Digital Mazes and Spatial Reasoning: Using Colour and Movement to Explore the 4th Dimension

This chapter focuses on innovative developments of four-dimensional digital mazes, examining how these mazes tap into the ideas of mathematician and fiction writer Charles Hinton (1853-1907) who wrote extensively on perception of a 4th geometric dimension. Hinton treats mathematical objects as physical and material movements, and draws on non-Euclidean geometry to argue for a virtual dimension to matter. I discuss recent attempts to build digital mazes that develop spatial sense in four dimensions, and show how these are directly linked to Hinton’s ideas. I focus on how colour and movement in digital environments are used to develop a distinctive kind of spatial sense. This chapter sheds light on innovative uses of digital software for developing student spatial sense. My aim is to explicate the new materialism of Charles Hinton, contribute to discussions about the nature of spatial sense and spatial reasoning, and to point to possible directions for future research on inventive approaches to geometry

The development of path integration: combining estimations of distance and heading

Efficient daily navigation is underpinned by path integration, the mechanism by which we use self-movement information to update our position in space. This process is well-understood in adulthood, but there has been relatively little study of path integration in childhood, leading to an underrepresentation in accounts of navigational development. Previous research has shown that calculation of distance and heading both tend to be less accurate in children as they are in adults, although there have been no studies of the combined calculation of distance and heading that typifies naturalistic path integration. In the present study 5-year-olds and 7-year-olds took part in a triangle-completion task, where they were required to return to the startpoint of a multi-element path using only idiothetic information. Performance was compared to a sample of adult participants, who were found to be more accurate than children on measures of landing error, heading error, and distance error. 7-year-olds were significantly more accurate than 5-year-olds on measures of landing error and heading error, although the difference between groups was much smaller for distance error. All measures were reliably correlated with age, demonstrating a clear development of path integration abilities within the age range tested. Taken together, these data make a strong case for the inclusion of path integration within developmental models of spatial navigational processing

Representing 3D Space in Working Memory: Spatial Images from Vision, Hearing, Touch, and Language

The chapter deals with a form of transient spatial representation referred to as a spatial image. Like a percept, it is externalized, scaled to the environment, and can appear in any direction about the observer. It transcends the concept of modality, as it can be based on inputs from the three spatial senses, from language, and from long-term memory. Evidence is presented that supports each of the claimed properties of the spatial image, showing that it is quite different from a visual image. Much of the evidence presented is based on spatial updating. A major concern is whether spatial images from different input modalities are functionally equivalent— that once instantiated in working memory, the spatial images from different modalities have the same functional characteristics with respect to subsequent processing, such as that involved in spatial updating. Going further, the research provides some evidence that spatial images are amodal (i.e., do not retain modality-specific features)

Inferring the Transcriptional Landscape of Bovine Skeletal Muscle by Integrating Co-Expression Networks

Background: Despite modern technologies and novel computational approaches, decoding causal transcriptional regulation remains challenging. This is particularly true for less well studied organisms and when only gene expression data is available. In muscle a small number of well characterised transcription factors are proposed to regulate development. Therefore, muscle appears to be a tractable system for proposing new computational approaches. Methodology/Principal Findings: Here we report a simple algorithm that asks "which transcriptional regulator has the highest average absolute co-expression correlation to the genes in a co-expression module?" It correctly infers a number of known causal regulators of fundamental biological processes, including cell cycle activity (E2F1), glycolysis (HLF), mitochondrial transcription (TFB2M), adipogenesis (PIAS1), neuronal development (TLX3), immune function (IRF1) and vasculogenesis (SOX17), within a skeletal muscle context. However, none of the canonical pro-myogenic transcription factors (MYOD1, MYOG, MYF5, MYF6 and MEF2C) were linked to muscle structural gene expression modules. Co-expression values were computed using developing bovine muscle from 60 days post conception (early foetal) to 30 months post natal (adulthood) for two breeds of cattle, in addition to a nutritional comparison with a third breed. A number of transcriptional landscapes were constructed and integrated into an always correlated landscape. One notable feature was a 'metabolic axis' formed from glycolysis genes at one end, nuclear-encoded mitochondrial protein genes at the other, and centrally tethered by mitochondrially-encoded mitochondrial protein genes. Conclusions/Significance: The new module-to-regulator algorithm complements our recently described Regulatory Impact Factor analysis. Together with a simple examination of a co-expression module's contents, these three gene expression approaches are starting to illuminate the in vivo transcriptional regulation of skeletal muscle development

On the assessment of landmark salience for human navigation

In this paper, we propose a conceptual framework for assessing the salience of landmarks for navigation. Landmark salience is derived as a result of the observer’s point of view, both physical and cognitive, the surrounding environment, and the objects contained therein. This is in contrast to the currently held view that salience is an inherent property of some spatial feature. Salience, in our approach, is expressed as a three-valued Saliency Vector. The components that determine this vector are Perceptual Salience, which defines the exogenous (or passive) potential of an object or region for acquisition of visual attention, Cognitive Salience, which is an endogenous (or active) mode of orienting attention, triggered by informative cues providing advance information about the target location, and Contextual Salience, which is tightly coupled to modality and task to be performed. This separation between voluntary and involuntary direction of visual attention in dependence of the context allows defining a framework that accounts for the interaction between observer, environment, and landmark. We identify the low-level factors that contribute to each type of salience and suggest a probabilistic approach for their integration. Finally, we discuss the implications, consider restrictions, and explore the scope of the framework

Identifying Landmark Candidates Beyond Toy Examples : A Critical Discussion and Some Way Forward

Incorporating references to landmarks in navigation systems requires having data on potential landmarks in the first place. While there have been many approaches in the scientific literature for identifying landmark candidates, these have hardly been picked up in actual, running systems. One major obstacle for this to happen may be that most—if not all—approaches presented so far are not scalable due to their underlying data requirements. In this paper, I will critically discuss existing approaches in light of their scalability. I will then suggest a way forward to more scalable solutions by combining in a smart way aspects of different approaches