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.

Distance from forest edge affects bee pollinators in oilseed rape fields

Wild pollinators have been shown to enhance the pollination of Brassica napus(oilseed rape) and thus increase its market value. Several studies have previously shown that pollination services are greater in crops adjoining forest patches or other seminatural habitats than in crops completely surrounded by other crops. In this study, we investigated the specific importance of forest edges in providing potential pollinators in B. napus fields in two areas in France. Bees were caught with yellow pan traps at increasing distances from both warm and cold forest edges into B. napus fields during the blooming period. A total of 4594 individual bees, representing six families and 83 taxa, were collected. We found that both bee abundance and taxa richness were negatively affected by the distance from forest edge. However, responses varied between bee groups and edge orientations. The ITD (Inter-Tegular distance) of the species, a good proxy for bee foraging range, seems to limit how far the bees can travel from the forest edge. We found a greater abundance of cuckoo bees (Nomada spp.) of Andrena spp. and Andrena spp. males at forest edges, which we assume indicate suitable nesting sites, or at least mating sites, for some abundant Andrena species and their parasites (Fig. 1). Synthesis and Applications. This study provides one of the first examples in temperate ecosystems of how forest edges may actually act as a reservoir of potential pollinators and directly benefit agricultural crops by providing nesting or mating sites for important early spring pollinators. Policymakers and land managers should take forest edges into account and encourage their protection in the agricultural matrix to promote wild bees and their pollination services.

Atmospheric electric fields during the Carrington flare

Karen Aplin and Giles Harrison examine international records of the 1859 Carrington flare and consider what they mean for our understanding of space weather today. Space weather is increasingly recognized as a hazard to modern societies, and one way to assess the extent of its possible impact is through analysis of historic space weather events. One such event was the massive solar storm of late August and early September 1859. This is now widely known as the “Carrington flare” or “Carrington event” after the visual solar emissions on 1 September first reported by the Victorian astronomer Richard Carrington from his observatory in Redhill, Surrey (Carrington 1859). The related aurorae and subsequent effects on telegraph networks are well documented (e.g. Clark 2007, Boteler 2006), but use of modern techniques, such as analysis of nitrates produced by solar protons in ice cores to retrospectively assess the nature of the solar flare, has proved problematic (Wolff et al. 2012). This means that there is still very little quantitative information about the flare beyond magnetic observations (e.g. Viljanen et al. 2014).

Using an individual-based model to select among alternative foraging strategies of woodpigeons: data support a memory-based model with a flocking mechanism

Population modelling is increasingly recognised as a useful tool for pesticide risk assessment. For vertebrates that may ingest pesticides with their food, such as woodpigeon (Columba palumbus), population models that simulate foraging behaviour explicitly can help predicting both exposure and population-level impact. Optimal foraging theory is often assumed to explain the individual-level decisions driving distributions of individuals in the field, but it may not adequately predict spatial and temporal characteristics of woodpigeon foraging because of the woodpigeons’ excellent memory, ability to fly long distances, and distinctive flocking behaviour. Here we present an individual-based model (IBM) of the woodpigeon. We used the model to predict distributions of foraging woodpigeons that use one of six alternative foraging strategies: optimal foraging, memory-based foraging and random foraging, each with or without flocking mechanisms. We used pattern-oriented modelling to determine which of the foraging strategies is best able to reproduce observed data patterns. Data used for model evaluation were gathered during a long-term woodpigeon study conducted between 1961 and 2004 and a radiotracking study conducted in 2003 and 2004, both in the UK, and are summarised here as three complex patterns: the distributions of foraging birds between vegetation types during the year, the number of fields visited daily by individuals, and the proportion of fields revisited by them on subsequent days. The model with a memory-based foraging strategy and a flocking mechanism was the only one to reproduce these three data patterns, and the optimal foraging model produced poor matches to all of them. The random foraging strategy reproduced two of the three patterns but was not able to guarantee population persistence. We conclude that with the memory-based foraging strategy including a flocking mechanism our model is realistic enough to estimate the potential exposure of woodpigeons to pesticides. We discuss how exposure can be linked to our model, and how the model could be used for risk assessment of pesticides, for example predicting exposure and effects in heterogeneous landscapes planted seasonally with a variety of crops, while accounting for differences in land use between landscapes.

