Reduced basis isogeometric mortar approximations for eigenvalue problems in vibroacoustics

We simulate the vibration of a violin bridge in a multi-query context using reduced basis techniques. The mathematical model is based on an eigenvalue problem for the orthotropic linear elasticity equation. In addition to the nine material parameters, a geometrical thickness parameter is considered. This parameter enters as a 10th material parameter into the system by a mapping onto a parameter independent reference domain. The detailed simulation is carried out by isogeometric mortar methods. Weakly coupled patch-wise tensorial structured isogeometric elements are of special interest for complex geometries with piecewise smooth but curvilinear boundaries. To obtain locality in the detailed system, we use the saddle point approach and do not apply static condensation techniques. However within the reduced basis context, it is natural to eliminate the Lagrange multiplier and formulate a reduced eigenvalue problem for a symmetric positive definite matrix. The selection of the snapshots is controlled by a multi-query greedy strategy taking into account an error indicator allowing for multiple eigenvalues

Froth-like minimizers of a non local free energy functional with competing interactions

We investigate the ground and low energy states of a one dimensional non local free energy functional describing at a mean field level a spin system with both ferromagnetic and antiferromagnetic interactions. In particular, the antiferromagnetic interaction is assumed to have a range much larger than the ferromagnetic one. The competition between these two effects is expected to lead to the spontaneous emergence of a regular alternation of long intervals on which the spin profile is magnetized either up or down, with an oscillation scale intermediate between the range of the ferromagnetic and that of the antiferromagnetic interaction. In this sense, the optimal or quasi-optimal profiles are "froth-like": if seen on the scale of the antiferromagnetic potential they look neutral, but if seen at the microscope they actually consist of big bubbles of two different phases alternating among each other. In this paper we prove the validity of this picture, we compute the oscillation scale of the quasi-optimal profiles and we quantify their distance in norm from a reference periodic profile. The proof consists of two main steps: we first coarse grain the system on a scale intermediate between the range of the ferromagnetic potential and the expected optimal oscillation scale; in this way we reduce the original functional to an effective "sharp interface" one. Next, we study the latter by reflection positivity methods, which require as a key ingredient the exact locality of the short range term. Our proof has the conceptual interest of combining coarse graining with reflection positivity methods, an idea that is presumably useful in much more general contexts than the one studied here.Comment: 38 pages, 2 figure

Prior Mating Experience Modulates the Dispersal of Drosophila in Males More Than in Females

Cues from both an animal’s internal physiological state and its local environment may influence its decision to disperse. However, identifying and quantifying the causative factors underlying the initiation of dispersal is difficult in uncontrolled natural settings. In this study, we automatically monitored the movement of fruit flies and examined the influence of food availability, sex, and reproductive status on their dispersal between laboratory environments. In general, flies with mating experience behave as if they are hungrier than virgin flies, leaving at a greater rate when food is unavailable and staying longer when it is available. Males dispersed at a higher rate and were more active than females when food was unavailable, but tended to stay longer in environments containing food than did females. We found no significant relationship between weight and activity, suggesting the behavioral differences between males and females are caused by an intrinsic factor relating to the sex of a fly and not simply its body size. Finally, we observed a significant difference between the dispersal of the natural isolate used throughout this study and the widely-used laboratory strain, Canton-S, and show that the difference cannot be explained by allelic differences in the foraging gene

A guided tour of asynchronous cellular automata

Research on asynchronous cellular automata has received a great amount of attention these last years and has turned to a thriving field. We survey the recent research that has been carried out on this topic and present a wide state of the art where computing and modelling issues are both represented.Comment: To appear in the Journal of Cellular Automat

Functional divergence in the role of N-linked glycosylation in smoothened signaling

The G protein-coupled receptor (GPCR) Smoothened (Smo) is the requisite signal transducer of the evolutionarily conserved Hedgehog (Hh) pathway. Although aspects of Smo signaling are conserved from Drosophila to vertebrates, significant differences have evolved. These include changes in its active sub-cellular localization, and the ability of vertebrate Smo to induce distinct G protein-dependent and independent signals in response to ligand. Whereas the canonical Smo signal to Gli transcriptional effectors occurs in a G protein-independent manner, its non-canonical signal employs Gαi. Whether vertebrate Smo can selectively bias its signal between these routes is not yet known. N-linked glycosylation is a post-translational modification that can influence GPCR trafficking, ligand responsiveness and signal output. Smo proteins in Drosophila and vertebrate systems harbor N-linked glycans, but their role in Smo signaling has not been established. Herein, we present a comprehensive analysis of Drosophila and murine Smo glycosylation that supports a functional divergence in the contribution of N-linked glycans to signaling. Of the seven predicted glycan acceptor sites in Drosophila Smo, one is essential. Loss of N-glycosylation at this site disrupted Smo trafficking and attenuated its signaling capability. In stark contrast, we found that all four predicted N-glycosylation sites on murine Smo were dispensable for proper trafficking, agonist binding and canonical signal induction. However, the under-glycosylated protein was compromised in its ability to induce a non-canonical signal through Gαi, providing for the first time evidence that Smo can bias its signal and that a post-translational modification can impact this process. As such, we postulate a profound shift in N-glycan function from affecting Smo ER exit in flies to influencing its signal output in mice

