Colorings, determinants and Alexander polynomials for spatial graphs

A {\em balanced} spatial graph has an integer weight on each edge, so that the directed sum of the weights at each vertex is zero. We describe the Alexander module and polynomial for balanced spatial graphs (originally due to Kinoshita \cite{ki}), and examine their behavior under some common operations on the graph. We use the Alexander module to define the determinant and $p$-colorings of a balanced spatial graph, and provide examples. We show that the determinant of a spatial graph determines for which $p$ the graph is $p$-colorable, and that a $p$-coloring of a graph corresponds to a representation of the fundamental group of its complement into a metacyclic group $\Gamma(p,m,k)$. We finish by proving some properties of the Alexander polynomial.Comment: 14 pages, 7 figures; version 3 reorganizes the paper, shortens some of the proofs, and improves the results related to representations in metacyclic groups. This is the final version, accepted by Journal of Knot Theory and its Ramification

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Sin resume

The moving minimum audible angle is smaller during self motion than during source motion

We are rarely perfectly still: our heads rotate in three axes and move in three dimensions, constantly varying the spectral and binaural cues at the ear drums. In spite of this motion, static sound sources in the world are typically perceived as stable objects. This argues that the auditory system-in a manner not unlike the vestibulo-ocular reflex-works to compensate for self motion and stabilize our sensory representation of the world. We tested a prediction arising from this postulate: that self motion should be processed more accurately than source motion. We used an infrared motion tracking system to measure head angle, and real-time interpolation of head related impulse responses to create "head-stabilized" signals that appeared to remain fixed in space as the head turned. After being presented with pairs of simultaneous signals consisting of a man and a woman speaking a snippet of speech, normal and hearing impaired listeners were asked to report whether the female voice was to the left or the right of the male voice. In this way we measured the moving minimum audible angle (MMAA). This measurement was made while listeners were asked to turn their heads back and forth between ± 15° and the signals were stabilized in space. After this "self-motion" condition we measured MMAA in a second "source-motion" condition when listeners remained still and the virtual locations of the signals were moved using the trajectories from the first condition. For both normal and hearing impaired listeners, we found that the MMAA for signals moving relative to the head was ~1-2° smaller when the movement was the result of self motion than when it was the result of source motion, even though the motion with respect to the head was identical. These results as well as the results of past experiments suggest that spatial processing involves an ongoing and highly accurate comparison of spatial acoustic cues with self-motion cues

Developmental changes in sensitivity to spatial and temporal properties of sensory integration underlying body representation

The closer in time and space that two or more stimuli are presented, the more likely it is that they will be integrated together. A recent study by Hillock-Dunn and Wallace (2012) reported that the size of the visuo-auditory temporal binding window — the interval within which visual and auditory inputs are highly likely to be integrated — narrows over childhood. However, few studies have investigated how sensitivity to temporal and spatial properties of multisensory integration underlying body representation develops in children. This is not only important for sensory processes but has also been argued to underpin social processes such as empathy and imitation (Schütz-Bosbachet al., 2006). We tested 4 to 11 year-olds’ ability to detect a spatial discrepancy between visual and proprioceptive inputs (Experiment One) and a temporal discrepancy between visual and tactile inputs (Experiment Two) for hand representation. The likelihood that children integrated spatially separated visuo-proprioceptive information, and temporally asynchronous visuo-tactile information, decreased significantly with age. This suggests that spatial and temporal rules governing the occurrence of multisensory integration underlying body representation are refined with age in typical developmen

Equal Relabelings for PQ-Sided Dice

For m n-sided dice, we will call the sums m, m+1, m+2,..., mn the standard sums, and we will say that m n-sided dice have an equal relabeling if the dice can be labeled with positive integers in such a way that the standard sums are equally likely to occur. We will consider the case when n=pq for distinct primes

