Three-dimensional random Voronoi tessellations: From cubic crystal lattices to Poisson point processes

We perturb the SC, BCC, and FCC crystal structures with a spatial Gaussian noise whose adimensional strength is controlled by the parameter a, and analyze the topological and metrical properties of the resulting Voronoi Tessellations (VT). The topological properties of the VT of the SC and FCC crystals are unstable with respect to the introduction of noise, because the corresponding polyhedra are geometrically degenerate, whereas the tessellation of the BCC crystal is topologically stable even against noise of small but finite intensity. For weak noise, the mean area of the perturbed BCC and FCC crystals VT increases quadratically with a. In the case of perturbed SCC crystals, there is an optimal amount of noise that minimizes the mean area of the cells. Already for a moderate noise (a>0.5), the properties of the three perturbed VT are indistinguishable, and for intense noise (a>2), results converge to the Poisson-VT limit. Notably, 2-parameter gamma distributions are an excellent model for the empirical of of all considered properties. The VT of the perturbed BCC and FCC structures are local maxima for the isoperimetric quotient, which measures the degre of sphericity of the cells, among space filling VT. In the BCC case, this suggests a weaker form of the recentluy disproved Kelvin conjecture. Due to the fluctuations of the shape of the cells, anomalous scalings with exponents >3/2 is observed between the area and the volumes of the cells, and, except for the FCC case, also for a->0. In the Poisson-VT limit, the exponent is about 1.67. As the number of faces is positively correlated with the sphericity of the cells, the anomalous scaling is heavily reduced when we perform powerlaw fits separately on cells with a specific number of faces.

Spectrum of a Feinberg-Zee random hopping matrix

This paper provides a new proof of a theorem of Chandler-Wilde, Chonchaiya, and Lindner that the spectra of a certain class of infinite, random, tridiagonal matrices contain the unit disc almost surely. It also obtains an analogous result for a more general class of random matrices whose spectra contain a hole around the origin. The presence of the hole forces substantial changes to the analysis.

The trees and the bees: using enforcement and income projects to protect forests and rural livelihoods through spatial joint production

Forest managers in developing countries enforce extraction restrictions to limit forest degradation. In response, villagers may displace some of their extraction to other forests, which generates “leakage” of degradation. Managers also implement poverty alleviation projects to compensate for lost resource access or to induce conservation. We develop a model of spatial joint production of bees and fuelwood that is based on forest-compatible projects such as beekeeping in Thailand, Tanzania, and Mexico. We demonstrate that managers can better determine the amount and pattern of degradation by choosing the location of both enforcement and the forest-based activity.

Random-walk-based characterisation of multiple access interference in a DS/SSMA system

The problem of calculating the probability of error in a DS/SSMA system has been extensively studied for more than two decades. When random sequences are employed some conditioning must be done before the application of the central limit theorem is attempted, leading to a Gaussian distribution. The authors seek to characterise the multiple access interference as a random-walk with a random number of steps, for random and deterministic sequences. Using results from random-walk theory, they model the interference as a K-distributed random variable and use it to calculate the probability of error in the form of a series, for a DS/SSMA system with a coherent correlation receiver and BPSK modulation under Gaussian noise. The asymptotic properties of the proposed distribution agree with other analyses. This is, to the best of the authors' knowledge, the first attempt to propose a non-Gaussian distribution for the interference. The modelling can be extended to consider multipath fading and general modulation

Bayesian parameter estimation for latent Markov random fields and social networks

Undirected graphical models are widely used in statistics, physics and machine vision. However Bayesian parameter estimation for undirected models is extremely challenging, since evaluation of the posterior typically involves the calculation of an intractable normalising constant. This problem has received much attention, but very little of this has focussed on the important practical case where the data consists of noisy or incomplete observations of the underlying hidden structure. This paper specifically addresses this problem, comparing two alternative methodologies. In the first of these approaches particle Markov chain Monte Carlo (Andrieu et al., 2010) is used to efficiently explore the parameter space, combined with the exchange algorithm (Murray et al., 2006) for avoiding the calculation of the intractable normalising constant (a proof showing that this combination targets the correct distribution in found in a supplementary appendix online). This approach is compared with approximate Bayesian computation (Pritchard et al., 1999). Applications to estimating the parameters of Ising models and exponential random graphs from noisy data are presented. Each algorithm used in the paper targets an approximation to the true posterior due to the use of MCMC to simulate from the latent graphical model, in lieu of being able to do this exactly in general. The supplementary appendix also describes the nature of the resulting approximation.

