Algebraic entropy and the space of initial values for discrete dynamical systems

A method to calculate the algebraic entropy of a mapping which can be lifted to an isomorphism of a suitable rational surfaces (the space of initial values) are presented. It is shown that the degree of the $n$th iterate of such a mapping is given by its action on the Picard group of the space of initial values. It is also shown that the degree of the $n$th iterate of every Painlev\'e equation in sakai's list is at most $O(n^2)$ and therefore its algebraic entropy is zero.Comment: 10 pages, pLatex fil

Gopakumar-Vafa invariants via vanishing cycles

In this paper, we propose an ansatz for defining Gopakumar-Vafa invariants of Calabi-Yau threefolds, using perverse sheaves of vanishing cycles. Our proposal is a modification of a recent approach of Kiem-Li, which is itself based on earlier ideas of Hosono-Saito-Takahashi. We conjecture that these invariants are equivalent to other curve-counting theories such as Gromov-Witten theory and Pandharipande-Thomas theory. Our main theorem is that, for local surfaces, our invariants agree with PT invariants for irreducible one-cycles. We also give a counter-example to the Kiem-Li conjectures, where our invariants match the predicted answer. Finally, we give examples where our invariant matches the expected answer in cases where the cycle is non-reduced, non-planar, or non-primitive.Comment: 63 pages, many improvements of the exposition following referee comments, final version to appear in Inventione

Towards actionable international comparisons of health system performance: expert revision of the OECD framework and quality indicators

Objective To review and update the conceptual framework, indicator content and research priorities of the Organisation for Economic Cooperation and Development's (OECD) Health Care Quality Indicators (HCQI) project, after a decade of collaborative work. Design A structured assessment was carried out using a modified Delphi approach, followed by a consensus meeting, to assess the suite of HCQI for international comparisons, agree on revisions to the original framework and set priorities for research and development. Setting International group of countries participating to OECD projects. Participants Members of the OECD HCQI expert group. Results A reference matrix, based on a revised performance framework, was used to map and assess all seventy HCQI routinely calculated by the OECD expert group. A total of 21 indicators were agreed to be excluded, due to the following concerns: (i) relevance, (ii) international comparability, particularly where heterogeneous coding practices might induce bias, (iii) feasibility, when the number of countries able to report was limited and the added value did not justify sustained effort and (iv) actionability, for indicators that were unlikely to improve on the basis of targeted policy interventions. Conclusions The revised OECD framework for HCQI represents a new milestone of a long-standing international collaboration among a group of countries committed to building common ground for performance measurement. The expert group believes that the continuation of this work is paramount to provide decision makers with a validated toolbox to directly act on quality improvement strategie

On the Picard group of Enriques surfaces

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/46224/1/208_2005_Article_BF01456135.pd

Forty years on: clathrin-coated pits continue to fascinate

Clathrin mediated endocytosis (CME) is a fundamental process in cell biology and has been extensively investigated throughout the last several decades. Every cell biologist learns about it at some point during their education and the beauty of this process has led many of us to go deeper and make it the topic of our own research. Great progress has been made towards elucidating the mechanisms of CME and the field is becoming increasingly complex with several hundred new publications every year. This makes it easy to get lost in the vast amount of literature and to forget about the fundamentals of the field, based on the careful interpretation of simple observations made over 40 years ago. A study performed by Anderson, Brown and Goldstein in 1977 (Anderson et al., 1977) is a prime example of this. We therefore want to take a step back and examine how this seminal study was pivotal to our understanding of CME and its progression into ever increasing complexity over the last four decades

A genetic cause of Alzheimer disease: mechanistic insights from Down syndrome

Down syndrome, caused by an extra copy of chromosome 21, is associated with a greatly increased risk of early onset Alzheimer disease. It is thought that this risk is conferred by the presence of three copies of the gene encoding amyloid precursor protein (APP), an Alzheimer risk factor, although the possession of extra copies of other chromosome 21 genes may also play a role. Further study of the mechanisms underlying the development of Alzheimer disease in Down syndrome could provide insights into the mechanisms that cause dementia in the general population

Smooth rational curves on Enriques surfaces

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/46225/1/208_2005_Article_BF01455565.pd

Compactifications of the moduli space of plane quartics and two lines

We study the moduli space of triples (C,L₁,L₂) consisting of quartic curves C and lines L₁ and L₂. Specifically, we construct and compactify the moduli space in two ways: via geometric invariant theory (GIT) and by using the period map of certain lattice polarized K3 surfaces. The GIT construction depends on two parameters t₁ and t₂ which correspond to the choice of a linearization. For t₁=t₂=1 we describe the GIT moduli explicitly and relate it to the construction via K3 surfaces

Synaptic vesicle recycling is unaffected in the Ts65Dn mouse model of Down syndrome

Down syndrome (DS) is the most common genetic cause of intellectual disability, and arises from trisomy of human chromosome 21. Accumulating evidence from studies of both DS patient tissue and mouse models has suggested that synaptic dysfunction is a key factor in the disorder. The presence of several genes within the DS trisomy that are either directly or indirectly linked to synaptic vesicle (SV) endocytosis suggested that presynaptic dysfunction could underlie some of these synaptic defects. Therefore we determined whether SV recycling was altered in neurons from the Ts65Dn mouse, the best characterised model of DS to date. We found that SV exocytosis, the size of the SV recycling pool, clathrin-mediated endocytosis, activity-dependent bulk endocytosis and SV generation from bulk endosomes were all unaffected by the presence of the Ts65Dn trisomy. These results were obtained using battery of complementary assays employing genetically-encoded fluorescent reporters of SV cargo trafficking, and fluorescent and morphological assays of fluid-phase uptake in primary neuronal culture. The absence of presynaptic dysfunction in central nerve terminals of the Ts65Dn mouse suggests that future research should focus on the established alterations in excitatory / inhibitory balance as a potential route for future pharmacotherapy