High-temperature scaling limit for directed polymers on a hierarchical lattice with bond disorder

Diamond "lattices" are sequences of recursively-defined graphs that provide a network of directed pathways between two fixed root nodes, $A$ and $B$. The construction recipe for diamond graphs depends on a branching number $b\in \mathbb{N}$ and a segmenting number $s\in \mathbb{N}$, for which a larger value of the ratio $s/b$ intuitively corresponds to more opportunities for intersections between two randomly chosen paths. By attaching i.i.d. random variables to the bonds of the graphs, I construct a random Gibbs measure on the set of directed paths by assigning each path an "energy" given by summing the random variables along the path. For the case $b=s$, I propose a scaling regime in which the temperature grows along with the number of hierarchical layers of the graphs, and the partition function (the normalization factor of the Gibbs measure) appears to converge in law. I prove that all of the positive integer moments of the partition function converge in this limiting regime. The motivation of this work is to prove a functional limit theorem that is analogous to a previous result obtained in the $b<s$ case.Comment: 28 pages, 1 figur

Terrigenous Fe input and biogenic sedimentation in the glacial and interglacial equatorial Pacific Ocean

Many ocean regions important to the global carbon budget, including the equatorial Pacific Ocean, have low chlorophyll concentrations despite high levels of conventional nutrients. Iron may instead be the limiting nutrient, and elevated input of terrigenous Fe during windy glacial episodes has been hypothesized to stimulate oceanic productivity through time and thus regulate the oceanic and atmospheric CO2 balance. To test whether particulate Fe input is related to the accumulation of biogenic matter in one important low chlorophyll‐high nutrient area, that is, the equatorial Pacific Ocean, we present results from a suite of sediment cores that collectively record biogenic deposition through the last six glacial‐interglacial cycles (∼600,000 years). Our data set includes new chemical data on total Fe, terrigenous, and biogenic components in three cores as well as previously published mineralogic records of eolian input to the region. Chemical, spectral, and stratigraphic analysis indicates that (1) terrigenous input to the region shows no consistent pattern of either glacial or interglacial maxima, (2) the accumulation of particulate Fe is closely related to the accumulation of terrigenous matter (linear r2 = 0.81–0.98), (3) there are no coherent spectral relationships between Fe input and glacial periodicity (i.e., δ18O) in any of the orbital frequency bands, (4) the linear and cross‐spectral correlations between Fe or eolian input and CaCO3 concentration are most commonly the strongest observed relationships between Fe and any biogenic component, yet indicate a largely inverse pattern, with higher Fe being associated with low CaCO3, (5) there is no consistent linear r2 correlation or spectral coherence between the accumulation of Fe and that of CaCO3, Corg, or opal. Thus in total there is no relationship between terrigenous Fe input and sedimentary sequestering of carbon. Additionally, although we cannot specifically address the potential for changes in solubility of the terrigenous fraction that may be driven by a terrigenous compositional change, the Fe/Ti ratio (which monitors first‐order mineralogic changes) records only slight variations that also are linearly and spectrally unrelated to glacial periodicity, the bulk Fe flux, and the accumulation of any biogenic component. Finally, we find that the paleoceanographic flux of Fe is several order‐of‐magnitudes larger than modern observations of eolian Fe input, suggesting that the long‐term importance of Fe input by dust storms (which deliver Fe on the order of the sedimentary burial) may be underestimated. The removal of particulate terrigenous Fe from the recently discovered source within the Equatorial Undercurrent, however, remains unquantified and may also prove significant

Mapping same-sex couple family households in Australia

The map (1:1,218,987) accompanying this report is the first to depict the distribution of same-sex couple family households across Australia. The map and the report contribute to emerging scholarship combining critical geographies of sexualities with quantitative techniques and GIS in order to advance the political claims of sexual minorities. The data were collected through the 2006 Census and obtained via consultation with the Australian Bureau of Statistics. These data included the number of same-sex couple family households for all Statistical Divisions across Australia and for Statistical Sub-Divisions within metropolitan capital cities. Geographical concentrations of same-sex couple family households were determined by calculating the proportion of couple family households that were same-sex in each Statistical Division and Statistical Sub-Division, since the Census defines same-sex couples as a subset of couple family households. To visualise where the proportions fell above and below the national average, and thus where concentrations were found, these ratios were converted to location quotients using the Australian average as the denominator. The map combines different scales – Statistical Divisions and Statistical Sub-Divisions – to illustrate distributional patterns between inner-city and suburban areas, as well as between urban and regional localities, across Australia. While high concentrations are found in inner-cities, there are also significant suburban and regional concentrations, thus contesting assumptions about same-sex couples’ inner-city residential choices. Moreover, since same-sex couples were found in most Statistical Divisions, those areas below the national average cannot be considered devoid of these families, with implications for the effective operationalisation of equal rights legislation

