Neural Network Modeling of Constrained Spatial Interaction Flows: Design, Estimation, and Performance Issues

In this paper a novel modular product unit neural network architecture is presented to model singly constrained spatial interaction flows. The efficacy of the model approach is demonstrated for the origin constrained case of spatial interaction using Austrian interregional telecommunication traffic data. The model requires a global search procedure for parameter estimation, such as the Alopex procedure. A benchmark comparison against the standard origin constrained gravity model and the two–stage neural network approach, suggested by Openshaw (1998), illustrates the superiority of the proposed model in terms of the generalization performance measured by ARV and SRMSE.     

A Methodology for Neural Spatial Interaction Modeling

This paper attempts to develop a mathematically rigid and unified framework for neural spatial interaction modeling. Families of classical neural network models, but also less classical ones such as product unit neural network ones are considered for the cases of unconstrained and singly constrained spatial interaction flows. Current practice appears to suffer from least squares and normality assumptions that ignore the true integer nature of the flows and approximate a discrete‐valued process by an almost certainly misrepresentative continuous distribution. To overcome this deficiency we suggest a more suitable estimation approach, maximum likelihood estimation under more realistic distributional assumptions of Poisson processes, and utilize a global search procedure, called Alopex, to solve the maximum likelihood estimation problem. To identify the transition from underfitting to overfitting we split the data into training, internal validation, and test sets. The bootstrapping pairs approach with replacement is adopted to combine the purity of data splitting with the power of a resampling procedure to overcome the generally neglected issue of fixed data splitting and the problem of scarce data. In addition, the approach has power to provide a better statistical picture of the prediction variability. Finally, a benchmark comparison against the classical gravity models illustrates the superiority of both, the unconstrained and the origin constrained neural network model versions in terms of generalization performance measured by Kullback and Leibler's information criterion.     

DERIVATIVES OF FLOWS IN A DOUBLY CONSTRAINED GRAVITY MODEL

For many practical applications it is important to know how the flows in a doubly constrained gravity model react to slight variations in the predetermined marginal totals. The first-order approximation of these variations is a linear function on the set of feasible variations of marginal totals, i.e., the set of variations not violating the consistency constraint of the model. Several methods to find a matrix describing this linear function are developed and compared with former contributions to this issue. Finally, applicability of the methods to sensitivity and error propagation analysis is demonstrated.     

ON THE SENSITIVITY OF GRAVITY MODEL FORECASTS*

In this paper we present a procedure for estimating small changes in gravity model forecasts in response to small changes in input values (trip end totals and/or parameter values). The procedure can be used to derive covariance matrices from which confidence intervals may be obtained and which may be used for tests of hypotheses. While this type of problem has been addressed by others, our approach is the only one that is conveniently applicable to the doubly constrained model and can accommodate the large numbers of origin and destination zones one typically encounters.     

A Bayesian Approach to Modeling Binary Data: The Case of High‐Intensity Crime Areas

This paper reports the fitting of a number of Bayesian logistic models with spatially structured or/and unstructured random effects to binary data with the purpose of explaining the distribution of high‐intensity crime areas (HIAs) in the city of Sheffield, England. Bayesian approaches to spatial modeling are attracting considerable interest at the present time. This is because of the availability of rigorously tested software for fitting a certain class of spatial models. This paper considers issues associated with the specification, estimation, and validation, including sensitivity analysis, of spatial models using the WinBUGS software. It pays particular attention to the visualization of results. We discuss a map decomposition strategy and an approach that examines properties of the full posterior distribution. The Bayesian spatial model reported provides some interesting insights into the different factors underlying the existence of the three police‐defined HIAs in Sheffield.     

