Spatial Statistical Properties Research Articles

Numerical Analysis of Chaos in a Phononic Crystal Waveguide with Circular Inclusions of Real Materials

Phononic crystal waveguides (PnCW) have been of great interest due to their properties of manipulating or filtering the acoustic waves with which they interact. Similarly, the presence of the phenomenon of chaos in the classical transport of particles through billiards with analogous geometries has been investigated. With this in consideration, in the present work an acoustic system of a two-dimensional PnCW is modeled, composed of two plane-parallel plates and a periodic arrangement of circular cylindrical inclusions with acoustic surfaces of real materials. In this system, we use the numerical technique of the integral equation, which allows us to obtain the pressure field corresponding to the normal modes in a range of frequencies. In addition, spatial statistical properties of pressure intensity such as the autocorrelation function (ACF) and its standard deviation called correlation length were calculated. The results show that when the correlation length is very small, the system presents disordered patterns of field intensities. Thus under certain conditions, the system under consideration presents a chaotic behavior, similar to the corresponding classical system.

SYNTHESIS OF THE DIFFUSE RANDOM PRESSURE FIELD USING ACTIVE AND REACTIVE RADIATION MODES

This work investigates how active and reactive radiation modes can be used in the synthesis of random pressure fields developed on a rigid test panel. The active and reactive radiation modes are the eigenvectors of the real and imaginary part of the matrix that couples the sound power of the acoustic model. The matrix that couples the power is numerically obtained through finite element analysis of the vibroacoustic problem. The reduced modal matrix incorporated into the synthesis method allows regularization through the most efficient active and reactive radiation modes. The statistical properties of the diffuse pressure field are specified in its spectral density matrix, obtained from the simulation surface. By analyzing control metrics, for numerical simulations with and without regularization, it is possible to verify the feasibility of the acoustic model in generating a random pressure field, on a rigid test panel, whose spatial statistical properties are similar to those of the target pressure field.

Understanding the spatial statistical properties of a real estate listings point pattern in San José, Costa Rica

One should expect real estate sales, and properties listed as for sale, to be concentrated on market hotspots. Using data of real estate listings from San José, Costa Rica, this expected clustering is examined using point pattern processes of detached housing, apartments, and vacant lots. Non-stationary G and J functions describe the patterns and their interactions. Potential determinants of the point pattern were selected based on previous studies and theory. Their effect on the point pattern was estimated using an inhomogeneous Poisson model, with its intensity a lognormal function of the determinants. Results show detached houses, apartments, and lots are all clustered point patterns. The cross density (joint G function) of houses with apartments and with lots exhibits clustering, suggesting the patterns are related; however, the cross density of apartments and lots is no different from a Poisson distribution (they are not related). The inhomogeneous Poisson model with Euclidean distance to the central business district (CBD), nearest municipal center, and nearest main road, as well as elevation and slope, proved better than homogeneous Poisson models in explaining the point patterns of houses, apartments, and lots.

Effect of optical spatial coherence on localized spin angular momentum density in tightly focused light [Invited

Optical coherence is one of the most fundamental characteristics of light and has been viewed as a powerful tool for governing the spatial, spectral, and temporal statistical properties of optical fields during light-matter interactions. In this work, we use the optical coherence theory developed by Emil Wolf as well as the Richards-Wolf's vectorial diffraction method to numerically study the effect of optical coherence on the localized spin density of a tightly focused partially coherent vector beam. We find that both the transverse spin and longitudinal spin, with the former induced by the out-of-phase longitudinal field generated during strong light focusing and the latter induced by the vortex phase in the incident beam, are closely related to the optical coherence of the incident beam, i.e., with the decrease of the transverse spatial coherence width of the incident beam, the magnitude of the spin density components decreases as well. The numerical findings are interpreted well with the two-dimensional degrees of polarization between any two of the three orthogonal field components of the tightly focused field. We also explore the roles of the topological charge of the vortex phase on enhancing the spin density for the partially coherent tightly focused field. The effect of the incident beam's initial polarization state is also discussed.

