The Euler number of OGradys 10-dimensional symplectic manifold

Wir berechnen die Eulerzahl der 10-dimensionalen exzeptionellen irreduziblen symplektischen Mannigfaltigkeit, die von O Grady konstruiert wurde. Die Idee besteht darin, zunächst eine Lagrangefaserung zu konstruieren und dann die Eulerzahlen der Fasern zu berechnen. Es stellt sich heraus, dass fast alle Fasern die Eulerzahl 0 haben, und deswegen reduziert sich das Problem auf die Berechnung der Eulerzahlen der übrigen Fasern. Diese Fasern sind Modulräume von halbstabilen Garben auf singulären Kurven. Der Hauptteil dieser Dissertation ist der Berechnung der Eulerzahlen dieser Modulräume gewidmet. Diese Resultate sind von unabhängigem Interesse.

On the Chern number of I-admissible filtrations of ideals

Let I be an m-primary ideal of a Noetherian local ring (R, m) of positive dimension. The coefficient e(1)(I) of the Hilbert polynomial of an I-admissible filtration I is called the Chern number of I. A formula for the Chern number has been derived involving the Euler characteristic of subcomplexes of a Koszul complex. Specific formulas for the Chern number have been given in local rings of dimension at most two. These have been used to provide new and unified proofs of several results about e(1)(I).

Static analysis of Euler-Bernoulli beams with multiple unilateral cracks under combined axial and transverse loads

The paper deals with the static analysis of pre-damaged Euler-Bernoulli beams with any number of unilateral cracks and subjected to tensile or compression forces combined with arbitrary transverse loads. The mathematical representation of cracks with a bilateral behaviour (i.e. always open) via Dirac delta functions is extended by introducing a convenient switching variable, which allows each crack to be open or closed depending on the sign of the axial strain at the crack centre. The proposed model leads to analytical solutions, which depend on four integration constants (to be computed by enforcing the boundary conditions) along with the Boolean switching variables associated with the cracks (whose role is to turn on and off the additional flexibility due to the presence of the cracks). An efficient computational procedure is also presented and numerically validated. For this purpose, the proposed approach is applied to two pre-damaged beams, with different damage and loading conditions, and the results so obtained are compared against those given by a standard finite element code (in which the correct opening of the cracks is pre-assigned), always showing a perfect agreement. © 2013 Elsevier Ltd. All rights reserved.

Smoothing a Discrete Hazard Function for the Number of Patients Colonized with Methicillin-Resistance Staphylococcus Aureus in an Intensive Care Unit

A new method for estimating the time to colonization of Methicillin-resistant Staphylococcus Aureus (MRSA) patients is developed in this paper. The time to colonization of MRSA is modelled using a Bayesian smoothing approach for the hazard function. There are two prior models discussed in this paper: the first difference prior and the second difference prior. The second difference prior model gives smoother estimates of the hazard functions and, when applied to data from an intensive care unit (ICU), clearly shows increasing hazard up to day 13, then a decreasing hazard. The results clearly demonstrate that the hazard is not constant and provide a useful quantification of the effect of length of stay on the risk of MRSA colonization which provides useful insight.

Measuring episodic memory: A novel approach with an indefinite number of alternative forms

Both clinical practice and clinical research settings can require successive administrations of a memory test, particularly when following the trajectory of suspected memory decline in older adults. However, relatively few verbal episodic memory tests have alternative forms. We set out to create a broad based memory test to allow for the use of an essentially unlimited number of alternative forms. Four tasks for inclusion in such a test were developed. These tasks varied the requirement for recall as opposed to recognition, the need to form an association between unrelated words, and the need to discriminate the most recent list from earlier lists, all of which proved useful. A total of 115 participants completed the battery of tests and were used to show that the test could differentiate between older and younger adults; a sub-sample of 73 participants completed alternative forms of the tests to determine test-retest reliability and the amount of learning to learn.

Scaling for the Prandtl number of the natural convection boundary layer of an inclined flat plate under uniform surface heat flux

An improved scaling analysis and direct numerical simulations are performed for the unsteady natural convection boundary layer adjacent to a downward facing inclined plate with uniform heat flux. The development of the thermal or viscous boundary layers may be classified into three distinct stages: a start-up stage, a transitional stage and a steady stage, which can be clearly identified in the analytical as well as the numerical results. Previous scaling shows that the existing scaling laws of the boundary layer thickness, velocity and steady state time scale for the natural convection flow on a heated plate of uniform heat flux provide a very poor prediction of the Prandtl number dependency of the flow. However, those scalings perform very well with Rayleigh number and aspect ratio dependency. In this study, a modified Prandtl number scaling is developed using a triple layer integral approach for Pr > 1. It is seen that in comparison to the direct numerical simulations, the modified scaling performs considerably better than the previous scaling.

