Distance Weighting Function Research Articles

Spatially explicit predictions using spatial eigenvector maps

Abstract In this paper, we explain how to obtain sets of descriptors of the spatial variation, which we call “predictive Moran's eigenvector maps” (pMEM), that can be used to make spatially explicit predictions for any environmental variables, biotic or abiotic. It unites features of a method called “Moran's eigenvector maps” (MEM) and those of spatial interpolation, and produces sets of descriptors that can be used with any other modelling method, such as regressions, support vector machines, regression trees, artificial neural networks and so on. The pMEM are the predictive eigenvectors produced by using a distance‐weighting function (DWF) in the construction of MEM. Seven types of pMEM, each associated with one of seven different DWFs, were defined and studied. We performed a simulation study to determine the power of different types of pMEM eigenfunctions at making accurate predictions for spatially structured variables. We exemplified the application of the method to the prediction of the spatial distribution of 35 Oribatid mites living in a peat moss (Sphagnum) mat on the shore of a Laurentian lake. We also provide an R language package called pMEM to make calculations easily available to end users. The results indicate that anyone of the pMEMs obtained from the different DWFs could be the best suited one to predict spatial variability in a given data set. Their application to the prediction of mite distributions highlights the capability of pMEMs for predicting distributions, and for providing spatially explicit estimates of environmental variables that are useful for predicting distributions.

Improving word vector model with part‐of‐speech and dependency grammar information

Part-of-speech (POS) and dependency grammar (DG) are the basic components of natural language processing. However, current word vector models have not made full use of both POS information and DG information, and hence the models’ performances are limited to some extent. The authors first put forward the concept of POS vector, and then, based on continuous bag-of-words (CBOW), constructed four models: CBOW + P, CBOW + PW, CBOW + G, and CBOW + G + P to incorporate POS information and DG information into word vectors. The CBOW + P and CBOW + PW models are based on POS tagging, the CBOW + G model is based on DG parsing, and the CBOW + G + P model is based on POS tagging and DG parsing. POS information is integrated into the training process of word vectors through the POS vector to solve the problem of the POS similarity being difficult to measure. The POS vector correlation coefficient and distance weighting function are used to train the POS vector as well as the word vector. DG information is used to correct the information loss caused by fixed context windows. Dependency relations weight is used to measure the difference of dependency relations. Experiments demonstrated the superior performance of their models while the time complexity is still kept the same as the base model of CBOW.

Self-organization in aggregating robot swarms: A DW-KNN topological approach

In certain swarm applications, where the inter-agent distance is not the only factor in the collective behaviours of the swarm, additional properties such as density could have a crucial effect. In this paper, we propose applying a Distance-Weighted K-Nearest Neighbouring (DW-KNN) topology to the behaviour of robot swarms performing self-organized aggregation, in combination with a virtual physics approach to keep the robots together. A distance-weighted function based on a Smoothed Particle Hydrodynamic (SPH) interpolation approach, which is used to evaluate the robot density in the swarm, is applied as the key factor for identifying the K-nearest neighbours taken into account when aggregating the robots. The intra virtual physical connectivity among these neighbours is achieved using a virtual viscoelastic-based proximity model. With the ARGoS based-simulator, we model and evaluate the proposed approach, showing various self-organized aggregations performed by a swarm of N foot-bot robots. Also, we compared the aggregation quality of DW-KNN aggregation approach to that of the conventional KNN approach and found better performance.

How to quantify a distance‐dependent landscape effect on a biological response

Abstract To quantify the effect of the surrounding landscape context on a biological response at a site, most studies measure landscape variables within discs centred on this biological response (threshold‐based method, TBM). This implicitly assumes that the effect of a unit area of the landscape is consistent up to a threshold distance beyond which it drops to zero. However, it seems more likely that the landscape effect declines with increasing distance from the biological response point. Here, we develop a method to quantify landscape context effects by weighting the landscape variables by functions that decrease with distance. We illustrate the method using abundance data on birds and insects, and compare the results to the threshold approach. We defined distance weighting functions by the function family (e.g. negative exponential, Gaussian…) and by the parameters for this function. We developed a method to simultaneously estimate the parameters characterizing the effect of the landscape variables and the parameters of the best weighting functions. For each test dataset, we determined which weighting function (family and parameters) had the most support, by optimizing the model AIC. The distance‐weighted method (DWM) improved model support over the TBM in three of four datasets, with the exponential power function selected as the best weighing function in all three cases. The observed differences between estimations of landscape context effects by the distance‐weighted and the threshold methods have significant implications for landscape management. For example, the DWM suggests that managing a landscape for 90% of its effect on a focal population requires an area over five times larger than the area estimated by the threshold method, a situation that might apply for priority conservation of few remnant populations of a severely endangered species. In contrast, management for 30% of the landscape effect requires only about half the area estimated using the threshold method, a situation that might apply to a management situation with limited resources or low political/societal support. The DWM is applicable to any species‐habitat relationship. More comparisons are needed to determine the situations in which distance‐weighted estimation of landscape context effects is warranted over the simpler threshold method.