Molecular dynamics study on the equilibrium magnetization properties and structure of ferrofluids

We investigate in detail the initial susceptibility, magnetization curves, and microstructure of ferrofluids in various concentration and particle dipole moment ranges by means of molecular dynamics simulations. We use the Ewald summation for the long-range dipolar interactions, take explicitly into account the translational and rotational degrees of freedom, coupled to a Langevin thermostat. When the dipolar interaction energy is comparable with the thermal energy, the simulation results on the magnetization properties agree with the theoretical predictions very well. For stronger dipolar couplings, however, we find systematic deviations from the theoretical curves. We analyze in detail the observed microstructure of the fluids under different conditions. The formation of clusters is found to enhance the magnetization at weak fields and thus leads to a larger initial susceptibility. The influence of the particle aggregation is isolated by studying ferro-solids, which consist of magnetic dipoles frozen in at random locations but which are free to rotate. Due to the artificial suppression of clusters in ferrosolids the observed susceptibility is considerably lowered when compared to ferrofluids.

Regional and monthly and clear-sky aerosol direct radiative effect (and forcing) derived from the GlobAEROSOL-AATSR satellite aerosol product

Using the GlobAEROSOL-AATSR dataset, estimates of the instantaneous, clear-sky, direct aerosol radiative effect and radiative forcing have been produced for the year 2006. Aerosol Robotic Network sun-photometer measurements have been used to characterise the random and systematic error in the GlobAEROSOL product for 22 regions covering the globe. Representative aerosol properties for each region were derived from the results of a wide range of literature sources and, along with the de-biased GlobAEROSOL AODs, were used to drive an offline version of the Met Office unified model radiation scheme. In addition to the mean AOD, best-estimate run of the radiation scheme, a range of additional calculations were done to propagate uncertainty estimates in the AOD, optical properties, surface albedo and errors due to the temporal and spatial averaging of the AOD fields. This analysis produced monthly, regional estimates of the clear-sky aerosol radiative effect and its uncertainty, which were combined to produce annual, global mean values of (−6.7±3.9)Wm−2 at the top of atmosphere (TOA) and (−12±6)Wm−2 at the surface. These results were then used to give estimates of regional, clear-sky aerosol direct radiative forcing, using modelled pre-industrial AOD fields for the year 1750 calculated for the AEROCOM PRE experiment. However, as it was not possible to quantify the uncertainty in the pre-industrial aerosol loading, these figures can only be taken as indicative and their uncertainties as lower bounds on the likely errors. Although the uncertainty on aerosol radiative effect presented here is considerably larger than most previous estimates, the explicit inclusion of the major sources of error in the calculations suggest that they are closer to the true constraint on this figure from similar methodologies, and point to the need for more, improved estimates of both global aerosol loading and aerosol optical properties.

Long-term variations in the magnetic fields of the Sun and the heliosphere: their origin, effects, and implications

Recent studies of the variation of geomagnetic activity over the past 140 years have quantified the "coronal source" magnetic flux F-s that leaves the solar atmosphere and enters the heliosphere and have shown that it has risen, on average, by an estimated 34% since 1963 and by 140% since 1900. This variation of open solar flux has been reproduced by Solanki et al. [2000] using a model which demonstrates how the open flux accumulates and decays, depending on the rate of flux emergence in active regions and on the length of the solar cycle. We here use a new technique to evaluate solar cycle length and find that it does vary in association with the rate of change of F-s in the way predicted. The long-term variation of the rate of flux emergence is found to be very similar in form to that in F-s, which may offer a potential explanation of why F-s appears to be a useful proxy for extrapolating solar total irradiance back in time. We also find that most of the variation of cosmic ray fluxes incident on Earth is explained by the strength of the heliospheric field (quantified by F-s) and use observations of the abundance of the isotope Be-10 (produced by cosmic rays and deposited in ice sheets) to study the decrease in F-s during the Maunder minimum. The interior motions at the base of the convection zone, where the solar dynamo is probably located, have recently been revealed using the helioseismology technique and found to exhibit a 1.3-year oscillation. This periodicity is here reported in observations of the interplanetary magnetic field and geomagnetic activity but is only present after 1940, When present, it shows a strong 22-year variation, peaking near the maximum of even-numbered sunspot cycles and showing minima at the peaks of odd-numbered cycles. We discuss the implications of these long-term solar and heliospheric variations for Earth's environment.

