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

GIMAP6 is required for T cell maintenance and efficient autophagy in mice

The GTPases of the immunity-associated proteins (GIMAP) GTPases are a family of proteins expressed strongly in the adaptive immune system. We have previously reported that in human cells one member of this family, GIMAP6, interacts with the ATG8 family member GABARAPL2, and is recruited to autophagosomes upon starvation, suggesting a role for GIMAP6 in the autophagic process. To study this possibility and the function of GIMAP6 in the immune system, we have established a mouse line in which the Gimap6 gene can be inactivated by Cre-mediated recombination. In mice bred to carry the CD2Cre transgene such that the Gimap6 gene was deleted within the T and B cell lineages there was a 50-70% reduction in peripheral CD4(+) and CD8(+) T cells. Analysis of splenocyte-derived proteins from these mice indicated increased levels of MAP1LC3B, particularly the lipidated LC3-II form, and S405-phosphorylation of SQSTM1. Electron microscopic measurements of Gimap6(-/-) CD4(+) T cells indicated an increased mitochondrial/cytoplasmic volume ratio and increased numbers of autophagosomes. These results are consistent with autophagic disruption in the cells. However, Gimap6(-/-) T cells were largely normal in character, could be effectively activated in vitro and supported T cell-dependent antibody production. Treatment in vitro of CD4(+) splenocytes from GIMAP6(fl/fl) ERT2Cre mice with 4-hydroxytamoxifen resulted in the disappearance of GIMAP6 within five days. In parallel, increased phosphorylation of SQSTM1 and TBK1 was observed. These results indicate a requirement for GIMAP6 in the maintenance of a normal peripheral adaptive immune system and a significant role for the protein in normal autophagic processes. Moreover, as GIMAP6 is expressed in a cell-selective manner, this indicates the potential existence of a cell-restricted mode of autophagic regulation.Peer reviewe

Spectral estimates for saddle point matrices arising in weak constraint four-dimensional variational data assimilation

We consider the large-sparse symmetric linear systems of equations that arise in the solution of weak constraint four-dimensional variational data assimilation, a method of high interest for numerical weather prediction. These systems can be written as saddle point systems with a $3 \times 3$ block structure but block eliminations can be performed to reduce them to saddle point systems with a $2 \times 2$ block structure, or further to symmetric positive definite systems. In this paper, we analyse how sensitive the spectra of these matrices are to the number of observations of the underlying dynamical system. We also obtain bounds on the eigenvalues of the matrices. Numerical experiments are used to confirm the theoretical analysis and bounds

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

Stochastic B-series and order conditions for exponential integrators

We discuss stochastic differential equations with a stiff linear part and their approximation by stochastic exponential integrators. Representing the exact and approximate solutions using B-series and rooted trees, we derive the order conditions for stochastic exponential integrators. The resulting general order theory covers both It\^{o} and Stratonovich integration

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

RNAi-Mediated Knock-Down of Arylamine N-acetyltransferase-1 Expression Induces E-cadherin Up-Regulation and Cell-Cell Contact Growth Inhibition

Arylamine N-acetyltransferase-1 (NAT1) is an enzyme that catalyzes the biotransformation of arylamine and hydrazine substrates. It also has a role in the catabolism of the folate metabolite p-aminobenzoyl glutamate. Recent bioinformatics studies have correlated NAT1 expression with various cancer subtypes. However, a direct role for NAT1 in cell biology has not been established. In this study, we have knocked down NAT1 in the colon adenocarcinoma cell-line HT-29 and found a marked change in cell morphology that was accompanied by an increase in cell-cell contact growth inhibition and a loss of cell viability at confluence. NAT1 knock-down also led to attenuation in anchorage independent growth in soft agar. Loss of NAT1 led to the up-regulation of E-cadherin mRNA and protein levels. This change in E-cadherin was not attributed to RNAi off-target effects and was also observed in the prostate cancer cell-line 22Rv1. In vivo, NAT1 knock-down cells grew with a longer doubling time compared to cells stably transfected with a scrambled RNAi or to parental HT-29 cells. This study has shown that NAT1 affects cell growth and morphology. In addition, it suggests that NAT1 may be a novel drug target for cancer therapeutics

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