To balance the examination of large quantities of data with the di#culty of comprehending such quantities, we propose a geometric approach to detection enhanced by a visual component. Visually presented information can encode large amounts of complex, interrelated data, can be quanti#ed and manipulated, and is something that human beings naturally process well. Limitations of traditional intrusion detection system #IDS# techniques are as much a function of the abilityofahuman to process large amounts of information as they are limitations of the techniques themselves. In this paper, we present a discussion of a geometric model which appears to be useful in performing many of the activities used in traditional intrusion detection while including a useful visualization.

The results of two experiments suggest that strong constraints on the ability to imagine rotations extend to the perception of rotations. Participants viewed stereographic perspective views of rotating squares, regular polyhedra, and a variety of polyhedral generalized cones, and attempted to indicate the orientation of the axis and planes of rotation in terms of one of the 13 canonical directions in 3D space. When the axis and planes of a rotation were aligned with principal directions of the environment, participants could indicate the orientation of the motion well. When a rotation was oblique to the environment, the orientation of the object to the motion made a very large difference to performance. Participants were fast and accurate when the object was a generalized cone about the axis of rotation or was elongated along the axis. Variation of the amount of rotation and reflection symmetry of the object about the axis of rotation was not powerful. The study of motion and spatial transformation has long been central in mathematics and the physical sciences, and recently it has become the focus of much work in the study of perception and spatial cognition. Rotation, for example, is a fundamental form of motion (e.g., Gibson, 1957; Shepard, 1984), and the study of mental imagery has benefited greatly from the investigation of mental imagery of rotation (see Shepard & Cooper, 1982). Across the study of spatial cognition, it has become clear that some forms of spatiotemporal structure are cognitively simple for the typical person, whereas other forms are quite complex and difficult. This distinction is familiar from work on the spatial organization of elementary forms (e.g., Garner, 1974; Palmer, 1977; Wertheimer, 1950), but it applies also to a great variety of familiar or three-dimensional (3D) structures and

A fullerene F n is a 3-regular (or cubic) polyhedral carbon molecule for which the n vertices - the carbons atoms - are arranged in 12 pentagons and ( n 2 \Gamma 10) hexagons. Only a finite number of fullerenes are expected to be, up to scale, isometrically embeddable into a hypercube. Looking for the list of such fullerenes, we first check the embeddability of all fullerenes F n for n ! 60 and of all preferable fullerenes C n for n ! 86 and their duals. Then, we consider some infinite families, including fullerenes with icosahedral symmetry, which describe virus capsids, onion-like metallic clusters and geodesic domes. Quasi-embeddings and fullerene analogues are considered. We also present some results on chemically relevant polyhedra such as coordination polyhedra and cluster polyhedra. Finally we conjecture that the list of known embeddable fullerenes is complete and present its relevance to the Katsura model for vesicles cells. Contents 1 Introduction and Basic Properties 2 1...

Physical reasoning is strongly influenced by various parameters of orientation. The authors report 3 experiments in which this phenomenon was explored for a particularly elementary transformation: the formation of a line from the intersection of 2 planes. Participants perceived pairs of planar surfaces (disks) in a variety of orientations in 3-D space and indicated the orientations of the edges that would result if the surfaces interpenetrated. The ranges of error and response time were large. Performance depended on whether the orientation of the edge that would be formed was the same as components of the orientations of the perceived surfaces, the degree to which the orientation of the edge would be canonical in the environment, and whether the angle between the surfaces would be perpendicular. The results are discussed in the context of a general approach to orientation in perception and physical reasoning. When the relations among things in the world might be seen in one way but instead are seen in another, visual perception may be said to be a type of description (Pani, in press). Such situations occur consistently in perceptions that involve orientation. As a simple example, if the shape in Figure 1 is oriented as shown at the left, it is seen to have a pointed top and bottom and uniform orientations of edges and surfaces about one of its object axes. When the same shape is oriented as shown at the right, it appears to have a flat top and bottom and nonuniform orientations of edges and surfaces. Thus, a single object is seen to have different qualitative properties, those of a regular "dipyramid " or those of an "antiprism, " depending on the object axis that is used to determine the orientations of edges and surfaces

Abstract not found