Spatial weights matrices used in quantitative geography furnish maps with their individual latent eigenvectors, whose geographic distributions portray distinct spatial autocorrelation (SA) ...components. These polygon patterns on maps have specific meaning, partially in terms of geographic scale, which this article describes. The goal of this description is to enable spatial analysts to better understand and interpret these maps individually, as well as mixtures of them, when accounting for SA in a spatial analysis. Linear combinations of Moran eigenvector maps supply a powerful and relatively simple tool that can explain SA in regression residuals, with an ability to render reasonably accurate reproductions of empirical geographic distributions with or without the aid of substantive covariates. The focus of this article is positive SA, the most commonly encountered nature of autocorrelation in georeferenced data. The principal innovative contribution of this article is establishing a better clarification of what the synthetic SA variates extracted from spatial weights matrices epitomize with regard to global, regional, and local clusters of similar values on a map. This article shows that the Getis-Ord G
i
* statistic provides a useful tool for classifying Moran eigenvector maps into these three qualitative categories, illustrating findings with a range of specimen geographic landscapes.
A class of spectral Moran measures An, Li-Xiang; He, Xing-Gang
Journal of functional analysis,
01/2014, Letnik:
266, Številka:
1
Journal Article
Recenzirano
Odprti dostop
Let {Dk}k=1∞ be a sequence of digit sets in N and let {bk}k=1∞ be a sequence of integer numbers bigger than 1. We call the family {fk,Dk(x)=bk−1(x+d):d∈Dk,k⩾1} a Moran iterated function system (IFS), ...which is a natural generalization of an IFS. We prove, under certain conditions in terms of (bk,Dk), that the associated Moran measure μ is a spectral measure, i.e., there exists a countable set Λ⊂N such that {e2πiλx:λ∈Λ} is an orthonormal basis for L2(μ).
Letμ=μ{Rn,Bn}=δR1−1B1⁎δ(R2R1)−1B2⁎⋯ be a Borel probability measure with a compact support, where Rn∈M2(Z), Bn⊂Z2 and (Rn,Bn,Ln) forms a Hadamard triple for all n≥1. In this paper, we consider the ...existence of exponential orthogonal basis in L2(μ). We extend the concept of equi-positive family in 1 to higher dimensions, and provide a new idea to characterize the spectrality of such measures. In details, we study the spectrality and non-spectrality of Moran-Sierpinski type measures specifically under some necessary assumptions. The partial findings of several previous studies are extended by this study, such as Cantor-Moran measures (An-Fu-Lai 1, An-He-He 3), Moran-Sierpinski type measures (Wang-Dong 47) and Moran-Cantor-Dust type measures (Chen-Liu-Su-Wang 9).
The oil palm (Elaeis guineensis) is a very important source of vegetable oil worldwide. While oil palm cultivation is not currently economically significant in Brazil, there is immense growth ...potential for this crop in the Amazon region, with no need for deforestation. Fatal yellowing (FY) is a major phytosanitary barrier to the development of oil palm cultivation in the region. Many plantations have been devastated by FY, but its causes are unknown. The objective of this study was to analyze the spatial autocorrelation of FY in the oil palm crop by applying Moran's Index (I). The experiment was carried out on a large farm (>8000 ha) in the municipality of Acará, in the state of Pará (Brazil), with 139 plots of oil palm of different genetic materials and ages. The number of diseased plants per plot has been recorded since 2001 and used in the analysis. A positive autocorrelation of disease incidence was calculated based on the observations of the current study. By calculation of the Local Moran's I it was possible to identify the presence of high-incidence regions in the northeast and the central-west areas of the farm and low-incidence areas in the south and the north and in outlying plots. The approach described in this study was useful in identifying regions with the highest occurrence of FY, and could be useful in the management of this disease.
Based on data of 285 Chinese cities from 2003 to 2017, this paper mainly studies the impact of the spatial agglomeration of Foreign direct investment (FDI) on the green total factor productivity(TFP) ...of Chinese cities by SDM model. It is measured that China's urban green TFP generally has been developing well from 2003 to 2017, and progress in green technology plays an important role in improving urban green TFP. Both global Moran index and local Moran scatter plots show that FDI and green TFP are characterized by strong spatial agglomeration. This suggests green TFP is closely related to the spatial agglomeration of FDI in a region. The paper finds that FDI plays a positive role in promoting green TFP in high-high and high-low cluster cities, and the technology spillover effect of highly agglomerated FDI is more significant than that of decentralized FDI, thus promoting the upgrading and agglomeration of green TFP in itself and surrounding cities. The positive benefits of low-high and low-low cluster cities are not significant. Therefore, it is necessary to go beyond its policy of administrative regions and give full play to radiation effect of High-high FDI agglomeration cities and promote the green TFP of their surrounding cities.
