Antje Krumnack

The structural salience of landmarks: results from an on-line study and a virtual environment experiment

The term ‘structural salience’ refers to the characteristics of landmarks that are immediately related to navigation. One of the central aspects of this kind of salience is where a landmark is located at an intersection. Klippel and Winter (2005) developed a mathematical measure that describes the ideal position of a landmark at an intersection. In the first experiment (on-line study) we examined the four different landmark positions from a birds-eye perspective and in the second experiment (virtual environment) from an egocentric perspective. We compare our results with Klippel and Winters model and provide some evidence to support their assumptions empirically.

2008 Special Issue: Deducing logical relationships between spatially registered cortical parcellations under conditions of uncertainty

We propose a new technique, called Spatial Objective Relational Transformation (SORT), as an automated approach for derivation of logical relationships between cortical areas in different brain maps registered in the same Euclidean space. Recently, there have been large amounts of voxel-based three-dimensional structural and functional imaging data that provide us with coordinate-based information about the location of differently defined areas in the brain, whereas coordinate-independent, parcellation-based mapping is still commonly used in the majority of animal tracing and mapping studies. Because of the impact of voxel-based imaging methods and the need to attribute their features to coordinate-independent brain entities, this mapping becomes increasingly important. Our motivation here is not to make vague statements where more precise spatial statements would be better, but to find criteria for the identity (or other logical relationships) between areas that were delineated by different methods, in different individuals, or mapped to three-dimensional space using different deformation algorithms. The relevance of this problem becomes immediately obvious as one superimposes and compares different datasets in multimodal databases (e.g. CARET, http://brainmap.wustl.edu/caret), where voxel-based data are registered to surface nodes exploited by the procedure presented here. We describe the SORT algorithm and its implementation in the Java 2 programming language (http://java.sun.com/, which we make available for download. We give an example of practical use of our approach, and validate the SORT approach against a database of the coordinate-independent statements and inferences that have been deduced using alternative techniques.

Shapley ratings in brain networks

Recent applications of network theory to brain networks as well as the expanding empirical databases of brain architecture spawn an interest in novel techniques for analyzing connectivity patterns in the brain. Treating individual brain structures as nodes in a directed graph model permits the application of graph theoretical concepts to the analysis of these structures within their large-scale connectivity networks. In this paper, we explore the application of concepts from graph and game theory toward this end. Specifically, we utilize the Shapley value principle, which assigns a rank to players in a coalition based upon their individual contributions to the collective profit of that coalition, to assess the contributions of individual brain structures to the graph derived from the global connectivity network. We report Shapley values for variations of a prefrontal network, as well as for a visual cortical network, which had both been extensively investigated previously. This analysis highlights particular nodes as strong or weak contributors to global connectivity. To understand the nature of their contribution, we compare the Shapley values obtained from these networks and appropriate controls to other previously described nodal measures of structural connectivity. We find a strong correlation between Shapley values and both betweenness centrality and connection density. Moreover, a stepwise multiple linear regression analysis indicates that approximately 79% of the variance in Shapley values obtained from random networks can be explained by betweenness centrality alone. Finally, we investigate the effects of local lesions on the Shapley ratings, showing that the present networks have an immense structural resistance to degradation. We discuss our results highlighting the use of such measures for characterizing the organization and functional role of brain networks.

Criteria for optimizing cortical hierarchies with continuous ranges.

In a recent paper (Reid et al., 2009) we introduced a method to calculate optimal hierarchies in the visual network that utilizes continuous, rather than discrete, hierarchical levels, and permits a range of acceptable values rather than attempting to fit fixed hierarchical distances. There, to obtain a hierarchy, the sum of deviations from the constraints that define the hierarchy was minimized using linear optimization. In the short time since publication of that paper we noticed that many colleagues misinterpreted the meaning of the term “optimal hierarchy”. In particular, a majority of them were under the impression that there was perhaps only one optimal hierarchy, but a substantial difficulty in finding that one. However, there is not only more than one optimal hierarchy but also more than one option for defining optimality. Continuing the line of this work we look at additional options for optimizing the visual hierarchy: minimizing the number of violated constraints and minimizing the maximal size of a constraint violation using linear optimization and mixed integer programming. The implementation of both optimization criteria is explained in detail. In addition, using constraint sets based on the data from Felleman and Van Essen (1991), optimal hierarchies for the visual network are calculated for both optimization methods.

Spatial belief revision

Belief revision is the process of changing ones beliefs when a newly acquired fact contradicts the existing belief set. Psychological research on belief revision mostly used conditional reasoning problems in which an inconsistency arises between a fact, contradicting a valid conclusion, and the conditional and categorical premises. In this paper, we present a new experimental paradigm in which we explore how people change their mind about the location of objects in space. The participants received statements that described the spatial relations between a set of objects. From these premises they drew a conclusion which then, in the next step, was contradicted by a new, irrefutable fact. The participants’ task was to decide which of the objects to relocate and which one to leave at its initial position. We hypothesised that this spatial revision process is based on mental models and is affected by the functional asymmetry between reference objects (RO) and the located objects (LO) of spatial relations. The results from two experiments corroborate this hypothesis. We found that individuals have a strong preference to relocate the LO of the premises, but avoid relocating the RO. This is a novel finding and opens up new avenues of research on how humans mentally revise their beliefs about spatial relations between entities in the world.

A Connectivity Rating for Vertices in Networks

We compute the influence of a vertex on the connectivity structure of a directed network by using Shapley value theory. In general, the computation of such ratings is highly inefficient. We show how the computation can be managed for many practically interesting instances by a decomposition of large networks into smaller parts. For undirected networks, we introduce an algorithm that computes all vertex ratings in linear time, if the graph is cycle composed or chordal.