Autocorrelation Estimates Research Articles

Spatial patterns of electoral support in the 2023 general election in Poland

RESEARCH OBJECTIVE: This article focuses on identifying the spatial patterns of electoral support for the main political actors, and searching for adequate determinants that explain this distribution of support, based on the results of the 2023 general election in Poland. THE RESEARCH PROBLEM AND METHODS: Is there a relationship between the basic morphological features of the voting space in Poland and the hierarchy of the settlement structure, along with the arrangement of regions associated with the country’s historical and political heritage? The methods used in the study include analysis of descriptive statistics, estimation of spatial autocorrelation, discriminant analysis, and cartographic methods. PROCESS OF ARGUMENTATION: The research process involves a two-stage procedure: 1) identifying a general picture of spatial variation in electoral support for selected groupings, and basic clustering patterns of electoral support; and 2) estimating links between the observed patterns of support and their presumed determinants; that is, the country’s settlement hierarchy and historical-political divisions. RESEARCH RESULTS: The spatial variability of the support indicators is characterised by a distinctive territorial distribution, based on the units of the settlement system and the boundaries of former historical divisions. The nature of this linkage indicates the changing layout of the voting space, associated with the increasing polarisation of citizens’ political preferences. CONCLUSIONS, INNOVATIONS, AND RECOMMENDATIONS: The current pattern of urban-rural differentiation is related to the different preferences of metropolitan (over 20,000 inhabitants) and rural or small-town (up to 20,000 inhabitants) communities. The east-west heterogeneity of Poland’s voting space is increasing due to similarities of preferences among the inhabitants of former Austrian and Russian Poland, on the one hand, and Prussian Poland and the Recovered Territories, on the other.

Seasonal variation in the ranging behavior of elephants in the Laikipia-Samburu ecosystem.

African savanna elephants are a highly mobile species that ranges widely across the diversity of ecosystems they inhabit. In xeric environments, elephant movement patterns are largely dictated by the availability of water and suitable forage resources, which can drive strong seasonal changes in their movement behavior. In this study, we analyzed a unique movement dataset from 43 collared elephants, collected over a period of 10 years, to assess the degree to which seasonal changes influences home range size of elephants in the semi-arid, Laikipia-Samburu ecosystem of northern Kenya. Auto-correlated Kernel Density Estimation (AKDE) was used to estimate elephants' seasonal home range size. For each individual elephant, we also calculated seasonal home range shifts, as the distance between wet season home range centroids and dry season home range centroids. Core areas (50% AKDE isopleths) of all individual elephants ranged from 3 to 1743 km2 whereas total home range sizes (the 95% AKDE isopleths) ranged between 15 and 10,677 km2. Core areas and home range sizes were 67% and 61% larger, respectively, during the wet season than during the dry season. On average, the core area centroids for all elephants were 17 km away from the nearest river (range 0.2-150.3 km). Females had their core areas closer to the river than males (13.5 vs. 27.5 km). Females differed from males in their response to seasonal variation. Specifically, females tended to occupy areas farther from the river during the wet season, while males occupied areas further from the river during the dry season. Our study highlights how elephants adjust their space use seasonally, which can be incorporated into conservation area planning in the face of increased uncertainty in rainfall patterns due to climate change.

Home range and habitat selection of wolves recolonising central European human‐dominated landscapes

Decades of persecution has resulted in the long‐term absence of grey wolves Canis lupus from most European countries. However, recent changes in both legislation and public attitudes toward wolves has eased the pressure, allowing wolves to rapidly re‐establish territories in their previous central European habitats over the last 20 years. Unfortunately, these habitats are now heavily altered by humans. Understanding the spatial ecology of wolves in such highly modified environments is crucial, given the high potential for conflict and the need to reconcile their return with multiple human concerns. We equipped 20 wolves, originating from seven packs in six central European regions, with GPS collars, allowing us to calculate monthly average home range sizes for 14 of the animals of 213.3 km2 using autocorrelated kernel density estimation. We then used ESA WorldCover data to assess the mosaic of available habitats used within each home range. Our data confirmed a general seasonal pattern for breeding individuals, with smaller apparent home ranges during the reproduction phase, and no specific pattern for non‐breeders. Predictably, our wolves showed a general preference for remote areas, and especially forests, though some wolves within military training areas also showed a broader preference for grassland, possibly influenced by local land use and high availability of prey. Our results provide a comprehensive insight into the ecology of wolves during their re‐colonisation of central Europe. Though wolves are spreading relatively quickly across central European landscapes, their permanent reoccupation remains uncertain due to conflicts with the human population. To secure the restoration of European wolf populations, further robust biological data, including data on spatial ecology, will be needed to clearly identify any management implications.

