arXiv subjects

Aaron Wagner

Publications and source records attributed to Aaron Wagner.

3 recordsLinked to original sources

arXiv2026

Entropy power inequalities in compact groups

Suppose $X,Y$ are independent random variables with values in a compact abelian group $(G,+)$. We examine the following two entropy power-type inequalities: $h(X+Y)\geq \frac{1}{2}h(X)+\frac{1}{2}h(Y)$ and $h(X+Y)\geq \max\{h(X),h(Y)\}$, where the entropy $h(Z)$ of a $G$-valued random variable $Z$ is defined in terms of its density with respect to Haar measure on $G$. For groups that are either connected or finite with no nontrivial subgroups, we precisely characterize the cases of equality and establish explicit, quantitative stability estimates in terms of relative entropy for these two inequalities. The main tools are a generalization of an entropic inequality obtained by Green, Manners and Tao (2023) for discrete entropy, and a harmonic-analytic estimate for the chi-squared contraction coefficient in connected compact groups. As an application, we derive exponential convergence rates to the uniform distribution in relative entropy for random walks on connected compact abelian groups.

math.PR↗

arXiv2026

LASER: Level-Based Asynchronous Scheduling and Execution Regime for Spatiotemporally Constrained Multi-Robot Timber Manufacturing

Automating large-scale manufacturing in domains like timber construction requires multi-robot systems to manage tightly coupled spatiotemporal constraints, such as collision avoidance and process-driven deadlines. This paper introduces LASER (Level-based Asynchronous Scheduling and Execution Regime), a complete framework for scheduling and executing complex assembly tasks, demonstrated on a screw-press gluing application for timber slab manufacturing. Our central contribution is to integrate a barrier-based mechanism into a constraint programming (CP) scheduling formulation that partitions tasks into spatiotemporally disjoint sets, which we define as levels. This structure enables robots to execute tasks in parallel and asynchronously within a level, synchronizing only at level barriers, which guarantees collision-free operation by construction and provides robustness to timing uncertainties. To solve this formulation for large problems, we propose two specialized algorithms: an iterative temporal-relaxation approach for heterogeneous task sequences and a bi-level decomposition for homogeneous tasks that balances workload. We validate the LASER framework by fabricating a full-scale 2.4m x 6m timber slab with a two-robot system mounted on parallel linear tracks, successfully coordinating 108 subroutines and 352 screws under tight adhesive time windows. Computational studies show our method scales steadily with size compared to a monolithic approach.

cs.RO↗

arXiv2021

Selection of inverse gamma and half-t priors for hierarchical models: sensitivity and recommendations

While the importance of prior selection is well understood, establishing guidelines for selecting priors in hierarchical models has remained an active, and sometimes contentious, area of Bayesian methodology research. Choices of hyperparameters for individual families of priors are often discussed in the literature, but rarely are different families of priors compared under similar models and hyperparameters. Using simulated data, we evaluate the performance of inverse gamma and half-$t$ priors for estimating the standard deviation of random effects in three hierarchical models: the 8-schools model, a random intercepts longitudinal model, and a simple multiple outcomes model. We compare the performance of the two prior families using a range of prior hyperparameters, some of which have been suggested in the literature, and others that allow for a direct comparison of pairs of half-$t$ and inverse-gamma priors. Estimation of very small values of the random effect standard deviation led to convergence issues especially for the half-$t$ priors. For most settings, we found that the posterior distribution of the standard deviation had smaller bias under half-$t$ priors than under their inverse-gamma counterparts. Inverse gamma priors generally gave similar coverage but had smaller interval lengths than their half-$t$ prior counterparts. Our results for these two prior families will inform prior specification for hierarchical models, allowing practitioners to better align their priors with their respective models and goals.

stat.ME↗