Shape optimization for quadratic functionals and states with random right-hand sides

In this work, we investigate a particular class of shape optimization problems under uncertainties on the input parameters. More precisely, we are interested in the minimization of the expectation of a quadratic objective in a situation where the state function depends linearly on a random input parameter. This framework covers important objectives such as tracking-type functionals for elliptic second order partial differential equations and the compliance in linear elasticity. We show that the robust objective and its gradient are completely and explicitly determined by low-order moments of the random input. We then derive a cheap, deterministic algorithm to minimize this objective and present model cases in structural optimization

Bernoulli free boundary problems under uncertainty: the convex case

The present article is concerned with solving Bernoulli's exterior free boundary problem in case of an interior boundary which is random. We provide a new regularity result on the map that sends a parametrization of the inner boundary to a parametrization of the outer boundary. Moreover, by assuming that the interior boundary is convex, also the exterior boundary is convex, which enables to identify the boundaries with support functions and to determine their expectations. We in particular construct a confidence region for the outer boundary based on Aumann's expectation and provide a numerical method to compute it

An extremal eigenvalue problem for the Wentzell–Laplace operator

International audienceWe consider the question of giving an upper bound for the first nontrivial eigenvalue of the Wentzell-Laplace operator of a domain $\Omega$, involving only geometrical informations. We provide such an upper bound, by generalizing Brock's inequality concerning Steklov eigenvalues, and we conjecture that balls maximize the Wentzell eigenvalue, in a suitable class of domains, which would improve our bound. To support this conjecture, we prove that balls are critical domains for the Wentzell eigenvalue, in any dimension, and that they are local maximizers in dimension 2 and 3, using an order two sensitivity analysis. We also provide some numerical evidence

Soils Drowned in Water Impoundments: A New Frontier

Water impoundments have major impacts on biogeochemical cycles at the local and global scales. However, although reservoirs flood soils, their biogeochemical evolution below water and its ecological consequences are very poorly documented. We took advantage of the complete emptying of the Guerlédan Reservoir (Brittany, France) to compare the composition of soils flooded for 84 years with that of adjacent non-flooded soils used as reference, in 3 situations contrasted by their soil type (Cambisol and Podzol) and initial land-use (forest or grassland). In the annual drawdown zone, upper horizons of submerged soils are eroded, especially near the upper shore and on slopes. In the permanently drowned area, silty sediments cover drowned soils. Compared to reference soils, forest soils drowned for 84 years maintain their original morphological differentiation, but colors are dull, and the humus (O horizons) have virtually disappeared. Spodic horizons are depleted in poorly crystallized iron minerals while the accumulation of amorphous aluminum compounds remains unchanged. Soil bulk density increases as well as pH while total phosphorus content is almost unchanged. On the other hand, the pH of drowned grassland soils is lower by almost one unit, and the total phosphorus content was halved compared to reference soils. In this context, in addition to the effects of flooding, differences are attributed to post-1950 changes in agricultural practices i.e., liming and fertilization. Organic matter stocks decrease by almost 40%. This rate is similar in Cambisols and Podzols. Assuming that carbon was lost as CO2 and CH4, the corresponding flux averaged over the reservoir's life is close to global areal estimates of CO2 emissions in temperate reservoirs and offsets a significant proportion of the carbon burial in reservoir sediments. Hence, flooded soils contribute significantly to the GHG budget of reservoirs, provide original long-term experimental sites to measure the effects of anoxia on soils and contain archives of past soil properties

Dimension reduction in heterogeneous parametric spaces with application to naval engineering shape design problems