Angular Integral Autocorrelation for Speed Estimation in Shear-Wave Elastography

The utilization of a reverberant shear-wave field in shear-wave elastography has emerged as a promising technique for achieving robust shear-wave speed (SWS) estimation. However, many types of estimators cannot accurately measure SWS within such a complicated 3D wave field. This study introduces an advanced autocorrelation estimator based on angular integration known as the angular integral autocorrelation (AIA) approach to address this issue. The AIA approach incorporates all the autocorrelation data from various angles during measurements, resulting in enhanced robustness to both noise and imperfect distributions in SWS estimation. The effectiveness of the AIA estimator for SWS estimation is first validated using a k-Wave simulation of a stiff branching tube in a uniform background. Furthermore, the AIA estimator is applied to ultrasound elastography experiments, magnetic resonance imaging (MRI) experiments, and optical coherence tomography (OCT) studies across a range of different excitation frequencies on tissues and phantoms, including in vivo scans. The results verify the capacity of the AIA approach to enhance the accuracy of SWS estimation and the signal-to-noise ratio (SNR), even within an imperfect reverberant shear-wave field. Compared to simple autocorrelation approaches, the AIA approach can also successfully visualize and define lesions while significantly improving the estimated SWS and SNR in homogeneous background materials and providing improved elastic contrast between structures within the scans. These findings demonstrate the robustness and effectiveness of the AIA approach across a wide range of applications, including ultrasound elastography, magnetic resonance elastography (MRE), and optical coherence elastography (OCE), for accurately identifying the elastic properties of biological tissues in diverse excitation scenarios.

Abstract P322: Mapping Geographic Variation in Hypertension Prevalence in United States Congressional Districts Using Spatial Modeling

Introduction: Using spatial methods to explore drivers of hypertension (HTN) risks, commonalities, and differences across geographical areas can be assessed to inform future public health research and advocacy efforts. Objectives: To examine ecological associations between social determinants of health (SDoH), space, and HTN across congressional districts (CDs) in effect for the 118th US Congress. Methods: We obtained aggregate district-level data from Congressional District Health Dashboard on health behaviors, exposures, and outcomes for US CDs in 2019. Primary outcome was HTN prevalence, defined as proportion of adults who self-reported diagnosed HTN. Exposure variables were SDoH: health outcomes (diabetes, obesity, frequent physical and mental distress), health behaviors (physical activity, binge drinking, smoking), clinical care (routine checkups), and physical environment (air pollution). We fitted a hierarchical Bayesian Besag-York-Mollié model using the integrated nested Laplace approximation (INLA) method, which allowed the estimation of spatial autocorrelation of HTN prevalence at CDs level, accounting for SDoH. Results: Across 421 CDs, we found a variation in the modeled linear proportion of 83% across the CDs in the United States after adjusting for known HTN risk factors at the CDs level. A notable degree of variation in HTN prevalence exists within specific CDs, independent of recognized risk factors ( Figure ). These unmeasured variables act as confounding elements, and districts with darker shading indicate increased HTN attributed to the district, while lighter, red-shaded districts exhibit a reduced district-specific proportion of HTN. Conclusions: Our findings show significant geographic variation of HTN beyond known risk factors which underscores the significance of adopting a spatial perspective to understand HTN prevalence. It emphasizes the necessity for tailored public health interventions that consider the unique geographic context of each CDs.

