On asymptotic behavior at infinity and the finite section method for integral equations on the half-line

e consider integral equations on the half-line of the form and the finite section approximation to x obtained by replacing the infinite limit of integration by the finite limit β. We establish conditions under which, if the finite section method is stable for the original integral equation (i.e. exists and is uniformly bounded in the space of bounded continuous functions for all sufficiently large β), then it is stable also for a perturbed equation in which the kernel k is replaced by k + h. The class of perturbations allowed includes all compact and some non-compact perturbations of the integral operator. Using this result we study the stability and convergence of the finite section method in the space of continuous functions x for which ()()()=−∫∞dttxt,sk)s(x0()syβxβx()sxsp+1 is bounded. With the additional assumption that ()(tskt,sk−≤ where ()()(),qsomefor,sassOskandRLkq11>+∞→=∈− we show that the finite-section method is stable in the weighted space for ,qp≤≤0 provided it is stable on the space of bounded continuous functions. With these results we establish error bounds in weighted spaces for x - xβ and precise information on the asymptotic behaviour at infinity of x. We consider in particular the case when the integral operator is a perturbation of a Wiener-Hopf operator and illustrate this case with a Wiener-Hopf integral equation arising in acoustics.

Clare Balding: the televisual face of London 2012

This piece discusses the performance of television presenter Claire Balding during her coverage of the Olympics and Paralympics of London 2012. It suggests that her success with viewers was connected with her persona as a television personality, which combined professional skill with intimacy and immediacy. It argues that Balding represented the face of contemporary public service broadcasting – one that bridges both the BBC and Channel 4’s brand identities – through her research and authority, combined with interaction with her audience with social media.

Building resilience in the face of recurring environmental crisis in African Sahel

The present food shortages in the Horn of Africa and the West African Sahel are affecting 31 million people. Such continuing and future crises require that people in the region adapt to an increasing and potentially irreversible global sustainability challenge. Given this situation and that short-term weather and seasonal climate forecasting have limited skill for West Africa, the Rainwatch project illustrates the value of near real-time monitoring and improved communication for the unfavourable 2011 West African monsoon, the resulting severe drought-induced humanitarian impacts continuing into 2012, and their exacerbation by flooding in 2012. Rainwatch is now coupled with a boundary organization (Africa Climate Exchange, AfClix) with the aim of integrating the expertise and actions of relevant institutions, agencies and stakeholders to broker ground-based dialogue to promote resilience in the face of recurring crisis.

Social approach in preschool children with Williams syndrome: the role of the face

Background Indiscriminate social approach behaviour is a salient aspect of the Williams syndrome (WS) behavioural phenotype. The present study examines approach behaviour in preschoolers with WS and evaluates the role of the face in WS social approach behaviour. Method Ten preschoolers with WS (aged 3-6 years) and two groups of typically developing children, matched to the WS group on chronological or mental age, participated in an observed play session. The play session incorporated social and non-social components including two components that assessed approach behaviour towards strangers, one in which the stranger’s face could be seen and one in which the stranger’s face was covered. Results In response to the non-social aspects of the play session, the WS group behaved similarly to both control groups. In contrast, the preschoolers with WS were significantly more willing than either control group to engage with a stranger, even when the stranger’s face could not be seen. Conclusion The findings challenge the hypothesis that an unusual attraction to the face directly motivates social approach behaviour in individuals with WS.

Contributions of maternal and infant factors to infant responding to the Still Face paradigm: a longitudinal study

Early mother–infant interactions are characterised by periods of synchronous interaction that are interrupted by periods of mismatch; the experience of such mismatches and their subsequent repair is held to facilitate the development of infant self-regulatory capacities (Tronick, Als, Adamson, Wise, & Brazelton, 1978). Infant responding to such interactive challenge is assumed to be a function of both maternal behaviour and pre-existing infant characteristics. However, the latter has received relatively little attention. In a prospective longitudinal study of a sample comprising high and low adversity dyads (n = 122), we examined the contributions of both maternal sensitivity and neonatal irritability to infant behavioural and physiological responding to the interactive challenge of the Still Face paradigm. Results indicated that higher levels of maternal sensitivity were associated with more regulated infant behaviour during the Still Face paradigm. Neonatal irritability also predicted poorer behavioural and heart rate recovery following the Still Face challenge. Furthermore, there was an interaction such that irritable infants with insensitive mothers showed the worst behavioural outcomes. The findings highlight the importance of the interplay between maternal and infant characteristics in determining dyadic responding.

