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.

Sparse polynomial approximation in positive order Sobolev spaces with bounded mixed derivatives and applications to elliptic problems with random loading

In the present paper we study the approximation of functions with bounded mixed derivatives by sparse tensor product polynomials in positive order tensor product Sobolev spaces. We introduce a new sparse polynomial approximation operator which exhibits optimal convergence properties in L2 and tensorized View the MathML source simultaneously on a standard k-dimensional cube. In the special case k=2 the suggested approximation operator is also optimal in L2 and tensorized H1 (without essential boundary conditions). This allows to construct an optimal sparse p-version FEM with sparse piecewise continuous polynomial splines, reducing the number of unknowns from O(p2), needed for the full tensor product computation, to View the MathML source, required for the suggested sparse technique, preserving the same optimal convergence rate in terms of p. We apply this result to an elliptic differential equation and an elliptic integral equation with random loading and compute the covariances of the solutions with View the MathML source unknowns. Several numerical examples support the theoretical estimates.

On the spectra and pseudospectra of a class of non-self-adjoint random matrices and operators

In this paper we develop and apply methods for the spectral analysis of non-selfadjoint tridiagonal infinite and finite random matrices, and for the spectral analysis of analogous deterministic matrices which are pseudo-ergodic in the sense of E. B. Davies (Commun. Math. Phys. 216 (2001), 687–704). As a major application to illustrate our methods we focus on the “hopping sign model” introduced by J. Feinberg and A. Zee (Phys. Rev. E 59 (1999), 6433–6443), in which the main objects of study are random tridiagonal matrices which have zeros on the main diagonal and random ±1’s as the other entries. We explore the relationship between spectral sets in the finite and infinite matrix cases, and between the semi-infinite and bi-infinite matrix cases, for example showing that the numerical range and p-norm ε - pseudospectra (ε > 0, p ∈ [1,∞] ) of the random finite matrices converge almost surely to their infinite matrix counterparts, and that the finite matrix spectra are contained in the infinite matrix spectrum Σ. We also propose a sequence of inclusion sets for Σ which we show is convergent to Σ, with the nth element of the sequence computable by calculating smallest singular values of (large numbers of) n×n matrices. We propose similar convergent approximations for the 2-norm ε -pseudospectra of the infinite random matrices, these approximations sandwiching the infinite matrix pseudospectra from above and below.

On the barrier properties of the cornea: a microscopy study of the penetration of fluorescently labeled nanoparticles, polymers, and sodium fluorescein

Overcoming the natural defensive barrier functions of the eye remains one of the greatest challenges of ocular drug delivery. Cornea is a chemical and mechanical barrier preventing the passage of any foreign bodies including drugs into the eye, but the factors limiting penetration of permeants and nanoparticulate drug delivery systems through the cornea are still not fully understood. In this study, we investigate these barrier properties of the cornea using thiolated and PEGylated (750 and 5000 Da) nanoparticles, sodium fluorescein, and two linear polymers (dextran and polyethylene glycol). Experiments used intact bovine cornea in addition to bovine cornea de-epithelialized or tissues pretreated with cyclodextrin. It was shown that corneal epithelium is the major barrier for permeation; pretreatment of the cornea with β-cyclodextrin provides higher permeation of low molecular weight compounds, such as sodium fluorescein, but does not enhance penetration of nanoparticles and larger molecules. Studying penetration of thiolated and PEGylated (750 and 5000 Da) nanoparticles into the de-epithelialized ocular tissue revealed that interactions between corneal surface and thiol groups of nanoparticles were more significant determinants of penetration than particle size (for the sizes used here). PEGylation with polyethylene glycol of a higher molecular weight (5000 Da) allows penetration of nanoparticles into the stroma, which proceeds gradually, after an initial 1 h lag phase.

Spatio-temporal variations of ozone and nitrogen dioxide concentrations under urban trees and in a nearby open area

The evergreen Quercus ilex L. is one of the most common trees in Italian urban environments and is considered effective in the uptake of particulate and gaseous atmospheric pollutants. However, the few available estimates on O3 and NO2 removal by urban Q. ilex originate from model-based studies (which indicate NO2/O3 removal capacity of Q. ilex) and not from direct measurements of air pollutant concentrations. Thus, in the urban area of Siena (central Italy) we began long-term monitoring of O3/NO2 concentrations using passive samplers at a distance of 1, 5, 10 m from a busy road, under the canopies of Q. ilex and in a nearby open-field. Measurements performed in the period June 2011-October 2013 showed always a greater decrease of NO2 concentrations under the Q. ilex canopy than in the open-field transect. Conversely, a decrease of average O3 concentrations under the tree canopy was found only in autumn after the typical Mediterranean post-summer rainfalls. Our results indicate that interactions between O3/NO2 concentrations and trees in Mediterranean urban ecosystems are affected by temporal variations in climatic conditions. We argue therefore that the direct measurement of atmospheric pollutant concentrations should be chosen to describe local changes of aerial pollution.