ERAM 모델의 거리가중치 도입 및 적용에 관한 연구

The purpose of this study is to verify whether to improve the explanatory power by introducing and applying distance-weighting concept to the ERAM model, one of spatial analysis techniques. Introduction of distance-weighting to the ERAM model was tried in an existing study, but it showed lower explanatory power than the original ERAM model, to which distance-weighting concept is not applied. In the existing research, movement distance is in reverse proportion to accessibility, which is problematic. Moreover, this study proposed new distance-weighting functions, not the reciprocal of distance(1/D) from the existing study. The original ERAM model, the existing distance-weighted ERAM model, and the distance-weighted ERAM model with newly proposed distance-weighting functions in this study were used for analyzing two regions in Seoul, Insadong and Myeongdong. In these regions, the correlation tests between the analysis results and the pedestrian movement rate showed that the distance-weighted ERAM model with the newly proposed distance-weighting functions has higher explanatory power than the original ERAM Model and the existing distance-weighted ERAM Model. In particular, the case of applying 'W=1-D/250' function as distance-weighting function showed the highest explanatory power among the three functions proposed in this study. This study reveals that the distance-weighting concept can contribute to improve the explanatory power of the ERAM model to human movement behavior, which opposes to conclusion of the existing study. However, further studies need to be done more deeply and extensively to find out the final form of distance-weighting function.

Building Development and Roads: Implications for the Distribution of Stone Curlews across the Brecks

BackgroundSubstantial new housing and infrastructure development planned within England has the potential to conflict with the nature conservation interests of protected sites. The Breckland area of eastern England (the Brecks) is designated as a Special Protection Area for a number of bird species, including the stone curlew (for which it holds more than 60% of the UK total population). We explore the effect of buildings and roads on the spatial distribution of stone curlew nests across the Brecks in order to inform strategic development plans to avoid adverse effects on such European protected sites.MethodologyUsing data across all years (and subsets of years) over the period 1988-2006 but restricted to habitat areas of arable land with suitable soils, we assessed nest density in relation to the distances to nearest settlements and to major roads. Measures of the local density of nearby buildings, roads and traffic levels were assessed using normal kernel distance-weighting functions. Quasi-Poisson generalised linear mixed models allowing for spatial auto-correlation were fitted.ResultsSignificantly lower densities of stone curlew nests were found at distances up to 1500m from settlements, and distances up to 1000m or more from major (trunk) roads. The best fitting models involved optimally distance-weighted variables for the extent of nearby buildings and the trunk road traffic levels.SignificanceThe results and predictions from this study of past data suggests there is cause for concern that future housing development and associated road infrastructure within the Breckland area could have negative impacts on the nesting stone curlew population. Given the strict legal protection afforded to the SPA the planning and conservation bodies have subsequently agreed precautionary restrictions on building development within the distances identified and used the modelling predictions to agree mitigation measures for proposed trunk road developments.

Spatial autocorrelation in honeybee foraging activity reveals optimal focus scale for predicting agro-environmental scheme efficiency