The concept of exchangeability in ensemble forecasting

A set of random variables is exchangeable if its joint distribution function is invariant under permutation of the arguments. The concept of exchangeability is discussed, with a view towards potential application in evaluating ensemble forecasts. It is argued that the paradigm of ensembles being an independent draw from an underlying distribution function is probably too narrow; allowing ensemble members to be merely exchangeable might be a more versatile model. The question is discussed whether established methods of ensemble evaluation need alteration under this model, with reliability being given particular attention. It turns out that the standard methodology of rank histograms can still be applied. As a first application of the exchangeability concept, it is shown that the method of minimum spanning trees to evaluate the reliability of high dimensional ensembles is mathematically sound.

Distributed hoeffding trees for pocket data mining

Collaborative mining of distributed data streams in a mobile computing environment is referred to as Pocket Data Mining PDM. Hoeffding trees techniques have been experimentally and analytically validated for data stream classification. In this paper, we have proposed, developed and evaluated the adoption of distributed Hoeffding trees for classifying streaming data in PDM applications. We have identified a realistic scenario in which different users equipped with smart mobile devices run a local Hoeffding tree classifier on a subset of the attributes. Thus, we have investigated the mining of vertically partitioned datasets with possible overlap of attributes, which is the more likely case. Our experimental results have validated the efficiency of our proposed model achieving promising accuracy for real deployment.

Thorn-dwelling ants provide antiherbivore defence for camelthorn trees, Vachellia erioloba, in Namibia

Ants are widely employed by plants as an antiherbivore defence. A single host plant can associate with multiple, symbiotic ant species, although usually only a single ant species at a time. Different plant-ant species may vary in the degree to which they defend their host plant. In Kenya, ant–acacia interactions are well studied, but less is known about systems elsewhere in Africa. A southern African species, Vachellia erioloba, is occupied by thorn-dwelling ants from three different genera. Unusually, multiple colonies of all these ants simultaneously and stably inhabit trees. We investigated if the ants on V. erioloba (i) deter insect herbivores; (ii) differ in their effectiveness depending on the identity of the herbivore; and (iii) protect the tree against an important herbivore, the larvae of the lepidopteran Gonometa postica. We show that experimental exclusion of ants leads to greater levels of herbivory on trees. The ants inhabiting V. erioloba are an effective deterrent against hemipteran and coleopteran, but not lepidopteran herbivores. Defensive services do not vary among ant species, but only Crematogaster ants exhibit aggression towards G. postica. This highlights the potential of the V. erioloba–ant mutualism for studying ant–plant interactions that involve multiple, simultaneously resident thorn-dwelling ant species.

Probability of survival in a random exchange economy with dependent agents

In this paper I analyze the general equilibrium in a random Walrasian economy. Dependence among agents is introduced in the form of dependency neighborhoods. Under the uncertainty, an agent may fail to survive due to a meager endowment in a particular state (direct effect), as well as due to unfavorable equilibrium price system at which the value of the endowment falls short of the minimum needed for survival (indirect terms-of-trade effect). To illustrate the main result I compute the stochastic limit of equilibrium price and probability of survival of an agent in a large Cobb-Douglas economy.

Soil injections of carbohydrates improve fine root growth of established urban trees

Four established mature tree species (Aesculus hippocastanum L., Betula pendula Roth., Primus avium L. and Quercus rohur L.) commonly planted in UK urban landscapes were subjected to soil injections of the carbohydrate sucrose at 25, 50 and 70g per litre of water. Fine root dry weight was recorded at month 5 following soil injections. Soil injections of sucrose significantly increased fine root dry weight compared to controls, however; growth responses were influenced by species and the concentration of sucrose applied. Results indicate soil injections of sucrose ≥ 50g litre of water may be able to improve root growth of established mature trees. Such a response is desirable as root damage following construction is a frequent problem encountered by established trees growing in UK towns and cities.

