Modified Semi-Classical Methods for Nonlinear Quantum Oscillations Problems

We develop a modified semi-classical approach to the approximate solution of Schrodinger's equation for certain nonlinear quantum oscillations problems. At lowest order, the Hamilton-Jacobi equation of the conventional semi-classical formalism is replaced by an inverted-potential-vanishing-energy variant thereof. Under smoothness, convexity and coercivity hypotheses on its potential energy function, we prove, using the calculus of variations together with the Banach space implicit function theorem, the existence of a global, smooth `fundamental solution'. Higher order quantum corrections, for ground and excited states, are computed through the integration of associated systems of linear transport equations, and formal expansions for the corresponding energy eigenvalues obtained by imposing smoothness on the quantum corrections to the eigenfunctions. For linear oscillators our expansions naturally truncate, reproducing the well-known solutions for the energy eigenfunctions and eigenvalues. As an application, we calculate a number of terms in the corresponding expansions for the one-dimensional anharmonic oscillators of quartic, sectic, octic, and dectic types and find that our eigenvalue expansions agree with those of Rayleigh/Schrodinger theory, whereas our wave functions more accurately capture the more-rapid-than-gaussian decay. For the quartic oscillator our results strongly suggest that the ground state energy eigenvalue expansion and its associated wave function expansion are Borel summable to yield natural candidates for the actual exact ground state solution and its energy. Our techniques for proving the existence of the crucial `fundamental solution' to the relevant Hamilton Jacobi equation admit infinite dimensional generalizations. In a parallel project we shall show how this construction can be carried out for the Yang-Mills equations in Minkowski spacetime

CAMAU Project: Research Report (April 2018)

‘Learning about Progression’ is a suite of research-based resources designed to provide evidence to support the building of learning progression frameworks in Wales. ‘Learning about Progression’ seeks to deepen our understanding of current thinking about progression and to explore different purposes that progression frameworks can serve to improve children and young people’s learning. These resources include consideration of how this evidence relates to current developments in Wales and derives a series of principles to serve as touchstones to make sure that, as practices begin to develop, they stay true to the original aspirations of A Curriculum for Wales – A Curriculum for Life. It also derives, from the review of evidence, a number of fundamental questions for all those involved in the development of progression frameworks to engage

CAMAU Project: Research Report (April 2018)

‘Learning about Progression’ is a suite of research-based resources designed to provide evidence to support the building of learning progression frameworks in Wales. ‘Learning about Progression’ seeks to deepen our understanding of current thinking about progression and to explore different purposes that progression frameworks can serve to improve children and young people’s learning. These resources include consideration of how this evidence relates to current developments in Wales and derives a series of principles to serve as touchstones to make sure that, as practices begin to develop, they stay true to the original aspirations of A Curriculum for Wales – A Curriculum for Life. It also derives, from the review of evidence, a number of fundamental questions for all those involved in the development of progression frameworks to engage

Targeting DNA Damage Response and Replication Stress in Pancreatic Cancer

Background and aims: Continuing recalcitrance to therapy cements pancreatic cancer (PC) as the most lethal malignancy, which is set to become the second leading cause of cancer death in our society. The study aim was to investigate the association between DNA damage response (DDR), replication stress and novel therapeutic response in PC to develop a biomarker driven therapeutic strategy targeting DDR and replication stress in PC. Methods: We interrogated the transcriptome, genome, proteome and functional characteristics of 61 novel PC patient-derived cell lines to define novel therapeutic strategies targeting DDR and replication stress. Validation was done in patient derived xenografts and human PC organoids. Results: Patient-derived cell lines faithfully recapitulate the epithelial component of pancreatic tumors including previously described molecular subtypes. Biomarkers of DDR deficiency, including a novel signature of homologous recombination deficiency, co-segregates with response to platinum (P < 0.001) and PARP inhibitor therapy (P < 0.001) in vitro and in vivo. We generated a novel signature of replication stress with which predicts response to ATR (P < 0.018) and WEE1 inhibitor (P < 0.029) treatment in both cell lines and human PC organoids. Replication stress was enriched in the squamous subtype of PC (P < 0.001) but not associated with DDR deficiency. Conclusions: Replication stress and DDR deficiency are independent of each other, creating opportunities for therapy in DDR proficient PC, and post-platinum therapy

SARS-CoV-2 B.1.617.2 Delta variant replication and immune evasion

Abstract: The B.1.617.2 (Delta) variant of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) was first identified in the state of Maharashtra in late 2020 and spread throughout India, outcompeting pre-existing lineages including B.1.617.1 (Kappa) and B.1.1.7 (Alpha)1. In vitro, B.1.617.2 is sixfold less sensitive to serum neutralizing antibodies from recovered individuals, and eightfold less sensitive to vaccine-elicited antibodies, compared with wild-type Wuhan-1 bearing D614G. Serum neutralizing titres against B.1.617.2 were lower in ChAdOx1 vaccinees than in BNT162b2 vaccinees. B.1.617.2 spike pseudotyped viruses exhibited compromised sensitivity to monoclonal antibodies to the receptor-binding domain and the amino-terminal domain. B.1.617.2 demonstrated higher replication efficiency than B.1.1.7 in both airway organoid and human airway epithelial systems, associated with B.1.617.2 spike being in a predominantly cleaved state compared with B.1.1.7 spike. The B.1.617.2 spike protein was able to mediate highly efficient syncytium formation that was less sensitive to inhibition by neutralizing antibody, compared with that of wild-type spike. We also observed that B.1.617.2 had higher replication and spike-mediated entry than B.1.617.1, potentially explaining the B.1.617.2 dominance. In an analysis of more than 130 SARS-CoV-2-infected health care workers across three centres in India during a period of mixed lineage circulation, we observed reduced ChAdOx1 vaccine effectiveness against B.1.617.2 relative to non-B.1.617.2, with the caveat of possible residual confounding. Compromised vaccine efficacy against the highly fit and immune-evasive B.1.617.2 Delta variant warrants continued infection control measures in the post-vaccination era