A New Perspective about Moran's Coefficient: Spatial Autocorrelation as a Linear Regression Problem. Moran系数的新视角：空间自相关视为线性回归问题

The computation of Moran's index of spatial autocorrelation requires the definition of a spatial weighting matrix. The eigendecomposition of this doubly centered matrix (i.e., one that forces the sums of all rows and columns to equal zero) has interesting properties that have been exploited in various contexts: distribution properties of the Moran coefficient (MC), spatial filtering in linear models, generalized linear models, and multivariate analysis. In this article, this eigendecomposition is used to propose a new view of MC based on its interpretation in the simple context of linear regression. I use this interpretation to demonstrate the different properties of MC and also the inefficiency of this index in some situations involving simultaneous positive and negative spatial autocorrelation. I propose some new statistics and procedures for testing spatial autocorrelation, and conduct a simulation study to evaluate these new approaches.     

Travel-Time Constraints on Destination-Choice Sets

The importance of travel-time constraints in spatial choice is widely recognized in the literature of geography and related disciplines, but little work has been done toward developing operational models of spatial choice wherein these constraints and their effects are made explicit. The purpose of the paper is to test the accuracy of predictions produced by a destination choice model that does not take explicit account of travel constraints under the assumption that observed choices are made from choice sets delineated by a constraint of maximum travel time. Observed choices are generated by simulation from a new random utility model consistent with the constrained nature of individual choice sets. Results show that the characteristics of constraints are a decisive factor in the accuracy of the unconstrained choice model. Choice probabilities of the constrained reality are predicted with a reasonably good accuracy in some instances, but predictions are less impressive, and even poor, in many others.     

Gifts given, gifts taken: The behavioral ecology of nonmarket, intragroup exchange

Behavioral ecologists combine evolutionary models of mechanism and ecological models of circumstance to analyze the origins and forms of intragroup exchange among social foragers, a category that includes primates, hominids, and recent and modern hunter-gatherers. Evolutionary mechanisms encompass individual, sexual, reciprocal, kin, group, and cultural selection; models of circumstance include tolerated theft, scrounging, marginal value, trade, show-offs, and risk reduction. After a critical review, I develop a partial synthesis of these models. The results show that exchange behaviors have multicausal origins and they likely will be diverse due to differing combinations of mechanism and circumstance. They also help explain seemingly unique features of foraging economies, including constrained production and routine demand sharing.     

Continuous Characterization of the Planform Geometry and Curvature of Meandering Rivers

The complex feedback between process and form that governs planform migration of meandering rivers is still incompletely understood. Current theoretical models aimed at predicting planform migration relate the rate of meander migration at a particular location to the channel curvature at and upstream of that location. However, these models are still incapable of reproducing complex forms of bend development, such as compound loops. Evaluation of such models requires a representation of planform curvature better than that provided by traditional methods where the curvature is calculated from directional change between the successive digitized points—an approach that provides a discrete representation of curvature dependent on the density of the digitized points used to characterize the channel planform. This article presents and evaluates a methodology that provides a continuous functional representation of the planform geometry and curvature of meandering rivers. The method involves the fitting of splines, specifically parametric cubic splines (PCSs), to discrete digitization data of the channel centerline (CL) and the arc-length parameterization of the resulting composite curve. The arc-length parameterized PCS-interpolated curve is then used to compute analytically the channel CL location and curvature for any value of the streamwise axis. Evaluation of the method involves examination of the effects of digitization interval size and digitization error on the characterization of the planform geometry and curvature using PCS fitting. The derivation of curvature values from continuous planform function for any location and any spatial interval overcomes the reliance either on average bend curvature values or on discrete curvature values based on digitized points.     

Probabilistic, Maximal Covering Location—Allocation Models forCongested Systems

When dealing with the design of service networks, such as health andemergency medical services, banking or distributed ticket-selling services, the location of servicecenters has a strong influence on the congestion at each of them, and, consequently, on thequality of service. In this paper, several probabilistic maximal coveringlocation—allocation models with constrained waiting time for queue length are presentedto consider service congestion. The first model considers the location of a given number ofsingle-server centers such that the maximum population is served within a standard distance, andnobody stands in line for longer than a given time or with more than a predetermined number ofother users. Several maximal coverage models are then formulated with one or more servers perservice center. A new heuristic is developed to solve the models and tested in a 30-node network.     

