A mathematical theory of stochastic microlensing. II. Random images, shear, and the Kac-Rice formula

Continuing our development of a mathematical theory of stochastic microlensing, we study the random shear and expected number of random lensed images of different types. In particular, we characterize the first three leading terms in the asymptotic expression of the joint probability density function (pdf) of the random shear tensor due to point masses in the limit of an infinite number of stars. Up to this order, the pdf depends on the magnitude of the shear tensor, the optical depth, and the mean number of stars through a combination of radial position and the star's mass. As a consequence, the pdf's of the shear components are seen to converge, in the limit of an infinite number of stars, to shifted Cauchy distributions, which shows that the shear components have heavy tails in that limit. The asymptotic pdf of the shear magnitude in the limit of an infinite number of stars is also presented. All the results on the random microlensing shear are given for a general point in the lens plane. Extending to the general random distributions (not necessarily uniform) of the lenses, we employ the Kac-Rice formula and Morse theory to deduce general formulas for the expected total number of images and the expected number of saddle images. We further generalize these results by considering random sources defined on a countable compact covering of the light source plane. This is done to introduce the notion of global expected number of positive parity images due to a general lensing map. Applying the result to microlensing, we calculate the asymptotic global expected number of minimum images in the limit of an infinite number of stars, where the stars are uniformly distributed. This global expectation is bounded, while the global expected number of images and the global expected number of saddle images diverge as the order of the number of stars. © 2009 American Institute of Physics.

Designing Climate Mitigation Policy

This paper provides an exhaustive review of critical issues in the design of climate mitigation policy by pulling together key findings and controversies from diverse literatures on mitigation costs, damage valuation, policy instrument choice, technological innovation, and international climate policy. We begin with the broadest issue of how high assessments suggest the near and medium term price on greenhouse gases would need to be, both under cost-effective stabilization of global climate and under net benefit maximization or Pigouvian emissions pricing. The remainder of the paper focuses on the appropriate scope of regulation, issues in policy instrument choice, complementary technology policy, and international policy architectures.

Defective lymphocyte chemotaxis in beta-arrestin2- and GRK6-deficient mice.

Lymphocyte chemotaxis is a complex process by which cells move within tissues and across barriers such as vascular endothelium and is usually stimulated by chemokines such as stromal cell-derived factor-1 (CXCL12) acting via G protein-coupled receptors. Because members of this receptor family are regulated ("desensitized") by G protein-coupled receptor kinase (GRK)-mediated receptor phosphorylation and beta-arrestin binding, we examined signaling and chemotactic responses in splenocytes derived from knockout mice deficient in various beta-arrestins and GRKs, with the expectation that these responses might be enhanced. Knockouts of beta-arrestin2, GRK5, and GRK6 were examined because all three proteins are expressed at high levels in purified mouse CD3+ T and B220+ B splenocytes. CXCL12 stimulation of membrane GTPase activity was unaffected in splenocytes derived from GRK5-deficient mice but was increased in splenocytes from the beta-arrestin2- and GRK6-deficient animals. Surprisingly, however, both T and B cells from beta-arrestin2-deficient animals and T cells from GRK6-deficient animals were strikingly impaired in their ability to respond to CXCL12 both in transwell migration assays and in transendothelial migration assays. Chemotactic responses of lymphocytes from GRK5-deficient mice were unaffected. Thus, these results indicate that beta-arrestin2 and GRK6 actually play positive regulatory roles in mediating the chemotactic responses of T and B lymphocytes to CXCL12.

People who expect to enter psychotherapy are prone to believing that they have forgotten memories of childhood trauma and abuse.

We asked 1004 undergraduates to estimate both the probability that they would enter therapy and the probability that they experienced but could not remember incidents of potentially life-threatening childhood traumas or physical and sexual abuse. We found a linear relation between the expectation of entering therapy and the belief that one had, but cannot now remember, childhood trauma and abuse. Thus individuals who are prone to seek psychotherapy are also prone to accept a suggested memory of childhood trauma or abuse as fitting their expectations. In multiple regressions predicting the probability of forgotten memories of childhood traumas and abuse, the expectation of entering therapy remained as a substantial predictor when self-report measures of mood, anxiety, post-traumatic stress disorder symptom severity, and trauma exposure were included.

