An exploration of the equivalent weights particle filter

Particle filters are fully non-linear data assimilation techniques that aim to represent the probability distribution of the model state given the observations (the posterior) by a number of particles. In high-dimensional geophysical applications the number of particles required by the sequential importance resampling (SIR) particle filter in order to capture the high probability region of the posterior, is too large to make them usable. However particle filters can be formulated using proposal densities, which gives greater freedom in how particles are sampled and allows for a much smaller number of particles. Here a particle filter is presented which uses the proposal density to ensure that all particles end up in the high probability region of the posterior probability density function. This gives rise to the possibility of non-linear data assimilation in large dimensional systems. The particle filter formulation is compared to the optimal proposal density particle filter and the implicit particle filter, both of which also utilise a proposal density. We show that when observations are available every time step, both schemes will be degenerate when the number of independent observations is large, unlike the new scheme. The sensitivity of the new scheme to its parameter values is explored theoretically and demonstrated using the Lorenz (1963) model.

Supplementary feeding of wild birds indirectly affects ground beetle populations in suburban gardens

Supplementary feeding of wild birds by domestic garden-holders is a globally widespread and popular form of human–wildlife interaction, particularly in urban areas. Vast amounts of energy are thus being added to garden ecosystems. However, the potential indirect effects of this activity on non-avian species have been little studied to date, with the only two previous studies taking place under experimentally manipulated conditions. Here we present the first evidence of a localised depletive effect of wild bird feeding on ground beetles (Coleoptera: Carabidae) in suburban gardens under the usual feeding patterns of the garden-holders. We trapped significantly fewer ground beetles directly under bird-feeding stations than in matched areas of habitat away from feeders. Video analysis also revealed significantly higher activity by ground-foraging birds under the feeding stations than in the control areas. Small mammal trapping revealed no evidence that these species differ in abundance between gardens with and without bird feeders. We therefore suggest that local increases in ground-foraging activity by bird species whose diets encompass arthropods as well as seed material are responsible for the reduction in ground beetle numbers. Our work therefore illustrates that providing food for wild birds can have indirect negative effects on palatable prey species under typical conditions.

The composite-tendency RAW filter in semi-implicit integrations

The time discretization in weather and climate models introduces truncation errors that limit the accuracy of the simulations. Recent work has yielded a method for reducing the amplitude errors in leapfrog integrations from first-order to fifth-order. This improvement is achieved by replacing the Robert--Asselin filter with the RAW filter and using a linear combination of the unfiltered and filtered states to compute the tendency term. The purpose of the present paper is to apply the composite-tendency RAW-filtered leapfrog scheme to semi-implicit integrations. A theoretical analysis shows that the stability and accuracy are unaffected by the introduction of the implicitly treated mode. The scheme is tested in semi-implicit numerical integrations in both a simple nonlinear stiff system and a medium-complexity atmospheric general circulation model, and yields substantial improvements in both cases. We conclude that the composite-tendency RAW-filtered leapfrog scheme is suitable for use in semi-implicit integrations.

Automated algorithms for multilayer thin film filter design using metamaterials

Currently, infrared filters for astronomical telescopes and satellite radiometers are based on multilayer thin film stacks of alternating high and low refractive index materials. However, the choice of suitable layer materials is limited and this places limitations on the filter performance that can be achieved. The ability to design materials with arbitrary refractive index allows for filter performance to be greatly increased but also increases the complexity of design. Here a differential algorithm was used as a method for optimised design of filters with arbitrary refractive indices, and then materials are designed to these specifications as mono-materials with sub wavelength structures using Bruggeman’s effective material approximation (EMA).

