Operating LISA as a Sagnac interferometer

A phase-locking configuration for LISA is proposed that provides a significantly simpler mode of operation. The scheme provides one Sagnac signal readout inherently insensitive to laser frequency noise and optical bench motion for a non-rotating LISA array. This Sagnac output is also insensitive to clock noise, requires no time shifting of data, nor absolute arm length knowledge. As all measurements are made at one spacecraft, neither clock synchronization nor exchange of phase information between spacecraft is required. The phase-locking configuration provides these advantages for only one Sagnac variable yet retains compatibility with the baseline approach for obtaining the other TDI variables. The orbital motion of the LISA constellation is shown to produce a 14 km path length difference between the counter-propagating beams in the Sagnac interferometer. With this length difference a laser frequency noise spectral density of 1 Hz/$\sqrt{\rm Hz}$ would consume the entire optical path noise budget of the Sagnac variables. A significant improvement of laser frequency stability (currently at 30 Hz/$\sqrt{\rm Hz}$) would be needed for full-sensitivity LISA operation in the Sagnac mode. Alternatively, an additional level of time-delay processing could be applied to remove the laser frequency noise. The new time-delayed combinations of the phase measurements are presented.Comment: 8 pages, 2 figure

Orbit categories, classifying spaces, and generalized homotopy fixed points

We give a new description of Rosenthal's generalized homotopy fixed point spaces as homotopy limits over the orbit category. This is achieved using a simple categorical model for classifying spaces with respect to families of subgroups.Comment: 10 pages. Version 4: various improvements to the exposition based on comments from the referee and edito

Selected Challenges From Spatial Statistics For Spatial Econometricians

Griffith and Paelinck (2011) present selected non-standard spatial statistics and spatial econometrics topics that address issues associated with spatial econometric methodology. This paper addresses the following challenges posed by spatial autocorrelation alluded to and/or derived from the spatial statistics topics of this book: the Gaussian random variable Jacobian term for massive datasets; topological features of georeferenced data; eigenvector spatial filtering-based georeferenced data generating mechanisms; and, interpreting random effects.Artykuł prezentuje wybrane, niestandardowe statystyki przestrzenne oraz zagadnienia ekonometrii przestrzennej. Rozważania teoretyczne koncentrują się na wyzwaniach wynikających z autokorelacji przestrzennej, nawiązując do pojęć Gaussowskiej zmiennej losowej, topologicznych cech danych georeferencyjnych, wektorów własnych, filtrów przestrzennych, georeferencyjnych mechanizmów generowania danych oraz interpretacji efektów losowych

Colouring exact distance graphs of chordal graphs

For a graph $G=(V,E)$ and positive integer $p$, the exact distance-$p$ graph $G^{[\natural p]}$ is the graph with vertex set $V$ and with an edge between vertices $x$ and $y$ if and only if $x$ and $y$ have distance $p$. Recently, there has been an effort to obtain bounds on the chromatic number $\chi(G^{[\natural p]})$ of exact distance-$p$ graphs for $G$ from certain classes of graphs. In particular, if a graph $G$ has tree-width $t$, it has been shown that $\chi(G^{[\natural p]}) \in \mathcal{O}(p^{t-1})$ for odd $p$, and $\chi(G^{[\natural p]}) \in \mathcal{O}(p^{t}\Delta(G))$ for even $p$. We show that if $G$ is chordal and has tree-width $t$, then $\chi(G^{[\natural p]}) \in \mathcal{O}(p\, t^2)$ for odd $p$, and $\chi(G^{[\natural p]}) \in \mathcal{O}(p\, t^2 \Delta(G))$ for even $p$. If we could show that for every graph $H$ of tree-width $t$ there is a chordal graph $G$ of tree-width $t$ which contains $H$ as an isometric subgraph (i.e., a distance preserving subgraph), then our results would extend to all graphs of tree-width $t$. While we cannot do this, we show that for every graph $H$ of genus $g$ there is a graph $G$ which is a triangulation of genus $g$ and contains $H$ as an isometric subgraph.Comment: 11 pages, 2 figures. Versions 2 and 3 include minor changes, which arise from reviewers' comment

