Search

Entropy production in stochastic mechanical systems is examined here with strict bounds on its rate. Stochastic mechanical systems include pure diffusions in Euclidean space or on Lie groups, as well as systems evolving on phase space for which the fluctuation-dissipation theorem applies, i.e., return-to-equilibrium processes. Two separate ways for ensembles of such mechanical systems forced by noise to reach equilibrium are examined here. First, a restorative potential and damping can be applied, leading to a classical return-to-equilibrium process wherein energy taken out by damping can balance the energy going in from the noise. Second, the process evolves on a compact configuration space (such as random walks on spheres, torsion angles in chain molecules, and rotational Brownian motion) lead to long-time solutions that are constant over the configuration space, regardless of whether or not damping and random forcing balance. This is a kind of potential-free equilibrium distribution resulting from topological constraints. Inertial and noninertial (kinematic) systems are considered. These systems can consist of unconstrained particles or more complex systems with constraints, such as rigid-bodies or linkages. These more complicated systems evolve on Lie groups and model phenomena such as rotational Brownian motion and nonholonomic robotic systems. In all cases, it is shown that the rate of entropy production is closely related to the appropriate concept of Fisher information matrix of the probability density defined by the Fokker–Planck equation. Classical results from information theory are then repurposed to provide computable bounds on the rate of entropy production in stochastic mechanical systems.

In this paper, we aim at improving the computational efficiency of graph convolutional networks (GCNs) for learning on point clouds. The basic graph convolution that is typically composed of a $K$-nearest neighbor (KNN) search and a multilayer perceptron (MLP) is examined. By mathematically analyzing the operations there, two findings to improve the efficiency of GCNs are obtained. (1) The local geometric structure information of 3D representations propagates smoothly across the GCN that relies on KNN search to gather neighborhood features. This motivates the simplification of multiple KNN searches in GCNs. (2) Shuffling the order of graph feature gathering and an MLP leads to equivalent or similar composite operations. Based on those findings, we optimize the computational procedure in GCNs. A series of experiments show that the optimized networks have reduced computational complexity, decreased memory consumption, and accelerated inference speed while maintaining comparable accuracy for learning on point clouds. Code will be available at \url{https://github.com/ofsoundof/EfficientGCN.git}.

In November 2012, the eleventh Workshop on Distributed Autonomous Robotic Systems (DARS 2012) was held in Baltimore, Maryland on the campus of Johns Hopkins University. Previous DARS workshops were held in 1992, 1994, and 1996 in Riken, Wako, Japan; Karlsruhe, Germany (1998); Knoxville, Tennessee, USA (2000); Fukuoka, Japan (2002); Toulouse, France (2004); Minneapolis, Minnesota, USA (2006); Tsukuba, Ibaraki, Japan (2008); and Lausanne, Switzerland (2010).