Local Mean Level Research Articles

Difference in the production and elemental composition of litter in Kandelia obovata mangrove forests due to site elevation

Site elevation is a crucial driver for mangrove restoration, and litter production restoration is a significantly important target of mangrove restoration, but little attention has been paid to impact of site elevation on the production and elemental composition of litter in the restored mangrove forests. This study compared the production and elemental composition of mangrove litter at the three intertidal elevations, to explore impacts of site elevation on the production and elemental composition of mangrove litter. Compared with the upper elevation site, significantly lower annual litter production was found at the lower elevation site. Leaf litter was the main component of litter, up to 60.49% of total litter production at the upper elevation site, while reproductive materials (flower and fruit) were the key part of litter and accounted for 50.80% (the lower elevation site) and 57.02% (the middle elevation site) of total litter production. As site elevation decreased, element stocks within total litter decreased by approximately 65.39% (organic carbon), 65.17% (total nitrogen) and 63.66% (total phosphorus), respectively, which was attributed more to element stocks within leaf litter instead of element stocks within the other litter. Results showed that site elevation decreases resulted in decreased litter production, altered composition percentages of litter production, and reduced element stocks within total litter. In the future mangrove restoration projects, it is advisable to prioritize upper elevation (above local mean level) for promoting litter production.

Estimation of the Spatial Weighting Matrix for Spatiotemporal Data under the Presence of Structural Breaks

ABSTRACT In this article, we propose a two-stage LASSO estimation approach for the estimation of a full spatial weight matrix of spatiotemporal autoregressive models. In addition, we allow for an unknown number of structural breaks in the local means of each spatial location. These locally varying mean levels, however, can easily be mistaken as spatial dependence and vice versa. Thus, the proposed approach jointly estimates the spatial dependence, all structural breaks, and the local mean levels. For selection of the penalty parameter, we propose a completely new selection criterion based on the distance between the empirical spatial autocorrelation and the spatial dependence estimated in the model. Through simulation studies, we will show the finite-sample performance of the estimators and provide practical guidance as to when the approach could be applied. Finally, the method will be illustrated by an empirical example of intra-city monthly real-estate prices in Berlin between 1995 and 2014. The spatial units will be defined by the respective postal codes. The new approach allows us to estimate local mean levels and quantify the deviation of the observed prices from these levels due to spatial spillover effects. In doing so, the entire spatial dependence structure is estimated on a data-driven basis. Supplementary materials for this article are available online.

Enhanced harmony search algorithm with circular region perturbation for global optimization problems

To improve the searching effectiveness of the harmony search (HS) algorithm, an enhanced harmony search algorithm with circular region perturbation (EHS_CRP) is proposed in this paper. In the EHS_CRP algorithm, a global and local dimension selection strategy is designed to accelerate the search speed of the algorithm. A selection learning operator based on the global and local mean level is proposed to improve the balance between exploration and exploitation. Circular region perturbation is employed to avoid the algorithm stagnation and get a better exploration region. To assess performance, the proposed algorithm is compared with 10 state-of-the-art swarm intelligent approaches in a large set of global optimization problems. The simulation results confirm that EHS_CRP has a significant advantage in terms of accuracy, convergence speed, stability and robustness. Moreover, EHS_CRP performs better than other tested methods in engineering design optimization problems. Thus, the EHS_CRP algorithm is a viable and reliable alternative for some difficult and multidimensional real-world problems.

Forecasting turbine problems by means of the state space framework

A forecasting system is set up to improve the diagnosis in a Condition Monitoring Programme of a critical turbine placed at an industrial plant. The system is based on a statistical model in a State Space framework, such that the local mean level of the vibration state of the equipment is estimated directly from the data, based on a continuous-time set up. This model is combined with a cost model in Conditioned Monitoring, by which the time of preventive replacement is produced when the minimum of the expected cost per unit of time is reached into the future. Such measure is a combination of the costs of failure, the costs of a preventive replacement and the probabilities of reaching the alarm levels fixed by some criteria. The system is estimated by Maximum Likelihood and thoroughly tested on the equipment. The main tests relate to statistical properties of the model residuals and a comprehensive comparison with an alternative system, namely a linear trend regression model in continuous time. The system produced a reasonable forecasting performance and sensible time of preventive replacement prediction and outperformed the alternative forecasting system.