Integrated Difference Autocorrelation: A Novel Approach to Estimate Shear Wave Speed in the Presence of Compression Waves.

In share wave elastography (SWE), the aim is to measure the velocity of shear waves, however unwanted compression waves and bulk tissue motion pose challenges in evaluating tissue stiffness. Conventional approaches often struggle to discriminate between shear and compression waves, leading to inaccurate shear wave speed (SWS) estimation. In this study, we propose a novel approach known as the integrated difference autocorrelation (IDA) estimator to accurately estimate reverberant SWS in the presence of compression waves and noise. The IDA estimator, unlike conventional techniques, computes the subtraction of velocity between neighboring particles, effectively minimizing the impact of long wavelength compression waves and other wide-area movements such as those caused by respiration. We evaluated the effectiveness of IDA by: (1) using k-Wave simulations of a branching cylinder in a soft background, (2) using ultrasound elastography on a breast phantom, (3) using ultrasound elastography in the human liver-kidney region, and (4) using magnetic resonance elastography (MRE) on a brain phantom. By applying IDA to unfiltered contaminated wave fields of simulation and elastography experiments, the estimated SWSs are in good agreement with the ground truth values (i.e., less than 2% error for the simulation, 9% error for ultrasound elastography of the breast phantom and 19% error for MRE). Our results demonstrate that IDA accurately estimates SWS, revealing the existence of a lesion, even in the presence of strong compression waves. IDA exhibits consistency in SWS estimation across different modalities and excitation scenarios, highlighting its robustness and potential clinical utility.

High‐resolution reservoir stochastic modelling based on optimized estimation of vertical autocorrelation

AbstractThe high‐resolution model of elastic properties is of great significance for fine reservoir characterization and precise oil and gas exploration. However, it is difficult to obtain a satisfactory high‐resolution reservoir model with the existing technologies. In this paper, a novel high‐resolution stochastic modelling strategy based on the fast Fourier transform moving average is proposed. In this strategy, several structural parameters are optimized to improve the rationality of the stochastic model, including vertical autocorrelation length, horizontal autocorrelation length, roughness factor and angle parameter. Among them, the optimization of the vertical autocorrelation length is crucial for vertical high‐resolution modelling. To this end, a nonlinear optimal inversion strategy of the vertical autocorrelation length is designed based on the idea of minimizing the spectral Jensen–Shannon divergence between the modelling result and the logging curve. However, nonlinear inversion is usually unstable, so it is necessary to introduce a regularization operator in the inversion to improve the stability. Considering that the heterogeneity of the subsurface medium is consistent or gradual within the stratums, but discontinuous and abrupt at the interfaces, edge‐preserving regularization is applied to obtain a blocky estimation of the vertical autocorrelation length. The optimal estimation experiment of the vertical autocorrelation length based on the measured logging data shows that the edge‐preserving regularization significantly improves the stability of the nonlinear optimal inversion, and blocky estimation results with sharp edges are obtained. Then, the optimized vertical autocorrelation length and the other structural parameters are applied to fast Fourier transform moving average modelling on an actual reservoir profile. The result shows that the resolution of the model is significantly improved, which realizes the fine reservoir characterization. In addition, the optimized structural parameters effectively constrain the small‐scale heterogeneity and ensure the rationality of the stochastic model.

Unlocking the triad of age, year, and cohort effects for stock assessment: Demonstration of a computationally efficient and reproducible framework using weight-at-age

Many demographic processes vary by age and over time, but are also hypothesized to exhibit cohort-specific patterns in variation; accounting for this variation within fisheries management remains a key challenge for contemporary stock assessments. Although there is evidence for time, age, and cohort-specific patterns in the variation of various components within stock assessment (e.g., selectivity, growth), methods are sparsely documented or are lacking to simultaneously estimate autocorrelation over time, among ages, and by cohort while also quantifying residual variation. We demonstrate an approach that facilitates the simultaneous estimation of autocorrelation for time, age, and cohort correlations, and provide two options to estimate the pointwise variance of this process (termed conditional and marginal variance). Using eastern Bering Sea walleye pollock (Gadus chalcogrammus) as a case-study, we develop factorial model formulations to demonstrate differences in predicted weight-at-age values from models that estimate different combinations of correlation parameters along three axes (age, year, cohort). We show that traditional model selection tools can be used to identify the relative evidence for, and magnitude of, age, time, and cohort correlations, and demonstrate that this method can be easily integrated as a routine option within next-generation stock assessments. Code to replicate our analysis is provided in a GitHub repository (https://github.com/chengmatt/GMRF_WAA), and includes a Template Model Builder function for assembling the precision matrix to facilitate easy adoption in other software packages.

