Decoupling the coupled DGLAP evolution equations: an analytic solution to pQCD

Using Laplace transform techniques, along with newly-developed accurate numerical inverse Laplace transform algorithms, we decouple the solutions for the singlet structure function $F_s(x,Q^2)$ and $G(x,Q^2)$ of the two leading-order coupled singlet DGLAP equations, allowing us to write fully decoupled solutions: F_s(x,Q^2)={\cal F}_s(F_{s0}(x), G_0(x)), G(x,Q^2)={\cal G}(F_{s0}(x), G_0(x)). Here ${\cal F}_s$ and $\cal G$ are known functions---found using the DGLAP splitting functions---of the functions $F_{s0}(x) \equiv F_s(x,Q_0^2)$ and $G_{0}(x) \equiv G(x,Q_0^2)$, the chosen starting functions at the virtuality $Q_0^2$. As a proof of method, we compare our numerical results from the above equations with the published MSTW LO gluon and singlet $F_s$ distributions, starting from their initial values at $Q_0^2=1 GeV^2$. Our method completely decouples the two LO distributions, at the same time guaranteeing that both distributions satisfy the singlet coupled DGLAP equations. It furnishes us with a new tool for readily obtaining the effects of the starting functions (independently) on the gluon and singlet structure functions, as functions of both $Q^2$ and $Q_0^2$. In addition, it can also be used for non-singlet distributions, thus allowing one to solve analytically for individual quark and gluon distributions values at a given $x$ and $Q^2$, with typical numerical accuracies of about 1 part in $10^5$, rather than having to evolve numerically coupled integral-differential equations on a two-dimensional grid in $x, Q^2$, as is currently done.Comment: 6 pages, 2 figure

Automatic landmarking for building biological shape models

We present a new method for automatic landmark extraction from the contours of biological specimens. Our ultimate goal is to enable automatic identification of biological specimens in photographs and drawings held in a database. We propose to use active appearance models for visual indexing of both photographs and drawings. Automatic landmark extraction will assist us in building the models. We describe the results of using our method on drawings and photographs of examples of diatoms, and present an active shape model built using automatically extracted data

A new numerical method for obtaining gluon distribution functions G(x,Q2)=xg(x,Q2)G(x,Q^2)=xg(x,Q^2), from the proton structure function F2γp(x,Q2)F_2^{\gamma p}(x,Q^2)

An exact expression for the leading-order (LO) gluon distribution function $G(x,Q^2)=xg(x,Q^2)$ from the DGLAP evolution equation for the proton structure function $F_2^{\gamma p}(x,Q^2)$ for deep inelastic $\gamma^* p$ scattering has recently been obtained [M. M. Block, L. Durand and D. W. McKay, Phys. Rev. D{\bf 79}, 014031, (2009)] for massless quarks, using Laplace transformation techniques. Here, we develop a fast and accurate numerical inverse Laplace transformation algorithm, required to invert the Laplace transforms needed to evaluate $G(x,Q^2)$, and compare it to the exact solution. We obtain accuracies of less than 1 part in 1000 over the entire $x$ and $Q^2$ spectrum. Since no analytic Laplace inversion is possible for next-to-leading order (NLO) and higher orders, this numerical algorithm will enable one to obtain accurate NLO (and NNLO) gluon distributions, using only experimental measurements of $F_2^{\gamma p}(x,Q^2)$.Comment: 9 pages, 2 figure

Sustained maintenance of somatotopic information in brain regions recruited by tactile working memory

To adaptively guide ongoing behavior, representations in working memory (WM) often have to be modified in line with changing task demands. We used event-related potentials (ERPs) to demonstrate that tactile WM representations are stored in modality-specific cortical regions, that the goal-directed modulation of these representations is mediated through hemispheric-specific activation of somatosensory areas, and that the rehearsal of somatotopic coordinates in memory is accomplished by modality-specific spatial attention mechanisms. Participants encoded two tactile sample stimuli presented simultaneously to the left and right hands, before visual retro-cues indicated which of these stimuli had to be retained to be matched with a subsequent test stimulus on the same hand. Retro-cues triggered a sustained tactile contralateral delay activity component with a scalp topography over somatosensory cortex contralateral to the cued hand. Early somatosensory ERP components to task-irrelevant probe stimuli (that were presented after the retro-cues) and to subsequent test stimuli were enhanced when these stimuli appeared at the currently memorized location relative to other locations on the cued hand, demonstrating that a precise focus of spatial attention was established during the selective maintenance of tactile events in WM. These effects were observed regardless of whether participants performed the matching task with uncrossed or crossed hands, indicating that WM representations in this task were based on somatotopic rather than allocentric spatial coordinates. In conclusion, spatial rehearsal in tactile WM operates within somatotopically organized sensory brain areas that have been recruited for information storage