•Green TFP is closely related to the spatial agglomeration of FDI in a region.•The impact of FDI on green TFP of different agglomeration cities is different.•Technology spillover effect of highly agglomerated FDI is more significant than that of decentralized FDI.
Motivated by the question of the impact of selective advantage in populations with skewed reproduction mechanisms, we study a Moran model with selection. We assume that there are two types of ...individuals, where the reproductive success of one type is larger than the other. The higher reproductive success may stem from either more frequent reproduction, or from larger numbers of offspring, and is encoded in a measure Λ for each of the two types. Λ-reproduction here means that a whole fraction of the population is replaced at a reproductive event. Our approach consists of constructing a Λ-asymmetric Moran model in which individuals of the two populations compete, rather than considering a Moran model for each population. Provided the measure are ordered stochastically, we can couple them. This allows us to construct the central object of this paper, the Λ−asymmetric ancestral selection graph, leading to a pathwise duality of the forward in time Λ-asymmetric Moran model with its ancestral process. We apply the ancestral selection graph in order to obtain scaling limits of the forward and backward processes, and note that the frequency process converges to the solution of an SDE with discontinuous paths. Finally, we derive a Griffiths representation for the generator of the SDE and use it to find a semi-explicit formula for the probability of fixation of the less beneficial of the two types.
Muller’s ratchet, in its prototype version, models a haploid, asexual population whose size N is constant over the generations. Slightly deleterious mutations are acquired along the lineages at a ...constant rate, and individuals carrying less mutations have a selective advantage. The classical variant considers fitness proportional selection, but other fitness schemes are conceivable as well. Inspired by the work of Etheridge et al. (2009) we propose a parameter scaling which fits well to the “near-critical” regime that was in the focus of Etheridge et al. (2009) (and in which the mutation–selection ratio diverges logarithmically as N→∞). Using a Moran model, we investigate the“rule of thumb” given in Etheridge et al. (2009) for the click rate of the “classical ratchet” by putting it into the context of new results on the long-time evolution of the size of the best class of the ratchet with (binary) tournament selection. This variant of Muller’s ratchet was introduced in González Casanova et al. (2023), and was analysed there in a subcritical parameter regime. Other than that of the classical ratchet, the size of the best class of the tournament ratchet follows an autonomous dynamics up to the time of its extinction. It turns out that, under a suitable correspondence of the model parameters, this dynamics coincides with the so called Poisson profile approximation of the dynamics of the best class of the classical ratchet.
Given a pair (R,D), where R={Ri}i=1∞ is a sequence of expanding matrix (i.e., all the eigenvalues of Ri have modulus strictly greater than 1), and D={Di}i=1∞⊆Z2. It is well known that there exists an ...infinite convolution generated by (R,D) which satisfies μR,D≔δR1−1D1∗δ(R2R1)−1D2∗⋯,we say that μR,D is a Moran measure if it convergent to a probability measure with compact support in a weak sense, where δE=1#E∑d∈Eδd is the uniformly discrete measure on E. In this paper, we consider the spectral properties of the Moran measure μR,D with R=b100b2, and #Di=p, where 1<b1,b2∈R and p is a prime number, supi∈N,d∈Di|d|<∞. Let B(p):≡{1pjk:1≤j,k≤p−1} and Z(δˆE)={x∈R2:δˆE(x)=0}. We show that under the conditions that Z(δˆDi)=⋃k=1φ(i)Zk(p)for some φ(i)∈N, where Zk(p)⊆B(p)+Z2 with (Zk(p)−Zk(p))∖Z2⊆Zk(p), and Zk(p)⁄⊆B(q)+Z2 for 0<q<p, 1≤k≤φ(i), {x∈0,1)2:|δˆDi(x)|=1}={00}. Then μR,D is a spectral measure if and only if R=pk100pk2 for some k1,k2∈N. This extends the results of Sierpinski-type measure considered by Dai et.al ACHA,2021. Also some sufficient conditions for μR,D being a spectral measure when p is not a prime number are given.
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