We present the results of the first application in the naval architecture field of a methodology based on active subspaces properties for parameter space reduction. The physical problem considered is the one of the simulation of the hydrodynamic flow past the hull of a ship advancing in calm water. Such problem is extremely relevant at the preliminary stages of the ship design, when several flow simulations are typically carried out by the engineers to assess the dependence of the hull total resistance on the geometrical parameters of the hull, and others related with flows and hull properties. Given the high number of geometric and physical parameters which might affect the total ship drag, the main idea of this work is to employ the active subspaces properties to identify possible lower dimensional structures in the parameter space. Thus, a fully automated procedure has been implemented to produce several small shape perturbations of an original hull CAD geometry, in order to exploit the resulting shapes and to run high fidelity flow simulations with different structural and physical parameters as well, and then collect data for the active subspaces analysis. The free form deformation procedure used to morph the hull shapes, the high fidelity solver based on potential flow theory with fully nonlinear free surface treatment, and the active subspaces analysis tool employed in this work have all been developed and integrated within SISSA mathLab as open source tools. The contribution will also discuss several details of the implementation of such tools, as well as the results of their application to the selected target engineering problem

Alternative splicing and nonsense-mediated decay regulate telomerase reverse transcriptase (TERT) expression during virus-induced lymphomagenesis in vivo

<p>Abstract</p> <p>Background</p> <p>Telomerase activation, a critical step in cell immortalization and oncogenesis, is partly regulated by alternative splicing. In this study, we aimed to use the Marek's disease virus (MDV) T-cell lymphoma model to evaluate TERT regulation by splicing during lymphomagenesis <it>in vivo</it>, from the start point to tumor establishment.</p> <p>Results</p> <p>We first screened cDNA libraries from the chicken MDV lymphoma-derived MSB-1 T- cell line, which we compared with B (DT40) and hepatocyte (LMH) cell lines. The chTERT splicing pattern was cell line-specific, despite similar high levels of telomerase activity. We identified 27 alternative transcripts of chicken TERT (chTERT). Five were in-frame alternative transcripts without <it>in vitro </it>telomerase activity in the presence of viral or chicken telomerase RNA (vTR or chTR), unlike the full-length transcript. Nineteen of the 22 transcripts with a premature termination codon (PTC) harbored a PTC more than 50 nucleotides upstream from the 3' splice junction, and were therefore predicted targets for nonsense-mediated decay (NMD). The major PTC-containing alternatively spliced form identified in MSB1 (ie10) was targeted to the NMD pathway, as demonstrated by UPF1 silencing. We then studied three splicing events separately, and the balance between in-frame alternative splice variants (d5f and d10f) plus the NMD target i10ec and constitutively spliced chTERT transcripts during lymphomagenesis induced by MDV indicated that basal telomerase activity in normal T cells was associated with a high proportion of in-frame non functional isoforms and a low proportion of constitutively spliced chTERT. Telomerase upregulation depended on an increase in active constitutively spliced chTERT levels and coincided with a switch in alternative splicing from an in-frame variant to NMD-targeted variants.</p> <p>Conclusions</p> <p>TERT regulation by splicing plays a key role in telomerase upregulation during lymphomagenesis, through the sophisticated control of constitutive and alternative splicing. Using the MDV T-cell lymphoma model, we identified a chTERT splice variant as a new NMD target.</p

Elevated aluminium concentration in acidified headwater streams lowers aquatic hyphomycete diversity and impairs leaf-litter breakdown.

Aquatic hyphomycetes play an essential role in the decomposition of allochthonous organic matter which is a fundamental process driving the functioning of forested headwater streams. We studied the effect of anthropogenic acidification on aquatic hyphomycetes associated with decaying leaves of Fagus sylvatica in six forested headwater streams (pH range, 4.3-7.1). Non-metric multidimensional scaling revealed marked differences in aquatic hyphomycete assemblages between acidified and reference streams. We found strong relationships between aquatic hyphomycete richness and mean Al concentration (r = -0.998, p < 0.0001) and mean pH (r = 0.962, p < 0.002), meaning that fungal diversity was severely depleted in acidified streams. By contrast, mean fungal biomass was not related to acidity. Leaf breakdown rate was drastically reduced under acidic conditions raising the issue of whether the functioning of headwater ecosystems could be impaired by a loss of aquatic hyphomycete species