Prebiotic feeding elevates central brain derived neurotrophic factor, N-methyl-D-aspartate receptor subunits and D-serine

The influence of the gut microbiota on brain chemistry has been convincingly demonstrated in rodents. In the absence of gut bacteria, the central expression of brain derived neurotropic factor, (BDNF), and N-methyl-d-aspartate receptor (NMDAR) subunits are reduced, whereas, oral probiotics increase brain BDNF, and impart significant anxiolytic effects. We tested whether prebiotic compounds, which increase intrinsic enteric microbiota, also affected brain BDNF and NMDARs. In addition, we examined whether plasma from prebiotic treated rats released BDNF from human SH-SY5Y neuroblastoma cells, to provide an initial indication of mechanism of action. Rats were gavaged with fructo-oligosaccharides (FOS), galacto-oligosaccharides (GOS) or water for five weeks, prior to measurements of brain BDNF, NMDAR subunits and amino acids associated with glutamate neurotransmission (glutamate, glutamine, and serine and alanine enantiomers). Prebiotics increased hippocampal BDNF and NR1 subunit expression relative to controls. The intake of GOS also increased hippocampal NR2A subunits, and frontal cortex NR1 and d-serine. Prebiotics did not alter glutamate, glutamine, l-serine, l-alanine or d-alanine concentrations in the brain, though GOSfeeding raised plasma d-alanine. Elevated levels of plasma peptide YY (PYY) after GOS intake was observed. Plasma from GOS rats increased the release of BDNF from SH-SY5Y cells, but not in the presence of PYY antisera. The addition of synthetic PYY to SH-SY5Y cell cultures, also elevated BDNF secretion. We conclude that prebiotic-mediated proliferation of gut microbiota in rats, like probiotics, increases brain BDNF expression, possibly through the involvement of gut hormones. The effect of GOS on components of central NMDAR signalling was greater than FOS, and may reflect the proliferative potency of GOS on microbiota. Our data therefore, provide a sound basis to further investigate the utility of prebiotics in the maintenance of brain health and adjunctive treatment of neuropsychiatric disorders.

Restrictive feeding practices and adiposity are differentially related to P3b cortical responses to food stimuli in children

Across two studies, we examined the association between adiposity, restrictive feeding practices and cortical processing bias to food stimuli in children. We assessed P3b event-related potential (ERP) during visual oddball tasks in which the frequently presented stimulus was non-food and the infrequently presented stimulus was either a food (Study 1) or non-food (Study 2) item. Children responded to the infrequently presented stimulus and accuracy and speed responses were collected. Restrictive feeding practices, children's height and weight were also measured. In Study 1, the difference in P3b amplitude for infrequently presented food stimuli, relative to frequently presented non-food stimuli, was negatively associated with adiposity and positively associated with restrictive feeding practices after controlling for adiposity. There was no association between P3b amplitude difference and adiposity or restriction in Study 2, suggesting that the effects seen in Study 1 were not due to general attentional processes. Taken together, our results suggest that attentional salience, as indexed by the P3b amplitude, may be important for understanding the neural correlates of adiposity and restrictive feeding practices in children.

Wild bird feeding in a large UK urban area: characteristics and estimates of energy input and individuals supported

Wild bird feeding is popular in domestic gardens across the world. Nevertheless, there is surprisingly little empirical information on certain aspects of the activity and no year-round quantitative records of the amounts and nature of the different foods provided in individual gardens. We sought to characterise garden bird feeding in a large UK urban area in two ways. First, we conducted face-to-face questionnaires with a representative cross-section of residents. Just over half fed birds, the majority doing so year round and at least weekly. Second, a two-year study recorded all foodstuffs put out by households on every provisioning occasion. A median of 628 kcal/garden/day was given. Provisioning level was not significantly influenced by weather or season. Comparisons between the data sets revealed significantly less frequent feeding amongst these ‘keen’ feeders than the face-to-face questionnaire respondents, suggesting that one-off questionnaires may overestimate provisioning frequency. Assuming 100% uptake, the median provisioning level equates to sufficient supplementary resources across the UK to support 196 million individuals of a hypothetical average garden-feeding bird species (based on 10 common UK garden-feeding birds’ energy requirements). Taking the lowest provisioning level recorded (101 kcal/day) as a conservative measure, 31 million of these average individuals could theoretically be supported.