Opportunistic Control Over Shared Wireless Channels

© 2015 IEEE.We consider a wireless control architecture with multiple control loops over a shared wireless medium. A scheduler observes the random channel conditions that each control system experiences over the shared medium and opportunistically selects systems to transmit at a set of non-overlapping frequencies. The transmit power of each system also adapts to channel conditions and determines the probability of successfully receiving and closing the loop. We formulate the optimal design of channel-aware scheduling and power allocation that minimize the total power consumption while meeting control performance requirements for all systems. In particular, it is required that for each control system a given Lyapunov function decreases at a specified rate in expectation over the random channel conditions. We develop an offline algorithm to find the optimal communication design, as well as an online protocol which selects scheduling and power variables based on a random observed channel sequence and converges almost surely to the optimal operating point. Simulations illustrate the power savings of our approach compared to other non-channel-aware schemes.

Entwicklungswege Jugendlicher zwischen Transition und Moratorium

Bisher stehen sich in der deutschen Jugendforschung mit dem Transitions- und Moratoriumsgedanken zwei Konzepte zur Beschreibung der Jugendphase gegenüber, deren ergänzender Charakter bisher kaum Beachtung gefunden hat. Um eine Verknüpfung leisten zu können, sollen beide Auffassungen von Jugend kurz skizziert und in die Beschreibung einer Typologie jugendlicher Entwicklungswege überführt werden. Im zweiten Teil werden auf der Basis von Sekundäranalysen empirische Evidenzen aufgezeigt, die eine Vertiefung der theoretischen Herangehensweise aussichtsreich erscheinen lassen. (DIPF/Orig.)

Automatic code generation of overlapped communications in a parallelisation tool

This paper addresses the exploitation of overlapping communication with calculation within parallel FORTRAN 77 codes for computational fluid dynamics (CFD) and computational structured dynamics (CSD). The obvious objective is to overlap interprocessor communication with calculation on each processor in a distributed memory parallel system and so improve the efficiency of the parallel implementation. A general strategy for converting synchronous to overlapped communication is presented together with tools to enable its automatic implementation in FORTRAN 77 codes. This strategy is then implemented within the parallelisation toolkit, CAPTools, to facilitate the automatic generation of parallel code with overlapped communications. The success of these tools are demonstrated on two codes from the NAS-PAR and PERFECT benchmark suites. In each case, the tools produce parallel code with overlapped communications which is as good as that which could be generated manually. The parallel performance of the codes also improve in line with expectation.

Scheduling parallel dedicated machines with the speeding-up resource

We consider a problem of scheduling jobs on m parallel machines. The machines are dedicated, i.e., for each job the processing machine is known in advance. We mainly concentrate on the model in which at any time there is one unit of an additional resource. Any job may be assigned the resource and this reduces its processing time. A job that is given the resource uses it at each time of its processing. No two jobs are allowed to use the resource simultaneously. The objective is to minimize the makespan. We prove that the two-machine problem is NP-hard in the ordinary sense, describe a pseudopolynomial dynamic programming algorithm and convert it into an FPTAS. For the problem with an arbitrary number of machines we present an algorithm with a worst-case ratio close to 3/2, and close to 3, if a job can be given several units of the resource. For the problem with a fixed number of machines we give a PTAS. Virtually all algorithms rely on a certain variant of the linear knapsack problem (maximization, minimization, multiple-choice, bicriteria). © 2008 Wiley Periodicals, Inc. Naval Research Logistics, 2008

Casual link and consensual arrangements in estoppel

Analyses the Court of Appeal decision in Powell v Benney on whether in a claim of proprietary estoppel the expectation of a couple that they would receive two properties owned, and promised to them, by a deceased friend was out of proportion to the detriment suffered by them in looking after the friend and improving his properties for their own use. Considers: (1) the approach to be taken to the requirement of a causal link between the assurance given and the conduct constituting the detriment relied on; and (2) consensual arrangements and estoppel equity.