Gibbs spatial process for characterization of filament interaction in ReRAM devices via photon emission microscopy

In this work, we investigate spatial statistical properties of filament patterns in resistive random-access memory (ReRAM) devices measured from a newly developed near-infrared photon emission microscopy (PEM) [Stellari et al., IEEE Electron Device Lett. 42, 828 (2021); Stellari et al., in Proceedings of the 47th International Symposium for Testing and Failure Analysis Conference (ISTFA) (ASM International, 2021), pp. 115–121]. Unlike previous reports on uncorrelated filaments [Stellari et al., IEEE Electron Device Lett. 42, 828 (2021); Wu et al., Appl. Phys. Lett. 99, 093502 (2011)], we report a strong clustering and non-Poisson pattern of filaments constructed from individual devices. A Poisson-mixture model incorporating the clustering (attractive) effect is introduced with an excellent agreement with the PEM data for global and nearest-neighbor spatial statistics. On the other hand, a two-filament pattern is also detected within the ReRAM devices. We found that both attractive and repulsive interactions among the filaments are required in a Gibbs process to explain the filament spatial distribution. We implemented a birth-death algorithm using a Markov-chain Monte Carlo approach and achieve good agreement with the PEM data using a generalized Morse potential.

Statistical properties of two-dimensional elastic turbulence.

We numerically investigate the spatial and temporal statistical properties of a dilute polymer solution in the elastic turbulence regime, i.e., in the chaotic flow state occurring at vanishing Reynolds and high Weissenberg numbers. We aim at elucidating the relations between measurements of flow properties performed in the spatial domain with the ones taken in the temporal domain, which is a key point for the interpretation of experimental results on elastic turbulence and to discuss the validity of Taylor's hypothesis. To this end, we carry out extensive direct numerical simulations of the two-dimensional Kolmogorov flow of an Oldroyd-B viscoelastic fluid. Static pointlike numerical probes are placed at different locations in the flow, particularly at the extrema of mean flow amplitude. The results in the fully developed elastic turbulence regime reveal large velocity fluctuations, as compared to the mean flow, leading to a partial breakdown of Taylor's frozen-field hypothesis. While second-order statistics, probed by spectra and structure functions, display consistent scaling behaviors in the spatial and temporal domains, the third-order statistics highlight robust differences. In particular the temporal analysis fails to capture the skewness of streamwise longitudinal velocity increments. Finally, we assess both the degree of statistical inhomogeneity and isotropy of the flow turbulent fluctuations as a function of scale. While the system is only weakly nonhomogenous in the cross-stream direction, it is found to be highly anisotropic at all scales.

Advanced Data Mining for Odour Emissions Monitoring: Experimental Peak-to-mean Calculations and Spectral Analysis of Data Derived from Ioms in Two Waste Treatment Plants

A landfill for non-hazardous waste and a composting plant were equipped with an integrated odour management system made up of instrumental Odour monitoring systems and automated air samplers. Collected data by the instrumental system cover a time span of 8 months and 9 months for the two plants, respectively, and have been used for investigating spatial distribution and statistical properties of peak-to-mean ratios; moreover, a new method of data analysis, not yet employed in the field of odour dispersion modelling, has been proposed. A peak-to-mean value is defined as the ratio between an hourly mediation time and the average duration of a single human breath (few seconds). Data derived from 0.033 Hz sampling frequency by IOMS were used to calculate peak-to-mean for the monitoring period for both plants; the size of samples analysed allowed the implementation of a statistical calculation methodology for peak-to-mean estimation, based on the construction of empirical probability density functions (PDF). Moreover, data collected from instruments installed in different areas of the plants, were used to evaluate how PDF of peak-to-mean values varies with the distance from the odour emission sources. The same data were also used to develop a new method of analysis based on time series processing through the use of the Fourier Transform. Spectral analysis, sometimes used for meteorological variables, more recently has been applied in the study of air pollution data, although this type of analysis makes a decisive contribution to the understanding of cyclical behaviour in the observed data and provides information on temporal and spatial scales of such mechanisms. The aim is therefore to define a viable methodology to time series of odour concentration data collected at the fence of a plant, to be used to gather information on periodic odour variations. Interesting results, which related some periodic behaviours in odour emissions to working periods and composting phases, were observed, demonstrating the usefulness of such methodology to assess whether odour fluctuations are caused by atmospheric conditions variability or plant management operations.

A Kriged Compressive Sensing Approach to Reconstruct Acoustic Fields From Measurements Collected by Underwater Vehicles

This article presents a kriged compressive sensing (KCS) approach to reconstruct acoustic fields using measurements collected by underwater mobile sensing platforms. The KCS approach has two steps. First, initial estimates are obtained from a kriging method by leveraging spatial statistical correlation properties of the acoustic fields. Second, selected initial estimates, treated as virtual samples, are combined with the measurements to perform field reconstruction through compressive sensing. To differentiate the fidelity between real measurements and virtual samples, we use the kriging variance to determine weight coefficients for the virtual samples estimated from kriging. Simulation results show that the proposed KCS approach can improve the reconstruction performance, in terms of the peak signal-to-noise ratio and structural similarity metrics. The KCS performance has been validated based on the acoustic intensity measurements collected by an autonomous underwater vehicle in a lake. The KCS methods have also been applied to process the ambient sound level measurements collected by an underwater glider in the South China Sea. The proposed KCS method leads to better performance than either the compressive sensing or the kriging method alone.

