26 research outputs found
Generalizations of Ripley's K-function with Application to Space Curves
The intensity function and Ripley's K-function have been used extensively in
the literature to describe the first and second moment structure of spatial
point sets. This has many applications including describing the statistical
structure of synaptic vesicles. Some attempts have been made to extend Ripley's
K-function to curve pieces. Such an extension can be used to describe the
statistical structure of muscle fibers and brain fiber tracks. In this paper,
we take a computational perspective and construct new and very general variants
of Ripley's K-function for curves pieces, surface patches etc. We discuss the
method from [Chiu, Stoyan, Kendall, & Mecke 2013] and compare it with our
generalizations theoretically, and we give examples demonstrating the
difference in their ability to separate sets of curve pieces.Comment: 9 pages & 8 figure
Characterizing Crown Struture of Three Interior Northwest Conifer Species Using Terrestrial Laser Scanning
Emerging interests in wildland fire behavior and risk, bioenergy utilization, carbon sequestration, and wildlife conservation increasingly rely on accurate assessments of the amount and location of biomass within the dominant plants on the landscape, often at finer scales than traditional methods have provided. At the tree scale, current studies often distribute biomass uniformly through simple volumes (e.g., cones and cylinders). However, biomass is heterogeneous at a variety of scales from needle clusters to groups of trees. This thesis presents techniques for using terrestrial laser scanning data to define crown profiles and describe within-crown heterogeneity in Pseudotusga menziesii, Pinus ponderosa, and Abies lasiocarpa of the Interior Northwest. Crown profiles were modeled using parametric curves applied to crown-length normalized laser point clouds, dimensioned by height above ground and distance from bole-centroids. A crown-base metric was derived from the laser data and compared to conventional field measurements. For all species, a modified Weibull curve fit crown points with significantly smaller error than a beta curve, cone, or cylinder; crown profile Weibull curves were species-specific and not interchangeable without producing signifcantly greater error. Within-crown patterning was described using a 3-D form of the Ripley’s K function. Ripley’s K analysis detected maximum clustering occuring at scales of 1.25 – 2.50 percent of crown length (e.g., 25-50 cm radius clusters in a 20 meter crown). P. ponderosa demonstrated clustering over the largest range of scales and to the greatest degree, while A. lasiocarpa exhibited clustering over the smallest range of scales. The scale of clustering did not change when points roughly corresponding to branchwood were excluded from the analysis. This study provides groundwork for predicting the spatial distribution of biomass with tree crowns. Limitations of the work include uncertainty regarding the impacts of occlusion of inner crowns and the relationships between laser points and foliage-branch elements, and the lack of spatial explicitness inherent to Ripley’s K. Future work should examine these issues with an eye toward refinement of predictive models linking traditional biomass allometry with spatial arrangement of canopy material
GTM: the generative topographic mapping
This thesis describes the Generative Topographic Mapping (GTM) --- a non-linear latent variable model, intended for modelling continuous, intrinsically low-dimensional probability distributions, embedded in high-dimensional spaces. It can be seen as a non-linear form of principal component analysis or factor analysis. It also provides a principled alternative to the self-organizing map --- a widely established neural network model for unsupervised learning --- resolving many of its associated theoretical problems. An important, potential application of the GTM is visualization of high-dimensional data. Since the GTM is non-linear, the relationship between data and its visual representation may be far from trivial, but a better understanding of this relationship can be gained by computing the so-called magnification factor. In essence, the magnification factor relates the distances between data points, as they appear when visualized, to the actual distances between those data points. There are two principal limitations of the basic GTM model. The computational effort required will grow exponentially with the intrinsic dimensionality of the density model. However, if the intended application is visualization, this will typically not be a problem. The other limitation is the inherent structure of the GTM, which makes it most suitable for modelling moderately curved probability distributions of approximately rectangular shape. When the target distribution is very different to that, theaim of maintaining an `interpretable' structure, suitable for visualizing data, may come in conflict with the aim of providing a good density model. The fact that the GTM is a probabilistic model means that results from probability theory and statistics can be used to address problems such as model complexity. Furthermore, this framework provides solid ground for extending the GTM to wider contexts than that of this thesis
Vesica: using Neolithic British ritual art and architecture as a model for making contemporary art
Merged with duplicate record 10026.1/646 on 08.03.2017 by CS (TIS)Can the creative practices of British Neolithic art and architecture be used in the making
of contemporary art? This dissertation describes my practice making works of art based
on the Neolithic model, presented in a gallery setting and occasionally in the landscape.
