Multilateral inversion of A_r, C_r and D_r basic hypergeometric series

In [Electron. J. Combin. 10 (2003), #R10], the author presented a new basic hypergeometric matrix inverse with applications to bilateral basic hypergeometric series. This matrix inversion result was directly extracted from an instance of Bailey's very-well-poised 6-psi-6 summation theorem, and involves two infinite matrices which are not lower-triangular. The present paper features three different multivariable generalizations of the above result. These are extracted from Gustafson's A_r and C_r extensions and of the author's recent A_r extension of Bailey's 6-psi-6 summation formula. By combining these new multidimensional matrix inverses with A_r and D_r extensions of Jackson's 8-phi-7 summation theorem three balanced very-well-poised 8-psi-8 summation theorems associated with the root systems A_r and C_r are derived.Comment: 24 page

A new multivariable 6-psi-6 summation formula

By multidimensional matrix inversion, combined with an A_r extension of Jackson's 8-phi-7 summation formula by Milne, a new multivariable 8-phi-7 summation is derived. By a polynomial argument this 8-phi-7 summation is transformed to another multivariable 8-phi-7 summation which, by taking a suitable limit, is reduced to a new multivariable extension of the nonterminating 6-phi-5 summation. The latter is then extended, by analytic continuation, to a new multivariable extension of Bailey's very-well-poised 6-psi-6 summation formula.Comment: 16 page

Phytoplankton community responses in a shallow lake following lanthanum-bentonite application

The release of phosphorus (P) from bed sediments to the overlying water can delay the recovery of lakes for decades following reductions in catchment contributions, preventing water quality targets being met within timeframes set out by environmental legislation (e.g. EU Water Framework Directive: WFD). Therefore supplementary solutions for restoring lakes have been explored, including the capping of sediment P sources using a lanthanum (La)-modified bentonite clay to reduce internal P loading and enhance the recovery process. Here we present results from Loch Flemington where the first long-term field trial documenting responses of phytoplankton community structure and abundance, and the UK WFD phytoplankton metric to a La-bentonite application was performed. A Before-After-Control-Impact (BACI) analysis was used to distinguish natural variability from treatment effect and confirmed significant reductions in the magnitude of summer cyanobacterial blooms in Loch Flemington, relative to the control site, following La-bentonite application. However this initial cyanobacterial response was not sustained beyond two years after application, which implied that the reduction in internal P loading was short-lived; several possible explanations for this are discussed. One reason is that this ecological quality indicator is sensitive to inter-annual variability in weather patterns, particularly summer rainfall and water temperature. Over the monitoring period, the phytoplankton community structure of Loch Flemington became less dominated by cyanobacteria and more functionally diverse. This resulted in continual improvements in the phytoplankton compositional and abundance metrics, which were not observed at the control site, and may suggest an ecological response to the sustained reduction in filterable reactive phosphorus (FRP) concentration following La-bentonite application. Overall, phytoplankton classification indicated that the lake moved from poor to moderate ecological status but did not reach the proxy water quality target (i.e. WFD Good Ecological Status) within four years of the application. As for many other shallow lakes, the effective control of internal P loading in Loch Flemington will require further implementation of both in-lake and catchment-based measures. Our work emphasizes the need for appropriate experimental design and long-term monitoring programmes, to ascertain the efficacy of intervention measures in delivering environmental improvements at the field scale

Nonlinear Differential Equations Satisfied by Certain Classical Modular Forms

A unified treatment is given of low-weight modular forms on \Gamma_0(N), N=2,3,4, that have Eisenstein series representations. For each N, certain weight-1 forms are shown to satisfy a coupled system of nonlinear differential equations, which yields a single nonlinear third-order equation, called a generalized Chazy equation. As byproducts, a table of divisor function and theta identities is generated by means of q-expansions, and a transformation law under \Gamma_0(4) for the second complete elliptic integral is derived. More generally, it is shown how Picard-Fuchs equations of triangle subgroups of PSL(2,R) which are hypergeometric equations, yield systems of nonlinear equations for weight-1 forms, and generalized Chazy equations. Each triangle group commensurable with \Gamma(1) is treated.Comment: 40 pages, final version, accepted by Manuscripta Mathematic

Delivering energy efficiency and carbon reduction schemes in England: Lessons from Green Deal Pioneer Places

Against a background of growing international and national carbon reduction legislation, the UK government introduced the “Green Deal” to deliver a significant increase in housing energy efficiency and reduction in carbon emissions. This paper reflects on one English local authority's experience delivering a programme intended to foster local interest in the Green Deal. Drawing on social surveys and pre and post Green Deal intervention interviews with five demonstrator homes (households that applied to receive a Green Deal package fully funded by the scheme, providing a test bed for the Green Deal recruitment and installation process), this paper shows that awareness and understanding of the Green Deal scheme is low. There is opposition to the cost of finance offered but a strong interest in improving household warmth and for funding improvements through payments added to the electricity bill. Demonstrator home residents perceived Green Deals had improved the warmth and quality of their home, but saving money was the primary motivator for their involvement, not increasing warmth. Whilst Green Deal has not delivered the level of success that was hoped, much can be learned from the scheme to improve future energy efficiency schemes that will be necessary to deliver emission reduction commitments

Changes in Serological Immunology Measures in UK and Kenyan Adults Post-controlled Human Malaria Infection.

