TY - JOUR AB - 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. AU - Shehu, Yekini ID - 6596 IS - 4 JF - Results in Mathematics SN - 1422-6383 TI - Convergence results of forward-backward algorithms for sum of monotone operators in Banach spaces VL - 74 ER - TY - JOUR AB - 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. AU - Hannezo, Edouard B AU - Heisenberg, Carl-Philipp J ID - 6601 IS - 1 JF - Cell SN - 00928674 TI - Mechanochemical feedback loops in development and disease VL - 178 ER - TY - JOUR AB - 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. AU - Fischer, Julian L ID - 6617 IS - 2 JF - Archive for Rational Mechanics and Analysis SN - 0003-9527 TI - The choice of representative volumes in the approximation of effective properties of random materials VL - 234 ER - TY - JOUR AB - 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. AU - Glanc, Matous AU - Fendrych, Matyas AU - Friml, Jiří ID - 6611 IS - 6 JF - Biomolecules TI - PIN2 polarity establishment in arabidopsis in the absence of an intact cytoskeleton VL - 9 ER - TY - JOUR AB - This paper establishes an asymptotic formula with a power-saving error term for the number of rational points of bounded height on the singular cubic surface of ℙ3ℚ given by the following equation 𝑥0(𝑥21+𝑥22)−𝑥33=0 in agreement with the Manin-Peyre conjectures. AU - De La Bretèche, Régis AU - Destagnol, Kevin N AU - Liu, Jianya AU - Wu, Jie AU - Zhao, Yongqiang ID - 6620 IS - 12 JF - Science China Mathematics SN - 16747283 TI - On a certain non-split cubic surface VL - 62 ER -