A classification of spanning surfaces for alternating links

A classification of spanning surfaces for alternating links is provided up to genus, orientability, and a new invariant that we call aggregate slope. That is, given an alternating link, we determine all possible combinations of genus, orientability, and aggregate slope that a surface spanning that link can have. To this end, we describe a straightforward algorithm, much like Seifert's Algorithm, through which to construct certain spanning surfaces called layered surfaces. A particularly important subset of these will be what we call basic layered surfaces. We can alter these surface by performing the entirely local operations of adding handles and/or crosscaps, each of which increases genus. The main result then shows that if we are given an alternating projection P(L) and a surface S spanning L, we can construct a surface T spanning L with the same genus, orientability, and aggregate slope as S that is a basic layered surface with respect to P, except perhaps at a collection of added crosscaps and/or handles. Furthermore, S must be connected if L is non-splittable. This result has several useful corollaries. In particular, it allows for the determination of nonorientable genus for alternating links. It also can be used to show that mutancy of alternating links preserves nonorientable genus. And it allows one to prove that there are knots that have a pair of minimal nonorientable genus spanning surfaces, one boundary-incompressible and one boundary-compressible.Comment: 31 pages, 34 figure

Free associative composition: Practice led research into composition techniques that help enable free association.

The original compositions presented in this portfolio are the product of practice led research into developing and implementing composition techniques that enable free association. This com-mentary outlines the different approaches I have taken and the reasoning behind them

Another dimension from LiDAR – Obtaining foliage density from full waveform data

LiDAR tells the user where surfaces are, not what they are. In this study we investigate the potential for waveform LiDAR to provide more information on the nature of the returns over forestry. Waveform LiDAR was acquired for ten Pinus radiata plots in a New Zealand plantation, along with comprehensive leaf area sampling in 2m vertical bands. The decay rate of each waveform peak was shown to be a useful tool for estimating foliage density, and has potential for identifying regions containing ground and understorey. Leaf Area Density (LAD) is an expression of foliage density per unit height, and a relationship between waveform decay rate and LAD was developed with an R2 of 56%. Incorporating the proportion of discrete LiDAR that fell in that band (which itself has an R2 of 50%) improves this model to explain 69% of the variation in LAD. This is a good result, especially given the costs and difficulties in measuring leaf area directly. As foliage density varies dramatically on a fine scale it was not possible to differentiate the nature of every single LiDAR return – but by averaging over a small area local variation in LAD could be easily mapped. Ground returns could be distinguished as having short decays, and broad leafed understorey typically had values between those of the canopy and ground, although surface roughness and slope make it impossible to robustly identify single returns. This study produced a useful model for estimating LAD in Pinus radiata which could easily be extended to other coniferous species

Extracting More Data from LiDAR in Forested Areas by Analyzing Waveform Shape

Light Detection And Ranging (LiDAR) in forested areas is used for constructing Digital Terrain Models (DTMs), estimating biomass carbon and timber volume and estimating foliage distribution as an indicator of tree growth and health. All of these purposes are hindered by the inability to distinguish the source of returns as foliage, stems, understorey and the ground except by their relative positions. The ability to separate these returns would improve all analyses significantly. Furthermore, waveform metrics providing information on foliage density could improve forest health and growth estimates. In this study, the potential to use waveform LiDAR was investigated. Aerial waveform LiDAR data were acquired for a New Zealand radiata pine plantation forest, and Leaf Area Density (LAD) was measured in the field. Waveform peaks with a good signal-to-noise ratio were analyzed and each described with a Gaussian peak height, half-height width, and an exponential decay constant. All parameters varied substantially across all surface types, ruling out the potential to determine source characteristics for individual returns, particularly those with a lower signal-to-noise ratio. However, pulses on the ground on average had a greater intensity, decay constant and a narrower peak than returns from coniferous foliage. When spatially averaged, canopy foliage density (measured as LAD) varied significantly, and was found to be most highly correlated with the volume-average exponential decay rate. A simple model based on the Beer-Lambert law is proposed to explain this relationship, and proposes waveform decay rates as a new metric that is less affected by shadowing than intensity-based metrics. This correlation began to fail when peaks with poorer curve fits were included