The ecology and conservation of green turtles (Chelonia mydas) in New Zealand : a thesis submitted in partial fulfilment of the requirements for the degree of Doctor of Philosophy in Marine Ecology at Massey University, Albany, New Zealand

Historically, little consideration has been given to the occurrence, ecology or conservation of the green turtle (Chelonia mydas) in temperate New Zealand. Located geographically at the southern boundary of the distributional range of green turtles in the southwestern Pacific, reports of this species in New Zealand are often overlooked as occasional visitors or stragglers incidentally carried by ocean currents. This convention may be reasonable when considering the temperature constrained distribution of this poikilothermic marine reptile. Despite this, green turtles have been reported in New Zealand waters for more than 100 years, yet no study has undertaken any in depth investigation as to their occurrence in this region. Therefore, this thesis investigated the presence of green turtles in New Zealand waters to test the hypothesis that their occurrence is ephemeral and incidental. Opportunistic data and samples collected between 1895 and 2013 was collated, reviewed and analysed to investigate several lines of empirical enquiry, including spatio-temporal distribution, population structure, genetic origin, diet composition and anthropogenic effects. Sighting, stranding, and incidental capture revealed a year round presence of post-pelagic immature juveniles to large sub-adult green turtles across northern New Zealand (ca. 34°-38° S). Such occurrence exists despite sea surface temperatures averaging only 14 C during austral winters. The aggregation exhibited a female:male sex ratio of 1.7:1 which is similar to that reported from proximate warm temperate foraging grounds in eastern Australia. Size frequency data indicated that green turtles recruit to neritic habitats of the North Island at ca. 40.8 cm curved carapace length. This reflects a natural postoceanic settlement pattern rather than oceanic-phase stragglers incidentally blown ashore by storm and other stochastic events. Supporting this rationale for natural recruitment, diet component data demonstrates that once green turtles settle into New Zealand’s nearshore coastal habitats, they transition to a benthic foraging strategy. Notably, green turtles in New Zealand do not ontogenetically transition from omnivory to obligate herbivory with age, but instead consume a variable diet of primarily macroalgae and benthic macro invertebrates. Overall, the confirmation of feeding in New Zealand substantially extends the southern foraging limit for green turtles in the Pacific Ocean. Genetic analyses of ~770 base pair sequences of mitochondrial (mt) DNA was conducted on 42 stranded green turtles to characterize the genetic structure of this aggregation. Results identified 15 haplotypes including one orphan haplotype from widely dispersed green turtle stocks across the western, central, and eastern Pacific Ocean. When compared to other regional nesting rookeries and foraging grounds, the New Zealand aggregation exemplified its unique composition, predominantly due to the large proportion of haplotypes from the endemic eastern Pacific clade. These results provide a genetic link to east Pacific stocks in the southwestern Pacific; identifying previously undefined regional connectivity and trans-oceanic dispersal for eastern Pacific green turtles. In order to assess potential human impacts, gross necropsies were conducted on green turtles found stranded in northern New Zealand between 2007 and 2013. Anthropogenic effects predominantly associated with the ingestion of plastic marine debris were identified as the likely cause for the majority of strandings in the North Island. Propeller strike and incidental capture in recreational fisheries were further shown to impact green turtles, particularly for turtles inhabiting neritic habitats adjacent to densely populated urban centres of northeastern New Zealand. Overall, data presented here supports the hypothesis that New Zealand northern neritic habitats provide a transitional developmental habitat for immature green turtles at the edge of their range in the southwestern Pacific Ocean. Genetic analysis reveals this aggregation is unique when compared to other regional foraging grounds, exhibiting links to discrete genetic stocks from across the Pacific Ocean. In addition, the cause of the exponential increase in records observed over time remains unclear, therefore warrants further research and monitoring of this endangered marine reptile; particularly in light of climate-mediated environmental change presently experienced in the region