Bandwidth selection for estimating the two-point correlation function of a spatial point pattern using AMSE

Author(s):  
Ji Meng Loh ◽  
Woncheol Jang
2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
D. Chicherin ◽  
J. M. Henn ◽  
E. Sokatchev ◽  
K. Yan

Abstract We present a method for calculating event shapes in QCD based on correlation functions of conserved currents. The method has been previously applied to the maximally supersymmetric Yang-Mills theory, but we demonstrate that supersymmetry is not essential. As a proof of concept, we consider the simplest example of a charge-charge correlation at one loop (leading order). We compute the correlation function of four electromagnetic currents and explain in detail the steps needed to extract the event shape from it. The result is compared to the standard amplitude calculation. The explicit four-point correlation function may also be of interest for the CFT community.


2021 ◽  
Vol 10 (1) ◽  
Author(s):  
Mariem Ben-Said

Abstract Background Ecological processes such as seedling establishment, biotic interactions, and mortality can leave footprints on species spatial structure that can be detectable through spatial point-pattern analysis (SPPA). Being widely used in plant ecology, SPPA is increasingly carried out to describe biotic interactions and interpret pattern-process relationships. However, some aspects are still subjected to a non-negligible debate such as required sample size (in terms of the number of points and plot area), the link between the low number of points and frequently observed random (or independent) patterns, and relating patterns to processes. In this paper, an overview of SPPA is given based on rich and updated literature providing guidance for ecologists (especially beginners) on summary statistics, uni-/bi-/multivariate analysis, unmarked/marked analysis, types of marks, etc. Some ambiguities in SPPA are also discussed. Results SPPA has a long history in plant ecology and is based on a large set of summary statistics aiming to describe species spatial patterns. Several mechanisms known to be responsible for species spatial patterns are actually investigated in different biomes and for different species. Natural processes, plant environmental conditions, and human intervention are interrelated and are key drivers of plant spatial distribution. In spite of being not recommended, small sample sizes are more common in SPPA. In some areas, periodic forest inventories and permanent plots are scarce although they are key tools for spatial data availability and plant dynamic monitoring. Conclusion The spatial position of plants is an interesting source of information that helps to make hypotheses about processes responsible for plant spatial structures. Despite the continuous progress of SPPA, some ambiguities require further clarifications.


2011 ◽  
Vol 417 (3) ◽  
pp. 2206-2215 ◽  
Author(s):  
A. P. Cooper ◽  
S. Cole ◽  
C. S. Frenk ◽  
A. Helmi

2013 ◽  
Vol 21 ◽  
pp. 138-139
Author(s):  
SHOTARO SHIBA

The AGT-W relation is a conjecture of the nontrivial duality between 4-dim quiver gauge theory and 2-dim conformal field theory. We verify a part of this conjecture for all the cases of quiver gauge groups by studying on the property of 3-point correlation function of conformal theory. We also mention the relation to [Formula: see text] algebra as one of the promising direction towards the proof of the remaining part.


2012 ◽  
Vol 6 (6) ◽  
pp. 4673-4693 ◽  
Author(s):  
H. Löwe ◽  
F. Riche ◽  
M. Schneebeli

Abstract. Finding relevant microstructural parameters beyond the density is a longstanding problem which hinders the formulation of accurate parametrizations of physical properties of snow. Towards a remedy we address the effective thermal conductivity tensor of snow via known anisotropic, second-order bounds. The bound provides an explicit expression for the thermal conductivity and predicts the relevance of a microstructural anisotropy parameter Q which is given by an integral over the two-point correlation function and unambiguously defined for arbitrary snow structures. For validation we compiled a comprehensive data set of 167 snow samples. The set comprises individual samples of various snow types and entire time series of metamorphism experiments under isothermal and temperature gradient conditions. All samples were digitally reconstructed by micro-computed tomography to perform microstructure-based simulations of heat transport. The incorporation of anisotropy via Q considerably reduces the root mean square error over the usual density-based parametrization. The systematic quantification of anisotropy via the two-point correlation function suggests a generalizable route to incorporate microstructure into snowpack models. We indicate the inter-relation of the conductivity to other properties and outline a potential impact of Q on dielectric constant, permeability and adsorption rate of diffusing species in the pore space.


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