On Approximations of the Curve Shortening Flow and of the Mean Curvature Flow based on the DeTurck trick

In this paper we discuss novel numerical schemes for the computation of the curve shortening and mean curvature flows that are based on special reparametrizations. The main idea is to use special solutions to the harmonic map heat flow in order to reparametrize the equations of motion. This idea is widely known from the Ricci flow as the DeTurck trick. By introducing a variable time scale for the harmonic map heat flow, we obtain families of numerical schemes for the reparametrized flows. For the curve shortening flow this family unveils a surprising geometric connection between the numerical schemes in [5] and [9]. For the mean curvature flow we obtain families of schemes with good mesh properties similar to those in [3]. We prove error estimates for the semi-discrete scheme of the curve shortening flow. The behaviour of the fully-discrete schemes with respect to the redistribution of mesh points is studied in numerical experiments. We also discuss possible generalizations of our ideas to other extrinsic flows

The major transcriptional regulatory protein of herpes simplex virus type 1 includes a protease resistant DNA binding domain

Herpes simplex virus type 1 expresses five immediateearly (IE) polypeptides. In the absence of functional Vmw175 (the product of IE gene 3) activation of transcription of later classes of viral genes and repression of IE gene expression does not occur. The recognition of specific DNA sequences by Vmw175 requires, as determined by sensitivity to mutation, a part of the protein highly conserved in the corresponding proteins of related herpes viruses. However, mutations in other parts of the protein can also disrupt specific DNA binding. This paper shows that the DNA binding domain of Vmw175 can be liberated as a functional unit by digestion with proteinase K. Analysis of mutant Vmw175 proteinsshowed that the proteinase K resistant domain has an amino terminus between amino acid residues 229 and 292, while its carboxy terminus is between residues 495 and 518. Mutations outside this region which affect DNA binding by the intact protein do not eliminate binding of the proteinase K resistant domain. This implies that direct DNA binding by Vmw175 involves a linear subsection of the polypeptide, and that mutations in other parts of the polypeptide which affect DNA binding of the whole protein do so by indirect means

Second order splitting of a class of fourth order PDEs with point constraints

We formulate a well-posedness and approximation theory for a class of generalised saddle point problems with a specific form of constraints. In this way we develop an approach to a class of fourth order elliptic partial differential equations with point constraints using the idea of splitting into coupled second order equations. An approach is formulated using a penalty method to impose the constraints. Our main motivation is to treat certain fourth order equations involving the biharmonic operator and point Dirichlet constraints for example arising in the modelling of biomembranes on curved and flat surfaces but the approach may be applied more generally. The theory for well-posedness and approximation is presented in an abstract setting. Several examples are described together with some numerical experiments

Hormone replacement therapy

Martha Hickey, Jane Elliott, Sonia Louise Daviso

Hierarchical Reverberation Mapping

Reverberation mapping (RM) is an important technique in studies of active galactic nuclei (AGN). The key idea of RM is to measure the time lag $\tau$ between variations in the continuum emission from the accretion disc and subsequent response of the broad line region (BLR). The measurement of $\tau$ is typically used to estimate the physical size of the BLR and is combined with other measurements to estimate the black hole mass $M_{\rm BH}$. A major difficulty with RM campaigns is the large amount of data needed to measure $\tau$. Recently, Fine et al (2012) introduced a new approach to RM where the BLR light curve is sparsely sampled, but this is counteracted by observing a large sample of AGN, rather than a single system. The results are combined to infer properties of the sample of AGN. In this letter we implement this method using a hierarchical Bayesian model and contrast this with the results from the previous stacked cross-correlation technique. We find that our inferences are more precise and allow for more straightforward interpretation than the stacked cross-correlation results.Comment: Accepted for publication in MNRAS Letters. 5 pages, 5 figures. Source code for this paper is available at https://github.com/eggplantbren/RMH

An abstract framework for parabolic PDEs on evolving spaces

We present an abstract framework for treating the theory of well-posedness of solutions to abstract parabolic partial differential equations on evolving Hilbert spaces. This theory is applicable to variational formulations of PDEs on evolving spatial domains including moving hypersurfaces. We formulate an appropriate time derivative on evolving spaces called the material derivative and define a weak material derivative in analogy with the usual time derivative in fixed domain problems; our setting is abstract and not restricted to evolving domains or surfaces. Then we show well-posedness to a certain class of parabolic PDEs under some assumptions on the parabolic operator and the data.Comment: 38 pages. Minor typos correcte

Phase Separation of Saturated and Mono-unsaturated Lipids as determined from a Microscopic Model

A molecular model is proposed of a bilayer consisting of fully saturated DPPC and mono unsaturated DOPC. The model not only encompasses the constant density within the hydrophobic core of the bilayer, but also the tendency of chain segments to align. It is solved within self-consistent field theory. A model bilayer of DPPC undergoes a main chain transition to a gel phase, while a bilayer of DOPC does not do so above zero degrees centigrade because of the double bond which disrupts order. We examine structural and thermodynamic properties of these membranes and find our results in reasonable accord with experiment. In particular, order-parameter profiles are in good agreement with NMR experiments. A phase diagram is obtained for mixtures of these lipids in a membrane at zero tension. The system undergoes phase separation below the main-chain transition temperature of the saturated lipid. Extensions to the ternary DPPC, DOPC, and cholesterol system are outlined.Comment: 29 pages, 4 figures, 1 table. revised versio

Mapping of transcription termination within the S segment of SFTS phlebovirus facilitated the generation of NSs-deletant viruses

SFTS phlebovirus (severe fever with thrombocytopenia syndrome virus; SFTSV) is an emerging tick-borne bunyavirus that was first reported in China in 2009. Here we report the generation of a recombinant SFTSV (rHB29NSsKO) that cannot express the viral non-structural protein (NSs) upon infection of cells in culture. We show that rHB29NSsKO replication kinetics are greater in interferon (IFN)-incompetent cells and that the virus is unable to suppress IFN induced in response to viral replication. The data confirm for the first time in the context of virus infection that NSs acts as a virally encoded IFN antagonist and that NSs is dispensable for virus replication. Using 3’ RACE we mapped the 3’ -end of the N and NSs mRNAs, showing that the mRNAs terminate within the coding region of the opposite open reading frame. We show that the 3’ end of the N mRNA terminates upstream of a 5’ -GCCAGCC-3’ motif present in the viral genomic RNA. With this knowledge, and using virus-like particles, we could demonstrate that the last 36 nt of the NSs ORF were needed to ensure the efficient termination of the N mRNA and were required for recombinant virus rescue. We demonstrate it is possible to recover viruses lacking NSs, expressing just a 12 amino acid NSs peptide or viruses encoding eGFP or a NSs-eGFP fusion protein in the NSs locus. This opens the possibility for further studies of NSs and potentially the design of attenuated viruses for vaccination studies