Auditory spatial representations of the world are compressed in blind humans

Compared to sighted listeners, blind listeners often display enhanced auditory spatial abilities such as localization in azimuth. However, less is known about whether blind humans can accurately judge distance in extrapersonal space using auditory cues alone. Using virtualization techniques, we show that auditory spatial representations of the world beyond the peripersonal space of blind listeners are compressed compared to those for normally sighted controls. Blind participants overestimated the distance to nearby sources, and underestimated the distance to remote sound sources, in both reverberant and anechoic environments, and for speech, music and noise signals. Functions relating judged and actual virtual distance were well fitted by compressive power functions, indicating that the absence of visual information regarding the distance of sound sources may prevent accurate calibration of the distance information provided by auditory signals

Clementine

Erstdruck (anonym): Leipzig (F. A Brockhaus) 1843

The role of visual experience in the emergence of cross-modal correspondences

Cross-modal correspondences describe the widespread tendency for attributes in one sensory modality to be consistently matched to those in another modality. For example, high pitched sounds tend to be matched to spiky shapes, small sizes, and high elevations. However, the extent to which these correspondences depend on sensory experience (e.g. regularities in the perceived environment) remains controversial. Two recent studies involving blind participants have argued that visual experience is necessary for the emergence of correspondences, wherein such correspondences were present (although attenuated) in late blind individuals but absent in the early blind. Here, using a similar approach and a large sample of early and late blind participants (N=59) and sighted controls (N=63), we challenge this view. Examining five auditory-tactile correspondences, we show that only one requires visual experience to emerge (pitch-shape), two are independent of visual experience (pitch-size, pitch-weight), and two appear to emerge in response to blindness (pitch-texture, pitch-softness). These effects tended to be more pronounced in the early blind than late blind group, and the duration of vision loss among the late blind did not mediate the strength of these correspondences. Our results suggest that altered sensory input can affect cross-modal correspondences in a more complex manner than previously thought and cannot solely be explained by a reduction in visually-mediated environmental correlations. We propose roles of visual calibration, neuroplasticity and structurally-innate associations in accounting for our findings

Keeping up appearances: a comparative approach to aesthetics and the politics of public planning

This research examines the politics of land use planning debates and compares how aesthetic ideals and values associated with a landscape impact public planning decisions in rural Chatham County, North Carolina and the traditionally agrarian Dutch Green Heart. Landscapes and the associated aesthetic values often emerge in these debates simply as attractive places, views and vistas, or synonyms for natural and ecological environments. The aesthetic ideals and attachment to particular landscapes, however, act as diacritical markers indicative of a specific social imaginary that is rooted in time and space. In this dissertation, I argue that battles over landscape ideals such as the preservation of the rural character in Chatham County elicit powerful emotive responses from residents. These emotional responses are embedded within socio-historic beliefs and practices that both implicitly and explicitly reflect deeply ingrained class and race-based components. The aesthetic ideals introduced by so-called newcomers since the 1980s and the recent battle to preserve the rural character of the region indelibly marks the landscape. The privileging of aesthetic ideals in Chatham's planning documents and public debates masks unintended economic, class, and potentially race-based exclusionary practices and fosters a divisive social imaginary in the region. The aesthetic ideals promoted in the Green Heart region, however, actually unified Dutch support during the late 1990s as the European Union consolidated. The Dutch Green Heart emerged in public discourse as an idealized landscape that embodied Dutch ingenuity and perseverance. It acted as a central national identity marker at a time when the push towards integration and co-operation within the European Union decreased national sovereignty, and threatened the social and economic position of the Netherlands. Landscapes emerge in this research as sites of contestation and ongoing debate that link people, polity, and place. The aesthetic privileging of a particular landscape in planning decisions is, therefore, neither benign nor apolitical

Von Geschlecht zu Geschlecht 1. Erster Teil: Der Freiherr

Erstdruck: Berlin (Otto Janke) 1864. : Neue revidierte Ausgab