Splash singularities for the one-phase Muskat problem in stable regimes

This paper shows finite time singularity formation for the Muskat problem in a stable regime. The framework we exhibit is with a dry region, where the density and the viscosity are set equal to 0 (the gradient of the pressure is equal to (0, 0)) in the complement of the fluid domain. The singularity is a splash-type: a smooth fluid boundary collapses due to two different particles evolve to collide at a single point. This is the first example of a splash singularity for a parabolic problem.Ministerio de Ciencia e InnovaciónEuropean Research CouncilNational Science FoundationOffice of Naval Researc

Finite time singularities for the free boundary incompressible Euler equations

In this paper, we prove the existence of smooth initial data for the 2D free boundary incompressible Euler equations (also known for some particular scenarios as the water wave problem), for which the smoothness of the interface breaks down in finite time into a splash singularity or a splat singularity.Ministerio de Ciencia e InnovaciónEuropean Research CouncilNational Science Foundatio

Splash singularity for water waves

We exhibit smooth initial data for the two-dimensional (2D) waterwave equation for which we prove that smoothness of the interface breaks down in finite time. Moreover, we show a stability result together with numerical evidence that there exist solutions of the 2D water-wave equation that start from a graph, turn over, and collapse in a splash singularity (self-intersecting curve in one point) in finite time.Ministerio de Ciencia e InnovaciónEuropean Research CouncilNational Science Foundatio

Structural stability for the splash singularities of the water waves problem

In this paper we show a structural stability result for water waves. The main motivation for this result is that we would like to exhibit a water wave whose interface starts as a graph and ends in a splash. Numerical simulations lead to an approximate solution with the desired behaviour. The stability result will conclude that near the approximate solution to water waves there is an exact solution.Ministerio de Ciencia e InnovaciónInstituto de Ciencias Matemáticas Severo OchoaEuropean Research CouncilNational Science Foundatio

Turning waves and breakdown for incompressible flows

We consider the evolution of an interface generated between two immiscible, incompressible, and irrotational fluids. Specifically we study the Muskat and water wave problems. We show that starting with a family of initial data given by (α, f0(α)), the interface reaches a regime in finite time in which is no longer a graph. Therefore there exists a time ∗t where the solution of the free boundary problem parameterized as s (α, f(α, t)) blows up:: k∂αfkL∞(t∗) = ∞. In particular, for the Muskat problem, this result allows us to reach an unstable regime, for which the Rayleigh-Taylor condition changes sign and the solution breaks down.Ministerio de Ciencia e InnovaciónEuropean Research CouncilNational Science FoundationOffice of Naval Researc

Finite time singularities for water waves with surface tension

Here we consider the 2D free boundary incompressible Euler equation with surface tension. We prove that the surface tension does not prevent a finite time splash or splat singularity, i.e. that the curve touches itself either in a point or along an arc. To do so, the main ingredients of the proof are a transformation to desingularize the curve and a priori energy estimates.Ministerio de Ciencia e InnovaciónEuropean Research CouncilNational Science Foundatio

AlN-based BAW resonators with CNT electrodes for gravimetric biosensing

Solidly mounted resonators (SMRs) with a top carbon nanotubes (CNTs) surface coating that doubles as an electrode and as a sensing layer have been fabricated. The influence of the CNTs on the frequency response of the resonators was studied by direct comparison to identical devices with a top metallic electrode. It was found that the CNTs introduced significantly less mass load on the resonators and these devices exhibited a greater quality factor, Q (>2000, compared to ∼1000 for devices with metal electrodes), which increases the gravimetric sensitivity of the devices by allowing the tracking of smaller frequency shifts. Protein solutions with different concentrations were loaded on the top of the resonators and their responses to mass-load from physically adsorbed coatings were investigated. Results show that resonators using CNTs as the top electrode exhibited a higher frequency change for a given load (∼0.25 MHz cm2 ng−1) compared to that of a metal thin film electrode (∼0.14 MHz cm2 ng−1), due to the lower mass of the CNT electrodes and their higher active surface area compared to that of a thin film metal electrode. It is therefore concluded that the use of CNT electrodes on resonators for their use as gravimetric biosensors is a significant improvement over metallic electrodes that are normally employed

Rucaparib for patients with platinum-sensitive, recurrent ovarian carcinoma (ARIEL3): post-progression outcomes and updated safety results from a randomised, placebo-controlled, phase 3 trial

