@article{6609, abstract = {Mechanical systems facilitate the development of a hybrid quantum technology comprising electrical, optical, atomic and acoustic degrees of freedom1, and entanglement is essential to realize quantum-enabled devices. Continuous-variable entangled fields—known as Einstein–Podolsky–Rosen (EPR) states—are spatially separated two-mode squeezed states that can be used for quantum teleportation and quantum communication2. In the optical domain, EPR states are typically generated using nondegenerate optical amplifiers3, and at microwave frequencies Josephson circuits can serve as a nonlinear medium4,5,6. An outstanding goal is to deterministically generate and distribute entangled states with a mechanical oscillator, which requires a carefully arranged balance between excitation, cooling and dissipation in an ultralow noise environment. Here we observe stationary emission of path-entangled microwave radiation from a parametrically driven 30-micrometre-long silicon nanostring oscillator, squeezing the joint field operators of two thermal modes by 3.40 decibels below the vacuum level. The motion of this micromechanical system correlates up to 50 photons per second per hertz, giving rise to a quantum discord that is robust with respect to microwave noise7. Such generalized quantum correlations of separable states are important for quantum-enhanced detection8 and provide direct evidence of the non-classical nature of the mechanical oscillator without directly measuring its state9. This noninvasive measurement scheme allows to infer information about otherwise inaccessible objects, with potential implications for sensing, open-system dynamics and fundamental tests of quantum gravity. In the future, similar on-chip devices could be used to entangle subsystems on very different energy scales, such as microwave and optical photons.}, author = {Barzanjeh, Shabir and Redchenko, Elena and Peruzzo, Matilda and Wulf, Matthias and Lewis, Dylan and Arnold, Georg M and Fink, Johannes M}, journal = {Nature}, pages = {480--483}, publisher = {Nature Publishing Group}, title = {{Stationary entangled radiation from micromechanical motion}}, doi = {10.1038/s41586-019-1320-2}, volume = {570}, year = {2019}, } @article{6596, abstract = {It is well known that many problems in image recovery, signal processing, and machine learning can be modeled as finding zeros of the sum of maximal monotone and Lipschitz continuous monotone operators. Many papers have studied forward-backward splitting methods for finding zeros of the sum of two monotone operators in Hilbert spaces. Most of the proposed splitting methods in the literature have been proposed for the sum of maximal monotone and inverse-strongly monotone operators in Hilbert spaces. In this paper, we consider splitting methods for finding zeros of the sum of maximal monotone operators and Lipschitz continuous monotone operators in Banach spaces. We obtain weak and strong convergence results for the zeros of the sum of maximal monotone and Lipschitz continuous monotone operators in Banach spaces. Many already studied problems in the literature can be considered as special cases of this paper.}, author = {Shehu, Yekini}, issn = {1420-9012}, journal = {Results in Mathematics}, number = {4}, publisher = {Springer}, title = {{Convergence results of forward-backward algorithms for sum of monotone operators in Banach spaces}}, doi = {10.1007/s00025-019-1061-4}, volume = {74}, year = {2019}, } @article{6601, abstract = {There is increasing evidence that both mechanical and biochemical signals play important roles in development and disease. The development of complex organisms, in particular, has been proposed to rely on the feedback between mechanical and biochemical patterning events. This feedback occurs at the molecular level via mechanosensation but can also arise as an emergent property of the system at the cellular and tissue level. In recent years, dynamic changes in tissue geometry, flow, rheology, and cell fate specification have emerged as key platforms of mechanochemical feedback loops in multiple processes. Here, we review recent experimental and theoretical advances in understanding how these feedbacks function in development and disease.}, author = {Hannezo, Edouard B and Heisenberg, Carl-Philipp J}, issn = {00928674}, journal = {Cell}, number = {1}, pages = {12--25}, publisher = {Elsevier}, title = {{Mechanochemical feedback loops in development and disease}}, doi = {10.1016/j.cell.2019.05.052}, volume = {178}, year = {2019}, } @article{6617, abstract = {The effective large-scale properties of materials with random heterogeneities on a small scale are typically determined by the method of representative volumes: a sample of the random material is chosen—the representative volume—and its effective properties are computed by the cell formula. Intuitively, for a fixed sample size it should be possible to increase the accuracy of the method by choosing a material sample which captures the statistical properties of the material particularly well; for example, for a composite material consisting of two constituents, one would select a representative volume in which the volume fraction of the constituents matches closely with their volume fraction in the overall material. Inspired by similar attempts in materials science, Le Bris, Legoll and Minvielle have designed a selection approach for representative volumes which performs remarkably well in numerical examples of linear materials with moderate contrast. In the present work, we provide a rigorous analysis of this selection approach for representative volumes in the context of stochastic homogenization of linear elliptic equations. In particular, we prove that the method essentially never performs worse than a random selection of the material sample and may perform much better if the selection criterion for the material samples is chosen suitably.}, author = {Fischer, Julian L}, issn = {1432-0673}, journal = {Archive for Rational Mechanics and Analysis}, number = {2}, pages = {635–726}, publisher = {Springer}, title = {{The choice of representative volumes in the approximation of effective properties of random materials}}, doi = {10.1007/s00205-019-01400-w}, volume = {234}, year = {2019}, } @article{6611, abstract = {Cell polarity is crucial for the coordinated development of all multicellular organisms. In plants, this is exemplified by the PIN-FORMED (PIN) efflux carriers of the phytohormone auxin: The polar subcellular localization of the PINs is instructive to the directional intercellular auxin transport, and thus to a plethora of auxin-regulated growth and developmental processes. Despite its importance, the regulation of PIN polar subcellular localization remains poorly understood. Here, we have employed advanced live-cell imaging techniques to study the roles of microtubules and actin microfilaments in the establishment of apical polar localization of PIN2 in the epidermis of the Arabidopsis root meristem. We report that apical PIN2 polarity requires neither intact actin microfilaments nor microtubules, suggesting that the primary spatial cue for polar PIN distribution is likely independent of cytoskeleton-guided endomembrane trafficking.}, author = {Glanc, Matous and Fendrych, Matyas and Friml, Jiří}, journal = {Biomolecules}, number = {6}, publisher = {MDPI}, title = {{PIN2 polarity establishment in arabidopsis in the absence of an intact cytoskeleton}}, doi = {10.3390/biom9060222}, volume = {9}, year = {2019}, }