Trust, leadership and economic necessity in post-compulsory education

Trust is a complex concept that has increasingly been debated in academic research (Kramer and Tyler, 1996). Research on 'trust and leadership' (Caldwell and Hayes, 2007) has suggested, unsurprisingly, that leadership behaviours influence 'follower' perceptions of leaders' trustworthiness. The development of 'ethical stewardship' amongst leaders may foster high trust situations (Caldwell, Hayes, Karri and Bernal, 2008), yet studies on the erosion of teacher professionalism in UK post-compulsory education have highlighted the distrust that arguably accompanies 'new managerialism', performativity and surveillance within a climate of economic rationalisation established by recent deterministic skills-focused government agendas for education (Avis, 2003; Codd, 1999, Deem, 2004, DFES, 2006). Given the shift from community to commercialism identified by Collinson and Collinson (2005) in a global economic environment characterised by uncertainty and rapid change, trust is, simultaneously, increasingly important and progressively both more fragile and limited in a post compulsory education sector dominated by skills-based targets and inspection demands. Building on such prior studies, this conference paper reports on the analysis of findings from a 2007-8 funded research study on 'trust and leadership' carried out in post-compulsory education. The research project collected and analysed case study interview and survey data from the lifelong learning sector, including selected tertiary, further and higher education (FE and HE) institutions. We interviewed 18 UK respondents from HE and FE, including principals, middle managers, first line managers, lecturers and researchers, supplementing and cross-checking this with a small number of survey responses (11) on 'trust and leadership' and a larger number (241) of survey responses on more generalised leadership issues in post-compulsory education. A range of facilitators and enablers of trust and their relationship to leadership were identified and investigated. The research analysed the ways in which interviewees defined the concept of 'trust' and the extent to which they identified that trust was a mediating factor affecting leadership and organisational performance. Prior literature indicates that trust involves a psychological state in which, despite dependency, risk and vulnerability, trustors have some degree of confident expectation that trustees will behave in benevolent rather than detrimental ways. The project confirmed the views of prior researchers (Mayer, Davis and Schoorman, 1995) that, since trust inevitably involves potential betrayal, estimations of leadership 'trustworthiness' are based on followers' cognitive and affective perceptions of the reliability, competence, benevolence and reputation of leaders. During the course of the interviews it also became clear that some interviewees were being managed in more or less transaction-focused, performative, audit-dominated cultures in which trust was not regarded as particularly important: while 'cautious trust' existed, collegiality flourished only marginally in small teams. Economic necessity and survival were key factors influencing leadership and employee behaviours, while an increasing distance was reported between senior managers and their staff. The paper reflects on the nature of the public sector leadership and management environment in post-compulsory education reported by interviewees and survey respondents. Leadership behaviours to build trust are recommended, including effective communication, honesty, integrity, authenticity, reliability and openness. It was generally felt that building trust was difficult in an educational environment largely determined by economic necessity and performativity. Yet, despite this, the researchers did identify a number of examples of high trust leadership situations that are worthy of emulation.

Student Experience of E-Learning (SEEL)

The Student Experience of E-Learning project (SEEL) was an institutional response to the university’s HEA/JISC Benchmarking exercise (Ryan and Kandler, 2007). The study had a social constructivist approach which recognised the importance of listening to the student voice (JISC 2007) within the University of Greenwich context, to interpret the student experience of e-learning. Nearly 1000 students responded to an online survey on their approaches to, and their use of, learning technology. The quantitative and qualitative questions used included identifying study patterns, using specific online tools, within the context of learning and beyond, and student’s attitudes towards using e-learning in their studies. Initially, individual responses to questions were analysed in depth, giving a general indication of the student experience. Further depth was applied through a filtering mechanism, beginning with a cross-slicing of individual student responses to produce cameos. Audio logs and individual interviews were drawn from these cameos. Analysis of the cameos is in progress but has already revealed some unexpected results. There was a mismatch between students’ expectations of the university’s use of technology and their experiences and awareness of its possible use in other contexts. Students recognised the importance of social interaction as a vehicle for learning (Vygotsky 1978, Bruner 2006) but expressed polarised views on the use of social networking sites such as Facebook for e-learning. Their experiences in commercial contexts led them to see the university VLE as unimaginative and the tutors’ use of it as lacking in vision. Whereas analysis of the individual questions provided a limited picture, the cameos gave a truer reflection of the students lived experiences and identified a gulf between the university’s provision and the students’ expectation of e-learning and their customary use of technology. However it is recognised that the very nature of an online survey necessarily excludes students who chose not to engage, either through lack of skills or through disillusionment and this would constitute a separate area for study.

