A 'Darboux theorem' for derived schemes with shifted symplectic structure

We prove a 'Darboux theorem' for derived schemes with symplectic forms of degree $k<0$, in the sense of Pantev, Toen, Vaquie and Vezzosi arXiv:1111.3209. More precisely, we show that a derived scheme $X$ with symplectic form $\omega$ of degree $k$ is locally equivalent to (Spec $A,\omega'$) for Spec $A$ an affine derived scheme whose cdga $A$ has Darboux-like coordinates in which the symplectic form $\omega'$ is standard, and the differential in $A$ is given by Poisson bracket with a Hamiltonian function $H$ in $A$ of degree $k+1$. When $k=-1$, this implies that a $-1$-shifted symplectic derived scheme $(X,\omega)$ is Zariski locally equivalent to the derived critical locus Crit$(H)$ of a regular function $H:U\to{\mathbb A}^1$ on a smooth scheme $U$. We use this to show that the underlying classical scheme of $X$ has the structure of an 'algebraic d-critical locus', in the sense of Joyce arXiv:1304.4508. In the sequels arXiv:1211.3259, arXiv:1305.6428, arXiv:1312.0090, arXiv:1504.00690, 1506.04024 we will discuss applications of these results to categorified and motivic Donaldson-Thomas theory of Calabi-Yau 3-folds, and to defining new Donaldson-Thomas type invariants of Calabi-Yau 4-folds, and to defining 'Fukaya categories' of Lagrangians in algebraic symplectic manifolds using perverse sheaves, and we will extend the results of this paper and arXiv:1211.3259, arXiv:1305.6428 from (derived) schemes to (derived) Artin stacks, and to give local descriptions of Lagrangians in $k$-shifted symplectic derived schemes. Bouaziz and Grojnowski arXiv:1309.2197 independently prove a similar 'Darboux Theorem'.Comment: 54 pages. (v4) Final version to appear in Journal of the AM

Inter-rater reliability and validity of the Australian Football League\u27s kicking and handball tests

Talent identification tests used at the Australian Football League’s National Draft Combine assess the capacities of athletes to compete at a professional level. Tests created for the National Draft Combine are also commonly used for talent identification and athlete development in development pathways. The skills tests created by the Australian Football League required players to either handball (striking the ball with the hand) or kick to a series of 6 randomly generated targets. Assessors subjectively rate each skill execution giving a 0-5 score for each disposal. This study aimed to investigate the inter-rater reliability and validity of the skills tests at an adolescent sub-elite level. Male Australian footballers were recruited from sub-elite adolescent teams (n=121, age=15.7 ± 0.3 years, height=1.77 ± 0.07 m, mass=69.17 ± 8.08 kg). The coaches (n=7) of each team were also recruited. Inter-rater reliability was assessed using Inter-class correlations (ICC) and Limits of Agreement analysis. Both the kicking (ICC=0.96, P\u3c0.01) and handball tests (ICC=0.89, P\u3c0.01) demonstrated strong reliability and acceptable levels of absolute agreement. Content validity was determined by examining test scores sensitivity to laterality and distance. Concurrent validity was assessed by comparing coaches’ perceptions of skill to actual test outcomes. Multivariate analysis of variance (MANOVA) examined the main effect of laterality, with scores on the dominant hand (P=0.04) and foot (P\u3c0.01) significantly higher compared to the non-dominant side. Follow-up univariate analysis showing significant differences at every distance in the kicking test. A poor correlation was found between coaches’ perceptions of skill and testing outcomes. The results of this study demonstrate both skill tests demonstrate acceptable inter-rater reliable. Partial content validity was confirmed for the kicking test, however further research is required to confirm validity of the handball test

Multi-segment trunk models used to investigate the crunch factor in golf and their relationship with selected swing and launch parameters

The use of multi-segment trunk models to investigate the crunch factor in golf may be warranted. The first aim of the study was to investigate the relationship between the trunk and lower trunk for crunch factor related variables (trunk lateral bending and trunk axial rotation velocity). The second aim was to determine the level of association between crunch factor related variables with swing (clubhead velocity) and launch (launch angle). Thirty five high level amateur male golfers (Mean ± SD: age = 23.8 ± 2.1 years, registered golfing handicap = 5 ± 1.9) without low back pain had kinematic data collected from their golf swing using a 10- camera motion analysis system operating at 500 Hz. Clubhead velocity and launch angle were collected using a validated real-time launch monitor. A positive relationship was found between the trunk and lower trunk for axial rotation velocity (r(35) = .47, p\u3c .01). Crosscorrelation analysis revealed a strong coupling relationship for the crunch factor (R2 21 = 0.98) between the trunk and lower trunk. Using generalised linear model analysis, it was evident that faster clubhead velocities and lower launch angles of the golf ball were related to reduced lateral bending of the lower trunk

An Investigation of Technique and Equipment Factors Associated with Clubhead Speed in Golf