Spatial-temporal differentiation of coupling coordination degree for green finance and green innovation efficiency: a case study in China.

Continued investment in finance and innovation is beneficial to economic development, and the joining of green system can accelerate the process of economic recovery from environmental distress. To better enhance the relationship of green finance and green innovation, it is vital to demonstrate the synergy between the two thoroughly. Thirty provinces in China are selected to examine the coupling coordination relationship between the two, specifically testing the spatial aggregation and evolutionary differences in the coupling coordination by adopting the coupling coordination degree (CCD) model, spatial autocorrelation, and kernel density estimation. Conclusions of the paper show that green finance is calculated by the EW-TOPSIS method, and the overall score of provinces is low. Using super-SBM model to evaluate green innovation, the uneven distribution of efficiency is obvious, although it is gradually increasing. The CCD in most provinces is in low-level or basic coordination, with significant regional heterogeneity. The global Moran's index becomes gradually evident with time. The local Moran scatter diagram presents a downward trend from east to west, but with more L-L aggregation provinces emerging in 2020. The center of the national kernel density curve gradually shifts to the right, indicating that the national overall synergy level is improving. Deepening the understanding of the empirical results facilitates the formulation of reasonable policies that fit the four major regions.

Modelling Outflow Remittances in the Digital Era: A Subnational Analysis of Russia

Relevance. The outflow of funds from the Russian economy, including remittances, can have a significant impact on the country's economic development. The influence of digital technologies and the heterogeneity of Russian regions further complicate the study of factors affecting remittance outflows. This study aims to address this research gap by examining the spatial effects of remittance outflows from Russia at the regional level within the context of digital transformation. Research Objective. The primary objective of this paper is to investigate whether spatial effects exist in the outflow of remittances from Russia at the regional level and how digitalization affects this phenomenon. By exploring spatial autocorrelation and fitting spatial models, we aim to understand the mutual influence and interdependence of regions in cross-border remittances. Data and Methods. The study utilizes open annual data from the Bank of Russia on cross-border remittances and data from the Federal State Statistics Service of the Russian Federation. The research methodology includes spatial autocorrelation estimation and the application of spatial models. Results. Our findings indicate that the digitalization of business transactions leads to a decline in cross-border remittances that do not involve payment systems. This finding primarily relates to the relatively low share of non-resident remittances within formal remittances. The results underscore the importance of considering spatial differentiation among regions in terms of remittance volume when formulating regional policies. Furthermore, the study reveals a shifting trend towards the emergence of major centers for outgoing transfers in the Far Eastern part of Russia and an increase in remittance volumes from border regions in the European part of Russia. Conclusions. The policy implications of this study highlight the need to encourage the participation of the population's savings in the domestic economy. This can be achieved through measures aimed at facilitating internal investment and financial inclusion.

Investigating the statistical error on autocorrelation for operational modal analysis

Autocorrelation is commonly used in signal processing for analyzing time signals, however the shape and magnitude of its statistical error, caused by its estimation from finite length measurements, is rarely addressed. Previous research showed that in the general case, the error on the autocorrelation estimator of an arbitrary signal is inversely proportional to the square root of the signal length. For operational modal analysis of linear systems under unknown ambient excitation, this error seems to present a peculiar shape influencing the estimation of damping ratios. In this paper the error on autocorrelation for a linear, time-invariant system subjected to white Gaussian noise is analytically and numerically studied. It is found to be very similar to the system’s response to an ambient noise, thus with a frequency content close to that of the expected autocorrelation itself. An upper bound of error magnitude is found for each mode of the system. Then, the resulting error on damping computations is investigated through numerical simulations applied to a two degrees of freedom mechanical system. Numerical outcomes show good agreement with the theoretical part and are then supported by experimental data of a prestressed concrete bridge under ambient traffic. This study allows for a better understanding and quantification of the inaccuracy on damping ratios computation through techniques using autocorrelation in time domain, notably the logarithmic decrement or time–frequency domain decomposition based on wavelet analysis.

