Abelian networks II. Halting on all inputs

Abelian networks are systems of communicating automata satisfying a local commutativity condition. We show that a finite irreducible abelian network halts on all inputs if and only if all eigenvalues of its production matrix lie in the open unit disk.Comment: Supersedes sections 5 and 6 of arXiv:1309.3445v1. To appear in Selecta Mathematic

Abelian networks III. The critical group

The critical group of an abelian network is a finite abelian group that governs the behavior of the network on large inputs. It generalizes the sandpile group of a graph. We show that the critical group of an irreducible abelian network acts freely and transitively on recurrent states of the network. We exhibit the critical group as a quotient of a free abelian group by a subgroup containing the image of the Laplacian, with equality in the case that the network is rectangular. We generalize Dhar's burning algorithm to abelian networks, and estimate the running time of an abelian network on an arbitrary input up to a constant additive error.Comment: supersedes sections 7 and 8 of arXiv:1309.3445v1. To appear in the Journal of Algebraic Combinatoric

Local optical field variation in the neighborhood of a semiconductor micrograting

The local optical field of a semiconductor micrograting (GaAs, 10x10 micro m) is recorded in the middle field region using an optical scanning probe in collection mode at constant height. The recorded image shows the micro-grating with high contrast and a displaced diffraction image. The finite penetration depth of the light leads to a reduced edge resolution in the direction to the illuminating beam direction while the edge contrast in perpendicular direction remains high (~100nm). We use the discrete dipole model to calculate the local optical field to show how the displacement of the diffraction image increases with increasing distance from the surface.Comment: 12 pages, 3 figure

A systematic implementation of image processing algorithms on configurable computing hardware

Configurable computing hardware has many advantages over both general-purpose processors and application specific hardware. However, the difficulty of using this type of hardware has limited its use. An automated system for implementing image Processing applications in configurable hardware, called CHAMPION, is under development at the University of Tennessee. CHAMPION will map applications in the Khoros Cantata graphical programming environment to hardware. A relatively complex automatic target recognition (ATR) application was manually mapped from Cantata to a commercially available configurable computing platform. This manual implementation was done to assist in the development of function libraries and hardware for use in the CHAMPION systems, as well as to develop procedures to perform the application mapping. The mapping techniques used were developed in such a way that they could serve as the basis for the automated system. Many important considerations for the mapping process were identified and included in the mapping algorithms. The manual mapping was successful, allowing the ATR application to be run on a Wildforce-XL configurable computing board. The successful application implementation validated the basic hardware design and mapping concepts to be used in CHAMPION. Nearly a tenfold performance increase was realized in the hardware implementation and performance bottlenecks were identified which should enable even greater performance improvements to be realized in the automated system. The manual implementation also helped to identify some of the challenges that must be overcome to complete the development of the automated system

Maximum Entropy RL (Provably) Solves Some Robust RL Problems

Many potential applications of reinforcement learning (RL) require guarantees that the agent will perform well in the face of disturbances to the dynamics or reward function. In this paper, we prove theoretically that standard maximum entropy RL is robust to some disturbances in the dynamics and the reward function. While this capability of MaxEnt RL has been observed empirically in prior work, to the best of our knowledge our work provides the first rigorous proof and theoretical characterization of the MaxEnt RL robust set. While a number of prior robust RL algorithms have been designed to handle similar disturbances to the reward function or dynamics, these methods typically require adding additional moving parts and hyperparameters on top of a base RL algorithm. In contrast, our theoretical results suggest that MaxEnt RL by itself is robust to certain disturbances, without requiring any additional modifications. While this does not imply that MaxEnt RL is the best available robust RL method, MaxEnt RL does possess a striking simplicity and appealing formal guarantees.Comment: Blog post and videos: https://bair.berkeley.edu/blog/2021/03/10/maxent-robust-rl/. arXiv admin note: text overlap with arXiv:1910.0191