Fully discrete finite element data assimilation method for the heat equation

We consider a finite element discretization for the reconstruction of the final state of the heat equation, when the initial data is unknown, but additional data is given in a sub domain in the space time. For the discretization in space we consider standard continuous affine finite element approximation, and the time derivative is discretized using a backward differentiation. We regularize the discrete system by adding a penalty of the $H^1$-semi-norm of the initial data, scaled with the mesh-parameter. The analysis of the method uses techniques developed in E. Burman and L. Oksanen, Data assimilation for the heat equation using stabilized finite element methods, arXiv, 2016, combining discrete stability of the numerical method with sharp Carleman estimates for the physical problem, to derive optimal error estimates for the approximate solution. For the natural space time energy norm, away from $t=0$, the convergence is the same as for the classical problem with known initial data, but contrary to the classical case, we do not obtain faster convergence for the $L^2$-norm at the final time

Syncrip/hnRNP Q is required for activity-induced Msp300/Nesprin-1 expression and new synapse formation.

Memory and learning involve activity-driven expression of proteins and cytoskeletal reorganization at new synapses, requiring posttranscriptional regulation of localized mRNA a long distance from corresponding nuclei. A key factor expressed early in synapse formation is Msp300/Nesprin-1, which organizes actin filaments around the new synapse. How Msp300 expression is regulated during synaptic plasticity is poorly understood. Here, we show that activity-dependent accumulation of Msp300 in the postsynaptic compartment of the Drosophila larval neuromuscular junction is regulated by the conserved RNA binding protein Syncrip/hnRNP Q. Syncrip (Syp) binds to msp300 transcripts and is essential for plasticity. Single-molecule imaging shows that msp300 is associated with Syp in vivo and forms ribosome-rich granules that contain the translation factor eIF4E. Elevated neural activity alters the dynamics of Syp and the number of msp300:Syp:eIF4E RNP granules at the synapse, suggesting that these particles facilitate translation. These results introduce Syp as an important early acting activity-dependent regulator of a plasticity gene that is strongly associated with human ataxias

GpABC: a Julia package for approximate Bayesian computation with Gaussian process emulation

Motivation Approximate Bayesian computation (ABC) is an important framework within which to infer the structure and parameters of a systems biology model. It is especially suitable for biological systems with stochastic and nonlinear dynamics, for which the likelihood functions are intractable. However, the associated computational cost often limits ABC to models that are relatively quick to simulate in practice. Results We here present a Julia package, GpABC, that implements parameter inference and model selection for deterministic or stochastic models using i) standard rejection ABC or ABC-SMC, or ii) ABC with Gaussian process emulation. The latter significantly reduces the computational cost. Availability and Implementation https://github.com/tanhevg/GpABC.jl Supplementary information Supplementary data are available at Bioinformatics online

The exon junction complex is required for definition and excision of neighboring introns in Drosophila

Splicing of pre-mRNAs results in the deposition of the exon junction complex (EJC) upstream of exon-exon boundaries. The EJC plays crucial post-splicing roles in export, translation, localization, and nonsense-mediated decay of mRNAs. It also aids faithful splicing of pre-mRNAs containing large introns, albeit via an unknown mechanism. Here, we show that the core EJC plus the accessory factors RnpS1 and Acinus aid in definition and efficient splicing of neighboring introns. This requires prior deposition of the EJC in close proximity to either an upstream or downstream splicing event. If present in isolation, EJC-dependent introns are splicing-defective also in wild-type cells. Interestingly, the most affected intron belongs to the piwi locus, which explains the reported transposon desilencing in EJC-depleted Drosophila ovaries. Based on a transcriptome-wide analysis, we propose that the dependency of splicing on the EJC is exploited as a means to control the temporal order of splicing events

Observation of twin beam correlations and quadrature entanglement by frequency doubling in a two-port resonator

We demonstrate production of quantum correlated and entangled beams by second harmonic generation in a nonlinear resonator with two output ports. The output beams at wavelength 428.5 nm exhibit 0.9 dB of nonclassical intensity correlations and 0.3 dB of entanglement.Comment: 5 pages, 7 figure

A genetic screen based on in vivo RNA imaging reveals centrosome-independent mechanisms for localizing gurken transcripts in Drosophila

We have screened chromosome arm 3L for ethyl methanesulfonate-induced mutations that disrupt localization of fluorescently labeled gurken (grk) messenger (m)RNA, whose transport along microtubules establishes both major body axes of the developing Drosophila oocyte. Rapid identification of causative mutations by single-nucleotide polymorphism recombinational mapping and whole-genomic sequencing allowed us to define nine complementation groups affecting grk mRNA localization and other aspects of oogenesis, including alleles of elg1, scaf6, quemao, nudE, Tsc2/gigas, rasp, and Chd5/Wrb, and several null alleles of the armitage Piwi-pathway gene. Analysis of a newly induced kinesin light chain allele shows that kinesin motor activity is required for both efficient grk mRNA localization and oocyte centrosome integrity. We also show that initiation of the dorsoanterior localization of grk mRNA precedes centrosome localization, suggesting that microtubule self-organization contributes to breaking axial symmetry to generate a unique dorsoventral axis

Covariant Generalisation of Codazzi-Raychaudhuri and Area Change Equations for Relativistic Branes

In this paper we derive the generalisations of Gauss-Codazzi, Raychaudhuri and area change equations for classical relativistic branes and multidimensional fluids in arbitrary background manifolds with metricity and torsion. The kinematical description we develop is fully covariant and based on the use of projection tensors tilted with respect to the brane worldsheets.Comment: 29 pages, LaTe

Pulses of Notch activation synchronise oscillating somite cells and entrain the zebrafish segmentation clock

Formation of somites, the rudiments of vertebrate body segments, is an oscillatory process governed by a gene-expression oscillator, the segmentation clock. This operates in each cell of the presomitic mesoderm (PSM), but the individual cells drift out of synchrony when Delta/Notch signalling fails, causing gross anatomical defects. We and others have suggested that this is because synchrony is maintained by pulses of Notch activation, delivered cyclically by each cell to its neighbours, that serve to adjust or reset the phase of the intracellular oscillator. This, however, has never been proved. Here, we provide direct experimental evidence, using zebrafish containing a heat-shock-driven transgene that lets us deliver artificial pulses of expression of the Notch ligand DeltaC. In DeltaC-defective embryos, in which endogenous Notch signalling fails, the artificial pulses restore synchrony, thereby rescuing somite formation. The spacing of segment boundaries produced by repetitive heat-shocking varies according to the time interval between one heat-shock and the next. The induced synchrony is manifest both morphologically and at the level of the oscillations of her1, a core component of the intracellular oscillator. Thus, entrainment of intracellular clocks by periodic activation of the Notch pathway is indeed the mechanism maintaining cell synchrony during somitogenesis