A substantial honeybee decline is being observed worldwide. Agricultural intensification and loss of wild floral resources rank among the main factors contributing to this decline. Landscape enhancement of floral resources has been proposed as an agro-environmental scheme intended to provide honeybees with compensatory food sources in intensive agrosystems. Floral scheme efficiency has rarely been evaluated with respect to landscape context. In this study, we developed and validated a modeling tool to delineate the landscape areas likely to be associated with higher efficiency of floral enhancement schemes. In particular, the proximity of some landscape elements used by honeybees, either as foraging habitat or as visual landmark for orientation, may partly determine floral scheme efficiency. We investigated this issue using resource selection functions (RSFs), i.e. models that aim to predict the occurrence of foraging honeybees at floral patches as a function of the presence of keystone landscape elements in their proximity. However, deciding which landscape elements are effectively in the proximity or not is mostly a matter of subjectivity. The novelty of our approach resides in its use of a distance-weighting function to explicitly account for the spatial location of surrounding landscape elements. In that respect, a distance function should be scaled on movement patterns of foraging organisms. Herein, we inferred movement patterns from the autocorrelative properties of honeybee foraging activity. This modeling approach was developed on Phacelia ( Phacelia tanacetifolia) field margin strips, a typical “honeybee-friendly” floral scheme. A foraging survey conducted on 170 Phacelia plots (2 m × 2 m) from 17 Phacelia strips, all positioned within the foraging range of an experimental apiary, revealed that (i) the floral scheme efficiency is positively influenced by the presence of linear landscape elements such as hedgerows and forest edges, but negatively affected by the presence of alternative floral resources, and that (ii) weighting the relative importance of those landscape elements by incorporating a distance function into models considerably improved their predictive power. This modeling tool has the potential to help land managers optimizing their financial investment by avoiding low-efficiency landscape areas, or favoring high-efficiency ones, at the time of planning floral enhancement schemes.

Time-geographic density estimation for home range analysis

This research presents time-geographic density estimation (TGDE) as a new technique of animal home range analysis in geographic information science (GIS). TGDE combines methodologies of time geography and statistical density estimation to produce a continuous probability distribution of an object's spatial position over time. Once TGDE is applied to animal tracking data to create a density surface, home ranges and core areas can be delineated using specified contours of relative intensity (e.g., 95% or 50%). This article explores the use of TGDE for home range analysis using three data sets: a fixed-interval simulated data set and two variable-interval satellite tracks for a loggerhead sea turtle (Caretta caretta) corresponding to internesting and post-migration foraging periods. These applications are used to illustrate the influence of several parameters, including sample size, temporal sampling scheme, selected distance-weighted geoellipse function, and specified maximum velocity, on home range estimates. The results demonstrate how TGDE produces reasonable home range estimates even given irregular tracking data with wide temporal gaps. The advantages of TGDE as compared with traditional methods of home range estimation such as kernel density estimation are as follows: (1) intensities are not assigned to locations where the animal could not have been located given space and time constraints; (2) the density surface represents the actual uncertainty about an animal's spatial position during unsampled time periods; (3) the amount of smoothing applied is objectively specified based on the animal's movement velocity rather than arbitrarily chosen; and (4) uneven sampling intervals are easily accommodated since the density estimates are calculated based on the elapsed time between observed locations. In summary, TGDE is a useful method of home range estimation and shows promise for numerous applications to moving objects in GIS.

Application of Multidisciplinary Design Optimization Based on Approximation Model to Marine Supercharger Turbo

In this paper, the multidisciplinary design optimization based on Approximation Model for supercharge turbo is studied. Temperature and pressure loads are transferred to the solid model by distance-weighted function, and structure deformation is transferred to aerodynamic model by mesh regenerated method in order to avoid mesh aberration. The Multidisciplinary analysis (MDA) model of supercharge turbo considering aerodynamic, heat transfer, strength and vibration is obtained on the basis of information transferring, which is solved by iterated three times. The Kriging Approximation Model which fits the sample space accurately is employed in the MDO process to reduce computational cost. Results show that performance of supercharge turbo is improvement on the MDO system based on Approximation Model, meanwhile the computational time of the optimization system is saved. Also, this method is suitable for other Multidisciplinary Design Optimization problems.

Implications of bias evolution on measurements of the integrated Sachs-Wolfe effect: errors and biases in parameter estimation

The subject of this paper is a quantification of the impact of uncertainties in bias and bias evolution on the interpretation of measurements of the integrated Sachs-Wolfe effect, in particular on the estimation of cosmological parameters. We carry out a Fisher-matrix analysis for quantifying the degeneracies between the parameters of a dark energy cosmology and bias evolution, for the combination of the PLANCK microwave sky survey with the EUCLID main galaxy sample, where bias evolution b(a)=b_0+(1-a)b_a is modelled with two parameters b_0 and b_a. Using a realistic bias model introduces a characteristic suppression of the iSW-spectrum on large angular scales, due to the altered distance-weighting functions. The errors in estimating cosmological parameters if the data with evolving bias is interpreted in the framework of cosmologies with constant bias is quantified in an extended Fisher-formalism. We find that the best-fit values of all parameters are shifted by an amount comparable to the statistical accuracy: The estimation bias in units of the statistical accuracy amounts to 1.19 for Omega_m, 0.27 for sigma_8, and 0.72 for w for bias evolution with b_a=1. Leaving b_a open as a free parameter deteriorates the statistical accuracy, in particular on Omega_m and w.