Modeling the effect of mandatory district compactness on partisan gerrymanders

Geographic compactness standards have been offered as neutral and effective standards constraining redistricting. In this paper, we test this allegation. Redistricting is treated as a combinatoric optimization problem that is constrained by compactness rules. Computer models are used to analyze the results of applying compactness standards when political groups are geographically concentrated. Several population models are used to generate populations of voters, and arbitrary plans are created with combinatoric optimization algorithms. We find that compactness standards can be used to limit gerrymandering, but only if such standards require severe compactness. Compactness standards are not politically neutral—a geographically concentrated minority party will be affected by compactness standards much differently than a party supported by a geographically diffuse population. The particular effects of compactness standards depend on the institutional mechanism that creates districts.     

A Statistical Method for Analyzing the Spatial Relationship between the Distribution of Activity Points and the Distribution of Activity Continuously Distributed over a Region

This paper shows a statistical method for analyzing the spatial relationship between the distributions of two different kinds of activity in a region. One kind of activity is discretely distributed as points in a region (such as the distribution of retail stores), and the other kind of activity is continuously distributed over the region (such as the distribution of population). First, three models representing the relationship between the above two distributions are formulated. Second, statistical methods for fitting these models to data are developed and the measures of fitness are proposed. Third, using these measures, the relationship between the distributions of thirty-seven kinds of retail stores and the distribution of population is examined in a suburb of Osaka in Japan.     

STACKELBERG GAMES ON A NETWORK WITH COURNOT-NASH OLIGOPOLISTIC COMPETITORS

ABSTRACT. We formulate the spatial Stackelberg-Nash-Cournot competitive network equilibrium problem as a variational inequality constrained mathematical program. Our model differs from previous models of Stackelberg oligopolistic competition in that it employs explicit shipping decision variables and a general network topology. That is, the production and distribution decisions of the Stackelberg firm are determined simultaneously over a discrete network. We explore the existence of solutions to the proposed model, and we also numerically test a sensitivity analysis based algorithm. In particular, we illustrate how sensitivity analysis results can be used to generate the Cournot reaction necessary to solve the Stackelberg problem.     

Cost-efficient Reserve Site Selection Favoring Persistence of Threatened and Endangered Species

This article formulates and tests set covering and related models with spatial characteristics for selecting sites that provide habitat for species that are identified as "critical" (e.g., typically threatened, endangered, or rare), thereby enhancing their persistence. The first two models presented require the creation of a core area for each critical species and a buffer zone surrounding the core, with and without being constrained to include at least one representation of each and every common (i.e., noncritical) species. The final model aims at minimizing costs of protecting predetermined numbers of common species while all critical species remain covered and buffered. These models are implemented for occurrence data of terrestrial mammals in Oregon. They enable, among other things, a comparison between the budgetary impacts of reserve networks with and without buffering rings for critical species, and a determination of the marginal cost of common species protection.     

ELASTICITIES OF CONSTRAINED GRAVITY MODELS*

ABSTRACT Doubly constrained gravity models require a balancing procedure to make estimated origin and destination totals consistent. We show through a series of examples that not just the magnitudes but even the signs of derivatives and elasticities of gravity model flows depend on the specific balancing procedure used. Hence, if such elasticities are regarded as meaningful, then the balancing of origin and destination totals must be regarded as an integral part of the gravity theory itself.     

Providing Intergenerational Goods: Implementation of National Park System Plans in Canada and the United States

The provision of inter generational goods is a challenging task for democratic governments in that benefits arrive in the future but costs are borne in the present. Public agencies usually are assigned responsibility for providing such goods, but implementation of their long-term plans often is constrained by the short-term focus of other political actors. This argument is illustrated through a comparison of Canadian and American efforts to expand national park systems according to scientific criteria. Efforts in both nations have been constrained, albeit by different sets of institutional actors. The strong federal structure in Canada has enabled subnational actors to slow and compromise agency expansion plans. American agency efforts have been constrained by the acts of individual politicians at the federal level, particularly members of Congress     

