scholarly journals On the honeycomb conjecture for a class of minimal convex partitions

2018 ◽  
Vol 370 (10) ◽  
pp. 7149-7179 ◽  
Author(s):  
Dorin Bucur ◽  
Ilaria Fragalà ◽  
Bozhidar Velichkov ◽  
Gianmaria Verzini
Keyword(s):  
Convex Partitions ◽  
Minimal Convex

On minimal convex pairs of convex compact sets

1996 ◽  
Vol 67 (3) ◽  
pp. 226-238 ◽  
Author(s):  
Ryszard Urbański
Keyword(s):  
Convex Compact ◽  
Compact Sets ◽  
Minimal Convex ◽  
Convex Compact Sets

scholarly journals Population-level inference for home-range areas

2021 ◽  
Author(s):  
Christen Herbert Fleming ◽  
Iman Deznabi ◽  
Shauhin Alavi ◽  
Margaret C. Crofoot ◽  
Ben T. Hirsch ◽  
...  
Keyword(s):  
Home Range ◽  
Density Estimation ◽  
Kernel Density Estimation ◽  
Kernel Density ◽  
Population Level ◽  
Home Ranges ◽  
Tracking Data ◽  
Temporal Autocorrelation ◽  
Time Space ◽  
Minimal Convex

· Home-range estimates are a common product of animal tracking data, as each range informs on the area needed by a given individual. Population-level inference on home-range areas—where multiple individual home-ranges are considered to be sampled from a population—is also important to evaluate changes over time, space, or covariates, such as habitat quality or fragmentation, and for comparative analyses of species averages. Population-level home-range parameters have traditionally been estimated by first assuming that the input tracking data were sampled independently when calculating home ranges via conventional kernel density estimation (KDE) or minimal convex polygon (MCP) methods, and then assuming that those individual home ranges were measured exactly when calculating the population-level estimates. This conventional approach does not account for the temporal autocorrelation that is inherent in modern tracking data, nor for the uncertainties of each individual home-range estimate, which are often large and heterogeneous. · Here, we introduce a statistically and computationally efficient framework for the population-level analysis of home-range areas, based on autocorrelated kernel density estimation (AKDE), that can account for variable temporal autocorrelation and estimation uncertainty. · We apply our method to empirical examples on lowland tapir (Tapirus terrestris), kinkajou (Potos flavus), white‐nosed coati (Nasua narica), white-faced capuchin monkey (Cebus capucinus), and spider monkey (Ateles geoffroyi), and quantify differences between species, environments, and sexes. · Our approach allows researchers to more accurately compare different populations with different movement behaviors or sampling schedules, while retaining statistical precision and power when individual home-range uncertainties vary. Finally, we emphasize the estimation of effect sizes when comparing populations, rather than mere significance tests.

On the Minimal Convex Shell of a Convex Body

1993 ◽  
Vol 36 (4) ◽  
pp. 466-472 ◽  
Author(s):  
Carla Peri
Keyword(s):  
Convex Body ◽  
Spherical Shell ◽  
Minimal Convex ◽  
Convex Shell

AbstractFor any convex body C in ℝd we introduce the notion of the convex shell and we prove that there exists a unique "minimal" convex shell, extending the notion of the minimal spherical shell of C. Then we prove that a "typical" convex body touches the boundary of its minimal convex shell in precisely d + 2 points.

scholarly journals Finding equitable convex partitions of points in a polygon efficiently

2010 ◽  
Vol 6 (4) ◽  
pp. 1-19 ◽  
Author(s):  
John Gunnar Carlsson ◽  
Benjamin Armbruster ◽  
Yinyu Ye
Keyword(s):  
Convex Partitions

scholarly journals On convex partitions of polygonal regions

1999 ◽  
Vol 195 (1-3) ◽  
pp. 167-180 ◽  
Author(s):  
Horst Martini ◽  
Petru Soltan
Keyword(s):  
Convex Partitions

scholarly journals Finding minimal convex nested polygons

1989 ◽  
Vol 83 (1) ◽  
pp. 98-110 ◽  
Author(s):  
Alok Aggarwal ◽  
Heather Booth ◽  
Joseph O'Rourke ◽  
Subhash Suri ◽  
Chee K. Yap
Keyword(s):  
Minimal Convex
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