Taxon-related pollen source areas for lake basins in the southern Alps: an empirical approach

The pollen/vegetation relationship in broadleaved forests dominated by Castanea sativa was analysed using an empirical approach. The pollen content of surface sediments of three lake basins of different sizes (6.3, 22.2, and 101.2 ha) in Ticino (southern Switzerland) was used for a comparison with the surrounding vegetation. We surveyed the vegetation around the two small lakes, Lago di Origlio and Lago di Muzzano, and estimated the relative crown coverage of tree species. The regional vegetation outside the lake catchment (ca. >1 km) was determined with the data from the first Swiss National Forest Inventory. For the third large lake, basin of Ponte Tresa, we used only this latter approach for comparison with pollen data. We compare uncorrected and corrected pollen percentages with vegetational data that were processed with distance-weighting functions. To assess the degree of correspondence between pollen and vegetation data we define a ratio pollen/vegetation, which allows a comparison at the taxon level. The best fit between total pollen load and vegetation is reached for a distance from the lake shore of ca. 300 m for Lago di Origlio (150×350 m in size) and of ca. 600 m for Lago di Muzzano (300×750 m in size). Beside these general patterns, our analysis reveals taxon-specific pollen dispersal patterns that are in agreement with results from previous studies in northern Europe. Ratios of species with local (proximal) and long-distance (distal) pollen dispersal provide evidence that pollen dispersal mechanisms can influence the size of the taxon-related pollen source area, from small (100–400 m) to large (>5 km) for the same lake. The proportion of distal species increases with increasing lake size, highlighting the predominance of atmospheric pollen transport. We conclude that the large species-related differences in pollen source areas have to be taken into account when the provenance at a site is estimated and discussed.

Sub-pixel Target Mapping from Soft-classified, Remotely Sensed Imagery

A simple, efficient algorithm is presented for sub-pixel target mapping from remotely-sensed images. Following an initial random allocation of “soft” pixel proportions to “hard” subpixel binary classes, the algorithm works in a series of iterations, each of which contains three stages. For each pixel, for all sub-pixel locations, a distance-weighted function of neighboring sub-pixels is computed. Then, for each pixel, the sub-pixel representing the target class with the minimum value of the function, and the sub-pixel representing the background with the maximum value of the function are found. Third, these two sub-pixels are swapped if the swap results in an increase in spatial correlation between sub-pixels. The new algorithm predicted accurately when applied to simple simulated and real images. It represents an accessible tool that can be coded and applied readily by remote sensing investigators.

Reconstructing land cover from pollen assemblages from small lakes in Denmark

A calibration data set of AD 1800 pollen assemblages and land cover from 30 lake sites (3.5–33 ha) in Denmark is analysed. Canonical ordination (RDA) shows that the distance-weighted land cover of woodland, heathland and open field explain the highest proportion of the variation in the pollen data. Four different distance-weighting functions, 1, 1/ d, 1/ d 2 and an approximation of the Sugita model of pollen dispersal, are applied to the land-cover data, and the 1/ d function results in the strongest correlation between distance-weighted land cover and pollen proportions. Partial least squares (PLS) calibration is applied, and land cover around nine test sites (not included in the calibration data set) is reconstructed from pollen assemblages. The Extended R-value (ERV) model is applied to the pollen proportions and distance-weighted plant abundance inferred from the maps. Pollen productivity and background components are estimated from the calibration data set and used to reconstruct plant abundance around the test sites. The reconstructed land cover and plant abundance are compared with historical maps, and the performance of the two models is compared. Root-mean-squared errors for the two models are within the same ranges but tend to be slightly lower for the ERV model. Division of the data set into two regional subsets does not improve the reconstructions.