A mixed-method study to investigate the relationship between the number of social support people present during labour, women’s perceptions and birth outcomes

The birth of a baby is a significant event for women and their families, with the event being influenced by the prevailing social and cultural context. Historically, women throughout the world have given birth at home assisted by other women who helped them cope with the stress of labour and birth. In the middle of the twentieth century, the togetherness, caring and support that were provided within the social and cultural context of childbirth began to change; women in most developed countries, and to some extent in developing countries, laboured and gave birth in institutions that isolated them from the support of family and friends. This practice is referred to as the medical model of childbirth and, over time, birthing within this model has come to be viewed by women as a dehumanising experience. In an attempt to secure a more supportive experience, women began to demand the presence of a supportive companion; namely their partner. This event became the catalyst for a number of studies focusing on different types of support providers and their contribution to the phenomenon of social support during labour. More recently, it has become a common practice for some women to be supported during labour by a number of people from their social network. However, research on the influence of such supportive people on women’s experience of labour and birth and on birth outcomes is scarce. The aim of this study is to examine the influence of various support arrangements from a woman’s family and social network on her experience of labour and birth and on birth outcomes. The mixed-method study was conducted to answer three research questions: 1. Do women with more than one support person present during labour and birth have similar perceptions and experiences of support compared to women with one support person? 2. Do women with more than one support person present during labour and birth have similar birth outcomes compared to women with one support person? 3. Do women with different types of support providers during labour and birth have similar birth outcomes? Methods Phase one of this study developed, pilot tested and administered a newly developed instrument designed to measure women’s perceptions of supportive behaviours provided during labour. Specific birth outcome data were extracted from the medical records. Phase two consisted of in-depth interviews with a sample of women who had completed the survey. Results: The results identified a statistically significant relationship between women’s perceptions of social support and the number of support providers: women supported by one person only rated the supportive behaviours of that person more highly compared to women who were supported by a number of people. The results also identified that women supported by one person used less analgesia. An additional qualitative finding was that some women sacrificed the support of female relatives at the request of their partners. Conclusion: By using a mixed-method approach, this study found that women were selective in their choice of support providers, as they chose individuals with whom they had an enduring affectionate attachment. Women place more emphasis on a support person’s ability to fulfil their attachment needs of close proximity and a sense of security and safety, rather than their ability to provide the expected functional supportive behaviours.

History behind the IVF egg: Are women's comprehensive histories associated with the number of eggs collected, or fertilised normally, from repeated IVF cycles? [abstract]

Most studies of in vitro fertilisation (IVF) outcomes use cycle-based data and fail to account for women who use repeated IVF cycles. The objective of this study was to examine the association between the number of eggs collected (EC) and the percentage fertilised normally, and women’s self-reported medical, personal and social histories. This study involved a crosssectional survey of infertile women (aged 27-46 years) recruited from four privately-owned fertility clinics located in major cities of Australia. Regression modeling was used to estimate the mean EC and mean percentage of eggs fertilised normally: adjusted for age at EC. Appropriate statistical methods were used to take account of repeated IVF cycles by the same women. Among 121 participants who returned the survey and completed 286 IVF cycles, the mean age at EC was 35.2 years (SD 4.5). Women’s age at EC was strongly associated with the number of EC: <30 years, 11.7 EC; 30.0-< 35 years, 10.6 EC; 35.0-<40.0 years, 7.3 EC; 40.0+ years, 8.1 EC; p<.0001. Prolonged use of oral contraceptives was associated with lower numbers of EC: never used, 14.6 EC; 0-2 years, 11.7 EC; 3-5 years, 8.5 EC; 6þ years, 8.2 EC; p=.04. Polycystic ovary syndrome (PCOS) was associated with more EC: have PCOS, 11.5 EC; no, 8.3 EC; p=.01. Occupational exposures may be detrimental to normal fertilisation: professional roles, 58.8%; trade and service roles, 51.8%; manual and other roles, 63.3%; p=.02. In conclusion, women’s age remains the most significant characteristic associated with EC but not the percentage of eggs fertilised normally.

