scholarly journals Spatial modelling using a new class of nonstationary covariance functions

2006 ◽  
Vol 17 (5) ◽  
pp. 483-506 ◽  
Author(s):  
Christopher J. Paciorek ◽  
Mark J. Schervish
Keyword(s):  
Spatial Modelling ◽  
New Class ◽  
Covariance Functions ◽  
Nonstationary Covariance

scholarly journals A Note on the Properties of Generalised Separable Spatial Autoregressive Process

2009 ◽  
Vol 2009 ◽  
pp. 1-11 ◽  
Author(s):  
Mahendran Shitan ◽  
Shelton Peiris
Keyword(s):  
Three Dimensional ◽  
Real Data ◽  
Autoregressive Process ◽  
Spatial Modelling ◽  
Spectral Density Function ◽  
Data Sets ◽  
Additional Parameter ◽  
New Class ◽  
Spatial Autoregressive ◽  
Modelling And Forecasting

Spatial modelling has its applications in many fields like geology, agriculture, meteorology, geography, and so forth. In time series a class of models known as Generalised Autoregressive (GAR) has been introduced by Peiris (2003) that includes an index parameterδ. It has been shown that the inclusion of this additional parameter aids in modelling and forecasting many real data sets. This paper studies the properties of a new class of spatial autoregressive process of order 1 with an index. We will call this aGeneralised Separable Spatial Autoregressive(GENSSAR) Model. The spectral density function (SDF), the autocovariance function (ACVF), and the autocorrelation function (ACF) are derived. The theoretical ACF and SDF plots are presented as three-dimensional figures.

scholarly journals ACE of space: estimating genetic components of high-dimensional imaging data

Biostatistics ◽  
2019 ◽  
Author(s):  
Benjamin B Risk ◽  
Hongtu Zhu
Keyword(s):  
Cortical Thickness ◽  
Twin Studies ◽  
High Dimensional ◽  
Imaging Data ◽  
Covariance Functions ◽  
Genetic Components ◽  
Human Connectome Project ◽  
Nonstationary Covariance ◽  
Brain Structure And Function ◽  
And Function

SUMMARY It is of great interest to quantify the contributions of genetic variation to brain structure and function, which are usually measured by high-dimensional imaging data (e.g., magnetic resonance imaging). In addition to the variance, the covariance patterns in the genetic effects of a functional phenotype are of biological importance, and covariance patterns have been linked to psychiatric disorders. The aim of this article is to develop a scalable method to estimate heritability and the nonstationary covariance components in high-dimensional imaging data from twin studies. Our motivating example is from the Human Connectome Project (HCP). Several major big-data challenges arise from estimating the genetic and environmental covariance functions of functional phenotypes extracted from imaging data, such as cortical thickness with 60 000 vertices. Notably, truncating to positive eigenvalues and their eigenfunctions from unconstrained estimators can result in large bias. This motivated our development of a novel estimator ensuring positive semidefiniteness. Simulation studies demonstrate large improvements over existing approaches, both with respect to heritability estimates and covariance estimation. We applied the proposed method to cortical thickness data from the HCP. Our analysis suggests fine-scale differences in covariance patterns, identifying locations in which genetic control is correlated with large areas of the brain and locations where it is highly localized.

scholarly journals Reduction problems and deformation approaches to nonstationary covariance functions over spheres

2020 ◽  
Vol 14 (1) ◽  
pp. 890-916
Author(s):  
Emilio Porcu ◽  
Rachid Senoussi ◽  
Enner Mendoza ◽  
Moreno Bevilacqua
Keyword(s):  
Covariance Functions ◽  
Nonstationary Covariance

Implementation of geostatistical models for large spatiotemporal datasets using multi-resolution approximations

2021 ◽  
Author(s):  
Marius Appel ◽  
Edzer Pebesma
Keyword(s):  
Computation Time ◽  
Spatiotemporal Analysis ◽  
R Package ◽  
American Statistical Association ◽  
Environmental Data ◽  
Covariance Functions ◽  
Nonstationary Covariance ◽  
Geostatistical Models ◽  
Convolution Approach ◽  
Selection Of

