We investigate the relation between the physical world and its mental representation in the 'cognitive map', and test if this representation is image-like and complies with the laws of Euclidean geometry. We have developed a new experimental technique using 'impossible' virtual environments (VE) to directly influence the representational development. Subjects explore a number of VEs -- some 'normal', others with severe violations of Euclidean metrics or planar topology. We check if these manipulated properties cause problems in navigation performance. A consistent VE should be easily represented mentally in a map-like fashion, while a VE with severe violations should prove difficult. Surprisingly, we found no substantial influence of the impossible VEs on navigation performance, and forced-choice tests showed little evidence that subjects were aware of manipulations. This suggests that the representation does not resemble a two-dimensional image-like map. Alternatives to consider are sensorimotor and graph-like representations.

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We consider the problem of quantifying the degree of association between pairs of discrete event time series, with potential applications in forensic and cybersecurity settings. We focus in particular on the case where two associated event series exhibit temporal clustering such that the occurrence of one type of event at a particular time increases the likelihood that an event of the other type will also occur nearby in time.We pursue a non-parametric approach to the problem and investigate various score functions to quantify association, including characteristics of marked point processes and summary statistics of interevent times. Two techniques are proposed for assessing the significance of the measured degree of association: a populationbased approach to calculating score-based likelihood ratios when a sample from a relevant population is available, and a resampling approach to computing coincidental match probabilities when only a single pair of event series is available. The methods are applied to simulated data and to two real world data sets consisting of logs of computer activity and achieve accurate results across all data sets.

We investigate the hypothesis that the basic representation of space which underlies human navigation does not resemble an image-like map and is not restricted by the laws of Euclidean geometry. For this we developed a new experimental technique in which we use the properties of a virtual environment (VE) to directly influence the development of the representation. We compared the navigation performance of human observers under two conditions. Either the VE is consistent with the geometrical properties of physical space and could hence be represented in a map-like fashion, or it contains severe violations of Euclidean metric and planar topology, and would thus pose difficulties for the correct development of such a representation. Performance is not influenced by this difference, suggesting that a map-like representation is not the major basis of human navigation. Rather, the results are consistent with a representation which is similar to a non-planar graph augmented with path length information, or with a sensorimotor representation which combines sensory properties and motor actions. The latter may be seen as part of a revised view of perceptual processes due to recent results in psychology and neurobiology, which indicate that the traditional strict separation of sensory and motor systems is no longer tenable.

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