Tile Number and Space-Efficient Knot Mosaics

In this paper we introduce the concept of a space-efficient knot mosaic. That is, we seek to determine how to create knot mosaics using the least number of non-blank tiles necessary to depict the knot. This least number is called the tile number of the knot. We determine strict bounds for the tile number of a knot in terms of the mosaic number of the knot. In particular, if $t$ is the tile number of a prime knot with mosaic number $m$, then $5m-8 \leq t \leq m^2-4$ if $m$ is even and $5m-8 \leq t \leq m^2-8$ if $m$ is odd. We also determine the tile number of several knots and provide space-efficient knot mosaics for each of them.Comment: The original version of this article was split into two articles during refereein

落ちそむる梧桐(あおぎり)の葉 : 稲賀恵四郎（南畝, 1865-1901）の漢詩

The heart of this piece is a series of annotated translations of kanshi (poems in Chinese) by Inaga Keishirō (Nanpo, 1865–1901), an educator and amateur poet from Tottori prefecture. Eighty-six of Nanpo’s poems were rediscovered in 2000. The translators have deciphered the holograph poem texts and placed the poetry in context. Their introductory essay offers a biography of the poet and an outline of Meiji kanshi practice, and comments on developments in the world of kangaku. Kanshi during this period experienced its final flowering, remaining popular despite the trend toward modernity and Westernization and Japan’s gradual retreat from its Sinitic traditions. The kanshi renaissance of the Meiji era produced a large volume of appealing and lively poetry and reflected kanshi’s broadened demographic appeal. Several factors were at work, including educational reform and growth in the literacy rate, the reopening of contacts with China, expansion of the media, and a conservative reaction against modernization that set in during the 1880s. Much of Nanpo’s verse, like late Edo kanshi generally, displays a distinctively Japanese flavor; Chinese allusions are infrequent, as are conspicuous efforts to imitate past poets. His kanshi tend to be more conventional than novel or political in theme; in tone, the poems range from grave or melancholy to contented, even jocular. The introduction concludes with an analysis of Nanpo’s poetic style, topoi, diction, and his poetic persona. Despite the profusion of socio-political changes occurring around them, many kanshi poets in Meiji Japan remained content with traditional themes, even while giving the occasional nod to modernity. Nanpo was among these poets, who outnumbered the better known modernists of the kanshi world

Prediction of the probability of large fires in the Sydney region of south-eastern Australia using components of fire weather.

The probability of large-fire (\u3e= 1000 ha) ignition days, in the Sydney region, was examined using historical records. Relative influences of the ambient and drought components of the Forest Fire Danger Index (FFDI) on large fire ignition probability were explored using Bayesian logistic regression. The preferred models for two areas (Blue Mountains and Central Coast) were composed of the sum of FFDI (Drought Factor, DF = 1) (ambient component) and DF as predictors. Both drought and ambient weather positively affected the chance of large fire ignitions, with large fires more probable on the Central Coast than in the Blue Mountains. The preferred, additive combination of drought and ambient weather had a marked threshold effect on large-fire ignition and total area burned in both localities. This may be due to a landscape-scale increase in the connectivity of available fuel at high values of the index. Higher probability of large fires on the Central Coast may be due to more subdued terrain or higher population density and ignitions. Climate scenarios for 2050 yielded predictions of a 20-84% increase in potential large-fire ignitions days, using the preferred model

The proximal drivers of large fires: A Pyrogeographic study

Variations in global patterns of burning and fire regimes are relatively well measured, however, the degree of influence of the complex suite of biophysical and human drivers of fire remains controversial and incompletely understood. Such an understanding is required in order to support current fire management and to predict the future trajectory of global fire patterns in response to changes in these determinants. In this study we explore and compare the effects of four fundamental controls on fire, namely the production of biomass, its drying, the influence of weather on the spread of fire and sources of ignition. Our study area is southern Australia, where fire is currently limited by either fuel production or fuel dryness. As in most fire-prone environments, the majority of annual burned area is due to a relatively small number of large fires. We train and test an Artificial Neural Network’s ability to predict spatial patterns in the probability of large fires (>1,250 ha) in forests and grasslands as a function of proxies of the four major controls on fire activity. Fuel load is represented by predicted forested biomass and remotely sensed grass biomass, drying is represented by fraction of the time monthly potential evapotranspiration exceeds precipitation, weather is represented by the frequency of severe fire weather conditions and ignitions are represented by the average annual density of reported ignitions. The response of fire to these drivers is often non-linear. Our results suggest that fuel management will have limited capacity to alter future fire occurrence unless it yields landscape-scale changes in fuel amount, and that shifts between, rather than within, vegetation community types may be more important. We also find that increased frequency of severe fire weather could increase the likelihood of large fires in forests but decrease it in grasslands. These results have the potential to support long-term strategic planning and risk assessment by fire management agencies

Positive severity feedback between consecutive fires in dry eucalypt forests of southern Australia

