over existing algorithms. Nevertheless, researchers persist in using the same outdated feature extractors, and no attention has been given to the effects of different backbones yet. In this paper, we start back to the backbones proposing a comprehensive analysis of their intrinsic generalization capabilities, which so far have been ignored by the research community. We evaluate a wide variety of feature extractors, from standard residual solutions to transformer-based architectures, finding an evident linear correlation between large-scale single-domain classification accuracy and DG capability. Our extensive experimentation shows that by adopting competitive backbones in conjunction with effective data augmentation, plain ERM outperforms recent DG solutions and achieves state-of-the-art accuracy. Moreover, our additional qualitative studies reveal that novel backbones give more similar representations to same-class samples, separating different domains in the feature space. This boost in generalization capabilities leaves marginal room for DG algorithms. It suggests a new paradigm for investigating the problem, placing backbones in the spotlight and encouraging the development of consistent algorithms on top of them. The code is available at https://github.com/PIC4SeR/Back-to-Bones.

We extend the theory of dual Coxeter and Artin groups to all rank-three Coxeter systems, beyond the previously studied spherical and affine cases. Using geometric, combinatorial, and topological techniques, we show that rank-three noncrossing partition posets are EL-shellable lattices and give rise to Garside groups isomorphic to the associated standard Artin groups. Within this framework, we prove the $K(\pi, 1)$ conjecture, the triviality of the center, and the solubility of the word problem for rank-three Artin groups. Some of our constructions apply to general Artin groups; we hope they will help develop complete solutions to the $K(\pi, 1)$ conjecture and other open problems in the area.

Precision agriculture is rapidly attracting research to efficiently introduce automation and robotics solutions to support agricultural activities. Robotic navigation in vineyards and orchards offers competitive advantages in autonomously monitoring and easily accessing crops for harvesting, spraying and performing time-consuming necessary tasks. Nowadays, autonomous navigation algorithms exploit expensive sensors which also require heavy computational cost for data processing. Nonetheless, vineyard rows represent a challenging outdoor scenario where GPS and Visual Odometry techniques often struggle to provide reliable positioning information. In this work, we combine Edge AI with Deep Reinforcement Learning to propose a cutting-edge lightweight solution to tackle the problem of autonomous vineyard navigation without exploiting precise localization data and overcoming task-tailored algorithms with a flexible learning-based approach. We train an end-to-end sensorimotor agent which directly maps noisy depth images and position-agnostic robot state information to velocity commands and guides the robot to the end of a row, continuously adjusting its heading for a collision-free central trajectory. Our extensive experimentation in realistic simulated vineyards demonstrates the effectiveness of our solution and the generalization capabilities of our agent.

The development of precision agriculture has gradually introduced automation in the agricultural process to support and rationalize all the activities related to field management. In particular, service robotics plays a predominant role in this evolution by deploying autonomous agents able to navigate in fields while executing different tasks without the need for human intervention, such as monitoring, spraying and harvesting. In this context, global path planning is the first necessary step for every robotic mission and ensures that the navigation is performed efficiently and with complete field coverage. In this paper, we propose a learning-based approach to tackle waypoint generation for planning a navigation path for row-based crops, starting from a top-view map of the region-of-interest. We present a novel methodology for waypoint clustering based on a contrastive loss, able to project the points to a separable latent space. The proposed deep neural network can simultaneously predict the waypoint position and cluster assignment with two specialized heads in a single forward pass. The extensive experimentation on simulated and real-world images demonstrates that the proposed approach effectively solves the waypoint generation problem for both straight and curved row-based crops, overcoming the limitations of previous state-of-the-art methodologies., Comment: Accepted at ECML PKDD 2022