If golfers achieve long hitting distances whilst maintaining their accuracy they will gain a competitive advantage. To increase hitting distance, faster clubhead speed is required and this can potentially be achieved through a number of factors. Firstly, anthropometric factors such as height and physical factors such as trunk rotational power have been previously considered to be of importance. However, biomechanical factors such as; the X-factor (separation of the trunk-pelvis alignment when viewed in the transverse plane), have been a major focus of recent research. Further, the interaction of the golfer with the implement they hit with i.e. the golf club has also been examined in biomechanical studies. The broad aim of this doctoral research was to investigate how male high-level amateur golfers generate club head speed and this was examined in a series of five studies that examined technical and equipment factors. The first study of this thesis (Study I) developed a valid three-dimensional Cardan / Euler model to examine the kinematics of the trunk and lower trunk during the golf swing. This validation study involved; developing and validating models and related algorithms as well as making comparisons to static and dynamic postures. It was concluded that a lateral bending / flexion-extension / axial rotation (ZYX) order of rotation was the most suitable to quantify the X-factor and lower trunk movement in the golf swing. Previous research has shown conflicting relationships between golf swing kinematics (such as variables related to the X-factor) and clubhead speed, as well as what physical variables assist in generating clubhead speed. The second study of this thesis (Study II) had two aims. The first aim was to determine whether significant between-club (driver and five-iron) differences existed for trunk and lower trunk kinematics as well as launch conditions. The second aim was to determine which anthropometric, physical and trunk and lower trunk kinematic variables were most strongly associated with clubhead speed. Fifteen high level amateur male golfers (2.5 ± 1.9 handicap) had their trunk and lower trunk three-dimensional kinematics data quantified using the methods developed in Study I. Nine significant (p \u3c 0.002) between-club differences in swing kinematics were found; namely trunk and lower trunk flexion and lower trunk axial rotation, as well as ball velocity. Regression analyses explained 33.7 % and 66.7 % of the variance in clubhead speed for the driver and five-iron respectively, with both trunk and lower trunk variables showing associations with clubhead speed. No anthropometric (i.e. height) or physical (i.e. maximum trunk rotational speed) were associated with clubhead speed. The low amount of variance explained by clubhead speed for the driver in Study II stimulated further investigation. Studies III and IV were designed to develop a method to locate the kick point during the golf swing and examine the effect of kick point location on swing parameters and their related launch conditions, respectively. Study III involved two phases, Firstly, the level of agreement between two methods of determining the static kick point was determined. This showed that an algorithm using three-dimensional locations of markers placed on the golf club was a valid method to determine the location of the static kick point. In the second phase of testing, this method was used to determine the location of the dynamic kick point during the golf swing. Excellent between-trial reliability was found for this method. Further, differences were found for the dynamic kick point location when compared to the static kick point location. The main objective of Study IV was to determine whether drivers fitted with shafts having high and low kick points would alter selected swing parameters, and related launch conditions. Twelve high level amateur male golfers (1.2 ± 1.8 handicap) had three shots analysed for each of two drivers fitted with “stiff” shafts but these drivers had differing kick point location. Stiffness profiles of these shafts were also measured. Five swing parameters and their related launch conditions were measured using a real-time launch monitor. The driver fitted with the shaft containing the high kick point displayed a more negative (steeper) angle of attack, a lower launch angle and an increased spin rate when compared to a driver fitted with a low kick point In Study II, a relatively small amount of variance in clubhead speed was explained by the driver and it was the overall intention of the last study of this thesis (Study V) to attempt to explain more of this variance by examining both trunk and wrist kinematics. This was undertaken using two drivers containing differing kick point locations (low and high), with two separate regression models being produced. Twenty high-level amateur male golfers (1.9 ± 1.9 handicap) had their trunk and lower trunk three-dimensional kinematics data quantified as in Study II, but with the addition of a wrist segment. Four significant (p In conclusion, the methods developed for this thesis to analyse golf swing kinematics revealed a greater insight into how highly skilled golfers produce clubhead speed. Particularly, the results from Studies II and V revealed significant associations between lower trunk related variables and clubhead speed when using different clubs (driver vs. fiveiron) and the same club fitted with two shafts of different kick point location (driver). Also, the methods developed in Studies III and IV to investigate dynamic shaft profiles (deflection) in the downswing provided possible explanations as to how shaft performance in the downswing can influence swing parameters and their related launch conditions at ball impact

An examination of the correlation amongst trunk flexibility, x-factor and clubhead speed in skilled golfers