Large-scale fields and flows in the magnetosphere-ionosphere system

Advances in our understanding of the large-scale electric and magnetic fields in the coupled magnetosphere-ionosphere system are reviewed. The literature appearing in the period January 1991–June 1993 is sorted into 8 general areas of study. The phenomenon of substorms receives the most attention in this literature, with the location of onset being the single most discussed issue. However, if the magnetic topology in substorm phases was widely debated, less attention was paid to the relationship of convection to the substorm cycle. A significantly new consensus view of substorm expansion and recovery phases emerged, which was termed the ‘Kiruna Conjecture’ after the conference at which it gained widespread acceptance. The second largest area of interest was dayside transient events, both near the magnetopause and the ionosphere. It became apparent that these phenomena include at least two classes of events, probably due to transient reconnection bursts and sudden solar wind dynamic pressure changes. The contribution of both types of event to convection is controversial. The realisation that induction effects decouple electric fields in the magnetosphere and ionosphere, on time scales shorter than several substorm cycles, calls for broadening of the range of measurement techniques in both the ionosphere and at the magnetopause. Several new techniques were introduced including ionospheric observations which yield reconnection rate as a function of time. The magnetospheric and ionospheric behaviour due to various quasi-steady interplanetary conditions was studied using magnetic cloud events. For northward IMF conditions, reverse convection in the polar cap was found to be predominantly a summer hemisphere phenomenon and even for extremely rare prolonged southward IMF conditions, the magnetosphere was observed to oscillate through various substorm cycles rather than forming a steady-state convection bay.

The interconnection of the magnetic fields of the Earth and the sun

Magnetic reconnection facilitates the transfer of mass, energy, and momentum from the solar wind, through the Earth's magnetosphere and into the upper atmosphere. Recently, combined observations using both ground-based and satellite instruments have revealed much about how reconnection takes place. This new understanding has great signficance for systems which exploit, or operate within, the Earth's plasma environment, as well as for a wide variety of scientific studies.

A scalable expressive ensemble learning using Random Prism: a MapReduce approach

The induction of classification rules from previously unseen examples is one of the most important data mining tasks in science as well as commercial applications. In order to reduce the influence of noise in the data, ensemble learners are often applied. However, most ensemble learners are based on decision tree classifiers which are affected by noise. The Random Prism classifier has recently been proposed as an alternative to the popular Random Forests classifier, which is based on decision trees. Random Prism is based on the Prism family of algorithms, which is more robust to noise. However, like most ensemble classification approaches, Random Prism also does not scale well on large training data. This paper presents a thorough discussion of Random Prism and a recently proposed parallel version of it called Parallel Random Prism. Parallel Random Prism is based on the MapReduce programming paradigm. The paper provides, for the first time, novel theoretical analysis of the proposed technique and in-depth experimental study that show that Parallel Random Prism scales well on a large number of training examples, a large number of data features and a large number of processors. Expressiveness of decision rules that our technique produces makes it a natural choice for Big Data applications where informed decision making increases the user’s trust in the system.

