Estimating Pair Correlation Functions of Planar Cluster Processes

Stoyan, Dietrich; Stoyan, Helga

doi:10.1002/bimj.4710380302

Cited by 98 publications

(102 citation statements)

References 11 publications

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“…Nanoparticle labels appear to be sufficiently The clustering behaviour of HER2 was statistically analysed via the pair correlation function g(r) (Stoyan & Stoyan, 1996), calculated from all individual HER2 positions. These positions were automatically detected using a software tool designed by our group for this purpose.…”

Section: Model Of the Biotinylated Anti-her2 Affibody (Blue) Bindinmentioning

confidence: 99%

“…These positions were automatically detected using a software tool designed by our group for this purpose. The function g(r) measures the likelihood of a particle to be found within a certain radial distance with respect to a reference particle, whereby g(r) = 1 represents a random distribution, and a value >1 indicates clustering with a higher probability than random occurrence (Stoyan & Stoyan, 1996). In measurements incorporating 14,043 HER2 positions in eleven cells, a sharp peak in the g(r) function at 20 nm indicated that HER2 was clustered as a homodimer ( Figure 5A).…”

Section: Model Of the Biotinylated Anti-her2 Affibody (Blue) Bindinmentioning

confidence: 99%

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Membrane protein stoichiometry studied in intact mammalian cells

Jonge¹

2016

infocus

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Section: Model Of the Biotinylated Anti-her2 Affibody (Blue) Bindinmentioning

confidence: 99%

Section: Model Of the Biotinylated Anti-her2 Affibody (Blue) Bindinmentioning

confidence: 99%

Membrane protein stoichiometry studied in intact mammalian cells

Jonge¹

2016

infocus

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“…It is related to the K-function, but it is non-cumulative in character. The relation to the K-function is (Stoyan and Stoyan 1996):…”

Section: The Nearest-neighbour Distance Distribution Function (G-funcmentioning

confidence: 99%

Spatial statistics in ecological analysis: from indices to functions

Szmyt¹

2014

Silva Fenn.

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• Spatial statistics provides a quantitative description of natural variables distributed in space and time.• The objectives of spatial analysis are to detect spatial patterns and to confirm if a pattern found is significant. • Spatially explicit indices and functions may be applied depending on the information collected from the field. • Development of the specific software supports spatial analyses. AbstractThis paper presents a review of the most common methods in ecological studies aimed at spatial analysis of population structures (horizontal and vertical), based on point process statistics. Methods based on simple spatially explicit indices as well as more sophisticated methods relying on functions are described in a comprehensible manner. Simple indices revealing the information on spatial structure at the scale of the nearest neighbor can be easily implemented in practical forestry. On the other hand, spatial functions, based on much more detailed data, describe the spatial structure in terms of the spatial relationships between the natural processes and population structures and because of this complexity they are rarely used in forest practice. Including both methods in a single paper is also valuable from the potential reader's point of view saving their time for searching and choosing the appropriate method to make their spatial analysis. This paper can also serve as an initial guide for young researchers or those who are going to start their studies on spatial aspects of bio-systems. Avoiding the statistical and mathematical details makes this paper understandable for readers who are not statisticians or mathematicians. Readers will find many references related to each method described here, allowing them to find solutions to different problems observed in practice. This paper ends with a list of the most common specific software packages available to support spatial analysis.

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“…In addition to each point u in a spatial point process X, there may be an associated random variable m u called a mark. The process = {(u,m u ) : u ∈ X} is called a marked point process (Stoyan and Stoyan, 1996). It is commonly assumed in certain applications that the point process is stationary, i.e.…”

Section: Marked Spatial Point Patternsmentioning

confidence: 99%

Relationship between the spatial distribution of SMS messages reporting needs and building damage in 2010 Haiti disaster

Corbane

Lemoine

Kauffmann

2012

Nat. Hazards Earth Syst. Sci.

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Abstract. Just 4 days after the M = 7.1 earthquake on 12 January 2010, Haitians could send SMS messages about their location and urgent needs through the on-line mapping platform Ushahidi. This real-time crowdsourcing of crisis information provided direct support to key humanitarian resources on the ground, including Search and Rescue teams. In addition to its use as a knowledge base for rescue operations and aid provision, the spatial distribution of geolocated SMS messages may represent an early indicator on the spatial distribution and on the intensity of building damage.This work explores the relationship between the spatial patterns of SMS messages and building damage. The latter is derived from the detailed damage assessment of individual buildings interpreted in post-earthquake airborne photos. The interaction between SMS messages and building damage is studied by analyzing the spatial structure of the corresponding bivariate patterns.The analysis is performed through the implementation of cross Ripley's K-function which is suitable for characterizing the spatial structure of a bivariate pattern, and more precisely the spatial relationship between two types of point sets located in the same study area.The results show a strong attraction between the patterns exhibited by SMS messages and building damages. The interactions identified between the two patterns suggest that the geolocated SMS can be used as early indicators of the spatial distribution of building damage pattern. Accordingly, a statistical model has been developed to map the distribution of building damage from the geolocated SMS pattern.The study presented in this paper is the first attempt to derive quantitative estimates on the spatial patterns of novel crowdsourced information and correlate these to established methods in damage assessment using remote sensing data. The consequences of the study findings for rapid damage detection in post-emergency contexts are discussed.

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Estimating Pair Correlation Functions of Planar Cluster Processes

Cited by 98 publications

References 11 publications

Membrane protein stoichiometry studied in intact mammalian cells

Membrane protein stoichiometry studied in intact mammalian cells

Spatial statistics in ecological analysis: from indices to functions

Relationship between the spatial distribution of SMS messages reporting needs and building damage in 2010 Haiti disaster

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