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We study learning the directed acyclic graph (DAG) for linear structural equation models (SEMs) when the causal structure is a polytree. Under Gaussian polytree models, we derive sufficient sample-size conditions under which the Chow–Liu algorithm exactly recovers both the skeleton and the equivalence class (CPDAG). Matching information-theoretic lower bounds provide necessary conditions, yielding sharp characterizations of problem difficulty. We further analyze inverse correlation matrix estimation with error bounds depending on dimension and the number of v-structures, and extend to group linear polytrees. Comprehensive simulations and benchmark experiments demonstrate robustness when true graphs are only approximately polytrees. 

Objective: Physical and cognitive workloads and performance were studied for a corrective shared control (CSC) human–robot collaborative (HRC) sanding task. Background: Manual sanding is physically demanding. Collaborative robots (cobots) can potentially reduce physical stress, but fully autonomous implementation has been particularly challenging due to skill, task variability, and robot limitations. CSC is an HRC method where the robot operates semiautonomously while the human provides real-time corrections. Methods: Twenty laboratory participants removed paint using an orbital sander, both manually and with a CSC robot. A fully automated robot was also tested. Results: The CSC robot improved subjective discomfort compared to manual sanding in the upper arm by 29.5%, lower arm by 32%, hand by 36.5%, front of the shoulder by 24%, and back of the shoulder by 17.5%. Muscle fatigue measured using EMG, was observed in the medial deltoid and flexor carpi radialis for the manual condition. The composite cognitive workload on the NASA-TLX increased by 14.3% for manual sanding due to high physical demand and effort, while mental demand was 14% greater for the CSC robot. Digital imaging showed that the CSC robot outperformed the automated condition by 7.16% for uniformity, 4.96% for quantity, and 6.06% in total. Conclusions: In this example, we found that human skills and techniques were integral to sanding and can be successfully incorporated into HRC systems. Humans performed the task using the CSC robot with less fatigue and discomfort. Applications: The results can influence implementation of future HRC systems in manufacturing environments. 

Abstract The one-dimensional quantum breakdown model, which features spatially asymmetric fermionic interactions simulating the electrical breakdown phenomenon, exhibits an exponential U(1) symmetry and a variety of dynamical phases including many-body localization and quantum chaos with quantum scar states. We investigate the minimal quantum breakdown model with the minimal number of on-site fermion orbitals required for the interaction and identify a large number of local conserved charges in the model. We then reveal a mapping between the minimal quantum breakdown model in certain charge sectors and a quantum link model which simulates theU(1) lattice gauge theory and show that the local conserved charges map to the gauge symmetry generators. A special charge sector of the model further maps to the PXP model, which shows quantum many-body scars. This mapping unveils the rich dynamics in different Krylov subspaces characterized by different gauge configurations in the quantum breakdown model.