Discussion

This communication describes the new information that may be obtained by applying nonlinear analytical techniques to neurobiological time-series. Specifically, we consider the sequence of interspike intervals Ti (the "timing") of trains recorded from synaptically inhibited crayfish pacemaker neurons. As reported earlier, different postsynaptic spike train forms (sets of timings with shared properties) are generated by varying the average rate and/or pattern (implying interval dispersions and sequences) of presynaptic spike trains. When the presynaptic train is Poisson (independent exponentially distributed intervals), the form is "Poisson-driven" (unperturbed and lengthened intervals succeed each other irregularly). When presynaptic trains are pacemaker (intervals practically equal), forms are either "p:q locked" (intervals repeat periodically), "intermittent" (mostly almost locked but disrupted irregularly), "phase walk throughs" (intermittencies with briefer regular portions), or "messy" (difficult to predict or describe succinctly). Messy trains are either "erratic" (some intervals natural and others lengthened irregularly) or "stammerings" (intervals are integral multiples of presynaptic intervals). The individual spike train forms were analysed using attractor reconstruction methods based on the lagged coordinates provided by successive intervals from the time-series Ti. Numerous models were evaluated in terms of their predictive performance by a trial-and-error procedure: the most successful model was taken as best reflecting the true nature of the system's attractor. Each form was characterized in terms of its dimensionality, nonlinearity and predictability. (1) The dimensionality of the underlying dynamical attractor was estimated by the minimum number of variables (coordinates Ti) required to model acceptably the system's dynamics, i.e. by the system's degrees of freedom. Each model tested was based on a different number of Ti; the smallest number whose predictions were judged successful provided the best integer approximation of the attractor's true dimension (not necessarily an integer). Dimensionalities from three to five provided acceptable fits. (2) The degree of nonlinearity was estimated by: (i) comparing the correlations between experimental results and data from linear and nonlinear models, and (ii) tuning model nonlinearity via a distance-weighting function and identifying the either local or global neighborhood size. Lockings were compatible with linear models and stammerings were marginal; nonlinear models were best for Poisson-driven, intermittent and erratic forms. (3) Finally, prediction accuracy was plotted against increasingly long sequences of intervals forecast: the accuracies for Poisson-driven, locked and stammering forms were invariant, revealing irregularities due to uncorrelated noise, but those of intermittent and messy erratic forms decayed rapidly, indicating an underlying deterministic process. The excellent reconstructions possible for messy erratic and for some intermittent forms are especially significant because of their relatively low dimensionality (around 4), high degree of nonlinearity and prediction decay with time. This is characteristic of chaotic systems, and provides evidence that nonlinear couplings between relatively few variables are the major source of the apparent complexity seen in these cases. This demonstration of different dimensions, degrees of nonlinearity and predictabilities provides rigorous support for the categorization of different synaptically driven discharge forms proposed earlier on the basis of more heuristic criteria. This has significant implications. (1) It demonstrates that heterogeneous postsynaptic forms can indeed be induced by manipulating a few presynaptic variables. (2) Each presynaptic timing induces a form with characteristic dimensionality, thus breaking up the preparation into subsystems such that the physical variables in each operate as one

Automated contour mapping using triangular element data structures and an interpolant over each irregular triangular domain

Surface display techniques, including contour mapping, usually use an interpolant when data values are on a rectangular grid; but when values are irregularly located some form of assumed or estimated distance-weighting function is often used to estimate the "influence" of data points at other locations. If moving average (or some other) techniques are then applied, slopes may be zero at data points; extrema may fall at data points exclusively; or surfaces may not pass through data points.An alternative method is proposed whereby a map area is automatically divided into suitable triangular domains with a data point at each vertex. Surface estimation and contour plotting are then performed independently for each triangle using a measured or best-fit plane associated with each data point. The approach requires the utilization of three non-original aspects: 1) the derivation of a local homogeneous "area" coordinate system for any arbitrary triangle; 2) the construction of a data-structure linking each triangular domain with its three neighbouring triangles and three associated data points, and 3) the use of a "conforming" triangular finite-element interpolating function.Use of the first two of these concepts permits the economic generation and optimization of a triangular mesh from a set of data points. Optimization criteria used to define the "best" triangular partition are described in some detail, along with computer timing for this step. Use of the first and third concepts permits the interpolation of a smooth surface over the whole map area even though each triangular element is estimated and plotted independently. The requirements for a suitable interpolating function are discussed, and an interpolant is suggested that preserves elevation and slope at each data point as well as elevation and slope continuity between domains. Extrema need not be located at data points but are constrained by their associated planes. Contour line segments are produced by division of each triangle into N 2 sub-triangles, elevation estimation at each resulting node, and linear interpolation and plotting withing each sub-triangle. Resolution is then a function of N and local data point density. Extension of the method to higher dimensions is briefly discussed.