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

Adams

Barton

Bazzaz

Bradstock

Brosofske

Burnham

Camac

Clarke

Dubayah

Fornwalt

Gessler

Getis

Gill

Glenn

Gonzalez-Olabarria

Gordon

Hammill

Harpold

Jakubowksi

Kane

Keeley

Knox

Levick

Liyanage

McCarthy

Miller

Mitchard

Moore

Murphy

Nakagawa

Price

Purdie

Purdon

R Development Core Team

Rich

Tozer

Turner

Wasser

Watson

Zuur

English

arXiv

Abstract. There is a public perception that large high-severity wildfires decrease biodiversity and increase fire hazard by homogenizing vegetation composition and increasing the cover of mid-story vegetation. But a growing literature suggests that vegetation responses are nuanced. LiDAR technology provides a promising remote sensing tool to test hypotheses about post-fire vegetation regrowth because vegetation cover can be quantified within different height strata at fine scales over large areas. We assess the usefulness of airborne LiDAR data for measuring post-fire mid-story vegetation regrowth over a range of spatial resolutions (10 x 10 m, 30 x 30 m, 50 x 50 m, 100 x 100 m cell size) and investigate the effect of fire

severity on regrowth amount and spatial pattern following a mixed severity wildfire in Warrumbungle National Park, Australia. We predicted that recovery would be more vigorous in areas of high fire severity, because park managers observed dense post-fire regrowth in these areas. Moderate to strong positive associations were observed between LiDAR and field surveys of mid-story vegetation cover between 0.5–3.0 m. Thus our LiDAR survey was an apt representation of on-ground vegetation cover. LiDAR-derived mid-story vegetation cover was 22–40% lower in areas of low and moderate than high fire severity. Linear mixed-effects models showed that fire severity was among the strongest biophysical predictors of mid-story vegetation cover irrespective of spatial resolution. However much of the variance associated

with these models was unexplained, presumably because soil seed banks varied at finer scales than our LiDAR maps. Dense patches of mid-story vegetation regrowth were small (median size 0.01 ha) and evenly distributed between areas of low, moderate and high fire severity, demonstrating that high-severity fires do not homogenize vegetation cover. Our results are relevant for ecosystem conservation and fire management because they: indicate that native vegetation are responsive and resilient to high-severity fire, and show the usefulness of remote sensing tools such as LiDAR to monitor post-fire vegetation recovery over large areas in situ

Gordon, Christopher E. (R20465)

Price, Owen F.

Tasker, Elizabeth M.

Western Sydney ResearchDirect

Mapping and exploring variation in post-fire vegetation recovery following mixed severity wildfire using airborne LiDAR

There is a public perception that large high severity wildfires decrease biodiversity and increase fire hazard by homogenising vegetation composition and increasing the cover of mid-story vegetation. But a growing literature suggests that vegetation responses are nuanced. LiDAR technology provides a promising remote sensing tool to test hypotheses about post-fire vegetation regrowth because vegetation cover can be quantified within different height strata at fine-scales over large areas. We assess the usefulness of airborne LiDAR data for measuring post-fire mid-story vegetation regrowth over a range of spatial resolutions (10x10m, 30x30m, 50x50m, 100x100m cell size) and investigate the effect of fire severity on regrowth amount and spatial pattern following a mixed severity wildfire in Warrumbungle National Park, Australia. We predicted that recovery would be more vigorous in areas of high fire severity, because park managers observed dense post-fire regrowth in these areas. Moderate to strong positive associations were observed between LiDAR and field surveys of mid-story vegetation cover between 0.5–3m. Thus our LiDAR survey was an apt representation of on-ground vegetation cover. LiDAR-derived mid-story vegetation cover was 22–40% higher in areas of low and moderate than high fire severity. Linear mixed-effects models showed that fire severity was among the strongest biophysical predictors of mid-story vegetation cover irrespective of spatial resolution. However much of the variance associated with these models was unexplained, presumably because soil seedbanks varied at finer-scales than our LiDAR maps. Dense patches of mid-story vegetation regrowth were small (median size 0.01ha) and evenly distributed between areas of low, moderate and high fire severity, demonstrating that high severity fires do not homogenise vegetation cover. Our results are relevant for ecosystem conservation and fire management because they: indicate that native vegetation are responsive and resilient to high severity fire, and show the usefulness of remote sensing tools such as LiDAR to monitor post-fire vegetation recovery over large area in situ.Gordonetal_2017_EcolApp_DataData presented in the manuscript "Mapping and exploring variation in post-fire vegetation recovery following mixed severity wildfire using airborne LiDAR

Gordon, Christopher E.

NEUROSURGERY ENTHUSIASTIC WOMEN SOCIETY

Data from: Mapping and exploring variation in post-fire vegetation recovery following mixed severity wildfire using airborne LiDAR

ZENODO

Christopher E. Gordon

Owen F. Price

Elizabeth M. Tasker

Crossref

Ecological Applications

There is a public perception that large high severity wildfires decrease biodiversity and increase fire hazard by homogenising vegetation composition and increasing the cover of mid-story vegetation. But a growing literature suggests that vegetation responses are nuanced. LiDAR technology provides a promising remote sensing tool to test hypotheses about post-fire vegetation regrowth because vegetation cover can be quantified within different height strata at fine-scales over large areas. We assess the usefulness of airborne LiDAR data for measuring post-fire mid-story vegetation regrowth over a range of spatial resolutions (10x10m, 30x30m, 50x50m, 100x100m cell size) and investigate the effect of fire severity on regrowth amount and spatial pattern following a mixed severity wildfire in Warrumbungle National Park, Australia. We predicted that recovery would be more vigorous in areas of high fire severity, because park managers observed dense post-fire regrowth in these areas. Moderate to strong positive associations were observed between LiDAR and field surveys of mid-story vegetation cover between 0.5–3m. Thus our LiDAR survey was an apt representation of on-ground vegetation cover. LiDAR-derived mid-story vegetation cover was 22–40% higher in areas of low and moderate than high fire severity. Linear mixed-effects models showed that fire severity was among the strongest biophysical predictors of mid-story vegetation cover irrespective of spatial resolution. However much of the variance associated with these models was unexplained, presumably because soil seedbanks varied at finer-scales than our LiDAR maps. Dense patches of mid-story vegetation regrowth were small (median size 0.01ha) and evenly distributed between areas of low, moderate and high fire severity, demonstrating that high severity fires do not homogenise vegetation cover. Our results are relevant for ecosystem conservation and fire management because they: indicate that native vegetation are responsive and resilient to high severity fire, and show the usefulness of remote sensing tools such as LiDAR to monitor post-fire vegetation recovery over large area in situ

Electronic Archiving System

Dryad Digital Repository (Duke University)

https://ro.uow.edu.au/cgi/viewcontent.cgi?article=5974&amp;context=smhpapers