Adaptive query parallelization in multi-core column stores

With the rise of multi-core CPU platforms, their optimal utilization for in-memory OLAP workloads using column store databases has become one of the biggest challenges. Some of the inherent limi- tations in the achievable query parallelism are due to the degree of parallelism dependency on the data skew, the overheads incurred by thread coordination, and the hardware resource limits. Finding the right balance between the degree of parallelism and the multi-core utilizati

Stethoscope: A platform for interactive visual analysis of query execution plans

Searching for the performance bottleneck in an execution trace is an error prone and time consuming activity. Existing tools oer some comfort by providing a visual representation of trace for analysis. In this paper we present the Stethoscope, an interactive visual tool to inspect and analyze columnar database query performance, both online and online. It's unique interactive animated interface capitalizes the large dataflow graph representation of a query execution plan, augmented with query execution trace information. We demonstrate features of Stethoscope for both online and online analysis of long running queries. It helps in understanding where time goes, how optimizers perform, and how parallel processing on multi-core systems is exploited

A new numerical method for inverse Laplace transforms used to obtain gluon distributions from the proton structure function

We recently derived a very accurate and fast new algorithm for numerically inverting the Laplace transforms needed to obtain gluon distributions from the proton structure function $F_2^{\gamma p}(x,Q^2)$. We numerically inverted the function $g(s)$, $s$ being the variable in Laplace space, to $G(v)$, where $v$ is the variable in ordinary space. We have since discovered that the algorithm does not work if $g(s)\rightarrow 0$ less rapidly than $1/s$ as $s\rightarrow\infty$, e.g., as $1/s^\beta$ for $0<\beta<1$. In this note, we derive a new numerical algorithm for such cases, which holds for all positive and non-integer negative values of $\beta$. The new algorithm is {\em exact} if the original function $G(v)$ is given by the product of a power $v^{\beta-1}$ and a polynomial in $v$. We test the algorithm numerically for very small positive $\beta$, $\beta=10^{-6}$ obtaining numerical results that imitate the Dirac delta function $\delta(v)$. We also devolve the published MSTW2008LO gluon distribution at virtuality $Q^2=5$ GeV$^2$ down to the lower virtuality $Q^2=1.69$ GeV$^2$. For devolution, $\beta$ is negative, giving rise to inverse Laplace transforms that are distributions and not proper functions. This requires us to introduce the concept of Hadamard Finite Part integrals, which we discuss in detail.Comment: 16 pages, 2 figures; title and abstract changed, typos correcte

Mature-aged men’s experiences of higher education: Australia and England compared

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Mountain child: systematic literature review.

Objectives This systematic review identifies and reviews both peer-reviewed and 'grey' literature, across a range of disciplines and from diverse sources, relating to the condition of children living in mountain communities in low- and middle-income countries. Findings The literature on poverty in these communities does not generally focus on the particular vulnerabilities of children or the impact of intersecting vulnerabilities on the most marginalised members of communities. However, this literature does contribute analyses of the broader context and variety of factors impacting on human development in mountainous areas. The literature on other areas of children's lives - health, nutrition, child mortality, education, and child labour - focuses more specifically on children's particular vulnerabilities or experiences. However, it sometimes lacks the broader analysis of the many interrelated characteristics of a mountainous environment which impact on children's situations. Themes Nevertheless, certain themes recur across many disciplines and types of literature, and point to some general conclusions: mountain poverty is influenced by the very local specificities of the physical environment; mountain communities are often politically and economically marginalised, particularly for the most vulnerable within these communities, including children; and mountain communities themselves are an important locus for challenging and interrupting cycles of increasing inequality and disadvantage. While this broad-scale review represents a modest first step, its findings provide the basis for further investigation