Estimating correlated observation error statistics using an ensemble transform Kalman filter

For certain observing types, such as those that are remotely sensed, the observation errors are correlated and these correlations are state- and time-dependent. In this work, we develop a method for diagnosing and incorporating spatially correlated and time-dependent observation error in an ensemble data assimilation system. The method combines an ensemble transform Kalman filter with a method that uses statistical averages of background and analysis innovations to provide an estimate of the observation error covariance matrix. To evaluate the performance of the method, we perform identical twin experiments using the Lorenz ’96 and Kuramoto-Sivashinsky models. Using our approach, a good approximation to the true observation error covariance can be recovered in cases where the initial estimate of the error covariance is incorrect. Spatial observation error covariances where the length scale of the true covariance changes slowly in time can also be captured. We find that using the estimated correlated observation error in the assimilation improves the analysis.

On the application of optimal wavelet filter banks for ECG signal classification

This paper discusses ECG signal classification after parametrizing the ECG waveforms in the wavelet domain. Signal decomposition using perfect reconstruction quadrature mirror filter banks can provide a very parsimonious representation of ECG signals. In the current work, the filter parameters are adjusted by a numerical optimization algorithm in order to minimize a cost function associated to the filter cut-off sharpness. The goal consists of achieving a better compromise between frequency selectivity and time resolution at each decomposition level than standard orthogonal filter banks such as those of the Daubechies and Coiflet families. Our aim is to optimally decompose the signals in the wavelet domain so that they can be subsequently used as inputs for training to a neural network classifier.

Widespread supplementary feeding in domestic gardens explains the return of reintroduced Red Kites Milvus milvus to an urban area

Reintroductions are used worldwide to mitigate biodiversity loss. One prominent case is a charismatic raptor of conservation concern, the Red Kite Milvus milvus. This species has been reintroduced across the UK over the last 25 years following its near extinction after centuries of persecution. The species was not expected to recolonize urban areas; its historical association with human settlements is attributed to scavenging on human waste and refuse, a resource now greatly reduced on the streets of modern Western cities. However, the species has become a common day-time visitor to a large conurbation centred on the town of Reading, southern England, approximately 20 km from the first English reintroduction site. Given a near-absence of breeding and roost sites, we investigated foraging opportunities and habitat associations that might explain use by Red Kites of this urban area. Surveys of discarded human foods and road-kill suggested that these could support at most 13−29 kites/day. Face-to-face surveys of a cross-section of residents revealed that 4.5% (equivalent to 4349 households) provided supplementary food for kites. Using estimates of per-household resource provision from another study, we calculated that this level is potentially sufficient to provision 142−320 kites, a substantial proportion of the total estimated to visit the conurbation each day (between 140 and 440). Road transects found positive associations between Red Kites and residential areas. We therefore suggest that the decision made by thousands of individuals to provide supplementary food for Red Kites is the primary factor explaining their day-time abundance in this urban area.

The lethal and sub-lethal consequences of entomopathogenic nematode infestation and exposure for adult pine weevils, Hylobius abietis (Coleoptera: Curculionidae)

Entomopathogenic nematodes (EPN) frequently kill their host within 1–2 days, and interest in EPN focuses mainly on their lethality. However, insects may take longer to die, or may fail to die despite being infected, but little is known about the effects of EPN infection on insects, other than death. Here we investigate both lethal and sub-lethal effects of infection by two EPN species, Steinernema carpocapsae and Heterorhabditis downesi, on adults of the large pine weevil, Hylobius abietis. Following 12 h nematode–weevil contact in peat, S. carpocapsae killed a significantly higher proportion of weevils (87–93%) than H. downesi (43–57%) at all concentrations tested. Less than 10% of weevils were dead within 2 days, and weevils continued to die for up to 10 days after exposure (LT50 of 3 days or more). In a separate experiment, live weevils dissected 6 days after a 24 h exposure to nematodes on filter paper harbored encapsulated and dead nematodes, showing that weevils could defend themselves against infection. Some live weevils also harbored live nematodes 6 days after they had been removed from the nematode infested medium. Feeding by weevils was not affected by infection with, or exposure to, either species of EPN. We discuss these results in relation to the use of EPN in biological control against H. abietis.

