A new div-curl result. Applications to the homogenization of elliptic systems and to the weak continuity of the Jacobian

In this paper a new div-curl result is established in an open set $\Omega$ of $\mathbb{R}^N$, $N\geq 2$, for the product of two sequences of vector-valued functions which are bounded respectively in $L^p(\Omega)^N$ and $L^q(\Omega)^N$, with ${1/p}+{1/q}=1+{1/(N-1)}$, and whose respectively divergence and curl are compact in suitable spaces. We also assume that the product converges weakly in $W^{-1,1}(\Omega)$. The key ingredient of the proof is a compactness result for bounded sequences in $W^{1,q}(\Omega)$, based on the imbedding of $W^{1,q}(S\_{N-1})$ into $L^{p'}(S\_{N-1})$ ($S\_{N-1}$ the unit sphere of $\mathbb{R}^N$) through a suitable selection of annuli on which the gradients are not too high, in the spirit of De Giorgi and Manfredi. The div-curl result is applied to the homogenization of equi-coercive systems whose coefficients are equi-bounded in $L^\rho(\Omega)$ for some \rho\textgreater{}{N-1\over 2} if N\textgreater{}2, or in $L^1(\Omega)$ if $N=2$. It also allows us to prove a weak continuity result for the Jacobian for bounded sequences in $W^{1,N-1}(\Omega)$ satisfying an alternative assumption to the $L^\infty$-strong estimate of Brezis and Nguyen. Two examples show the sharpness of the results

Asymptotic behavior of an elastic beam fixed on a small part of one of its extremities

We study the asymptotic behavior of the solution of an anisotropic, heterogeneous, linearized elasticity problem in a cylinder whose diameter $\epsilon$ tends to zero. The cylinder is assumed to be fixed (homogeneous Dirichlet boundary condition) on the whole of one of its extremities, but only on a small part (of size $\epsilon r^\epsilon$) of the second one; the Neumann boundary condition is assumed on the remainder of the boundary. We show that the result depends on $r^\epsilon$, and that there are 3 critical sizes, namely $r^\epsilon=\epsilon^3$, $r^\epsilon=\epsilon$, and $r^\epsilon=\epsilon^{1/3}$, and in total 7 different regimes. We also prove a corrector result for each behavior of $r^\epsilon$.Comment: Preliminary version of a Note to be published in a slightly abbreviated form in C. R. Acad. Sci. Paris, Ser. I, 338 (2004), pp. 975-98

Estimate of the pressure when its gradient is the divergence of a measure. Applications

International audienceIn this paper, a $W^{-1,N'}$ estimate of the pressure is derived when its gradient is the divergence of a matrix-valued measure on ${\mathbb R}^N$ , or on a regular bounded open set of ${\mathbb R}^N$ . The proof is based partially on the Strauss inequality [Strauss, Partial Differential Equations: Proc. Symp. Pure Math. 23 (1973) 207–214] in dimension two, and on a recent result of Bourgain and Brezis [J. Eur. Math. Soc. 9 (2007) 277–315] in higher dimension. The estimate is used to derive a representation result for divergence free distributions which read as the divergence of a measure, and to prove an existence result for the stationary Navier-Stokes equation when the viscosity tensor is only in L 1

Breakthrough Technologies Reshape the Ewing Sarcoma Molecular Landscape

Ewing sarcoma is a highly aggressive round cell mesenchymal neoplasm, most often occurring in children and young adults. At the molecular level, it is characterized by the presence of recurrent chromosomal translocations. In the last years, next-generation technologies have contributed to a more accurate diagnosis and a refined classification. Moreover, the application of these novel technologies has highlighted the relevance of intertumoral and intratumoral molecular heterogeneity and secondary genetic alterations. Furthermore, they have shown evidence that genomic features can change as the tumor disseminates and are influenced by treatment as well. Similarly, next-generation technologies applied to liquid biopsies will significantly impact patient management by allowing the early detection of relapse and monitoring response to treatment. Finally, the use of these novel technologies has provided data of great value in order to discover new druggable pathways. Thus, this review provides concise updates on the latest progress of these breakthrough technologies, underscoring their importance in the generation of key knowledge, prognosis, and potential treatment of Ewing SarcomaJunta de Andalucía, Consejería de Salud PI-0036-2017 y PI-0040-2017Fundación María García EstradaUniversidad de SevillaJuan de la Cierva Incorporación IJC-2018-036767-ILaboratorio de EdA compatible por el proyecto AECC GCB13-1578, ISCIIIFEDER PI14 / 01466, PI17 / 00464, CIBERONC CB16 / 12/00361Fundación CRIS Contra el Cánce

Cross-Resistance to Abiraterone and Enzalutamide in Castration Resistance Prostate Cancer Cellular Models Is Mediated by AR Transcriptional Reactivation