A new fuzzy rule based pixel organization scheme for optimal edge detection and impulse noise removal

Fuzzy sets provide a framework for incorporating human knowledge as an efficient unsupervised machine learning tool for problem solving. The approach discussed in this paper introduces a generalized transfer learning scheme using rule based fuzzy logic for edge detection in digital images. The spatial domain statistical properties of the image are explored as training data set and expressed in fuzzy format to obtain a decision function for optimal edge detection along with reduction of impulse noise. During fuzzy inference process, a specific linguistic value in input fuzzy set is selected in order to obtain an optimal range of second order difference which discriminates the edge pixels from the non-edge pixels. The proposed fuzzy rule based optimal edge pixel detection method in the presence of random valued impulse noise tends to sufficiently extract the edge pixels with out boosting the noisy pixels. The effectiveness of the proposed fuzzy rule based edge detection scheme is verified by testing it on various standard test images and comparing with existing edge detection techniques at different noise densities.

Spatial autocorrelation and data uncertainty in the American Community Survey: a critique

ABSTRACTWe argue that the use of American Community Survey (ACS) data in spatial autocorrelation statistics without considering error margins is critically problematic. Public health and geographical research has been slow to recognize high data uncertainty of ACS estimates, even though ACS data are widely accepted data sources in neighborhood health studies and health policies. Detecting spatial autocorrelation patterns of health indicators on ACS data can be distorted to the point that scholars may have difficulty in perceiving the true pattern. We examine the statistical properties of spatial autocorrelation statistics of areal incidence rates based on ACS data. In a case study of teen birth rates in Mecklenburg County, North Carolina, in 2010, Global and Local Moran’s I statistics estimated on 5-year ACS estimates (2006–2010) are compared to ground truth rate estimates on actual counts of births certificate records and decennial-census data (2010). Detected spatial autocorrelation patterns are found to be significantly different between the two data sources so that actual spatial structures are misrepresented. We warn of the possibility of misjudgment of the reality and of policy failure and argue for new spatially explicit methods that mitigate the biasedness of statistical estimations imposed by the uncertainty of ACS data.

Modelling local uncertainty in relations between birth weight and air quality within an urban area: combining geographically weighted regression with geostatistical simulation.

In this study, we combine known methods to present a new approach to assess local distributions of estimated parameters measuring associations between air quality and birth weight in the urban area of Sines (Portugal). To model exposure and capture short-distance variations in air quality, we use a Regression Kriging estimator combining air quality point data with land use auxiliary data. To assess uncertainty of exposure, the Kriging estimator is incorporated in a sequential Gaussian simulation algorithm (sGs) providing a set of simulated exposure maps with similar spatial structural dependence and statistical properties of observed data. Following the completion of the simulation runs, we fit a geographically weighted generalized linear model (GWGLM) for each mother's place of residence, using observed health data and simulated exposure data, and repeat this procedure for each simulated map. Once the fit of GWGLM with all exposure maps is finished, we take the distribution of local estimated parameters measuring associations between exposure and birth weight, thus providing a measure of uncertainty in the local estimates. Results reveal that the distribution of local parameters did not vary substantially. Combining both methods (GWGLM and sGs), however, we are able to incorporate local uncertainty on the estimated associations providing an additional tool for analysis of the impacts of place in health.

Stochastic modeling of coal fracture network by direct use of micro-computed tomography images

Characterization of coalbed methane reservoirs is a challenging task because of complex petrophysical properties of coal. Coal cleat system has a key role in permeability of gas through coalbed. Previous computational methods for characterization and modeling in coal formations do not account for the actual complexities in cleat systems as they commonly rely on simple statistical properties for describing the fractures. In this study, unlike the previous methods that try to extract some of the spatial statistical properties, the 2D/3D micro computed tomography images are used directly without any simplifications and assumptions. The generated models are compared to discrete fracture networks as one of the widely-used method for the modeling of such complex systems of coal cleats. Results show that the utilized algorithm produces visually satisfactory realizations of both coal matrix and cleat system. To quantify such similarities, autocorrelation functions, connectivity (with two distinct indices), average fracture length and orientation are computed. Moreover, permeabilities and porosities of the reconstructed samples are calculated and compared with the original sample. It is demonstrated that the proposed reconstruction method reproduces samples with similar statistical and petrophysical properties, but with different patterns of both coal porous region and fracture system. Finally, the proposed method and the DFN realizations are also compared extensively. The results of this study can be used for characterization of coal samples with any degree of complexity and heterogeneity by producing several realistic stochastic models. Consequently, petrophysical properties and their corresponding uncertainties can be evaluated more accurately.