<p>The multi-resolution approximation approach (MRA) [1] provides an efficient representation of Gaussian processes that scales beyond millions of observations. MRA leaves flexibility in the selection of covariance functions and allows to trade off computation time against prediction performance, depending on the selection of parameters. Recent work [2] has shown how MRA can be used for global spatiotemporal processes by integrating nonstationary covariance functions, where parameters vary over space and/or time following a kernel convolution approach. As such, MRA turns out to be a promising approach for geostatistical modelling of global spatiotemporal datasets, such as those coming from Earth observation satellites.</p><p>In this work, we show how MRA can be used for spatiotemporal analysis from a practical perspective. In the first part, we will discuss the influence of parameters (spatiotemporal shape of partitioning regions, the number of basis functions, and the number of partitioning levels) by analyzing a real world dataset. In the second part, we will present and discuss our implementation as an R package stmra[3]. We will demonstrate how traditional models as from the gstat package can be implemented efficiently with MRA, and how non-stationary models can be defined by users in a relatively simple way. </p><p>[1] Katzfuss, M. (2017). A multi-resolution approximation for massive spatial datasets. Journal of the American Statistical Association, 112(517), 201-214</p><p>[2] Appel, M., & Pebesma, E. (2020). Spatiotemporal multi-resolution approximations for analyzing global environmental data. Spatial Statistics, 38, 100465.</p><p>[3] https://github.com/appelmar/stmra</p>

In Situ microscopy of the anodic etching of silicon

1995 ◽  
Vol 53 ◽  
pp. 232-233
Author(s):  
Frances M. Ross ◽  
Peter C. Searson
Keyword(s):  
Composite Structures ◽  
High Surface ◽  
High Surface Area ◽  
Chemical Properties ◽  
Selective Etching ◽  
Silicon On Insulator ◽  
Second Phase ◽  
Porous Layers ◽  
New Class ◽  
Porous Semiconductors

Porous semiconductors represent a relatively new class of materials formed by the selective etching of a single or polycrystalline substrate. Although porous silicon has received considerable attention due to its novel optical properties1, porous layers can be formed in other semiconductors such as GaAs and GaP. These materials are characterised by very high surface area and by electrical, optical and chemical properties that may differ considerably from bulk. The properties depend on the pore morphology, which can be controlled by adjusting the processing conditions and the dopant concentration. A number of novel structures can be fabricated using selective etching. For example, self-supporting membranes can be made by growing pores through a wafer, films with modulated pore structure can be fabricated by varying the applied potential during growth, composite structures can be prepared by depositing a second phase into the pores and silicon-on-insulator structures can be formed by oxidising a buried porous layer. In all these applications the ability to grow nanostructures controllably is critical.

The microtubule associated protein (MAP) tau forms a new class of triple-stranded left-hand helical fibrous protein polymer

1992 ◽  
Vol 50 (1) ◽  
pp. 540-541
Author(s):  
G. C. Ruben ◽  
K. Iqbal ◽  
I. Grundke-Iqbal ◽  
H. Wisniewski ◽  
T. L. Ciardelli ◽  
...  
Keyword(s):  
Axial Ratio ◽  
Normal Structure ◽  
Paired Helical Filaments ◽  
Left Hand ◽  
New Class ◽  
Protein Polymer ◽  
Fibrous Protein ◽  
Protein Map ◽  
Neurotransmitter Transport ◽  
Alzheimer Neurofibrillary Tangles

In neurons, the microtubule associated protein, tau, is found in the axons. Tau stabilizes the microtubules required for neurotransmitter transport to the axonal terminal. Since tau has been found in both Alzheimer neurofibrillary tangles (NFT) and in paired helical filaments (PHF), the study of tau's normal structure had to preceed TEM studies of NFT and PHF. The structure of tau was first studied by ultracentrifugation. This work suggested that it was a rod shaped molecule with an axial ratio of 20:1. More recently, paraciystals of phosphorylated and nonphosphoiylated tau have been reported. Phosphorylated tau was 90-95 nm in length and 3-6 nm in diameter where as nonphosphorylated tau was 69-75 nm in length. A shorter length of 30 nm was reported for undamaged tau indicating that it is an extremely flexible molecule. Tau was also studied in relation to microtubules, and its length was found to be 56.1±14.1 nm.

Sign in / Sign up

Export Citation Format

Share Document