Extension of explicit formulas in Poissonian white noise analysis using harmonic analysis on configuration spaces

Harmonic analysis on configuration spaces is used in order to extend explicit expressions for the images of creation, annihilation, and second quantization operators in L2-spaces with respect to Poisson point processes to a set of functions larger than the space obtained by directly using chaos expansion. This permits, in particular, to derive an explicit expression for the generator of the second quantization of a sub-Markovian contraction semigroup on a set of functions which forms a core of the generator.

Stability results for the time-harmonic Maxwell equations with impedance boundary conditions

We consider the time-harmonic Maxwell equations with constant coefficients in a bounded, uniformly star-shaped polyhedron. We prove wavenumber-explicit norm bounds for weak solutions. This result is pivotal for convergence proofs in numerical analysis and may be a tool in the analysis of electromagnetic boundary integral operators.

Error analysis of Trefftz-discontinuous Galerkin methods for the time-harmonic Maxwell equations

In this paper, we extend to the time-harmonic Maxwell equations the p-version analysis technique developed in [R. Hiptmair, A. Moiola and I. Perugia, Plane wave discontinuous Galerkin methods for the 2D Helmholtz equation: analysis of the p-version, SIAM J. Numer. Anal., 49 (2011), 264-284] for Trefftz-discontinuous Galerkin approximations of the Helmholtz problem. While error estimates in a mesh-skeleton norm are derived parallel to the Helmholtz case, the derivation of estimates in a mesh-independent norm requires new twists in the duality argument. The particular case where the local Trefftz approximation spaces are built of vector-valued plane wave functions is considered, and convergence rates are derived.

Shoot yield drives phosphorus use efficiency in Brassica oleracea and correlates with root architecture traits

The environmental and financial costs of using inorganic phosphate fertilizers to maintain crop yield and quality are high. Breeding crops that acquire and use phosphorus (P) more efficiently could reduce these costs. The variation in shoot P concentration (shoot-P) and various measures of P use efficiency (PUE) were quantified among 355 Brassica oleracea L. accessions, 74 current commercial cultivars, and 90 doubled haploid (DH) mapping lines from a reference genetic mapping population. Accessions were grown at two or more external P concentrations in glasshouse experiments; commercial and DH accessions were also grown in replicated field experiments. Within the substantial species-wide diversity observed for shoot-P and various measures of PUE in B. oleracea, current commercial cultivars have greater PUE than would be expected by chance. This may be a consequence of breeding for increased yield, which is a significant component of most measures of PUE, or early establishment. Root development and architecture correlate with PUE; in particular, lateral root number, length, and growth rate. Significant quantitative trait loci associated with shoot-P and PUE occur on chromosomes C3 and C7. These data provide information to initiate breeding programmes to improve PUE in B. oleracea.

Atmosphere drives recent interannual variability of the Atlantic meridional overturning circulation at 26.5°N

The RAPID-MOCHA array has observed the Atlantic Meridional overturning circulation (AMOC) at 26.5°N since 2004. During 2009/2010, there was a transient 30% weakening of the AMOC driven by anomalies in geostrophic and Ekman transports. Here, we use simulations based on the Met Office Forecast Ocean Assimilation Model (FOAM) to diagnose the relative importance of atmospheric forcings and internal ocean dynamics in driving the anomalous geostrophic circulation of 2009/10. Data assimilating experiments with FOAM accurately reproduce the mean strength and depth of the AMOC at 26.5°N. In addition, agreement between simulated and observed stream functions in the deep ocean is improved when we calculate the AMOC using a method that approximates the RAPID observations. The main features of the geostrophic circulation anomaly are captured by an ensemble of simulations without data-assimilation. These model results suggest that the atmosphere played a dominant role in driving recent interannual variability of the AMOC.

Approximation by harmonic polynomials in star-shaped domains and exponential convergence of Trefftz hp-dGFEM

We study the approximation of harmonic functions by means of harmonic polynomials in two-dimensional, bounded, star-shaped domains. Assuming that the functions possess analytic extensions to a delta-neighbourhood of the domain, we prove exponential convergence of the approximation error with respect to the degree of the approximating harmonic polynomial. All the constants appearing in the bounds are explicit and depend only on the shape-regularity of the domain and on delta. We apply the obtained estimates to show exponential convergence with rate O(exp(−b square root N)), N being the number of degrees of freedom and b>0, of a hp-dGFEM discretisation of the Laplace equation based on piecewise harmonic polynomials. This result is an improvement over the classical rate O(exp(−b cubic root N )), and is due to the use of harmonic polynomial spaces, as opposed to complete polynomial spaces.