Statistical modeling of the high altitude platform dual-polarized MIMO propagation channel

In order to investigate the benefit of multiple-input multiple-output (MIMO) technique applying to the high altitude platform (HAP), a 2×2 MIMO statistical model, which can accurately describe the channel between HAP and high-speed train, is presented. And dual polarization diversity is particularly considered. Based on first-order three-state Markov chain, the single-input single-output (SISO) channel, a subset of the MIMO channel is first established. The ray tracing approach applied to the digital relief model (DRM) which covers the railway between Xi'an and Zhengzhou is used to obtain the state probability vector and matrix of the state transition probability. The proposed model considers both Doppler shift and temporal correlation, and the polarization correlation and spatial correlation statistical properties of large-scale fading and small-scale fading are analyzed. Moreover, useful numerical results on the MIMO HAP channel outage capacity are provided based on which, significant capacity gains with respect to the conventional SISO case are illustrated. Such statistical channel model can be applied to the future wireless communication system between HAP and high-speed train.

Asymptotic properties of spatial scan statistics under the alternative hypothesis

A common challenge for most spatial cluster detection methods is the lack of asymptotic properties to support their validity. As the spatial scan test is the most often used cluster detection method, we investigate two important properties in the method: the consistency and asymptotic local efficiency. We address the consistency by showing that the detected cluster converges to the true cluster in probability. We address the asymptotic local efficiency by showing that the spatial scan statistic asymptotically converges to the square of the maximum of a Gaussian random field, where the mean and covariance functions of the Gaussian random field depends on a function of at-risk population within and outside of the cluster. These conclusions, which are also supported by simulation and case studies, make it practical to precisely detect and characterize a spatial cluster.

Random spatial patterning of cone bipolar cell mosaics in the mouse retina.

Retinal bipolar cells spread their dendritic arbors to tile the retinal surface, extending them to the tips of the dendritic fields of their homotypic neighbors, minimizing dendritic overlap. Such uniform nonredundant dendritic coverage of these populations would suggest a degree of spatial order in the properties of their somal distributions, yet few studies have examined the patterning in retinal bipolar cell mosaics. The present study examined the organization of two types of cone bipolar cells in the mouse retina, the Type 2 cells and the Type 4 cells, and compared their spatial statistical properties with those of the horizontal cells and the cholinergic amacrine cells, as well as to random simulations of cells matched in density and constrained by soma size. The Delauney tessellation of each field was computed, from which nearest neighbor distances and Voronoi domain areas were extracted, permitting a calculation of their respective regularity indexes (RIs). The spatial autocorrelation of the field was also computed, from which the effective radius and packing factor (PF) were determined. Both cone bipolar cell types were found to be less regular and less efficiently packed than either the horizontal cells or cholinergic amacrine cells. Furthermore, while the latter two cell types had RIs and PFs in excess of those for their matched random simulations, the two types of cone bipolar cells had spatial statistical properties comparable to random distributions. An analysis of single labeled cone bipolar cells revealed dendritic arbors frequently skewed to one side of the soma, as would be expected from a randomly distributed population of cells with dendrites that tile. Taken together, these results suggest that, unlike the horizontal cells or cholinergic amacrine cells which minimize proximity to one another, cone bipolar cell types are constrained only by their physical size.

Multiscale Spatial and Temporal Statistical Properties of Rainfall in Central Arizona

Abstract The statistical properties of the rainfall regime in central Arizona are investigated using observations from the early 1980s of the Flood Control District of Maricopa County (FCDMC) network, currently consisting of 310 gauges ranging in elevation from 220 to 2325 m MSL. A set of techniques is applied to analyze the properties across a wide range of temporal scales (from 1 min to years) and the associated spatial variability. Rainfall accumulation is characterized by (i) high interannual variability, which is partially explained by teleconnections with El Niño–Southern Oscillation; (ii) marked seasonality, with two distinct maxima in summer (July–September) and winter (November–March); (iii) significant orographic control; and (iv) strong diurnal cycle in summer, peaking in early afternoon at higher elevations and at nighttime in lower desert areas. The annual maximum rainfall intensities occur in the summer months and increase with elevation, suggesting that higher terrain enhances the strength of thermal convective activity. The intergauge correlation of wintertime rainfall is high even at short aggregation times (<1 h) because of the widespread nature of the weather systems, while summer monsoonal thunderstorms are more localized in space and time. Spectral and scale invariance analyses show the presence of different scaling regimes in summer and winter, which are related to the typical meteorological phenomena of the corresponding time scales (frontal systems and isolated convective cells). Results of this work expand previous studies on the dominant meteorological features in the region and support the development of rainfall downscaling models from coarse products of climate, meteorological, or other statistical models.

