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

The author reviews the existing literature on density and crowding from a geographical perspective with a focus on the concerns of urban geographers. Several types of empirical studies are described and reviewed and research on models of crowding is outlined (ANNOTATION)

Population density, crowding and human behaviour:

This paper introduces procedures involving the recursive construction of Voronoi diagrams and Delaunay tessellations. In such constructions, Voronoi and Delaunay concepts are used to tessellate an object space with respect to a given set of generators and then the construction is repeated every time with a new generator set, which comprises members selected from the previous generator set plus features of the current tessellation. Such constructions are shown to provide an integrating conceptual framework for a number of disparate procedures, as well as extending the existing functionality of the basic Voronoi and Delaunay procedures to variable spatial resolutions. Further, because they are shown to be fractal in nature, it is suggested that this characteristic can be exploited in the development of new strategies for spatial modelling.

Recursive Voronoi Diagrams

Algorithms for Computing Voronoi Diagrams

Probability model approach to map pattern analysis

The quantitative revolution in geography in the 1960s and 1970s was an exciting time to be a post-graduate student. Like many social scientists, geographers at that time wanted to make the ‘intellectual music’ of science, the anthem of geography, from an orchestra of common methods and techniques. It is therefore with great appreciation that we thank Peter Haggett for providing retrospective comments on this volume as one of the conductors of the revolution. The term ‘maestro’ aptly applies to Peter and his many contributions, since the seminal work by Chorley and Haggett (1967) in Models in Geography was a catalyst and confirmation that models should be an integral part in the evolution of geographical knowledge. One of the features of the revolution was a massive borrowing of ideas from other disciplines under the umbrella of General Systems Theory. This enabled information on the properties of one real system to be used to present the properties of another little known system (Von Bertalanffy 1962). By the end of the 1970s, this reasoning by analogy had reached its zenith. Yet, the theoretical evolution of geographical models during the revolution was a haphazard but creative affair. One only has to look at the evolution of consumer spatial behaviour (Fig. 1) to appreciate the complex cross-fertilisation of different ideas that underpins this concept. This process was intellectually stimulating and good to be part of. However, in many ways, although the models were creative, they were naive in their appreciation of

Barry Boots

Papers

Population density, crowding and human behaviour:

Recursive Voronoi Diagrams

Algorithms for Computing Voronoi Diagrams

Probability model approach to map pattern analysis

The quantitative revolution plus 55 years: relevant, testable and reproducible modelling?