Approximation Algorithms for Geometric Networks

The main contribution of this thesis is approximation algorithms for several computational geometry problems. The underlying structure for most of the problems studied is a geometric network. A geometric network is, in its abstract form, a set of vertices, pairwise connected with an edge, such that the weight of this connecting edge is the Euclidean distance between the pair of points connected. Such a network may be used to represent a multitude of real-life structures, such as, for example, a set of cities connected with roads. Considering the case that a specific network is given, we study three separate problems. In the first problem we consider the case of interconnected `islands' of well-connected networks, in which shortest paths are computed. In the second problem the input network is a triangulation. We efficiently simplify this triangulation using edge contractions. Finally, we consider individual movement trajectories representing, for example, wild animals where we compute leadership individuals. Next, we consider the case that only a set of vertices is given, and the aim is to actually construct a network. We consider two such problems. In the first one we compute a partition of the vertices into several subsets where, considering the minimum spanning tree (MST) for each subset, we aim to minimize the largest MST. The other problem is to construct a $t$-spanner of low weight fast and simple. We do this by first extending the so-called gap theorem. In addition to the above geometric network problems we also study a problem where we aim to place a set of different sized rectangles, such that the area of their corresponding bounding box is minimized, and such that a grid may be placed over the rectangles. The grid should not intersect any rectangle, and each cell of the grid should contain at most one rectangle. All studied problems are such that they do not easily allow computation of optimal solutions in a feasible time. Instead we consider approximation algorithms, where near-optimal solutions are produced in polynomial time. In addition to the above geometric network problems we also study a problem where we aim to place a set of different sized rectangles, such that the area of their corresponding bounding box is minimized, and such that a grid may be placed over the rectangles. The grid should not intersect any rectangle, and each cell of the grid should contain at most one rectangle. All studied problems are such that they do not easily allow computation of optimal solutions in a feasible time. Instead we consider approximation algorithms, where near-optimal solutions are produced in polynomial time

Space transformation for understanding group movement

We suggest a methodology for analyzing movement behaviors of individuals moving in a group. Group movement is analyzed at two levels of granularity: the group as a whole and the individuals it comprises. For analyzing the relative positions and movements of the individuals with respect to the rest of the group, we apply space transformation, in which the trajectories of the individuals are converted from geographical space to an abstract 'group space'. The group space reference system is defined by both the position of the group center, which is taken as the coordinate origin, and the direction of the group's movement. Based on the individuals' positions mapped onto the group space, we can compare the behaviors of different individuals, determine their roles and/or ranks within the groups, and, possibly, understand how group movement is organized. The utility of the methodology has been evaluated by applying it to a set of real data concerning movements of wild social animals and discussing the results with experts in animal ethology

How context influences the segmentation of movement trajectories - an experimental approach for environmental and behavioral context

In the digital information age where large amounts of movement data are generated daily through technological devices, such as mobile phones, GPS, and digital navigation aids, the exploration of moving point datasets for identifying movement patterns has become a research focus in GIScience (Dykes and Mountain 2003). Visual analytics (VA) tools, such as GeoVISTA Studio (Gahegan 2001), have been developed to explore large amounts of movement data based on the contention that VA combine computational methods with the outstanding human capabilities for pattern recognition, imagination, association, and reasoning (Andrienko et al. 2008). However, exploring, extracting and understanding the meaning encapsulated in movement data from a user perspective has become a major bottleneck, not only in GIScience, but in all areas of science where this kind of data is collected (Holyoak et al. 2008). Specifically the inherent complex and multidimensional nature of spatio-temporal data has not been sufficiently integrated into visual analytics tools. To ensure the inclusion of cognitive principles for the integration of space-time data, visual analytics has to consider how users conceptualize and understand movement data (Fabrikant et al. 2008). A review on cognitively motivated work exemplifies the urgent need to identify how humans make inferences and derive knowledge from movement data. In order to enhance visual analytics tools by integrating cognitive principles we have to first ask to what extent cognitive factors influence our understanding, reasoning, and analysis of movement pattern extraction. It is especially important to comprehend human knowledge construction and reasoning about spatial and temporal phenomena and processes. This paper proposes an experimental approach with human subject testing to evaluate the importance of contextual information in visual displays of movement patterns. This research question is part of a larger research project, with two main objectives, namely * getting a better understanding of how humans process spatio-temporal information * and empirically validating guidelines to improve the design of visual analytics tools to enhance visual data exploration