Minor structural abnormalities in the infant face disrupt neural processing: a unique window into early caregiving responses

Infant faces elicit early, specific activity in the orbitofrontal cortex (OFC), a key cortical region for reward and affective processing. A test of the causal relationship between infant facial configuration and OFC activity is provided by naturally occurring disruptions to the face structure. One such disruption is cleft lip, a small change to one facial feature, shown to disrupt parenting. Using magnetoencephalography, we investigated neural responses to infant faces with cleft lip compared with typical infant and adult faces. We found activity in the right OFC at 140 ms in response to typical infant faces but diminished activity to infant faces with cleft lip or adult faces. Activity in the right fusiform face area was of similar magnitude for typical adult and infant faces but was significantly lower for infant faces with cleft lip. This is the first evidence that a minor change to the infant face can disrupt neural activity potentially implicated in caregiving.

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.

Visual search for basic emotional expressions in autism; impaired processing of anger, fear and sadness, but a typical happy face advantage

Facial expression recognition was investigated in 20 males with high functioning autism (HFA) or Asperger syndrome (AS), compared to typically developing individuals matched for chronological age (TD CA group) and verbal and non-verbal ability (TD V/NV group). This was the first study to employ a visual search, “face in the crowd” paradigm with a HFA/AS group, which explored responses to numerous facial expressions using real-face stimuli. Results showed slower response times for processing fear, anger and sad expressions in the HFA/AS group, relative to the TD CA group, but not the TD V/NV group. Reponses to happy, disgust and surprise expressions showed no group differences. Results are discussed with reference to the amygdala theory of autism.

High-level face adaptation without awareness

When a visual stimulus is suppressed from awareness, processing of the suppressed image is necessarily reduced. Although adaptation to simple image properties such as orientation still occurs, adaptation to high-level properties such as face identity is eliminated. Here we show that emotional facial expression continues to be processed even under complete suppression, as indexed by substantial facial expression aftereffects.

Stated willingness-to-pay for organic fruit and pesticide ban: an evaluation using both web-based and face-to-face interviewing

Income growth in highly industrialised countries has resulted in consumer choice of foodstuffs no longer being primarily influenced by basic factors such as price and organoleptic features. From this perspective, the present study sets out to evaluate how and to what extent consumer choice is influenced by the possible negative effects on health and environment caused by the consumption of fruit containing deposits of pesticides and chemical products. The study describes the results of a survey which explores and estimates consumer willingness to pay in two forms: a yearly contribution for the abolition of the use of pesticides on fruit, and a premium price for organically grown apples guaranteed by a certified label. The same questionnaire was administered to two samples. The first was a conventional face-to-face survey of customers of large retail outlets located around Bologna (Italy); the second was an Internet sample. The discrete choice data were analysed by means of probit and tobit models to estimate the utility consumers attribute to organically grown fruit and to a pesticide ban. The research also addresses questions of validity and representativeness as a fundamental problem in web-based surveys.

Half-remembered quotations from mostly forgotten speeches: the limits of Labour’s European policy discourse

This article uses discourse analysis to study the continuities in British foreign policy thinking within the Labour party from the 1960s to the present day. Using representative extracts from speeches by Hugh Gaitskell, Harold Wilson, Tony Blair and Gordon Brown, it identifies the ideational consis- tencies in the leaders’ attitudes to: Empire; federalism in the EEC/EU; and laying down conditions that have to be met before any constructive engagement with ‘Europe’ can be countenanced. We argue that these consistencies, spanning a 50-year period, exemplify a certain stagnation both within Labour’s European discourses and within British foreign policy thinking more widely. We develop the idea that Labour party thinking has been crucially framed by both small ‘c’ conser- vative and upper-case Conservative ideology, popularised by Winston Churchill in his ‘three circles’ model of British foreign policy.