Adaptive sizing of populations and number of islands in distributed genetic algorithms

Deciding the appropriate population size and number of is- lands for distributed island-model genetic algorithms is often critical to the algorithm’s success. This paper outlines a method that automatically searches for good combinations of island population sizes and the number of islands. The method is based on a race between competing parameter sets, and collaborative seeding of new parameter sets. This method is applicable to any problem, and makes distributed genetic algorithms easier to use by reducing the number of user-set parameters. The experimental results show that the proposed method robustly and reliably finds population and islands settings that are comparable to those found with traditional trial-and-error approaches.

Towards Bayesian experimental design for nonlinear models that require a large number of sampling times

The use of Bayesian methodologies for solving optimal experimental design problems has increased. Many of these methods have been found to be computationally intensive for design problems that require a large number of design points. A simulation-based approach that can be used to solve optimal design problems in which one is interested in finding a large number of (near) optimal design points for a small number of design variables is presented. The approach involves the use of lower dimensional parameterisations that consist of a few design variables, which generate multiple design points. Using this approach, one simply has to search over a few design variables, rather than searching over a large number of optimal design points, thus providing substantial computational savings. The methodologies are demonstrated on four applications, including the selection of sampling times for pharmacokinetic and heat transfer studies, and involve nonlinear models. Several Bayesian design criteria are also compared and contrasted, as well as several different lower dimensional parameterisation schemes for generating the many design points.

Resequencing and fine-mapping of the chromosome 12q13-14 locus associated with multiple sclerosis refines the number of implicated genes

Multiple sclerosis (MS) is a common chronic inflammatory disease of the central nervous system. Susceptibility to the disease is affected by both environmental and genetic factors. Genetic factors include haplotypes in the histocompatibility complex (MHC) and over 50 non-MHC loci reported by genome-wide association studies. Amongst these, we previously reported polymorphisms in chromosome 12q13-14 with a protective effect in individuals of European descent. This locus spans 288 kb and contains 17 genes, including several candidate genes which have potentially significant pathogenic and therapeutic implications. In this study, we aimed to fine-map this locus. We have implemented a two-phase study: a variant discovery phase where we have used next-generation sequencing and two target-enrichment strategies [long-range polymerase chain reaction (PCR) and Nimblegen's solution phase hybridization capture] in pools of 25 samples; and a genotyping phase where we genotyped 712 variants in 3577 healthy controls and 3269 MS patients. This study confirmed the association (rs2069502, P = 9.9 × 10−11, OR = 0.787) and narrowed down the locus of association to an 86.5 kb region. Although the study was unable to pinpoint the key-associated variant, we have identified a 42 (genotyped and imputed) single-nucleotide polymorphism haplotype block likely to harbour the causal variant. No evidence of association at previously reported low-frequency variants in CYP27B1 was observed. As part of the study we compared variant discovery performance using two target-enrichment strategies. We concluded that our pools enriched with Nimblegen's solution phase hybridization capture had better sensitivity to detect true variants than the pools enriched with long-range PCR, whilst specificity was better in the long-range PCR-enriched pools compared with solution phase hybridization capture enriched pools; this result has important implications for the design of future fine-mapping studies.

Mice selectively bred for High and Low fear behavior show differences in the number of pMAPK (p44/42 ERK) expressing neurons in lateral amygdala following Pavlovian fear conditioning

Individual variability in the acquisition, consolidation and extinction of conditioned fear potentially contributes to the development of fear pathology including posttraumatic stress disorder (PTSD). Pavlovian fear conditioning is a key tool for the study of fundamental aspects of fear learning. Here, we used a selected mouse line of High and Low Pavlovian conditioned fear created from an advanced intercrossed line (AIL) in order to begin to identify the cellular basis of phenotypic divergence in Pavlovian fear conditioning. We investigated whether phosphorylated MAPK (p44/42 ERK/MAPK), a protein kinase required in the amygdala for the acquisition and consolidation of Pavlovian fear memory, is differentially expressed following Pavlovian fear learning in the High and Low fear lines. We found that following Pavlovian auditory fear conditioning, High and Low line mice differ in the number of pMAPK-expressing neurons in the dorsal sub nucleus of the lateral amygdala (LAd). In contrast, this difference was not detected in the ventral medial (LAvm) or ventral lateral (LAvl) amygdala sub nuclei or in control animals. We propose that this apparent increase in plasticity at a known locus of fear memory acquisition and consolidation relates to intrinsic differences between the two fear phenotypes. These data provide important insights into the micronetwork mechanisms encoding phenotypic differences in fear. Understanding the circuit level cellular and molecular mechanisms that underlie individual variability in fear learning is critical for the development of effective treatment of fear-related illnesses such as PTSD.