From Groups to Leaders and Back. Exploring Mutual Predictability Between Social Groups and Their Leaders

Recently, social theories and empirical observations identified small groups and leaders as the basic elements which shape a crowd. This leads to an intermediate level of abstraction that is placed between the crowd as a flow of people, and the crowd as a collection of individuals. Consequently, automatic analysis of crowds in computer vision is also experiencing a shift in focus from individuals to groups and from small groups to their leaders. In this chapter, we present state-of-the-art solutions to the groups and leaders detection problem, which are able to account for physical factors as well as for sociological evidence observed over short time windows. The presented algorithms are framed as structured learning problems over the set of individual trajectories. However, the way trajectories are exploited to predict the structure of the crowd is not fixed but rather learned from recorded and annotated data, enabling the method to adapt these concepts to different scenarios, densities, cultures, and other unobservable complexities. Additionally, we investigate the relation between leaders and their groups and propose the first attempt to exploit leadership as prior knowledge for group detection

Adults imitate to send a social signal

Humans are prolific imitators, even when copying may not be efficient. A variety of explanations have been advanced for this phenomenon, including that it is a side-effect of learning, that it arises from a lack of understanding of causality, to imitation being a mechanism to boost affiliation. This thesis systematically outlines the hypothesis that imitation is a social signal sent between interacting partners, which rests on testing whether our propensity to imitate is modulated by the social availability of the interaction partner (i.e., whether our interaction partner is watching us or not). I developed a dyadic block-moving paradigm that allowed us to test this hypothesis in a naturalistic manner in four behavioural and neuroimaging studies using functional near-infrared spectroscopy (fNIRS). I found that imitative fidelity was modulated by whether the interaction partner was watching the participant make their move or not, and this effect replicated across all four studies, in both neurotypicals and autistic participants. I also examined the neural correlates of responding to irrational actions, and of being watched. I found that being watched led to a robust deactivation in the right parietal cortex across both neurotypicals (in two studies) and autistic participants (one study). Among autistic participants we also found strong engagement in the left superior temporal sulcus (STS) when being watched. For responding to irrational actions, in one study of neurotypicals we found greater deactivation in the right superior parietal lobule (SPL) when making more irrational responses. In another study of autistic and neurotypical participants we found deactivation in the bilateral inferior parietal cortex (IPL) in neurotypicals when responding to irrational actions, while this deactivation appeared confined to the left IPL for autistic participants. Autistic participants also showed differentially higher engagement in the left occipitotemporal regions when responding to irrational actions. This thesis supports the social-signalling hypothesis of imitation and is accompanied by suggestions for future directions to explore this theory in more detail

Assessing Performance, Role Sharing, and Control Mechanisms in Human-Human Physical Interaction for Object Manipulation

abstract: Object manipulation is a common sensorimotor task that humans perform to interact with the physical world. The first aim of this dissertation was to characterize and identify the role of feedback and feedforward mechanisms for force control in object manipulation by introducing a new feature based on force trajectories to quantify the interaction between feedback- and feedforward control. This feature was applied on two grasp contexts: grasping the object at either (1) predetermined or (2) self-selected grasp locations (“constrained” and “unconstrained”, respectively), where unconstrained grasping is thought to involve feedback-driven force corrections to a greater extent than constrained grasping. This proposition was confirmed by force feature analysis. The second aim of this dissertation was to quantify whether force control mechanisms differ between dominant and non-dominant hands. The force feature analysis demonstrated that manipulation by the dominant hand relies on feedforward control more than the non-dominant hand. The third aim was to quantify coordination mechanisms underlying physical interaction by dyads in object manipulation. The results revealed that only individuals with worse solo performance benefit from interpersonal coordination through physical couplings, whereas the better individuals do not. This work showed that naturally emerging leader-follower roles, whereby the leader in dyadic manipulation exhibits significant greater force changes than the follower. Furthermore, brain activity measured through electroencephalography (EEG) could discriminate leader and follower roles as indicated power modulation in the alpha frequency band over centro-parietal areas. Lastly, this dissertation suggested that the relation between force and motion (arm impedance) could be an important means for communicating intended movement direction between biological agents.Dissertation/ThesisDoctoral Dissertation Biomedical Engineering 201