Establishment of a Time-Varying Modified Kanai-Tajimi Non Stationary Stochastic Model of Seismic Records Based on the S-transform

This article investigates the time-varying characteristics of seismic records. Time-varying amplitude and energy spectrums are defined to reflect the time-frequency dependence, and a general formulation of the S-transform is introduced. The S-transform is tested with various window functions to analyse the Kobe seismic records. The results indicate that using a complex window function with properly adjusted parameters gives favorable outcomes. Analyses of three soil sites show that sites with hard soil feature seismic records with shorter stationary durations, higher frequency centers, and broader frequency bands than other soil sites. The average time-varying spectrums of the seismic records are simulated using a uniform non stationary stochastic model and a time-varying modified non stationary Kanai-Tajimi stochastic model. Empirical formulas are established for the time-varying spectrums of the earthquake records from these sites by nonlinearly fitting stochastic models to the record data. The values of the time-varying spectrum factors for different earthquake intensities and sites agreeing with the Chinese Seismic Code are obtained. Based on these analyses and observations, we propose using the solutions to the stochastic models to simulate non stationary ground motions.     

The Location Invariance Theorem in Weberian Space Under Uncertainty

This paper examines the validity of the location invariance theorem in Weberian space under various types of uncertainty. The main results are: Given that the firm's location is constrained to remain at a specified distance from the output market, the optimal location is invariant to any change in product demand if and only if the production function is homothetic for a firm facing demand price uncertainty, or if the production function is homothetic and both inputs are risk-neutral for a firm facing technological uncertainty. Alternatively, given that the distance from the firm's location to the output market is a variable, location invariance occurs for a firm facing demand price uncertainty if the production function is linear homogeneous. In the presence of input price uncertainty the optimal location always varies with a change in product demand. The results can include those previously obtained for linear stochastic location models as special cases and some are new contributions to the literature.     

Queerly situated? Exploring negotiations of trans queer subjectivities at work and within community spaces in the UK

While traditional perspectives on transgender from some strands of feminism and within medical/psychoanalytical discourse have argued that transgender people conform to and reproduce gender stereotypes, queer theory has celebrated transgender as a site that highlights the social and cultural construction of ‘sex’ and ‘gender’ and, moreover, as a symbol of transgressive gender possibility. Both of these readings ignore the complexities of lived trans experiences and identifications. By evaluating a queer reading of trans through recent empirical research into transgender identities, I suggest that while trans identifications certainly queer binary models of ‘sex’ and ‘gender’, such transgressions are materially, culturally, socially and spatially contingent. The article draws on empirical research to explore the ways in which access to queer subjectivities is constrained by, and negotiated alongside, the locales of the workplace and community spaces.     

Nonparametric Significance Test for Discovery of Network‐Constrained Spatial Co‐Location Patterns

Spatial co‐location patterns are useful for understanding positive spatial interactions among different geographical phenomena. Existing methods for detecting spatial co‐location patterns are mostly developed based on planar space assumption; however, geographical phenomena related to human activities are strongly constrained by road networks. Although these methods can be simply modified to consider the constraints of networks by using the network distance or network partitioning scheme, user‐specified parameters or priori assumptions for determining prevalent co‐location patterns are still subjective. As a result, some co‐location patterns may be wrongly reported or omitted. Therefore, a nonparametric significance test without priori assumptions about the distributions of the spatial features is proposed in this article. Both point‐dependent and location‐dependent network‐constrained summary statistics are first utilized to model the distribution characteristics of the spatial features. Then, by using these summary statistics, a network‐constrained pattern reconstruction method is developed to construct the null model of the test, and the prevalence degree of co‐location patterns is modeled as the significance level. The significance test is evaluated using the facility points‐of‐interest data sets. Experiments and comparisons show that the significance test can effectively detect network‐constrained spatial co‐location patterns with less priori knowledge and outperforms two state‐of‐the‐art methods in excluding spurious patterns.