Extent Of Spatial Correlations Research Articles

Shape Transformers: Topology‐Independent 3D Shape Models Using Transformers

AbstractParametric 3D shape models are heavily utilized in computer graphics and vision applications to provide priors on the observed variability of an object's geometry (e.g., for faces). Original models were linear and operated on the entire shape at once. They were later enhanced to provide localized control on different shape parts separately. In deep shape models, nonlinearity was introduced via a sequence of fully‐connected layers and activation functions, and locality was introduced in recent models that use mesh convolution networks. As common limitations, these models often dictate, in one way or another, the allowed extent of spatial correlations and also require that a fixed mesh topology be specified ahead of time. To overcome these limitations, we present Shape Transformers, a new nonlinear parametric 3D shape model based on transformer architectures. A key benefit of this new model comes from using the transformer's self‐attention mechanism to automatically learn nonlinear spatial correlations for a class of 3D shapes. This is in contrast to global models that correlate everything and local models that dictate the correlation extent. Our transformer 3D shape autoencoder is a better alternative to mesh convolution models, which require specially‐crafted convolution, and down/up‐sampling operators that can be difficult to design. Our model is also topologically independent: it can be trained once and then evaluated on any mesh topology, unlike most previous methods. We demonstrate the application of our model to different datasets, including 3D faces, 3D hand shapes and full human bodies. Our experiments demonstrate the strong potential of our Shape Transformer model in several applications in computer graphics and vision.

Disease mapping and spatial regression with count data

In this paper, we provide critical reviews of methods suggested for the analysis of aggregate count data in the context of disease mapping and spatial regression. We introduce a new method for picking prior distributions, and propose a number of refinements of previously used models. We also consider ecological bias, mutual standardization, and choice of both spatial model and prior specification. We analyze male lip cancer incidence data collected in Scotland over the period 1975-1980, and outline a number of problems with previous analyses of these data. In disease mapping studies, hierarchical models can provide robust estimation of area-level risk parameters, though care is required in the choice of covariate model, and it is important to assess the sensitivity of estimates to the spatial model chosen, and to the prior specifications on the variance parameters. Spatial ecological regression is a far more hazardous enterprise for two reasons. First, there is always the possibility of ecological bias, and this can only be alleviated by the inclusion of individual-level data. For the Scottish data, we show that the previously used mean model has limited interpretation from an individual perspective. Second, when residual spatial dependence is modeled, and if the exposure has spatial structure, then estimates of exposure association parameters will change when compared with those obtained from the independence across space model, and the data alone cannot choose the form and extent of spatial correlation that is appropriate.

Reproducibility of the disordered vortex structure in twinned single crystals of YBCO

Bitter decorations of the vortices in twinned single crystal YBCO have been obtained to study the disordered structure formed on successive cooldowns of the sample under the same conditions of field and temperature. Between succesive decorations, the iron dots could be removed completely, giving a surface clean enough for further decoration. It was found that successive realizations of the disordered vortex state were very similar at long range, and differed mostly on short scales, compared to the average vortex separation. We have quantified the correlation between successive structures, and double sided decorations have been also performed to compare with the extent of spatial correlation in the applied field direction. The coincidence of the position of the vortices in successive realizations of the structure, is unexpected, and indicates an unusual behavior for a glassy system. Our technique makes it possible to image the position of the vortices in detail and repeatedly, providing us with a model amorphous system in which to study the reproducibility of the disordered structure.

The weak, the large, and the empty:: bringing order to concepts of spatial coherence in the Holstein polaron

We investigate polaron shape and size using electron–phonon correlation functions measured in 1D polaron ground states of the Holstein Hamiltonian. We use the Global–Local variational method as our primary quantitative tool, calling upon weak- and strong-coupling perturbation theories to assist in the interpretation of our results. The spatial extent of correlations is used to quantify polaron size, and is analyzed over a wide range of parameters. Distinct scaling behaviors are found below the self-trapping transition and above it, leading naturally to the notion of the polaron size as an order parameter for a self-trapping transition that becomes critical in the adiabatic limit. The archetypical structure characterizing polaron shape and size below the self-trapping transition is found to differ significantly from what might be expected from certain widely held views.

SPATIOTEMPORAL MODELS FOR SMALL‐AREA SOCIAL INDICATORS

ABSTRACT This paper investigates spatial effects in a generalized least squares regression model for small‐area social indicators. The significance of using spatial correlation in addition to an intermediate weighting (allowing for sampling and extraneous variation in the indicator) differs according to the index analyzed. It is greater for small‐area fertility (over 75S London wards) than for small‐area mortality. The model is extended in include serial as well as spatial correlation, then to spatial forecasting. The analyses show that the extent of spatial correlation can vary considerably according to (a) the specification of the form of spatial interaction, and (b) which independent variates are included. Further, spatial effects can be much reduced by including serial correlation.