Phase I control chart for individual autocorrelated data: application to prescription opioid monitoring

Phase I or retrospective process monitoring plays a key part in an overall statistical process monitoring (SPM) regime and is increasingly emphasized in the recent literature. At present, a lot of the data in a variety of settings (public and private sector organizations) are collected individually and sequentially and thus are serially correlated (or autocorrelated). Though a reasonable amount of work is available in the control charting literature for prospective (Phase II) autocorrelated data monitoring, very little work exists for the retrospective phase (Phase I). In this article, we present a Shewhart-type control chart for Phase I monitoring of individual autocorrelated data, assuming normality, with estimated parameters. The methodology, while developed and presented for the first-order autoregressive (AR(1)) model for simplicity, may be adapted to more general time series models. The correct charting constants, adjusted for autocorrelation and parameter estimation, are derived, and tabulated for a nominal in-control (IC) false alarm probability (FAP). Simulation results show that the proposed chart is favorably IC FAP robust and effective for reasonably small sample sizes, moderate autocorrelation, and some model miss-specifications, compared to other approaches. An illustration using some public health data involving prescription fentanyl transactions is provided to show the potential for broader areas of applications of the proposed methodology. Along with a summary and recommendations, some future research areas are indicated. An R package is developed and made available for implementing the proposed methodology on demand.

Multiple Unknown Emitters Direct Tracking With Distributed Sensor Arrays: Non-Homogeneous Data Fusion and Fast Position Update

This paper considers the problem of multiple unknown emitters tracking based on distributed sensor arrays. The most common two-step methods firstly track the intermediate parameters and then solve emitter positions. However, the two-step methods are suboptimal as ignoring the matching information. In this paper, we introduce the novel thought of Direct Position Determination (DPD) to the tracking problem and propose the Non-homogeneous Data Fusion and Fast Position Update (NDFFPU) algorithm. Firstly, the NDFFPU algorithm adapts to tracking scenarios by reducing the weights of past data in autocorrelation estimation. Thereafter, the non-homogeneity error of received data is eliminated in the difference co-array domain, which reduces the sensitivity to observation position. Finally, the NDFFPU algorithm fuses all difference array data and performs the Newton iteration to update the emitter positions with high speed. The NDFFPU algorithm avoids the drawbacks of both the intermediate parameter estimation and the complex peak-searching. Extensive numerical simulations demonstrate the superiority of the NDFFPU algorithm in utilized array aperture, computational complexity, tracking accuracy, and robustness.