Modelling Eggshell Maculation

The eggshells of many avian species are characterised by distinctive patterns of maculation, consisting of speckles, spots, blotches or streaks, the spatial-statistical properties of which vary considerably between (and often within) species. Understanding the mechanisms underlying the production of eggshell maculation would enable us to explore the costs and constraints on the evolution of maculation patterns, but as yet this area is surprisingly understudied. Here I present a simple model of eggshell maculation, which is based on the known biology of pigment deposition, and which can produce a range of realistic maculation patterns. In particular, it provides an explanation for previous observations of maculation heterogeneity and diversity, and allows testable predictions to be made regarding maculation patterns, including a possible signalling role.

Statistics of the electromagnetic response of a chaotic reverberation chamber

This article presents a study of the electromagnetic re- sponse of a chaotic reverberation chamber (RC) in the pres- ence of losses. By means of simulations and of experi- ments, the fluctuations in the maxima of the field obtained in a conventional mode-stirred RC are compared with those in a chaotic RC in the neighborhood of the Lowest Useable Frequency (LUF). The present work illustrates that the uni- versal spectral and spatial statistical properties of chaotic RCs allow to meet more adequately the criteria required by the Standard IEC 61000-4-21 to perform tests of electro- magnetic compatibility.

Spatial Coverage Cross-Tier Correlation Analysis for Heterogeneous Cellular Networks

In the search for improved coverage and capacity, cellular networks are currently undergoing a major transforma- tion. A thoroughly planned architecture comprised of macrocells served by large-coverage expensive base stations (BSs) is evolving toward a much more heterogeneous architecture where the macro- cell network is underlaid by one or several tiers of small cells deployed in an irregular and unplanned fashion using universal frequency reuse. Major challenges of this new scenario are the problems of intercell interference (ICI) and cell association. In this paper, these two problems are tackled in a novel way by analyzing and exploiting the inherent spatial cross-tier coverage correlation due to the cochannel ICI for a two-tier network. A mathematical framework for the representation of the two-tier coverage maps and their correlation is developed based on the spatial statistical properties of the signal quality measurements reported by the users to the base station. Several semivariogram-based estimation models are applied and cross-validated. Furthermore, a closed- form expression for the cross-tier coverage correlation function depending only on the estimator's parameters is obtained. In addition, a practical application of this framework is proposed. Cross-tier correlation information is exploited in the design of a new cell association policy based on cell-specific biasing for small cells. Numerical results show that the mathematical framework can provide accurate representations of the coverage fields and their correlation. Moreover, the performance of our proposed correlation-aware cell association policy is shown to be promising enough to encourage further research in this direction.

Object-Based Classification of Multi-temporal Images for Agricultural Crop Mapping in Karacabey Plain, Turkey

Abstract. The objective of this research is to classify major crop types cultivated in Karacabey Plain of north western Turkey using multitemporal Kompsat-2 and Envisat ASAR data with an object-based methodology. First a pansharpening algorithm is applied to each panchromatic and multispectral Kompsat-2 data to produce colour images having 1m spatial resolution. Next, Mean-Shift image segmentation procedure is applied to the pansharpened Kompsat-2 data with multiple parameter combinations. Multiple goodness measures are utilized to evaluate the object-based results. The optimum objects are then employed in object-based classifications of the single-date images. Next, single-date multispectral (MS) Kompsat-2 images and Kompsat-2 images along with the Envisat ASAR data are classified with the Support Vector Machines (SVMs) method. The training samples are provided automatically by the selected objects based on spatial statistical properties. Next, probability maps are generated for each image in pixel-based manner during the image classification operations. The maximum probabilities are then assigned to the pixels as class labels and the combined thematic maps (June-July, June-August, June-July-August) are generated in pixel-based and object-based manners. The produced thematic maps are evaluated through the confusion matrices and compared also with the results of parcel-based classifications using original agricultural parcels. Results indicate that the combined thematic maps of June-August and June-July- August provide the highest overall accuracy and kappa value approximately 92 % and 0.90, respectively.