Androgen deprivation therapy (ADT) and novel hormonal agents (NHAs) (Abiraterone and Enzalutamide) are the goal standard for metastatic prostate cancer (PCa) treatment. Although ADT is initially effective, a subsequent castration resistance status (CRPC) is commonly developed. The expression of androgen receptor (AR) alternative splicing isoforms (AR-V7 and AR-V9) has been associated to CRPC. However, resistance mechanisms to novel NHAs are not yet well understood. Androgen-dependent PCa cell lines were used to generate resistant models to ADT only or in combination with Abiraterone and/or Enzalutamide (concomitant models). Functional and genetic analyses were performed for each resistance model by real-time cell monitoring assays, flow cytometry and RT-qPCR. In androgen-dependent PCa cells, the administration of Abiraterone and/or Enzalutamide as first-line treatment involved a critical inhibition of AR activity associated with a significant cell growth inhibition. Genetic analyses on ADT-resistant PCa cell lines showed that the CRPC phenotype was accompanied by overexpression of AR full-length and AR target genes, but not necessarily AR-V7 and/or AR-V9 isoforms. These ADT resistant cell lines showed higher proliferation rates, migration and invasion abilities. Importantly, ADT resistance induced cross-resistance to Abiraterone and/or Enzalutamide. Similarly, concomitant models possessed an elevated expression of AR full-length and proliferation rates and acquired cross-resistance to its alternative NHA as second-line treatment.Instituto de Salud Carlos III PI17/00989European Regional Development Fund "A way to build Europe"Ramon y Cajal - Ministry of Economy and Competitiveness RYC-2015-18382Ministry of Education, Culture and Sport FPU14/05461University of Granad

Measurement of the cosmic ray spectrum above 4×10184{\times}10^{18} eV using inclined events detected with the Pierre Auger Observatory

A measurement of the cosmic-ray spectrum for energies exceeding $4{\times}10^{18}$ eV is presented, which is based on the analysis of showers with zenith angles greater than $60^{\circ}$ detected with the Pierre Auger Observatory between 1 January 2004 and 31 December 2013. The measured spectrum confirms a flux suppression at the highest energies. Above $5.3{\times}10^{18}$ eV, the "ankle", the flux can be described by a power law $E^{-\gamma}$ with index $\gamma=2.70 \pm 0.02 \,\text{(stat)} \pm 0.1\,\text{(sys)}$ followed by a smooth suppression region. For the energy ($E_\text{s}$) at which the spectral flux has fallen to one-half of its extrapolated value in the absence of suppression, we find $E_\text{s}=(5.12\pm0.25\,\text{(stat)}^{+1.0}_{-1.2}\,\text{(sys)}){\times}10^{19}$ eV.Comment: Replaced with published version. Added journal reference and DO

Energy Estimation of Cosmic Rays with the Engineering Radio Array of the Pierre Auger Observatory

The Auger Engineering Radio Array (AERA) is part of the Pierre Auger Observatory and is used to detect the radio emission of cosmic-ray air showers. These observations are compared to the data of the surface detector stations of the Observatory, which provide well-calibrated information on the cosmic-ray energies and arrival directions. The response of the radio stations in the 30 to 80 MHz regime has been thoroughly calibrated to enable the reconstruction of the incoming electric field. For the latter, the energy deposit per area is determined from the radio pulses at each observer position and is interpolated using a two-dimensional function that takes into account signal asymmetries due to interference between the geomagnetic and charge-excess emission components. The spatial integral over the signal distribution gives a direct measurement of the energy transferred from the primary cosmic ray into radio emission in the AERA frequency range. We measure 15.8 MeV of radiation energy for a 1 EeV air shower arriving perpendicularly to the geomagnetic field. This radiation energy -- corrected for geometrical effects -- is used as a cosmic-ray energy estimator. Performing an absolute energy calibration against the surface-detector information, we observe that this radio-energy estimator scales quadratically with the cosmic-ray energy as expected for coherent emission. We find an energy resolution of the radio reconstruction of 22% for the data set and 17% for a high-quality subset containing only events with at least five radio stations with signal.Comment: Replaced with published version. Added journal reference and DO

Measurement of the Radiation Energy in the Radio Signal of Extensive Air Showers as a Universal Estimator of Cosmic-Ray Energy

We measure the energy emitted by extensive air showers in the form of radio emission in the frequency range from 30 to 80 MHz. Exploiting the accurate energy scale of the Pierre Auger Observatory, we obtain a radiation energy of 15.8 \pm 0.7 (stat) \pm 6.7 (sys) MeV for cosmic rays with an energy of 1 EeV arriving perpendicularly to a geomagnetic field of 0.24 G, scaling quadratically with the cosmic-ray energy. A comparison with predictions from state-of-the-art first-principle calculations shows agreement with our measurement. The radiation energy provides direct access to the calorimetric energy in the electromagnetic cascade of extensive air showers. Comparison with our result thus allows the direct calibration of any cosmic-ray radio detector against the well-established energy scale of the Pierre Auger Observatory.Comment: Replaced with published version. Added journal reference and DOI. Supplemental material in the ancillary file