The composite-tendency Robert-Asselin-Williams (RAW) filter in semi-implicit integrations

Timediscretization in weatherandclimate modelsintroduces truncation errors that limit the accuracy of the simulations. Recent work has yielded a method for reducing the amplitude errors in leap-frog integrations from first-order to fifth-order.This improvement is achieved by replacing the Robert–Asselin filter with the Robert–Asselin–Williams (RAW) filter and using a linear combination of unfiltered and filtered states to compute the tendency term. The purpose of the present article is to apply the composite-tendency RAW-filtered leapfrog scheme to semi-implicit integrations. A theoretical analysis shows that the stability and accuracy are unaffected by the introduction of the implicitly treated mode. The scheme is tested in semi-implicit numerical integrations in both a simple nonlinear stiff system and a medium-complexity atmospheric general circulation model and yields substantial improvements in both cases. We conclude that the composite-tendency RAW-filtered leap-frog scheme is suitable for use in semi-implicit integrations.

The equivalent-weights particle filter in a high-dimensional system

In general, particle filters need large numbers of model runs in order to avoid filter degeneracy in high-dimensional systems. The recently proposed, fully nonlinear equivalent-weights particle filter overcomes this requirement by replacing the standard model transition density with two different proposal transition densities. The first proposal density is used to relax all particles towards the high-probability regions of state space as defined by the observations. The crucial second proposal density is then used to ensure that the majority of particles have equivalent weights at observation time. Here, the performance of the scheme in a high, 65 500 dimensional, simplified ocean model is explored. The success of the equivalent-weights particle filter in matching the true model state is shown using the mean of just 32 particles in twin experiments. It is of particular significance that this remains true even as the number and spatial variability of the observations are changed. The results from rank histograms are less easy to interpret and can be influenced considerably by the parameter values used. This article also explores the sensitivity of the performance of the scheme to the chosen parameter values and the effect of using different model error parameters in the truth compared with the ensemble model runs.

The effect of the equivalent-weights particle filter on dynamical balance in a primitive equation model

The disadvantage of the majority of data assimilation schemes is the assumption that the conditional probability density function of the state of the system given the observations [posterior probability density function (PDF)] is distributed either locally or globally as a Gaussian. The advantage, however, is that through various different mechanisms they ensure initial conditions that are predominantly in linear balance and therefore spurious gravity wave generation is suppressed. The equivalent-weights particle filter is a data assimilation scheme that allows for a representation of a potentially multimodal posterior PDF. It does this via proposal densities that lead to extra terms being added to the model equations and means the advantage of the traditional data assimilation schemes, in generating predominantly balanced initial conditions, is no longer guaranteed. This paper looks in detail at the impact the equivalent-weights particle filter has on dynamical balance and gravity wave generation in a primitive equation model. The primary conclusions are that (i) provided the model error covariance matrix imposes geostrophic balance, then each additional term required by the equivalent-weights particle filter is also geostrophically balanced; (ii) the relaxation term required to ensure the particles are in the locality of the observations has little effect on gravity waves and actually induces a reduction in gravity wave energy if sufficiently large; and (iii) the equivalent-weights term, which leads to the particles having equivalent significance in the posterior PDF, produces a change in gravity wave energy comparable to the stochastic model error. Thus, the scheme does not produce significant spurious gravity wave energy and so has potential for application in real high-dimensional geophysical applications.