LONG RANGE DEPENDENCE, UNBALANCED HAAR WAVELET TRANSFORMATION AND CHANGES IN LOCAL MEAN LEVEL

Long range dependent (LRD) stationary time series have historically served to model real time series with apparent changes in local mean level. A natural tool to study changes in local mean level is the unbalanced Haar wavelet transformation (UHT). In this work, UHT is used to study changes in local mean level in LRD models and several real and simulated time series exhibiting LRD. In particular, simulations for LRD models suggest that changes in local mean level occur at times essentially governed by a homogeneous Poisson arrival process, and only the local mean levels themselves inherit the LRD property of the original time series. These properties are compared with the analogous ones in several real and simulated time series. The results are mixed though generally in favor of LRD models. The approach based on UHT is also compared to several alternatives such as defining changes in local mean level through kernel smoothing. The interest throughout is mainly in very long time series such as those collected in the studies of data traffic over Internet.

Two Charts: Not One

ABSTRACT Difficulties can occur in the operation of traditional control charts. A principal reason for this is that the data coming from a typical operating process do not vary about a fixed mean. It is shown how by using a nonstationary model a continuously updated local mean level is provided. This can be used to produce (a) a bounded adjustment chart that tells you when to adjust the process to achieve maximum economy and (b) a Shewhart monitoring chart seeking assignable causes of trouble applied to the deviations from the local mean. Estimation of the mean and “standard deviation” are not required.

Modeling the Variability of Sydney Harbor Wind Measurements

The time-dependent behavior in the variability of wind measurements is investigated using bivariate generalized autoregressive conditional heteroscedastic models. These models express the current level of short-timescale wind variability in terms of previous observed values of the fluctuations from mean wind fields. As such, these models provide a useful descriptive model that can be applied to short-term forecasting of variability of wind fluctuations around local mean levels.

Universality of S-matrix correlations for deterministic plus random Hamiltonians.

We study S-matrix correlations for random matrix ensembles with a Hamiltonian H=H(0)+straight phi, in which H0 is a deterministic NxN matrix and straight phi belongs to a Gaussian random matrix ensemble. Using Efetov's supersymmetry formalism, we show that in the limit N-->infinity correlation functions of S-matrix elements are universal on the scale of the local mean level spacing: the dependence of H0 enters into these correlation functions only through the average S matrix and the average level density. This statement applies to each of the three symmetry classes (unitary, orthogonal, and symplectic).

Statistical issues in the analysis of disease mapping data.

In this paper we discuss a number of issues that are pertinent to the analysis of disease mapping data. As an illustrative example we consider the mapping of larynx cancer across electoral wards in the North West Thames region of the U.K. Bayesian hierarchical models are now frequently employed to carry out such mapping. In a typical situation, a three-stage hierarchical model is specified in which the data are modelled as a function of area-specific relative risks at stage one; the collection of relative risks across the study region are modelled at stage two; and at stage three prior distributions are assigned to parameters of the stage two distribution. Such models allow area-specific disease relative risks to be 'smoothed' towards global and/or local mean levels across the study region. However, these models contain many structural and functional assumptions at different levels of the hierarchy; we aim to discuss some of these assumptions and illustrate their sensitivity. When relative risks are the endpoint of interest, it is common practice to assume that, for each of the age-sex strata of a particular area, there is a common multiplier (the relative risk) acting upon each of the stratum-specific risks in that area; we will examine this proportionality assumption. We also consider the choices of models and priors at stages two and three of the hierarchy, the effect of outlying areas, and an assessment of the level of smoothing that is being carried out. For inference, we concentrate on the description of the spatial variability in relative risks and on the association between the relative risks of larynx cancer and an area-level measure of socio-economic status.