A moment problem for random discrete measures

Let X be a locally compact Polish space. A random measure on X is a probability measure on the space of all (nonnegative) Radon measures on X. Denote by K(X) the cone of all Radon measures η on X which are of the form η =

Recurrence and higher ergodic properties for quenched random Lorentz tubes in dimension bigger than two

We consider the billiard dynamics in a non-compact set of ℝ d that is constructed as a bi-infinite chain of translated copies of the same d-dimensional polytope. A random configuration of semi-dispersing scatterers is placed in each copy. The ensemble of dynamical systems thus defined, one for each global realization of the scatterers, is called quenched random Lorentz tube. Under some fairly general conditions, we prove that every system in the ensemble is hyperbolic and almost every system is recurrent, ergodic, and enjoys some higher chaotic properties.

Recurrence for quenched random Lorentz tubes

We consider the billiard dynamics in a striplike set that is tessellated by countably many translated copies of the same polygon. A random configuration of semidispersing scatterers is placed in each copy. The ensemble of dynamical systems thus defined, one for each global choice of scatterers, is called quenched random Lorentz tube. We prove that under general conditions, almost every system in the ensemble is recurrent.

Towards more precise sugar beet management based on geostatistical analysis of spatial variability within fields

Within-field variation in sugar beet yield and quality was investigated in three commercial sugar beet fields in the east of England to identify the main associated variables and to examine the possibility of predicting yield early in the season with a view to spatially variable management of sugar beet crops. Irregular grid sampling with some purposively-located nested samples was applied. It revealed the spatial variability in each sugar beet field efficiently. In geostatistical analyses, most variograms were isotropic with moderate to strong spatial dependency indicating a significant spatial variation in sugar beet yield and associated growth and environmental variables in all directions within each field. The Kriged maps showed spatial patterns of yield variability within each field and visual association with the maps of other variables. This was confirmed by redundancy analyses and Pearson correlation coefficients. The main variables associated with yield variability were soil type, organic matter, soil moisture, weed density and canopy temperature. Kriged maps of final yield variability were strongly related to that in crop canopy cover, LAI and intercepted solar radiation early in the growing season, and the yield maps of previous crops. Therefore, yield maps of previous crops together with early assessment of sugar beet growth may make an early prediction of within-field variability in sugar beet yield possible. The Broom’s Barn sugar beet model failed to account for the spatial variability in sugar yield, but the simulation was greatly improved when corrected for early canopy development cover and when the simulated yield was adjusted for weeds and plant population. Further research to optimize inputs to maximise sugar yield should target the irrigation and fertilizing of areas within fields with low canopy cover early in the season.

Systematic and random errors between collocated satellite ice water path observations

There remains large disagreement between ice-water path (IWP) in observational data sets, largely because the sensors observe different parts of the ice particle size distribution. A detailed comparison of retrieved IWP from satellite observations in the Tropics (!30 " latitude) in 2007 was made using collocated measurements. The radio detection and ranging(radar)/light detection and ranging (lidar) (DARDAR) IWP data set, based on combined radar/lidar measurements, is used as a reference because it provides arguably the best estimate of the total column IWP. For each data set, usable IWP dynamic ranges are inferred from this comparison. IWP retrievals based on solar reflectance measurements, in the moderate resolution imaging spectroradiometer (MODIS), advanced very high resolution radiometer–based Climate Monitoring Satellite Applications Facility (CMSAF), and Pathfinder Atmospheres-Extended (PATMOS-x) datasets, were found to be correlated with DARDAR over a large IWP range (~20–7000 g m -2 ). The random errors of the collocated data sets have a close to lognormal distribution, and the combined random error of MODIS and DARDAR is less than a factor of 2, which also sets the upper limit for MODIS alone. In the same way, the upper limit for the random error of all considered data sets is determined. Data sets based on passive microwave measurements, microwave surface and precipitation products system (MSPPS), microwave integrated retrieval system (MiRS), and collocated microwave only (CMO), are largely correlated with DARDAR for IWP values larger than approximately 700 g m -2 . The combined uncertainty between these data sets and DARDAR in this range is slightly less MODIS-DARDAR, but the systematic bias is nearly an order of magnitude.