The role of the harmonic vector average in motion integration

The local speeds of object contours vary systematically with the cosine of the angle between the normal component of the local velocity and the global object motion direction. An array of Gabor elements whose speed changes with local spatial orientation in accordance with this pattern can appear to move as a single surface. The apparent direction of motion of plaids and Gabor arrays has variously been proposed to result from feature tracking, vector addition and vector averaging in addition to the geometrically correct global velocity as indicated by the intersection of constraints (IOC) solution. Here a new combination rule, the harmonic vector average (HVA), is introduced, as well as a new algorithm for computing the IOC solution. The vector sum can be discounted as an integration strategy as it increases with the number of elements. The vector average over local vectors that vary in direction always provides an underestimate of the true global speed. The HVA, however, provides the correct global speed and direction for an unbiased sample of local velocities with respect to the global motion direction, as is the case for a simple closed contour. The HVA over biased samples provides an aggregate velocity estimate that can still be combined through an IOC computation to give an accurate estimate of the global velocity, which is not true of the vector average. Psychophysical results for type II Gabor arrays show perceived direction and speed falls close to the IOC direction for Gabor arrays having a wide range of orientations but the IOC prediction fails as the mean orientation shifts away from the global motion direction and the orientation range narrows. In this case perceived velocity generally defaults to the HVA.

Clonal expansion of early to mid-life mitochondrial DNA point mutations drives mitochondrial dysfunction during human ageing

Age-related decline in the integrity of mitochondria is an important contributor to the human ageing process. In a number of ageing stem cell populations, this decline in mitochondrial function is due to clonal expansion of individual mitochondrial DNA (mtDNA) point mutations within single cells. However the dynamics of this process and when these mtDNA mutations occur initially are poorly understood. Using human colorectal epithelium as an exemplar tissue with a well-defined stem cell population, we analysed samples from 207 healthy participants aged 17-78 years using a combination of techniques (Random Mutation Capture, Next Generation Sequencing and mitochondrial enzyme histochemistry), and show that: 1) non-pathogenic mtDNA mutations are present from early embryogenesis or may be transmitted through the germline, whereas pathogenic mtDNA mutations are detected in the somatic cells, providing evidence for purifying selection in humans, 2) pathogenic mtDNA mutations are present from early adulthood (<20 years of age), at both low levels and as clonal expansions, 3) low level mtDNA mutation frequency does not change significantly with age, suggesting that mtDNA mutation rate does not increase significantly with age, and 4) clonally expanded mtDNA mutations increase dramatically with age. These data confirm that clonal expansion of mtDNA mutations, some of which are generated very early in life, is the major driving force behind the mitochondrial dysfunction associated with ageing of the human colorectal epithelium.

What drives city branding?

The article revises the role of architecture and iconic buildings in the branding of urban spaces.

What drives ICT clustering in European Cities?

ICT clusters have attracted much attention because of their rapid growth and their value for other economic activities. Using a nested multi-level model, we examine how conditions at the country level and at the city level affect ICT clustering activity in 227 cities across 22 European countries. We test for the influence of three country regulations (starting a business, registering property, enforcing contracts) and two city conditions (proximity to university, network density) on ICT clustering. We consider heterogeneity within the sector and study two types of ICT activities: ICT product firms and ICT content firms. Our results indicate that country conditions and city conditions each have idiosyncratic implications for ICT clustering, and further, that these can vary by activities in ICT products or ICT content manufacturing.

On the structure of infinity-harmonic maps

Let H ∈ C 2(ℝ N×n ), H ≥ 0. The PDE system arises as the Euler-Lagrange PDE of vectorial variational problems for the functional E ∞(u, Ω) = ‖H(Du)‖ L ∞(Ω) defined on maps u: Ω ⊆ ℝ n → ℝ N . (1) first appeared in the author's recent work. The scalar case though has a long history initiated by Aronsson. Herein we study the solutions of (1) with emphasis on the case of n = 2 ≤ N with H the Euclidean norm on ℝ N×n , which we call the “∞-Laplacian”. By establishing a rigidity theorem for rank-one maps of independent interest, we analyse a phenomenon of separation of the solutions to phases with qualitatively different behaviour. As a corollary, we extend to N ≥ 2 the Aronsson-Evans-Yu theorem regarding non existence of zeros of |Du| and prove a maximum principle. We further characterise all H for which (1) is elliptic and also study the initial value problem for the ODE system arising for n = 1 but with H(·, u, u′) depending on all the arguments.

Science drives horticulture's progress and profit

Horticultural science linked with basic studies in biology, chemistry, physics and engineering has laid the foundation for advances in applied knowledge which are at the heart of commercial, environmental and social horticulture. In few disciplines is science more rapidly translated into applicable technologies than in the huge range of man’s activities embraced within horticulture which are discussed in this Trilogy. This chapter surveys the origins of horticultural science developing as an integral part of the 16th century “Scientific Revolution”. It identifies early discoveries during the latter part of the 19th and early 20th centuries which rationalized the control of plant growth, flowering and fruiting and the media in which crops could be cultivated. The products of these discoveries formed the basis on which huge current industries of worldwide significance are founded in fruit, vegetable and ornamental production. More recent examples of the application of horticultural science are used in an explanation of how the integration of plant breeding, crop selection and astute marketing highlighted by the New Zealand industry have retained and expanded the viability of production which supplies huge volumes of fruit into the world’s markets. This is followed by an examination of science applied to tissue and cell culture as an example of technologies which have already produced massive industrial applications but hold the prospect for generating even greater advances in the future. Finally, examples are given of nascent scientific discoveries which hold the prospect for generating horticultural industries with considerable future impact. These include systems modeling and biology, nanotechnology, robotics, automation and electronics, genetics and plant breeding, and more efficient and effective use of resources and the employment of benign microbes. In conclusion there is an estimation of the value of horticultural science to society.