Validating the reported random errors of ACE‐FTS measurements

In order to validate the reported precision of space‐based atmospheric composition measurements, validation studies often focus on measurements in the tropical stratosphere, where natural variability is weak. The scatter in tropical measurements can then be used as an upper limit on single‐profile measurement precision. Here we introduce a method of quantifying the scatter of tropical measurements which aims to minimize the effects of short‐term atmospheric variability while maintaining large enough sample sizes that the results can be taken as representative of the full data set. We apply this technique to measurements of O3, HNO3, CO, H2O, NO, NO2, N2O, CH4, CCl2F2, and CCl3F produced by the Atmospheric Chemistry Experiment–Fourier Transform Spectrometer (ACE‐FTS). Tropical scatter in the ACE‐FTS retrievals is found to be consistent with the reported random errors (RREs) for H2O and CO at altitudes above 20 km, validating the RREs for these measurements. Tropical scatter in measurements of NO, NO2, CCl2F2, and CCl3F is roughly consistent with the RREs as long as the effect of outliers in the data set is reduced through the use of robust statistics. The scatter in measurements of O3, HNO3, CH4, and N2O in the stratosphere, while larger than the RREs, is shown to be consistent with the variability simulated in the Canadian Middle Atmosphere Model. This result implies that, for these species, stratospheric measurement scatter is dominated by natural variability, not random error, which provides added confidence in the scientific value of single‐profile measurements.

Land use intensity and trees on farms in Malawi

Rapidly increasing population densities in Malawi have put a huge strain on the existing agricultural land and the surrounding woodland. Smallholder agriculture is the dominant economic activity of Malawi’s rural population and many farmers have been forced to cultivate marginal lands with less fertile soils, making conditions much more difficult to grow crops. Natural woodland is under increasing pressure from the opening of new lands for cultivation and the increased demand for firewood, timber and other woody resources, with rural households historically obtaining most of their complementary inputs and saleable commodities from nearby areas of forest (Arnold, 1997a). Despite this increasing pressure, woodlands are not being cleared indiscriminately; selected indigenous species are left standing in fields and around households. These are joined by exotic species that are planted and maintained. These trees provide products and services that are vital, yielding food, firewood, building materials and medicine, replenishing soil fertility and protecting against soil erosion. Following a Boserupian approach, this study attempts to establish the reality of a trajectory of enhanced on-farm tree planting and management as population pressure mounts and as part of a more general process of agricultural intensification. The study examines the combination of factors (social, economic, political and environmental) that either stimulate or discourage on-farm tree planting on smallholdings in Malawi, highlighting how woodland resource use changes over a gradient of land use intensity. This study gives a detailed insight into the way that tree planting and management in the smallholder farming system in Malawi works and identifies a trend of increased tree planting/management alongside an increase in agricultural intensification. However, there is no single ‘path’ of intensification; the link between agricultural change and tree planting is complex and there are many trajectories of intensification that a farmer may follow, dependent on his/her social or economic circumstances. The study recommends that agroforestry interventions give rigorous consideration to the needs of the local community, and the suitability of trees to address those needs, before embarking on programmes that advocate tree planting and management as a panacea.

Multi-vehicle planning using RRT-connect

The problem of planning multiple vehicles deals with the design of an effective algorithm that can cause multiple autonomous vehicles on the road to communicate and generate a collaborative optimal travel plan. Our modelling of the problem considers vehicles to vary greatly in terms of both size and speed, which makes it suboptimal to have a faster vehicle follow a slower vehicle or for vehicles to drive with predefined speed lanes. It is essential to have a fast planning algorithm whilst still being probabilistically complete. The Rapidly Exploring Random Trees (RRT) algorithm developed and reported on here uses a problem specific coordination axis, a local optimization algorithm, priority based coordination, and a module for deciding travel speeds. Vehicles are assumed to remain in their current relative position laterally on the road unless otherwise instructed. Experimental results presented here show regular driving behaviours, namely vehicle following, overtaking, and complex obstacle avoidance. The ability to showcase complex behaviours in the absence of speed lanes is characteristic of the solution developed.