DIRK Schemes with High Weak Stage Order

Runge-Kutta time-stepping methods in general suffer from order reduction: the observed order of convergence may be less than the formal order when applied to certain stiff problems. Order reduction can be avoided by using methods with high stage order. However, diagonally-implicit Runge-Kutta (DIRK) schemes are limited to low stage order. In this paper we explore a weak stage order criterion, which for initial boundary value problems also serves to avoid order reduction, and which is compatible with a DIRK structure. We provide specific DIRK schemes of weak stage order up to 3, and demonstrate their performance in various examples.Comment: 10 pages, 5 figure

Stability of central finite difference schemes for the Heston PDE

This paper deals with stability in the numerical solution of the prominent Heston partial differential equation from mathematical finance. We study the well-known central second-order finite difference discretization, which leads to large semi-discrete systems with non-normal matrices A. By employing the logarithmic spectral norm we prove practical, rigorous stability bounds. Our theoretical stability results are illustrated by ample numerical experiments

Overview of (pro-)Lie group structures on Hopf algebra character groups

Character groups of Hopf algebras appear in a variety of mathematical and physical contexts. To name just a few, they arise in non-commutative geometry, renormalisation of quantum field theory, and numerical analysis. In the present article we review recent results on the structure of character groups of Hopf algebras as infinite-dimensional (pro-)Lie groups. It turns out that under mild assumptions on the Hopf algebra or the target algebra the character groups possess strong structural properties. Moreover, these properties are of interest in applications of these groups outside of Lie theory. We emphasise this point in the context of two main examples: The Butcher group from numerical analysis and character groups which arise from the Connes--Kreimer theory of renormalisation of quantum field theories.Comment: 31 pages, precursor and companion to arXiv:1704.01099, Workshop on "New Developments in Discrete Mechanics, Geometric Integration and Lie-Butcher Series", May 25-28, 2015, ICMAT, Madrid, Spai

Disease progression in Plasmodium knowlesi malaria is linked to variation in invasion gene family members.

Emerging pathogens undermine initiatives to control the global health impact of infectious diseases. Zoonotic malaria is no exception. Plasmodium knowlesi, a malaria parasite of Southeast Asian macaques, has entered the human population. P. knowlesi, like Plasmodium falciparum, can reach high parasitaemia in human infections, and the World Health Organization guidelines for severe malaria list hyperparasitaemia among the measures of severe malaria in both infections. Not all patients with P. knowlesi infections develop hyperparasitaemia, and it is important to determine why. Between isolate variability in erythrocyte invasion, efficiency seems key. Here we investigate the idea that particular alleles of two P. knowlesi erythrocyte invasion genes, P. knowlesi normocyte binding protein Pknbpxa and Pknbpxb, influence parasitaemia and human disease progression. Pknbpxa and Pknbpxb reference DNA sequences were generated from five geographically and temporally distinct P. knowlesi patient isolates. Polymorphic regions of each gene (approximately 800 bp) were identified by haplotyping 147 patient isolates at each locus. Parasitaemia in the study cohort was associated with markers of disease severity including liver and renal dysfunction, haemoglobin, platelets and lactate, (r = ≥ 0.34, p =  <0.0001 for all). Seventy-five and 51 Pknbpxa and Pknbpxb haplotypes were resolved in 138 (94%) and 134 (92%) patient isolates respectively. The haplotypes formed twelve Pknbpxa and two Pknbpxb allelic groups. Patients infected with parasites with particular Pknbpxa and Pknbpxb alleles within the groups had significantly higher parasitaemia and other markers of disease severity. Our study strongly suggests that P. knowlesi invasion gene variants contribute to parasite virulence. We focused on two invasion genes, and we anticipate that additional virulent loci will be identified in pathogen genome-wide studies. The multiple sustained entries of this diverse pathogen into the human population must give cause for concern to malaria elimination strategists in the Southeast Asian region