Space use and site fidelity of wintering whooping cranes on the Texas Gulf Coast

AbstractThe Aransas‐Wood Buffalo population (the only non‐reintroduced, migratory population) of endangered whooping cranes (Grus americana) overwinters along the Texas Gulf Coast, USA. Understanding whooping crane space use on the wintering grounds reveals essential aspects of this species' ecology, which subsequently assists with conservation. Using global positioning system telemetry data from marked whooping cranes during 2009–2017, we fit continuous‐time stochastic process models to describe movement and home range using autocorrelated kernel density estimation (AKDE) and explored variation in home range size in relation to age, sex, reproductive status, and drought conditions. We used the Bhattacharyya coefficient of overlap and distance between home range centroids to quantify site fidelity. We examined the effects of time between winter home ranges and the sex of the crane on site fidelity using Bayesian mixed‐effects beta regression. Winter whooping crane 95% AKDE home range size averaged 30.1 ± 45.2 (SD) km2 (median = 14.3, range = 1.1–308.6). Home ranges of sub‐adult females were approximately 2 times larger than those of sub‐adult males or families. As drought worsened, home ranges typically expanded. Between consecutive years, the home ranges of an adult crane exhibited 68 ± 31% overlap (site fidelity), but fidelity to winter sites declined in subsequent winters. The overlap of adult home ranges with the nearest unrelated family averaged 33 ± 28%. As a whooping crane aged, overlap with its winter home range as a juvenile declined, regardless of sex. By 4 years of age, a whooping crane had approximately 14 ± 28% overlap with its juvenile winter home range. Limited evidence suggested male whooping cranes return to within 2 km of their juvenile home range by their fifth winter. Previous data obtained from aerial surveys led ecologists to assume that whooping crane families normally used small areas (~2 km2) and expressed persistent site fidelity. Our analyses showed <8% of families had home ranges ≤2 km2, with the average area 15 times greater, and waning site fidelity over time. Our work represents an analysis of whooping crane home ranges for this population, identifying past misconceptions of winter space use and resulting in better estimates of space requirements for future conservation efforts.

Performance Assessment of Row-Column Transverse Oscillation Tensor Velocity Imaging Using Computational Fluid Dynamics Simulation of Carotid Bifurcation Flow.

In this work, the accuracy of row-column tensor velocity imaging (TVI), i.e., 3-D vector flow imaging (VFI) in 3-D space over time, is quantified on a complex, clinically relevant flow. The quantification is achieved by transferring the flow simulated using computational fluid dynamics (CFD) to a Field II simulation environment, and this allows for a direct comparison between the actual and estimated velocities. The carotid bifurcation flow simulations were performed with a peak inlet velocity of 80 cm/s, nonrigid vessel walls, and a flow cycle duration of 1.2 s. The flow was simulated from two observation angles, and it was acquired using a 3-MHz 62+62 row-column addressed array (RCA) at a pulse repetition frequency ( fprf ) of 10 and 20 kHz. The tensor velocities were obtained at a frame rate of 208.3 Hz, at fprf = 10 kHz , and the results from two velocity estimators were compared. The two estimators were the directional transverse oscillation (TO) cross correlation estimator and the proposed autocorrelation estimator. Linear regression between the actual and estimated velocity components yielded, for the cross correlation estimator, an R 2 value in the range of 0.89-0.91, 0.46-0.77, and 0.91-0.97 for the x -, y -, and z -components, and 0.87-0.89, 0.40-0.83, and 0.91-0.96 when using the autocorrelation estimator. The results demonstrate that an RCA can, with just 62 receive channels, measure complex 3-D flow fields at a high volume rate.

Dynamics of Pinus wood prices for different timber assortments: comparison of stochastic processes

Understanding the dynamics of market prices for Pinus wood is a prerequisite for strategic decisions concerning forest investment plans since, in terms of the market, the exogenous risk to a project depends on timber assortments. The stochastic process that represents the best way of pricing the underlying asset therefore needs to be known. This study set out to compare Fractional Brownian Motion and Geometric Brownian Motion, through econometric tests, to understand the stochastic model that best represents the price behaviour of Pinus wood from planted forests in the state of Santa Catarina, Brazil, for the pricing of the underlying asset and valuation of the real options intrinsic to forest investment projects. The time series of prices, for the period from June 2017 to July 2019, relate to three assortments of Pinus wood used for multiple products. The recommended econometric tests to analyse the time series were for normality of the data, trend, autocorrelation, stationarity and fractional differential estimation. The time series were then modelled by means of stochastic processes in line with the econometric tests. The time series showed normal behaviour and indicated the presence of a positive trend and non-stationarity in the data. In addition, a true long memory was found in all series. Fractional Brownian Motion proved to be the most suitable stochastic process for modelling the prices of three forest timber assortments, given the non-stationary characteristics and true long memory of the time series for Pinus wood prices.