Mapping same-sex couple family households in Australia

The map (1:1,218,987) accompanying this report is the first to depict the distribution of same-sex couple family households across Australia. The map and the report contribute to emerging scholarship combining critical geographies of sexualities with quantitative techniques and GIS in order to advance the political claims of sexual minorities. The data were collected through the 2006 Census and obtained via consultation with the Australian Bureau of Statistics. These data included the number of same-sex couple family households for all Statistical Divisions across Australia and for Statistical Sub-Divisions within metropolitan capital cities. Geographical concentrations of same-sex couple family households were determined by calculating the proportion of couple family households that were same-sex in each Statistical Division and Statistical Sub-Division, since the Census defines same-sex couples as a subset of couple family households. To visualise where the proportions fell above and below the national average, and thus where concentrations were found, these ratios were converted to location quotients using the Australian average as the denominator. The map combines different scales – Statistical Divisions and Statistical Sub-Divisions – to illustrate distributional patterns between inner-city and suburban areas, as well as between urban and regional localities, across Australia. While high concentrations are found in inner-cities, there are also significant suburban and regional concentrations, thus contesting assumptions about same-sex couples’ inner-city residential choices. Moreover, since same-sex couples were found in most Statistical Divisions, those areas below the national average cannot be considered devoid of these families, with implications for the effective operationalisation of equal rights legislation

Drilling history and geology of the Lanipuna no. 6 geothermal test, Lanipuna prospect, Hawaii

Discussion of the drilling program and interpretation of downhole geology based on cuttings samples from the Lanipuna 6 well.For Barnwell Industries, Inc., Honolulu, Hawaii

Fixed lateral unicompartmental knee replacement is a reliable treatment for lateral compartment osteoarthritis after mobile-bearing medial unicompartmental replacement

Purpose: Lateral osteoarthritis following medial unicompartmental knee replacement (UKR) is usually treated with total knee replacement, however, lateral UKR is a less invasive option that preserves a well-functioning medial UKR. This study aimed to determine the 5-year outcome of the cemented Fixed Lateral Oxford UKR (FLO) when used for the treatment of severe lateral disease after medial Oxford unicompartmental knee replacement. Methods: Forty-four knees with lateral bone-on-bone osteoarthritis (n = 43) and avascular necrosis (n = 1) treated with the FLO following medial Oxford UKR were followed up prospectively. The Oxford Knee Score (OKS) and Tegner Activity Score (TAS) were collected pre- and post-operatively. Life-table analysis was used to determine survival rates. Results: The mean patient age at the time of FLO surgery was 74.4 years with a mean time of 12.1 years between the primary medial UKR and the conversion to a bi-UKR with a FLO. Mean follow-up of the FLO was 3.5 years. After FLO no intra-operative or medical complications, re-admissions, or mortality occurred. There was one reoperation in which a bearing was exchanged for a medial bearing dislocation. There were no revisions of the FLO, so the FLO survival rate at 5 years was 100% (24 at risk). The mean pre-operative OKS was 22, which significantly (p < 0.0001) improved to a mean of 42, 42, and 40 at 1, 2, and 5 years, respectively. The median TAS had a non-significant improvement from 2.5 (Range 0–8) pre-operatively to 2 (Range 1–6) at 5 years postoperatively. Conclusion: The FLO is a reliable treatment for lateral osteoarthritis following medial UKR. At 5 years there was a 100% survival of the FLO with a mean OKS of 40. Level of evidence: IV, Prospective Case Series

Evolution of the UV Excess in Early-Type Galaxies

We examine the UV emission from luminous early-type galaxies as a function of redshift. We perform a stacking analysis using Galaxy Evolution Explorer (GALEX) images of galaxies in the NOAO Deep Wide Field Survey (NDWFS) Bo\"otes field and examine the evolution in the UV colors of the average galaxy. Our sample, selected to have minimal ongoing star formation based on the optical to mid-IR SEDs of the galaxies, includes 1843 galaxies spanning the redshift range $0.05\leq z\leq0.65$. We find evidence that the strength of the UV excess decreases, on average, with redshift, and our measurements also show moderate disagreement with previous models of the UV excess. Our results show little evolution in the shape of the UV continuum with redshift, consistent either with the binary model for the formation of Extreme Horizontal Branch (EHB) stars or with no evolution in EHB morphology with look-back time. However, the binary formation model predicts that the strength of the UV excess should also be relatively constant, in contradiction with our measured results. Finally, we see no significant influence of a galaxy's environment on the strength of its UV excess.Comment: 30 pages, 10 figures; accepted by ApJ. Modified from original version to reflect referee's comment