The creative process is grounded on research into prehistoric British art and ritual
architecture and records my process of understanding the work of ancient Britons as a
framework for the concurrent process of making new objects for display. Without
extensive research and direct experience of the Neolithic art and architecture I would
not have been able to create the responsive work that has grown from it. I visited
dozens of sites in England, Scotland, and Ireland, immersing myself as much as
possible within them, on them and around them; I breathed the damp air and sheltered
from the rain under their roofs; I ate in them, I touched, measured and aligned them. I
visited them in daylight and at night; summer and winter; on solstices and ordinary days;
sometimes by car but mostly on foot. I read copious texts by academic archaeologists
in my effort to get into the minds of the people who made these places and got to know
the archaeological scene well enough to deliver a paper at the Theoretical Archaeology
Group Conference in 2005, taking questions from distinguished Professors Julian
Thomas and Mike Parker Pearson.
My research included the types of space that remain and explores patterns that exist
within the structures, interpreting, based on the archaeology, how the places Neolithic
people made might have been used in ritual; in addition it includes an exploration of the
decoration and phenomena of the spaces. The process of understanding the Neolithic
shaped and transformed my creative practice and profoundly affected my practice of
making art and introducing a shamanic theme into the way I share it. The work I make is
therefore a response to the ancient practices of the men and women, a collection of
objects that a Neolithic artist might make today.
Finally the thesis is concerned with identifying three strategies used by contemporary
artists; Reconstructing, "Artefacting", and Responding to Neolithic spaces, then
documents how these three strategies are used as models in the creation of the
practical work that corresponds with the written work. Issues of presentation are
explored at some length, born of the dilemmas I experienced when making decisions of
where and how to show people what I had made.Dartington College of Art
GIS and Archaeology: Bison Hunting Strategies in Southern Saskatchewan
Between 1988 and 1989, an intensive archaeological survey of a small drainage known as Roan Mare coulee in southern Saskatchewan was conducted by Dr. Ernest Walker (Walker 1990). Among the 120 archaeological sites in the area, seven bison kills and a vast array of associated drivelines were identified. This study focuses upon the spatial interaction amongst the kills, the drivelines and the local environment in relation to the bison hunting strategies used on the Northern Plains. This is done by modelling where bison are likely to move in the terrain as well as how the topography obstructs their line of sight.
As this problem covers a large spatial area and multiple different data sources, Geographic Information Systems (GIS) are integrated into the research design in the form of Least Cost Path and Viewshed analyses. Both archaeological data from Walker's survey and environmental data such as elevation and water sources served as the input datasets required by ArcGIS's spatial analysis tools. The results of the Least Cost Path analyses were compared visually to both the location and orientation of the driveline evidence, while the viewshed results were compared to the trap's location at the valley edge.
The results of this research showed that the drivelines found at Roan Mare coulee appear to be following the general orientation of the landscape at the broadest scales, and likely served to funnel bison over large distances. There also appear to be several locations on the landscape that are amenable to moving bison to several different sites. The viewshed evidence shows the smaller scale nuances between bison vision and the terrain in a hypothetical drive event. The differences in the viewable area available to the bison at each site likely played a role in the chosen strategy employed when that site was used. It is hoped that this style of research can be continued with higher quality data and additional variables to help clarify many of the subtleties found in a Plains bison drive
Engineering aperiodic spiral order for photonic-plasmonic device applications
Thesis (Ph.D.)--Boston UniversityDeterministic arrays of metal (i.e., Au) nanoparticles and dielectric nanopillars (i.e., Si and SiN) arranged in aperiodic spiral geometries (Vogel's spirals) are proposed as a novel platform for engineering enhanced photonic-plasmonic coupling and increased light-matter interaction over broad frequency and angular spectra for planar optical devices. Vogel's spirals lack both translational and orientational symmetry in real space, while displaying continuous circular symmetry (i.e., rotational symmetry of infinite order) in reciprocal Fourier space. The novel regime of "circular multiple light scattering" in finite-size deterministic structures will be investigated. The distinctive geometrical structure of Vogel spirals will be studied by a multifractal analysis, Fourier-Bessel decomposition, and Delaunay tessellation methods, leading to spiral structure optimization for novel localized optical states with broadband fluctuations in their photonic mode density. Experimentally, a number of designed passive and active spiral structures will be fabricated and characterized using dark-field optical spectroscopy, ellipsometry, and Fourier space imaging. Polarization-insensitive planar omnidirectional diffraction will be demonstrated and engineered over a large and controllable range of frequencies. Device applications to enhanced LEDs, novel lasers, and thin-film solar cells with enhanced absorption will be specifically targeted. Additionally, using Vogel spirals we investigate the direct (i.e. free space) generation of optical vortices, with well-defined and controllable values of orbital angular momentum, paving the way to the engineering and control of novel types of phase discontinuities (i.e., phase dislocation loops) in compact, chip-scale optical devices. Finally, we report on the design, modeling, and experimental demonstration of array-enhanced nanoantennas for polarization-controlled multispectral nanofocusing, nanoantennas for resonant near-field optical concentration of radiation to individual nanowires, and aperiodic double resonance surface enhanced Raman scattering substrates