Freshwater Pearl Mussel (Margaritifera Margaritifera) Host Choice and Behavioural Responses to Changes in Flow Regime

The endangered freshwater pearl mussel (Margaritifera margaritifera), one of the longest-lived invertebrates, are threatened globally. Scotland, UK, remains a stronghold, however even here the population is declining due to factors such as habitat degradation, pollution and pearl fishing. The study comprised two parts: field surveys of glochidia infection of host salmonid fish, and a novel laboratory flume based study of the mussel‟s behavioral responses to changes in flow regime. The intricate life cycle of M.margaritifera includes a parasitic stage as glochidia attached to gills of salmonids. The preferred host in Scotland is thought to be Salmo salar and Salmo trutta in the absence of S.salar. This has not, however, been empirically tested in the field. Eight rivers in NW Scotland were surveyed using standard electrofishing techniques and encysted glochidia counted. Results suggest S.trutta is the primary host fish for glochidia attachment in the rivers surveyed, which contradicts current accepted knowledge about host specificity of M.margaritifera. Mussel populations are often found in regulated rivers, however little data exists on response to changes in flow regime. The mussel's behavioral response to changes in flow were investigated in an experimental flume. Mussels buried significantly deeper in conditions of gradually increasing water velocity compared with rapid increases or where water velocity was constant. 68% of individual mussels washed out when the water velocity was rapidly increased. The findings are novel, provide initial recommendations for targeted management actions for the conservation of M.margaritifera both in Scotland and internationally, and highlight more research is required

Autumn Foods of White-Tailed Deer in Arkansas

Rumen contents from 65 hunter-harvested deer were collected and analyzed during 1985-86 to estimate the principal autumn foods consumed by white-tailed deer inhabiting the Ozark Mountains, Arkansas River Valley, and Gulf Coastal Plain regions of Arkansas. Deer in the Ozarks and Coastal Plain fed heavily on woody browse species, which comprised 99% of rumina identified from these 2 regions. Acorns were the primary food of deer in these heavily forested areas. Acorns and other woody browse were less important to deer inhabiting the Arkansas River Valley. In this region of interspersed agricultural fields and bottomland forests, soybeans and corn comprised 75% of the diet, and acorns accounted for only 2%

The RHIC azimuth quadrupole: "perfect liquid" or gluonic radiation?

Large elliptic flow at RHIC seems to indicate that ideal hydrodynamics provides a good description of Au-Au collisions, at least at the maximum RHIC energy. The medium formed has been interpreted as a nearly perfect (low-viscosity) liquid, and connections have been made to gravitation through string theory. Recently, claimed observations of large flow fluctuations comparable to participant eccentricity fluctuations seem to confirm the ideal hydro scenario. However, determination of the azimuth quadrupole with 2D angular autocorrelations, which accurately distinguish ``flow'' (quadrupole) from ``nonflow'' (minijets), contradicts conventional interpretations. Centrality trends may depend only on the initial parton geometry, and methods used to isolate flow fluctuations are sensitive instead mainly to minijet correlations. The results presented in this paper suggest that the azimuth quadrupole may be a manifestation of gluonic multipole radiation.Comment: 11 pages, 6 figure

Possible Suppression of Resonant Signals for Split-UED by Mixing at the LHC?

The mixing of the imaginary parts of the transition amplitudes of nearby resonances via the breakdown of the Breit-Wigner approximation has been shown to lead to potentially large modifications in the signal rates for new physics at colliders. In the case of suppression, this effect may be significant enough to lead to some new physics signatures being initially missed in searches at, e.g., the LHC. Here we explore the influence of this `width mixing' on the production of the nearly degenerate, level-2 Kaluza-Klein (KK) neutral gauge bosons present in Split-UED. We demonstrate that in this particular case large cross section modifications in the resonance region are necessarily absent and explain why this is so based on the group theoretical structure of the SM.Comment: 10 pages, 2 figures; discussion and references adde