Lagrangian perturbations and the matter bispectrum I: fourth-order model for non-linear clustering

We investigate the Lagrangian perturbation theory of a homogeneous and isotropic universe in the non-relativistic limit, and derive the solutions up to the fourth order. These solutions are needed for example for the next-to-leading order correction of the (resummed) Lagrangian matter bispectrum, which we study in an accompanying paper. We focus on flat cosmologies with a vanishing cosmological constant, and provide an in-depth description of two complementary approaches used in the current literature. Both approaches are solved with two different sets of initial conditions---both appropriate for modelling the large-scale structure. Afterwards we consider only the fastest growing mode solution, which is not affected by either of these choices of initial conditions. Under the reasonable approximation that the linear density contrast is evaluated at the initial Lagrangian position of the fluid particle, we obtain the nth-order displacement field in the so-called initial position limit: the nth order displacement field consists of 3(n-1) integrals over n linear density contrasts, and obeys self-similarity. Then, we find exact relations between the series in Lagrangian and Eulerian perturbation theory, leading to identical predictions for the density contrast and the peculiar-velocity divergence up to the fourth order.Comment: 31 pages, matches published version in JCAP, added an extra section which discusses and motivates the choice of initial conditions, extended the title for the sake of precisio

A formal theory for spatial representation and reasoning in biomedical ontologies

Objective: The objective of this paper is to demonstrate how a formal spatial theory can be used as an important tool for disambiguating the spatial information embodied in biomedical ontologies and for enhancing their automatic reasoning capabilities. Method and Materials: This paper presents a formal theory of parthood and location relations among individuals, called Basic Inclusion Theory (BIT). Since biomedical ontologies are comprised of assertions about classes of individuals (rather than assertions about individuals), we define parthood and location relations among classes in the extended theory BIT+Cl (Basic Inclusion Theory for Classes). We then demonstrate the usefulness of this formal theory for making the logical structure of spatial information more precise in two ontologies concerned with human anatomy: the Foundational Model of Anatomy (FMA) and GALEN. Results: We find that in both the FMA and GALEN, class-level spatial relations with different logical properties are not always explicitly distinguished. As a result, the spatial information included in these biomedical ontologies is often ambiguous and the possibilities for implementing consistent automatic reasoning within or across ontologies are limited. Conclusion: Precise formal characterizations of all spatial relations assumed by a biomedical ontology are necessary to ensure that the information embodied in the ontology can be fully and coherently utilized in a computational environment. This paper can be seen as an important beginning step toward achieving this goal, but much more work is along these lines is required

Ibrahim revisits Cape Town

Photocopied article from the newspaper The Daily Dispatch about Abdullah Ibrahim, a jazz musicia

Jazzman’s finest delivery

Photocopied article from the newspaper The Daily Dispatch about Albert Spaargaren, a jazz musician

Revival needs public support

Photocopied article from the newspaper The Daily Dispatch about the jazz music revival in East Londo

At the heart of Jonathan Butler

Photocopied article from the newspaper The Daily Dispatch about Jazz musician

Cape Town to host North Sea Jazz Festival

Photocopied article from the newspaper The Daily Dispatch about the North Sea Jazz Festival hosted by Cape Tow

Grammy winning jazz

Photocopied article from the newspaper The Daily Dispatch about Chucho Valdes, a jazz musician

Listening to pictures

Photocopied article from the newspaper The Daily Dispatch about the art of jazz photography of William Claxto