Skilled golfers are reported to be more flexible than lesser able golfers, which may assist in increased x-factor (shoulder – pelvis separation) at the top of the backswing. However, it is unknown if increased flexibility produces faster clubhead speed. The aim of this study was to investigate the correlations amongst trunk flexibility and x-factor, as well as the association between flexibility and clubhead speed in low handicap golfers. Fifteen low handicap male golfers who displayed a modern swing, had their trunk static anatomical end-range of motion (ROM) (flexibility) and driver swing kinematics were measured. Although Pearson correlations revealed trunk extension and lateral bending were moderately related to x-factor, axial rotation flexibility was not. A generalised linear model (GLM) reported three axial rotation flexibility variables and six golf swing kinematic variables were associated with faster clubhead speed. The Pearson correlation results suggests that skilled golfers who have increased axial rotation flexibility do not necessarily utilise it to increase x-factor, and the GLM results support the importance of multi-segment flexibility, and interaction for improving golf performance with skilled golfers

Philochoros and the tradition of local historical writing at Athens : genre, ideology and methodology in the reconstruction and literary presentation of attic history

Available from British Library Document Supply Centre- DSC:DXN054583 / BLDSC - British Library Document Supply CentreSIGLEGBUnited Kingdo

In silico comparative genomic analysis of GABAA receptor transcriptional regulation

<p>Abstract</p> <p>Background</p> <p>Subtypes of the GABA_Areceptor subunit exhibit diverse temporal and spatial expression patterns. <it>In silico </it>comparative analysis was used to predict transcriptional regulatory features in individual mammalian GABA_Areceptor subunit genes, and to identify potential transcriptional regulatory components involved in the coordinate regulation of the GABA_Areceptor gene clusters.</p> <p>Results</p> <p>Previously unreported putative promoters were identified for the β2, γ1, γ3, ε, θ and π subunit genes. Putative core elements and proximal transcriptional factors were identified within these predicted promoters, and within the experimentally determined promoters of other subunit genes. Conserved intergenic regions of sequence in the mammalian GABA_Areceptor gene cluster comprising the α1, β2, γ2 and α6 subunits were identified as potential long range transcriptional regulatory components involved in the coordinate regulation of these genes. A region of predicted DNase I hypersensitive sites within the cluster may contain transcriptional regulatory features coordinating gene expression. A novel model is proposed for the coordinate control of the gene cluster and parallel expression of the α1 and β2 subunits, based upon the selective action of putative Scaffold/Matrix Attachment Regions (S/MARs).</p> <p>Conclusion</p> <p>The putative regulatory features identified by genomic analysis of GABA_Areceptor genes were substantiated by cross-species comparative analysis and now require experimental verification. The proposed model for the coordinate regulation of genes in the cluster accounts for the head-to-head orientation and parallel expression of the α1 and β2 subunit genes, and for the disruption of transcription caused by insertion of a neomycin gene in the close vicinity of the α6 gene, which is proximal to a putative critical S/MAR.</p

Evidence against the Detectability of a Hippocampal Place Code Using Functional Magnetic Resonance Imaging

Individual hippocampal neurons selectively increase their firing rates in specific spatial locations. As a population, these neurons provide a decodable representation of space that is robust against changes to sensory- and path-related cues. This neural code is sparse and distributed, theoretically rendering it undetectable with population recording methods such as functional magnetic resonance imaging (fMRI). Existing studies nonetheless report decoding spatial codes in the human hippocampus using such techniques. Here we present results from a virtual navigation experiment in humans in which we eliminated visual- and path-related confounds and statistical limitations present in existing studies, ensuring that any positive decoding results would represent a voxel-place code. Consistent with theoretical arguments derived from electrophysiological data and contrary to existing fMRI studies, our results show that although participants were fully oriented during the navigation task, there was no statistical evidence for a place code

Management of European floodplain grasslands for plant biodiversity

European floodplain grasslands are characterized by periodic flooding and regular management, usually cutting and grazing as part of an agricultural system. Past losses and ecological degradation have been due largely to river regulation and either agricultural intensification or abandonment and have resulted in a substantial reduction in area across Europe. Nevertheless, the remaining resource supports considerable biodiversity and a high level of biological production. A better quantitative understanding of the functioning of these grasslands is required in order to establish effective conservation management within a sustainable land use system. The thesis examines the impact of key management factors on three important functional characteristics of the biodiversity of floodplain plant communities, namely plant diversity (measured by species diversity), cover (%) and primary production (above-ground biomass), on two floodplain grasslands of the River Trent, UK and a third on the the Luznice river, the Czech Republic. Field investigations of the effects of cutting, grazing, cessation of management, the influence of floodborne litter, and the impact of fertilizer nitrogen were undertaken over periods of between one and three seasons. These demonstrated that floodplain grassland plant communities are sensitive to variations in management and that impacts on communities are mediated particularly through effects on plant competition. Productive competitive species were encouraged both by abandonment and fertilizer application whereas cutting and grazing management, and the imposition of litter, favoured stress-tolerating perennials. Species diversity decreased both with high inputs of litter and additions of fertilizer. Plant community responses and competitive strategies of key species are discussed in the context of biodiversity conservation, ecological restoration and management of European floodplain grasslands