BACKGROUND: In ARIEL3, rucaparib maintenance treatment significantly improved progression-free survival versus placebo. Here, we report prespecified, investigator-assessed, exploratory post-progression endpoints and updated safety data. METHODS: In this ongoing (enrolment complete) randomised, placebo-controlled, phase 3 trial, patients aged 18 years or older who had platinum-sensitive, high-grade serous or endometrioid ovarian, primary peritoneal, or fallopian tube carcinoma and an Eastern Cooperative Oncology Group performance status of 0 or 1 who had received at least two previous platinum-based chemotherapy regimens and responded to their last platinum-based regimen were randomly assigned (2:1) to oral rucaparib (600 mg twice daily) or placebo in 28-day cycles using a computer-generated sequence (block size of six with stratification based on homologous recombination repair gene mutation status, progression-free interval following penultimate platinum-based regimen, and best response to most recent platinum-based regimen). Patients, investigators, site staff, assessors, and the funder were masked to assignments. The primary endpoint of investigator-assessed progression-free survival has been previously reported. Prespecified, exploratory outcomes of chemotherapy-free interval (CFI), time to start of first subsequent therapy (TFST), time to disease progression on subsequent therapy or death (PFS2), and time to start of second subsequent therapy (TSST) and updated safety were analysed (visit cutoff Dec 31, 2017). Efficacy analyses were done in all patients randomised to three nested cohorts: patients with BRCA mutations, patients with homologous recombination deficiencies, and the intention-to-treat population. Safety analyses included all patients who received at least one dose of study treatment. This trial is registered with ClinicalTrials.gov, NCT01968213. FINDINGS: Between April 7, 2014, and July 19, 2016, 564 patients were enrolled and randomly assigned to rucaparib (n=375) or placebo (n=189). Median follow-up was 28·1 months (IQR 22·0-33·6). In the intention-to-treat population, median CFI was 14·3 months (95% CI 13·0-17·4) in the rucaparib group versus 8·8 months (8·0-10·3) in the placebo group (hazard ratio [HR] 0·43 [95% CI 0·35-0·53]; p<0·0001), median TFST was 12·4 months (11·1-15·2) versus 7·2 months (6·4-8·6; HR 0·43 [0·35-0·52]; p<0·0001), median PFS2 was 21·0 months (18·9-23·6) versus 16·5 months (15·2-18·4; HR 0·66 [0·53-0·82]; p=0·0002), and median TSST was 22·4 months (19·1-24·5) versus 17·3 months (14·9-19·4; HR 0·68 [0·54-0·85]; p=0·0007). CFI, TFST, PFS2, and TSST were also significantly longer with rucaparib than placebo in the BRCA-mutant and homologous recombination-deficient cohorts. The most frequent treatment-emergent adverse event of grade 3 or higher was anaemia or decreased haemoglobin (80 [22%] patients in the rucaparib group vs one [1%] patient in the placebo group). Serious treatment-emergent adverse events were reported in 83 (22%) patients in the rucaparib group and 20 (11%) patients in the placebo group. Two treatment-related deaths have been previously reported in this trial; there were no new treatment-related deaths. INTERPRETATION: In these exploratory analyses over a median follow-up of more than 2 years, rucaparib maintenance treatment led to a clinically meaningful delay in starting subsequent therapy and provided lasting clinical benefits versus placebo in all three analysis cohorts. Updated safety data were consistent with previous reports. FUNDING: Clovis Oncology

The CRE1 carbon catabolite repressor of the fungus Trichoderma reesei: a master regulator of carbon assimilation

<p>Abstract</p> <p>Background</p> <p>The identification and characterization of the transcriptional regulatory networks governing the physiology and adaptation of microbial cells is a key step in understanding their behaviour. One such wide-domain regulatory circuit, essential to all cells, is carbon catabolite repression (CCR): it allows the cell to prefer some carbon sources, whose assimilation is of high nutritional value, over less profitable ones. In lower multicellular fungi, the C2H2 zinc finger CreA/CRE1 protein has been shown to act as the transcriptional repressor in this process. However, the complete list of its gene targets is not known.</p> <p>Results</p> <p>Here, we deciphered the CRE1 regulatory range in the model cellulose and hemicellulose-degrading fungus <it>Trichoderma reesei </it>(anamorph of <it>Hypocrea jecorina</it>) by profiling transcription in a wild-type and a delta-<it>cre1 </it>mutant strain on glucose at constant growth rates known to repress and de-repress CCR-affected genes. Analysis of genome-wide microarrays reveals 2.8% of transcripts whose expression was regulated in at least one of the four experimental conditions: 47.3% of which were repressed by CRE1, whereas 29.0% were actually induced by CRE1, and 17.2% only affected by the growth rate but CRE1 independent. Among CRE1 repressed transcripts, genes encoding unknown proteins and transport proteins were overrepresented. In addition, we found CRE1-repression of nitrogenous substances uptake, components of chromatin remodeling and the transcriptional mediator complex, as well as developmental processes.</p> <p>Conclusions</p> <p>Our study provides the first global insight into the molecular physiological response of a multicellular fungus to carbon catabolite regulation and identifies several not yet known targets in a growth-controlled environment.</p