Local and global modes of drug action in biochemical networks

It becomes increasingly accepted that a shift is needed from the traditional target-based approach of drug development to an integrated perspective of drug action in biochemical systems. We here present an integrative analysis of the interactions between drugs and metabolism based on the concept of drug scope. The drug scope represents the set of metabolic compounds and reactions that are potentially affected by a drug. We constructed and analyzed the scopes of all US approved drugs having metabolic targets. Our analysis shows that the distribution of drug scopes is highly uneven, and that drugs can be classified into several categories based on their scopes. Some of them have small scopes corresponding to localized action, while others have large scopes corresponding to potential large-scale systemic action. These groups are well conserved throughout different topologies of the underlying metabolic network. They can furthermore be associated to specific drug therapeutic properties

Secular evolution versus hierarchical merging: galaxy evolution along the Hubble sequence, in the field and rich environments

In the current galaxy formation scenarios, two physical phenomena are invoked to build disk galaxies: hierarchical mergers and more quiescent external gas accretion, coming from intergalactic filaments. Although both are thought to play a role, their relative importance is not known precisely. Here we consider the constraints on these scenarios brought by the observation-deduced star formation history on the one hand, and observed dynamics of galaxies on the other hand: the high frequency of bars and spirals, the high frequency of perturbations such as lopsidedness, warps, or polar rings. All these observations are not easily reproduced in simulations without important gas accretion. N-body simulations taking into account the mass exchange between stars and gas through star formation and feedback, can reproduce the data, only if galaxies double their mass in about 10 Gyr through gas accretion. Warped and polar ring systems are good tracers of this accretion, which occurs from cold gas which has not been virialised in the system's potential. The relative importance of these phenomena are compared between the field and rich clusters. The respective role of mergers and gas accretion vary considerably with environment.Comment: 18 pages, 8 figures, review paper to "Penetrating Bars through Masks of Cosmic Dust: the Hubble Tuning Fork Strikes a New Note", Pilanesberg, ed. D. Block et al., Kluwe

Definition of the σW regulon of Bacillus subtilis in the absence of stress

Bacteria employ extracytoplasmic function (ECF) sigma factors for their responses to environmental stresses. Despite intensive research, the molecular dissection of ECF sigma factor regulons has remained a major challenge due to overlaps in the ECF sigma factor-regulated genes and the stimuli that activate the different ECF sigma factors. Here we have employed tiling arrays to single out the ECF σW regulon of the Gram-positive bacterium Bacillus subtilis from the overlapping ECF σX, σY, and σM regulons. For this purpose, we profiled the transcriptome of a B. subtilis sigW mutant under non-stress conditions to select candidate genes that are strictly σW-regulated. Under these conditions, σW exhibits a basal level of activity. Subsequently, we verified the σW-dependency of candidate genes by comparing their transcript profiles to transcriptome data obtained with the parental B. subtilis strain 168 grown under 104 different conditions, including relevant stress conditions, such as salt shock. In addition, we investigated the transcriptomes of rasP or prsW mutant strains that lack the proteases involved in the degradation of the σW anti-sigma factor RsiW and subsequent activation of the σW-regulon. Taken together, our studies identify 89 genes as being strictly σW-regulated, including several genes for non-coding RNAs. The effects of rasP or prsW mutations on the expression of σW-dependent genes were relatively mild, which implies that σW-dependent transcription under non-stress conditions is not strictly related to RasP and PrsW. Lastly, we show that the pleiotropic phenotype of rasP mutant cells, which have defects in competence development, protein secretion and membrane protein production, is not mirrored in the transcript profile of these cells. This implies that RasP is not only important for transcriptional regulation via σW, but that this membrane protease also exerts other important post-transcriptional regulatory functions

Probing host pathogen cross-talk by transcriptional profiling of both Mycobacterium tuberculosis and infected human dendritic cells and macrophages

This study provides the proof of principle that probing the host and the microbe transcriptomes simultaneously is a valuable means to accessing unique information on host pathogen interactions. Our results also underline the extraordinary plasticity of host cell and pathogen responses to infection, and provide a solid framework to further understand the complex mechanisms involved in immunity to M. tuberculosis and in mycobacterial adaptation to different intracellular environments