Symmetry-Based Search Space Reduction For Grid Maps

In this paper we explore a symmetry-based search space reduction technique which can speed up optimal pathfinding on undirected uniform-cost grid maps by up to 38 times. Our technique decomposes grid maps into a set of empty rectangles, removing from each rectangle all interior nodes and possibly some from along the perimeter. We then add a series of macro-edges between selected pairs of remaining perimeter nodes to facilitate provably optimal traversal through each rectangle. We also develop a novel online pruning technique to further speed up search. Our algorithm is fast, memory efficient and retains the same optimality and completeness guarantees as searching on an unmodified grid map

Coverage, Continuity and Visual Cortical Architecture

The primary visual cortex of many mammals contains a continuous representation of visual space, with a roughly repetitive aperiodic map of orientation preferences superimposed. It was recently found that orientation preference maps (OPMs) obey statistical laws which are apparently invariant among species widely separated in eutherian evolution. Here, we examine whether one of the most prominent models for the optimization of cortical maps, the elastic net (EN) model, can reproduce this common design. The EN model generates representations which optimally trade of stimulus space coverage and map continuity. While this model has been used in numerous studies, no analytical results about the precise layout of the predicted OPMs have been obtained so far. We present a mathematical approach to analytically calculate the cortical representations predicted by the EN model for the joint mapping of stimulus position and orientation. We find that in all previously studied regimes, predicted OPM layouts are perfectly periodic. An unbiased search through the EN parameter space identifies a novel regime of aperiodic OPMs with pinwheel densities lower than found in experiments. In an extreme limit, aperiodic OPMs quantitatively resembling experimental observations emerge. Stabilization of these layouts results from strong nonlocal interactions rather than from a coverage-continuity-compromise. Our results demonstrate that optimization models for stimulus representations dominated by nonlocal suppressive interactions are in principle capable of correctly predicting the common OPM design. They question that visual cortical feature representations can be explained by a coverage-continuity-compromise.Comment: 100 pages, including an Appendix, 21 + 7 figure

CDDT: Fast Approximate 2D Ray Casting for Accelerated Localization

Localization is an essential component for autonomous robots. A well-established localization approach combines ray casting with a particle filter, leading to a computationally expensive algorithm that is difficult to run on resource-constrained mobile robots. We present a novel data structure called the Compressed Directional Distance Transform for accelerating ray casting in two dimensional occupancy grid maps. Our approach allows online map updates, and near constant time ray casting performance for a fixed size map, in contrast with other methods which exhibit poor worst case performance. Our experimental results show that the proposed algorithm approximates the performance characteristics of reading from a three dimensional lookup table of ray cast solutions while requiring two orders of magnitude less memory and precomputation. This results in a particle filter algorithm which can maintain 2500 particles with 61 ray casts per particle at 40Hz, using a single CPU thread onboard a mobile robot.Comment: 8 pages, 14 figures, ICRA versio

Methods of Hierarchical Clustering

We survey agglomerative hierarchical clustering algorithms and discuss efficient implementations that are available in R and other software environments. We look at hierarchical self-organizing maps, and mixture models. We review grid-based clustering, focusing on hierarchical density-based approaches. Finally we describe a recently developed very efficient (linear time) hierarchical clustering algorithm, which can also be viewed as a hierarchical grid-based algorithm.Comment: 21 pages, 2 figures, 1 table, 69 reference

The circumstellar disk of HH 30. Searching for signs of disk evolution with multi-wavelength modeling

Circumstellar disks are characteristic for star formation and vanish during the first few Myr of stellar evolution. During this time planets are believed to form in the dense midplane by growth, sedimentation and aggregation of dust. Indicators of disk evolution, such as holes and gaps, can be traced in the spectral energy distribution (SED) and spatially resolved images. We aim to construct a self-consistent model of HH 30 by fitting all available continuum observations simultaneously. New data sets not available in previous studies, such as high-resolution interferometric imaging with the Plateau de Bure Interferometer (PdBI) at lambda = 1.3 mm and SED measured with IRS on the Spitzer Space Telescope in the mid-infrared, put strong constraints on predictions and are likely to provide new insights into the evolutionary state of this object. A parameter study based on simulated annealing was performed to find unbiased best-fit models for independent observations made in the wavelength domain lambda ~ 1 micron ... 4 mm. The method essentially creates a Markov chain through parameter space by comparing predictions generated by our self-consistent continuum radiation transfer code MC3D with observations. We present models of the edge-on circumstellar disk of HH 30 based on observations from the near-infrared to mm-wavelengths that suggest the presence of an inner depletion zone with about 45 AU radius and a steep decline of mm opacity beyond 140 AU. Our modeling indicates that several modes of dust evolution such as growth, settling, and radial migration are taking place in this object. High-resolution observations of HH 30 at different wavelengths with next-generation observatories such as ALMA and JWST will enable the modeling of inhomogeneous dust properties and significantly expand our understanding of circumstellar disk evolution.Comment: Accepted for publication in Astronomy and Astrophysic