Cross-correlation quasi-gradient Doppler estimation for underwater acoustic OFDM mobile communications

Orthogonal Frequency Division Multiplexing (OFDM) has drawn comprehensive attention due to its capability of achieving high data rate and high spectrum efficiency in underwater acoustic communications. However, the widespread Doppler effect in underwater acoustic channel caused by mobile vehicles or time varying medium can lead to significant distortion and deteriorate the demodulation performance, thus Doppler estimation and compensation are needed for OFDM mobile communications. Generally Doppler effect can be accurately estimated by calculating the dominant correlation-peak or cross-ambiguity function (CAF) between received and transmitted signals. However, this type of method is computationally intensive because of the exhausting search on the two-dimensional (2D) delay and Doppler compression factor space, thus unsuitable for small underwater vehicles that equipped with limited computational payload. In this paper, quasi-gradient of cross-correlation is defined to derive the cross-correlation quasi-gradient (CCQG) iterative estimation algorithm to achieve low complexity Doppler estimation. Moreover, the smoothed quasi-gradient and variable Doppler interval are employed to accelerate the convergence rate as well as to avoid being trapped at a local maximum. Numerical simulations and mobile communication sea trial experiments demonstrate the effectiveness and robustness of the proposed algorithm by comparing to the conventional cross-correlation estimation, auto-correlation estimation, block estimation and BER search estimation strategies.

Autocorrelation‐informed home range estimation: A review and practical guide

AbstractModern tracking devices allow for the collection of high‐volume animal tracking data at improved sampling rates over very‐high‐frequency radiotelemetry. Home range estimation is a key output from these tracking datasets, but the inherent properties of animal movement can lead traditional statistical methods to under‐ or overestimate home range areas.The autocorrelated kernel density estimation (AKDE) family of estimators was designed to be statistically efficient while explicitly dealing with the complexities of modern movement data: autocorrelation, small sample sizes and missing or irregularly sampled data. Although each of these estimators has been described in separate technical papers, here we review how these estimators work and provide a user‐friendly guide on how they may be combined to reduce multiple biases simultaneously.We describe the magnitude of the improvements offered by these estimators and their impact on home range area estimates, using both empirical case studies and simulations, contrasting their computational costs.Finally, we provide guidelines for researchers to choose among alternative estimators and anRscript to facilitate the application and interpretation of AKDE home range estimates.

Inner-product quasilinear spaces with applications in signal processing

If certain characteristics of a non-deterministic signal are known, can some approximate results be obtained concerning the frequency, deterministic autocorrelation or other characteristics of the signal? The mathematical techniques we have developed allow us to obtain some approximate estimations of this type. In this way we use some new mathematical methods so called quasilinear functional analysis. Interval analysis also in the scope of this area and we use complex interval-valued signals in calculations. Especially, in this work, we give some special properties and results of inner-product quasilinear spaces which are generalizations of classical inner-product spaces. By this results we give easy examples of approximate estimations of deterministic autocorrelation of some semi non-deterministic signals or signals with inexact data. Further, we have constructed the space $\mathbb{I}l_{2}$ and we have showed that $\mathbb{I}l_{2}$ is an inner-product quasilinear space. This space provides a basis for an estimation of deterministic autocorrelation of the signals with inexact data.

Differentiation and progress of urban regionalization in China: Perspectives of land use and geography

The explosive population growth and economic development in cities have led to continuous but diverse urban regionalization. The resulting urban agglomerations (UAs) exhibit differentiation at both regional and local scales. Few studies have documented the disparities in UAs regarding land use and geography. In this study, we investigated the county-level land use features of 19 China's planned UAs by using a land use intensity (LUI) metric. We employed the spatial autocorrelation, inequality statistics, and imbalance estimation models to estimate the agglomeration, inequalities, and coordination of land use, and we combined those indicators to distinguish the development pattern of all UAs. Our findings revealed that spatial pattern of LUIs and their autocorrelations over time are closely associated with the evolution of urban regionalization. The widening gaps of land use exist more within the UAs than among them. Based on the LUI inequality and its relations to population and economy, UAs were classified into core-driven, differentiated, coordinated, and mismatched ones. Our conclusions highlighted that policy incentives for sustainable urbanization help decouple the synchronism of socioeconomic and LUI inequality.