When n identical randomly located nodes, each capable of transmitting at W bits per second and using a fixed range, form a wireless network, the throughput /spl lambda/(n) obtainable by each node for a randomly chosen destination is /spl Theta/(W//spl radic/(nlogn)) bits per second under a noninterference protocol. If the nodes are optimally placed in a disk of unit area, traffic patterns are optimally assigned, and each transmission's range is optimally chosen, the bit-distance product that can be transported by the network per second is /spl Theta/(W/spl radic/An) bit-meters per second. Thus even under optimal circumstances, the throughput is only /spl Theta/(W//spl radic/n) bits per second for each node for a destination nonvanishingly far away. Similar results also hold under an alternate physical model where a required signal-to-interference ratio is specified for successful receptions. Fundamentally, it is the need for every node all over the domain to share whatever portion of the channel it is utilizing with nodes in its local neighborhood that is the reason for the constriction in capacity. Splitting the channel into several subchannels does not change any of the results. Some implications may be worth considering by designers. Since the throughput furnished to each user diminishes to zero as the number of users is increased, perhaps networks connecting smaller numbers of users, or featuring connections mostly with nearby neighbors, may be more likely to be find acceptance.

/pdf/the-capacity-of-wireless-networks-1oibgdldgk.pdf

The capacity of wireless networks

Statistics for Spatial Data.

ilbstract. Autocorrelation is a very general statistical property of ecological variables observed across geographic space; its most common forms are patches and gradients. Spatial autocorrelation. which comes either from the physical forcing of environmental variables or from community processes, presents a problem for statistical testing because autocorrelated data violate the assumption of independence of most standard statistical procedures. The paper discusses first how autocorrelation in ecological variables can be described and measured. with emphasis on mapping techniques. Then. proper statistical testing in the presence of autocorrelation is briefly discussed. Finally. ways are presented of explicitly introducing spatial structures into ecological models. Two approaches are proposed: in the raw-data approach, the spatial structure takes the form of a polynomial of the x and .v geographic coordinates of the sampling stations; in the matrix approach. the spatial structure is introduced in the form of a geographic distance matrix among locations. These two approaches are compared in the concluding section. A table provides a list of computer programs available for spatial analysis.

https://www.jstor.org/stable/pdfplus/1939924.pdf

Spatial Autocorrelation: Trouble or New Paradigm?

Species distributional or trait data based on range map (extent-of-occurrence) or atlas survey data often display spatial autocorrelation, i.e. locations close to each other exhibit more similar values than those further apart. If this pattern remains present in the residuals of a statistical model based on such data, one of the key assumptions of standard statistical analyses, that residuals are independent and identically distributed (i.i.d), is violated. The violation of the assumption of i.i.d. residuals may bias parameter estimates and can increase type I error rates (falsely rejecting the null hypothesis of no effect). While this is increasingly recognised by researchers analysing species distribution data, there is, to our knowledge, no comprehensive overview of the many available spatial statistical methods to take spatial autocorrelation into account in tests of statistical significance. Here, we describe six different statistical approaches to infer correlates of species’ distributions, for both presence/absence (binary response) and species abundance data (poisson or normally distributed response), while accounting for spatial autocorrelation in model residuals: autocovariate regression; spatial eigenvector mapping; generalised least squares; (conditional and simultaneous) autoregressive models and generalised estimating equations. A comprehensive comparison of the relative merits of these methods is beyond the scope of this paper. To demonstrate each method’s implementation, however, we undertook preliminary tests based on simulated data. These preliminary tests verified that most of the spatial modeling techniques we examined showed good type I error control and precise parameter estimates, at least when confronted with simplistic simulated data containing

/pdf/methods-to-account-for-spatial-autocorrelation-in-the-5fbbuizhqs.pdf

Methods to account for spatial autocorrelation in the analysis of species distributional data : a review

This paper describes decentralized control laws for the coordination of multiple vehicles performing spatially distributed tasks. The control laws are based on a gradient descent scheme applied to a class of decentralized utility functions that encode optimal coverage and sensing policies. These utility functions are studied in geographical optimization problems and they arise naturally in vector quantization and in sensor allocation tasks. The approach exploits the computational geometry of spatial structures such as Voronoi diagrams.

/pdf/coverage-control-for-mobile-sensing-networks-3gs75qafnm.pdf

Coverage control for mobile sensing networks

Discrete-choice theory and logit models are evaluated for their usefulness in analyzing migration patterns in a zonal system. The authors "argue that spatial effects and more specifically the relative location of zones are not taken into account in such analyses. We therefore introduce a measure of spatial structure and advocate its usage as a predictor of migration in such models. In an example of intrametropolitan migration in Toronto [Canada] we demonstrate that this variable is not only significant but also it improves the performance of all the other variables with the greatest impact on the distance between zones. In addition inclusion of this variable improves the overall performance of the model in terms of residuals." (EXCERPT)

Incorporating the effects of spatial structure in discrete choice models of migration.

This paper is designed to review recent developments in choice modelling that offer promise for studying spatial choices. In particular, we focus on the ability of general choice models to account for a richer pattern of spatial substitution than afforded by early choice models. We argue that the generality offered by these choice models is sufficient to rethink the current view that spatial choice is a distinct field of inquiry. Our conclusion is that, while space complicates choice models, contemporary aspatial choice models are general enough to accommodate these complexities.

Spatial choice modelling: new opportunities to incorporate space into substitution patterns

Mountain pine beetle dispersal: The spatial-temporal interaction of infestations

The past decade has witnessed extensive development of measures that examine characteristics of spatial subsets (local spaces) defined with respect to a complete data set (global space). Such procedures have evolved independently in fields such as geography, GIS, cartography, remote sensing, and landscape ecology. Collectively, we label these procedures as local spatial methods. We focus on those methods that share a common goal of identifying subsets whose characteristics are statistically 'significant' in some way. We propose the concept of local spatial statistical analysis (LoSSA) both as an integrative structure for existing methods and as a framework that facilitates the development of new local and global statistics. By formalizing what is involved when a particular local statistic is used, LoSSA helps to reveal the key features and limitations of the procedure. These include a consideration of the nature of the spatial subsets, their spatial relationship to the complete data set, and the relationship between a given global statistic and the corresponding local statistics computed for the data set.

Local statistical spatial analysis: Inventory and prospect

We developed choice models to understand and predict the amount, timing, and locations of recreational fishing trips taken by anglers in northwestern Ontario, Canada. These models incorporated several improvements over previous models to account for complex patterns of spatial substitution among fishing sites, the context of fishing trips, and the importance of tradition and weather on the timing of trips. Joint models of fishing participation and site choice were developed for two resident populations of anglers from northern Ontario. For both populations, the three innovations provided significant improvements to the models and important information for understanding and predicting recreational fishing behaviors. The utility of the model to fisheries managers was illustrated through a management scenario that involved the restoration of walleyes Sander vitreus in a large water body. The forecasts suggested that the effect of this restoration on fishing effort at other waters was influenced by s...

Barry Boots

Papers

Incorporating the effects of spatial structure in discrete choice models of migration.

Spatial choice modelling: new opportunities to incorporate space into substitution patterns

Mountain pine beetle dispersal: The spatial-temporal interaction of infestations

Local statistical spatial analysis: Inventory and prospect

Predicting Fishing Participation and Site Choice While Accounting for Spatial Substitution, Trip Timing, and Trip Context