Symmetries of spatial graphs and Simon invariants

An ordered and oriented 2-component link L in the 3-sphere is said to be achiral if it is ambient isotopic to its mirror image ignoring the orientation and ordering of the components. Kirk-Livingston showed that if L is achiral then the linking number of L is not congruent to 2 modulo 4. In this paper we study orientation-preserving or reversing symmetries of 2-component links, spatial complete graphs on 5 vertices and spatial complete bipartite graphs on 3+3 vertices in detail, and determine the necessary conditions on linking numbers and Simon invariants for such links and spatial graphs to be symmetric.Comment: 16 pages, 14 figure

The What-And-Where Filter: A Spatial Mapping Neural Network for Object Recognition and Image Understanding

The What-and-Where filter forms part of a neural network architecture for spatial mapping, object recognition, and image understanding. The Where fllter responds to an image figure that has been separated from its background. It generates a spatial map whose cell activations simultaneously represent the position, orientation, ancl size of all tbe figures in a scene (where they are). This spatial map may he used to direct spatially localized attention to these image features. A multiscale array of oriented detectors, followed by competitve and interpolative interactions between position, orientation, and size scales, is used to define the Where filter. This analysis discloses several issues that need to be dealt with by a spatial mapping system that is based upon oriented filters, such as the role of cliff filters with and without normalization, the double peak problem of maximum orientation across size scale, and the different self-similar interpolation properties across orientation than across size scale. Several computationally efficient Where filters are proposed. The Where filter rnay be used for parallel transformation of multiple image figures into invariant representations that are insensitive to the figures' original position, orientation, and size. These invariant figural representations form part of a system devoted to attentive object learning and recognition (what it is). Unlike some alternative models where serial search for a target occurs, a What and Where representation can he used to rapidly search in parallel for a desired target in a scene. Such a representation can also be used to learn multidimensional representations of objects and their spatial relationships for purposes of image understanding. The What-and-Where filter is inspired by neurobiological data showing that a Where processing stream in the cerebral cortex is used for attentive spatial localization and orientation, whereas a What processing stream is used for attentive object learning and recognition.Advanced Research Projects Agency (ONR-N00014-92-J-4015, AFOSR 90-0083); British Petroleum (89-A-1204); National Science Foundation (IRI-90-00530, Graduate Fellowship); Office of Naval Research (N00014-91-J-4100, N00014-95-1-0409, N00014-95-1-0657); Air Force Office of Scientific Research (F49620-92-J-0499, F49620-92-J-0334

RUSSIAN VERBS OF SPATIAL ORIENTATION STAND, SIT, LIE

The semantics of Russian verbs of spatial orientation is far from being simple or trivial; complex spatial concepts categorized in these lexical items are based on a number of cognitive structures that emerge from different modes of man’s interaction with the environment

Differential recruitment of brain networks following route and cartographic map learning of spatial environments.

An extensive neuroimaging literature has helped characterize the brain regions involved in navigating a spatial environment. Far less is known, however, about the brain networks involved when learning a spatial layout from a cartographic map. To compare the two means of acquiring a spatial representation, participants learned spatial environments either by directly navigating them or learning them from an aerial-view map. While undergoing functional magnetic resonance imaging (fMRI), participants then performed two different tasks to assess knowledge of the spatial environment: a scene and orientation dependent perceptual (SOP) pointing task and a judgment of relative direction (JRD) of landmarks pointing task. We found three brain regions showing significant effects of route vs. map learning during the two tasks. Parahippocampal and retrosplenial cortex showed greater activation following route compared to map learning during the JRD but not SOP task while inferior frontal gyrus showed greater activation following map compared to route learning during the SOP but not JRD task. We interpret our results to suggest that parahippocampal and retrosplenial cortex were involved in translating scene and orientation dependent coordinate information acquired during route learning to a landmark-referenced representation while inferior frontal gyrus played a role in converting primarily landmark-referenced coordinates acquired during map learning to a scene and orientation dependent coordinate system. Together, our results provide novel insight into the different brain networks underlying spatial representations formed during navigation vs. cartographic map learning and provide additional constraints on theoretical models of the neural basis of human spatial representation

Three-dimensional cell to tissue assembly process

The present invention relates a 3-dimensional cell to tissue and maintenance process, more particularly to methods of culturing cells in a culture environment, either in space or in a gravity field, with minimum fluid shear stress, freedom for 3-dimensional spatial orientation of the suspended particles and localization of particles with differing or similar sedimentation properties in a similar spatial region