Hmgcr in the Corpus Allatum Controls Sexual Dimorphism of Locomotor Activity and Body Size via the Insulin Pathway in Drosophila

The insulin signaling pathway has been implicated in several physiological and developmental processes. In mammals, it controls expression of 3-Hydroxy-3-Methylglutaryl CoA Reductase (HMGCR), a key enzyme in cholesterol biosynthesis. In insects, which can not synthesize cholesterol de novo, the HMGCR is implicated in the biosynthesis of juvenile hormone (JH). However, the link between the insulin pathway and JH has not been established. In Drosophila, mutations in the insulin receptor (InR) decrease the rate of JH synthesis. It is also known that both the insulin pathway and JH play a role in the control of sexual dimorphism in locomotor activity. In studies here, to demonstrate that the insulin pathway and HMGCR are functionally linked in Drosophila, we first show that hmgcr mutation also disrupts the sexual dimorphism. Similarly to the InR, HMGCR is expressed in the corpus allatum (ca), which is the gland where JH biosynthesis occurs. Two p[hmgcr-GAL4] lines were therefore generated where RNAi was targeted specifically against the HMGCR or the InR in the ca. We found that RNAi-HMGCR blocked HMGCR expression, while the RNAi-InR blocked both InR and HMGCR expression. Each RNAi caused disruption of sexual dimorphism and produced dwarf flies at specific rearing temperatures. These results provide evidence: (i) that HMGCR expression is controlled by the InR and (ii) that InR and HMGCR specifically in the ca, are involved in the control of body size and sexual dimorphism of locomotor activity

Inositol 1,4,5- Trisphosphate Receptor Function in Drosophila Insulin Producing Cells

The Inositol 1,4,5- trisphosphate receptor (InsP3R) is an intracellular ligand gated channel that releases calcium from intracellular stores in response to extracellular signals. To identify and understand physiological processes and behavior that depends on the InsP3 signaling pathway at a systemic level, we are studying Drosophila mutants for the InsP3R (itpr) gene. Here, we show that growth defects precede larval lethality and both are a consequence of the inability to feed normally. Moreover, restoring InsP3R function in insulin producing cells (IPCs) in the larval brain rescues the feeding deficit, growth and lethality in the itpr mutants to a significant extent. We have previously demonstrated a critical requirement for InsP3R activity in neuronal cells, specifically in aminergic interneurons, for larval viability. Processes from the IPCs and aminergic domain are closely apposed in the third instar larval brain with no visible cellular overlap. Ubiquitous depletion of itpr by dsRNA results in feeding deficits leading to larval lethality similar to the itpr mutant phenotype. However, when itpr is depleted specifically in IPCs or aminergic neurons, the larvae are viable. These data support a model where InsP3R activity in non-overlapping neuronal domains independently rescues larval itpr phenotypes by non-cell autonomous mechanisms

Dopamine Modulates the Rest Period Length without Perturbation of Its Power Law Distribution in Drosophila melanogaster

We analyzed the effects of dopamine signaling on the temporal organization of rest and activity in Drosophila melanogaster. Locomotor behaviors were recorded using a video-monitoring system, and the amounts of movements were quantified by using an image processing program. We, first, confirmed that rest bout durations followed long-tailed (i.e., power-law) distributions, whereas activity bout durations did not with a strict method described by Clauset et al. We also studied the effects of circadian rhythm and ambient temperature on rest bouts and activity bouts. The fraction of activity significantly increased during subjective day and at high temperature, but the power-law exponent of the rest bout distribution was not affected. The reduction in rest was realized by reduction in long rest bouts. The distribution of activity bouts did not change drastically under the above mentioned conditions. We then assessed the effects of dopamine. The distribution of rest bouts became less long-tailed and the time spent in activity significantly increased after the augmentation of dopamine signaling. Administration of a dopamine biosynthesis inhibitor yielded the opposite effects. However, the distribution of activity bouts did not contribute to the changes. These results suggest that the modulation of locomotor behavior by dopamine is predominantly controlled by changing the duration of rest bouts, rather than the duration of activity bouts