Fire regimes have long-term effects on ecosystems which can be subtle, requiring study at a large spatial scale and temporal scale to fully appreciate. The way in which multiple fires interact to create a fire regime is poorly understood, and the relationship between the severities of consecutive fires has not been studied in Australia. By overlaying remotely sensed severity maps, our study investigated how the severity of a fire is influenced by previous fire severity. This was done by sampling points at 500-m spacing across 53 fires in dry eucalypt forests of southeast Australia, over a range of time since fire spanning every major fire season for 30 yr. Generalized additive models were used to determine the influence of previous severity on the probability of crown fire and understory fire, controlling for differences in time since fire, topography, and weather. We found that a crown fire is more than twice as likely after a previous crown fire than previous understory fire, and understory fire is more likely after previous understory fire. Our findings are in line with the results of studies from North America and suggest that severe fire promotes further fire. This may be evidence of a runaway positive feedback, which can drive ecological change, and lead to a mosaic of divergent vegetation, but research into more than two consecutive fires is needed to explore this. Our results also suggest that a low-severity prescribed fire may be a useful management option for breaking a cycle of crown fires

Wildfire and climate impacts tree hollow density in a temperate Australian forest

Tree hollows are an important landscape resource used by fauna for shelter, nesting, and predator avoidance. In fire-prone landscapes, wildfire and climate may impact hollow dynamics; however, assessments of their concurrent impacts are rare. We conducted a field survey at 80 sites in the Sydney Basin bioregion (Australia) to understand how fire frequency, fire severity, mean annual temperature, and mean annual precipitation concurrently impacted the site-density of small- (10 cm entry width) tree hollows and tree basal scars (which mediate hollow formation via invertebrate access to heartwood), when tree-size and dead/live status were considered. A unimodal relationship occurred between medium- and large-sized hollow densities and fire frequency and severity, respectively, with hollow densities greatest at intermediate frequencies/severities. Increases of 1.82, 1.43, and 1.17 hollows per site were observed between the 1 (reference) and 2, 2 and 3, and 3 and >3 fire frequency categories. Increases of 1.26, 1.75 and 0.75 hollows per site were observed between the low (reference) and moderate, moderate and high, and high and very high fire severity categories. Fire severity was also positively associated with basal scar density, with increases of 2.52, 8.15, and 8.47 trees per site between the low (reference) and moderate, moderate and high, and high and very high categories. A weak positive and stronger negative association was observed between mean annual temperature and small-sized hollow and basal scar density, respectively. Dead and medium-sized tree density was positively associated with medium-sized hollow and basal scar tree density, respectively. Collectively, our results suggest that wildfires, and in some cases climate, have diverse and size-specific impacts on tree hollow and basal scar density. Our results imply that fire regimes that allow for moderately severe wildfire will promote larger-sized tree hollows, which are a limiting resource for many fauna species

The role of Rnf in ion gradient formation in Desulfovibrio alaskensis

Rnf is a membrane protein complex that has been shown to be important in energy conservation. Here, Desulfovibrio alaskensis G20 and Rnf mutants of G20 were grown with different electron donor and acceptor combinations to determine the importance of Rnf in energy conservation and the type of ion gradient generated. The addition of the protonophore TCS strongly inhibited lactate-sulfate dependent growth whereas the sodium ionophore ETH2120 had no effect, indicating a role for the proton gradient during growth. Mutants in rnfA and rnfD were more sensitive to the protonophore at 5 µM than the parental strain, suggesting the importance of Rnf in the generation of a proton gradient. The electrical potential (ΔΨ), ΔpH and proton motive force were lower in the rnfA mutant than in the parental strain of D.alaskensis G20. These results provide evidence that the Rnf complex in D. alaskensis functions as a primary proton pump whose activity is important for growth.This work was supported by a grant from the Physical Biosciences program, DOE Office of Basic Energy Sciences, Chemical Sciences, Geosciences and Biosciences Division.Ye

How old is the Tasmanian cultural landscape? a test of landscape openness using quantitative land-cover reconstructions

Aim: To test competing hypotheses about the timing and extent of Holocene landscape opening using pollen-based quantitative land-cover estimates. Location: Dove Lake, Tasmanian Wilderness World Heritage Area, Australia. Methods: Fossil pollen data were incorporated into pollen dispersal models and corrected for differences in pollen productivity among key plant taxa. Mechanistic models (REVEALS-Regional Estimates of VEgetation Abundance from Large Sites) employing different models for pollen dispersal (Gaussian plume and Lagrangian stochastic models) were evaluated and applied in the Southern Hemisphere for the first time. Results: Validation of the REVEALS model with vegetation cover data suggests an overall better performance of the Lagrangian stochastic model. Regional land-cover estimates for forest and non-forest plant taxa show persistent landscape openness throughout the Holocene (average landscape openness similar to 50%). Gymnoschoenus sphaerocephalus, an indicator of moorland vegetation, shows higher values during the early Holocene (11.7-9 ka) and declines slightly through the mid-Holocene (9-4.5 ka) during a phase of partial landscape afforestation. Rain forest cover reduced (from similar to 40% to similar to 20%) during the period between 4.2-3.5 ka. Main conclusions: Pollen percentages severely under-represent landscape openness in western Tasmania and this bias has fostered an over-estimation of Holocene forest cover from pollen data. Treeless vegetation dominated Holocene landscapes of the Dove Lake area, allowing us to reject models of landscape evolution that invoke late-Holocene replacement of a rain forest-dominated landscape by moorland. Instead, we confirm a model of Late Pleistocene inheritance of open vegetation. Rapid forest decline occurred after c.4 ka, likely in response to regional moisture decline.Australian Research Council; AINSE AWARD [ALNGRA16024]; AINSE PGRA scholarship [12039]info:eu-repo/semantics/publishedVersio