Universality of random-matrix results for non-Gaussian ensembles.

We study random-matrix ensembles with a non-Gaussian probability distribution $P(H)\ensuremath{\sim}\mathrm{exp}[\ensuremath{-}N\mathrm{tr}V(H)]$, where $N$ is the dimension of the matrix $H$ and $V(H)$ is independent of $N$. Using Efetov's supersymmetry formalism, we show that in the limit $N\ensuremath{\rightarrow}\ensuremath{\infty}$ both energy level correlation functions and correlation functions of $S$-matrix elements are independent of $P(H)$ and hence universal on the scale of the local mean level spacing. This statement applies to each of the three generic ensembles (unitary, orthogonal, and symplectic). Universality is also found for correlation functions depending on some external parameter. Our results generalize previous work by Brezin and Zee [Nucl. Phys. B402, 613 (1993)].

Level clustering in the regular spectrum

In the regular spectrum of an f -dimensional system each energy level can be labelled with f quantum numbers originating in f constants of the classical motion. Levels with very different quantum numbers can have similar energies. We study the classical limit of the distribution P(S) of spacings between adjacent levels, using a scaling transformation to remove the irrelevant effects of the varying local mean level density. For generic regular systems P(S) = e -s , characteristic of a Poisson process with levels distributed at random. But for systems of harmonic oscillators, which possess the non-generic property that the ‘energy contours’ in action space are flat, P(S) does not exist if the oscillator frequencies are commensurable, and is peaked about a non-zero value of S if the frequencies are incommensurable, indicating some regularity in the level distribution; the precise form of P(S) depends on the arithmetic nature of the irrational frequency ratios. Numerical experiments on simple two-dimensional systems support these theoretical conclusions.

A Class of Matrix Ensembles

A class of random matrix ensembles is defined, with the purpose of providing a realistic statistical description of the Hamiltonian of a complicated quantum-mechanical system (such as a heavy nucleus) for which an approximate model Hamiltonian is known. An ensemble of the class is specified by the model Hamiltonian H0, an observed eigenvalue distribution-function r(E), and a parameter τ which may be considered to be a fictitious ``time.'' Each of H0, r(E), and τ may be chosen independently. The ensemble consists of matrices M which are obtained from H0 by an invariant random Brownian-motion process, lasting for a time τ and tending to pull the eigenvalues of M toward the distribution r(E). For small τ the ensemble allows only small perturbations of H0. As τ → ∞, the ensemble tends to a stationary limit independent of H0 and depending on r(E) alone. The following quantitative results are obtained. (1) It is proved that the global eigenvalue distribution in the limit τ → ∞ becomes identical with the observed distribution r(E). (2) A nonlinear partial differential equation is obtained for the global eigenvalue distribution ρ(E, τ) as a function of E and τ. Solution of this equation will show how the distribution changes from the initial form specified by H0 at τ = 0 to the final form r(E) at τ = ∞. Approximate solution shows that deviations of ρ(E, τ) from r(E) extending over an interval containing m eigenvalues will disappear exponentially as soon as τ is of the order of mD2, where D is the local mean level spacing. (3) Exact analytic expressions are obtained for the correlation functions representing the probabilities for finding n eigenvalues at assigned positions (E1, …, En) in the ensemble in the limit τ → ∞, irrespective of the positions of the remaining (N-n) eigenvalues. It is made plausible, but not proved, that these correlation functions tend to limits as N → ∞, which are universal functions independent of r(E). If proved, this statement would imply that the local statistical properties (spacing distributions, etc.) of eigenvalues in the ensemble become, when τ and N are both large, universal properties independent of the global eigenvalue distributions. In particular, the spacing distributions would be identical with those calculated for more special ensembles by Wigner, Gaudin, and Mehta.