A thematic cost-benefit analysis of a marine protected area

The implementation of Marine Protected Areas (MPAs) is ultimately a social endeavour to sustain or improve human well-being via the conservation of marine ecosystems. The degree to which ecological gains are realised can depend upon how economic, ecological and social costs (negative impacts) and benefits (positive impacts) are included in the designation and management process. Without the support of key stakeholder groups whose user rights have been affected by the creation of an MPA, human impacts cannot be reduced. This study analyses a three year dataset to understand the themes associated with the economic, environmental and social costs and benefits of an MPA in Lyme Bay, United Kingdom (UK) following its establishment in 2008. Methodologically, the paper presents an ecosystem based management framework for analysing costs and benefits. Two hundred and forty one individuals were interviewed via questionnaire between 2008 and 2010 to determine perceptions and the level of support towards the MPA. Results reveal that despite the contentious manner in which this MPA was established, support for the MPA is strong amongst the majority of stakeholder groups. The level of support and the reasons given for support vary between stakeholder groups. Overall, the stakeholders perceive the social, economic and environmental benefits of the MPA to outweigh the perceived costs. There have been clear social costs of the MPA policy and these have been borne by mobile and static gear fishermen and charter boat operators. Local support for this MPA bodes well for the development of a network of MPAs around the UK coast under the United Kingdom Marine and Coastal Access Act 2009. However, this initial optimism is at risk if stakeholder expectation is not managed and the management vacuum is not filled.

Monsoon oscillations regulate fertility of the Red Sea

Tropical ocean ecosystems are predicted to become warmer, more saline, and less fertile in a future Earth. The Red Sea, one of the warmest and most saline environments in the world, may afford insights into the function of the tropical ocean ecosystem in a changing planet. We show that the concentration of chlorophyll and the duration of the phytoplankton growing season in the Red Sea are controlled by the strength of the winter Arabian monsoon (through horizontal advection of fertile waters from the Indian Ocean). Furthermore, and contrary to expectation, in the last decade (1998–2010) the winter Red Sea phytoplankton biomass has increased by 75% during prolonged positive phases of the Multivariate El Niño–Southern Oscillation Index. A new mechanism is reported, revealing the synergy of monsoon and climate in regulating Red Sea greenness.

Assessing the conservation status of marine habitats: thoughts from a sandflat on the Isles of Scilly.

Statutory monitoring of the fauna of the ‘mudflats and sandflats not covered by seawater at low tide’ biotope complex on St Martin’s Flats, a part of the Isles of Scilly Complex Special Area of Conservation, was undertaken in 2000, 2004 and 2009. The targets set by Natural England for “characteristic biotopes” were that “composite species, abundance and diversity should not deviate significantly from an established baseline, subject to natural change”. The three specified biotopes could not be distinguished, and instead three assemblages were subjectively defined based on sediment surface features. There were statistically significant natural changes in diversity and species composition between years, especially in the association initially characterized by the razor-clam Ensis, and possible reasons for this are discussed. It is suggested that setting fixed local limits on natural variability is almost always impractical. Two possible approaches to distinguishing between natural and anthropogenic changes are suggested; a change in ecological condition as indicated by AMBI scores, and a significant change in average taxonomic distinctness (Δ+) compared with expectation. The determination of species biomasses as well as abundances might also open more possibilities for assessment. The practice of setting objectives for a marine SAC feature that include the range and number of biotopes cannot be supported, in view the difficulty in ascribing assemblages to recognised biotopes. A more realistic definition of species assemblages might best be gained from examination of the species that consistently make a substantial contribution to the Bray Curtis similarity among samples collected from specific sites.

Using WebCT to Support a Community of Practice

Reflecting a view of “teaching as both an intellectual and practical activity” the Queen’s University Bachelor of Education program has multi-week in-school practicum sessions separated by periods of on-campus course work. The expectation is that teacher candidates will bring together theory and practice as they reflect upon their daily classroom experiences. The reality often is that, while isolated from the university environment and caught up in the pressures of teaching, little deep reflection takes place. For reflection and critical examination of experience to occur, teacher candidates need to share and discuss on a daily basis their practice teaching experience. For the past few years, students in my secondary school mathematics curriculum course, through a WebCT based conference, have been provided, while away from campus, with a place for on-going sharing of teaching stories and dilemmas. In the Fall of 2004 eight-five percent of the class took part in the discussions, posting a total of 667 messages over a 9 week period. In an effort to increase the value of this practicum conference we have analysed the topic threads arising in the conversation, surveyed the participants concerning their impressions of the sharing experience, and conducted in-depth interviews with a sampling of the class. This session will present the results of this study and provide an opportunity to discuss ways in which an online discussion can support the building of community and the exchange of experience while students in professional programs are disbursed in practice/clinical settings.