Background: The timing of infection is closely determined in controlled human malaria infection (CHMI) studies, and as such they provide a unique opportunity to dissect changes in immunological responses before and after a single infection. The first Kenyan Challenge Study (KCS) (Pan African Clinical Trial Registry: PACTR20121100033272) was performed in 2013 with the aim of establishing the CHMI model in Kenya. This study used aseptic, cryopreserved, attenuated Plasmodium falciparum sporozoites administered by needle and syringe (PfSPZ Challenge) and was the first to evaluate parasite dynamics post-CHMI in individuals with varying degrees of prior exposure to malaria. Methods: We describe detailed serological and functional immunological responses pre- and post-CHMI for participants in the KCS and compare these with those from malaria-naïve UK volunteers who also underwent CHMI (VAC049) (ClinicalTrials.gov NCT01465048) using PfSPZ Challenge. We assessed antibody responses to three key blood-stage merozoite antigens [merozoite surface protein 1 (MSP1), apical membrane protein 1 (AMA1), and reticulocyte-binding protein homolog 5 (RH5)] and functional activity using two candidate measures of anti-merozoite immunity; the growth inhibition activity (GIA) assay and the antibody-dependent respiratory burst activity (ADRB) assay. Results:Clear serological differences were observed pre- and post-CHMI by ELISA between malaria-naïve UK volunteers in VAC049, and Kenyan volunteers who had prior malaria exposure. Antibodies to AMA1 and schizont extract correlated with parasite multiplication rate (PMR) post-CHMI in KCS. Serum from volunteer 110 in KCS, who demonstrated a dramatically reduced PMR in vivo, had no in vitro GIA prior to CHMI but the highest level of ADRB activity. A significant difference in ADRB activity was seen between KCS volunteers with minimal and definite prior exposure to malaria and significant increases were seen in ADRB activity post-CHMI in Kenyan volunteers. Quinine and atovaquone/proguanil, previously assumed to be removed by IgG purification, were identified as likely giving rise to aberrantly high in vitro GIA results. Conclusions: The ADRB activity assay is a promising functional assay that warrants further investigation as a measure of prior exposure to malaria and predictor of control of parasite growth. The CHMI model can be used to evaluate potential measures of naturally-acquired immunity to malaria

Human vaccination against Plasmodium vivax Duffy-binding protein induces strain-transcending antibodies

BACKGROUND. Plasmodium vivax is the most widespread human malaria geographically; however, no effective vaccine exists. Red blood cell invasion by the P. vivax merozoite depends on an interaction between the Duffy antigen receptor for chemokines (DARC) and region II of the parasite’s Duffy-binding protein (PvDBP_RII). Naturally acquired binding-inhibitory antibodies against this interaction associate with clinical immunity, but it is unknown whether these responses can be induced by human vaccination. METHODS. Safety and immunogenicity of replication-deficient chimpanzee adenovirus serotype 63 (ChAd63) and modified vaccinia virus Ankara (MVA) viral vectored vaccines targeting PvDBP_RII (Salvador I strain) were assessed in an open-label dose-escalation phase Ia study in 24 healthy UK adults. Vaccines were delivered by the intramuscular route in a ChAd63-MVA heterologous prime-boost regimen using an 8-week interval. RESULTS. Both vaccines were well tolerated and demonstrated a favorable safety profile in malaria-naive adults. PvDBP_RII–specific ex-vivo IFN-γ T cell, antibody-secreting cell, memory B cell, and serum IgG responses were observed after the MVA boost immunization. Vaccine-induced antibodies inhibited the binding of vaccine homologous and heterologous variants of recombinant PvDBP_RII to the DARC receptor, with median 50% binding-inhibition titers greater than 1:100. CONCLUSION. We have demonstrated for the first time to our knowledge that strain-transcending antibodies can be induced against the PvDBP_RII antigen by vaccination in humans. These vaccine candidates warrant further clinical evaluation of efficacy against the blood-stage P. vivax parasite

Dairy foods, calcium, and risk of breast cancer overall and for subtypes defined by estrogen receptor status: a pooled analysis of 21 cohort studies

Background: Epidemiologic studies examining the relations between dairy product and calcium intakes and breast cancer have been inconclusive, especially for tumor subtypes. Objective: To evaluate the associations between intakes of specific dairy products and calcium and risk of breast cancer overall and for subtypes defined by estrogen receptor (ER) status. Method: We pooled the individual-level data of over 1 million women who were followed for a maximum of 8-20 years across studies. Associations were evaluated for dairy product and calcium intakes and risk of incident invasive breast cancer overall (n = 37,861 cases) and by subtypes defined by ER status. Study-specific multivariable hazard ratios (HRs) were estimated and then combined using random-effects models. Results: Overall, no clear association was observed between the consumption of specific dairy foods, dietary (from foods only) calcium, and total (from foods and supplements) calcium, and risk of overall breast cancer. Although each dairy product showed a null or very weak inverse association with risk of overall breast cancer (P, test for trend >0.05 for all), differences by ER status were suggested for yogurt and cottage/ricotta cheese with associations observed for ER-negative tumors only (pooled HR = 0.90, 95% CI: 0.83, 0.98 comparing >= 60 g/d with = 25 g/d with Conclusion: Our study shows that adult dairy or calcium consumption is unlikely to associate with a higher risk of breast cancer and that higher yogurt and cottage/ricotta cheese intakes were inversely associated with the risk of ER-negative breast cancer, a less hormonally dependent subtype with poor prognosis. Future studies on fermented dairy products, earlier life exposures, ER-negative breast cancer, and different racial/ethnic populations may further elucidate the relation