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result(s) for
"Moran"
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Detecting Spatial Autocorrelation for a Small Number of Areas: a practical example
Moran’s
I
is commonly used to detect spatial autocorrelation in spatial data. However, Moran’s
I
may lead to underestimating spatial dependence when used for a small number of areas. This led to the development of Modified Moran’s
I
, which is designed to work when there are few areas. In this paper, both methods will be presented. Many R programs enable calculating Moran’s
I
, but to date, none have been available for calculating Modified Moran’s
I
. This paper aims to present both methods and provide the R code for calculating Modified Moran’s
I
, with an application to a case study of dengue fever across 14 regions in Makassar, Indonesia.
Journal Article
Spectrality of a class of Moran measures on the plane
Let
{
(
R
k
,
D
k
)
}
k
=
1
∞
be a sequence of pairs, where
D
k
=
{
0
,
1
,
…
,
q
k
-
1
}
(
1
,
1
)
T
is an integer vector set and
R
k
is an integer diagonal matrix or upper triangular matrix, i.e.,
R
k
=
s
k
0
0
t
k
or
R
k
=
u
k
1
0
v
k
. Associated with the sequence
{
(
R
k
,
D
k
)
}
k
=
1
∞
, Moran measure
μ
{
R
k
}
,
{
D
k
}
is defined by
μ
{
R
k
}
,
{
D
k
}
=
δ
R
1
-
1
D
1
*
δ
R
1
-
1
R
2
-
1
D
2
*
⋯
*
δ
R
1
-
1
R
2
-
1
⋯
R
k
-
1
D
k
*
⋯
.
In this paper, we consider the spectrality of
μ
{
R
k
}
,
{
D
k
}
. We prove that
μ
{
R
k
}
,
{
D
k
}
is a spectral measure under certain conditions in terms of
(
R
k
,
D
k
)
, i.e., there exists a Fourier basis for
L
2
(
μ
{
R
k
}
,
{
D
k
}
)
.
Journal Article
It had to be you
Years after their parents' murder, identical twin brothers, determined to clear one name at the expense of the other, ask Laura Moran and her Under Suspicion crew to solve this brutal crime and as they get close to the truth, they find the danger from the past finding its way into the present.
Book
Spatial-Temporal Analysis of Point Distribution Pattern of Schools Using Spatial Autocorrelation Indices in Bojnourd City
In recent years, attention has been given to the construction and development of new educational centers, but their spatial distribution across the cities has received less attention. In this study, the Average Nearest Neighbor (ANN) and the optimized hot spot analysis methods have been used to determine the general spatial distribution of the schools. Also, in order to investigate the spatial distribution of the schools based on the substructure variables, which include the school building area, the results of the general and local Moran and Getis Ord analyses have been investigated. A differential Moran index was also used to study the spatial-temporal variations of the schools’ distribution patterns based on the net per capita variable, which is the amount of school building area per student. The results of the Average Nearest Neighbor (ANN) analysis indicated that the general spatial patterns of the primary schools, the first high schools, and the secondary high schools in the years 2011, 2016, 2018, and 2021 are clustered. Applying the optimized hot spot analysis method also identified the southern areas and the suburbs as cold polygons with less-density. Also, the results of the differential Moran analysis showed the positive trend of the net per capita changes for the primary schools and first high schools. However, the result is different for the secondary high schools.
Journal Article
A unified perspective on some autocorrelation measures in different fields: A note
Using notions from linear algebraic graph theory, this article provides a unified perspective on some autocorrelation measures in different fields. They are as follows: (a) Orcutt’s first serial correlation coefficient, (b) Anderson’s first circular serial correlation coefficient, (c) Moran’s
, and (d) Moran’s
. The first two are autocorrelation measures for one-dimensional data equally spaced, such as time series data, and the last two are for spatial data. We prove that (a)–(c) are a kind of (d). For example, we show that (d) such that its spatial weight matrix equals the adjacency matrix of a path graph is the same as (a). The perspective is beneficial because studying the properties of (d) leads to studying the properties of (a)–(c) at the same time. For example, the bounds of (a)–(c) can be found from the bounds of (d).
Journal Article
Mechanisms of mast seeding
Mast seeding is a widespread and widely studied phenomenon. However, the physiological mechanisms that mediate masting events and link them to weather and plant resources are still debated. Here, we explore how masting is affected by plant resource budgets, fruit maturation success, and hormonal coordination of cues including weather and resources. There is little empirical support for the commonly stated hypothesis that plants store carbohydrates over several years to expend in a high-seed year. Plants can switch carbohydrates away from growth in high-seed years, and seed crops are more probably limited by nitrogen or phosphorus. Resources are clearly involved in the proximate mechanisms driving masting, but resource budget (RB) models cannot create masting in the absence of selection because some underlying selective benefit is required to set the level of a ‘full’ seed crop at greater than the annual resource increment. Economies of scale (EOSs) provide the ultimate factor selecting for masting, but EOSs probably always interact with resources, which modify the relationship between weather cues and reproduction. Thus, RB and EOS models are not alternative explanations for masting – both are required. Experiments manipulating processes that affect mast seeding will help clarify the physiological mechanisms that underlie mast seeding.
Journal Article