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 - TY - JOUR AB - The environment changes constantly at various time scales and, in order to survive, species need to keep adapting. Whether these species succeed in avoiding extinction is a major evolutionary question. Using a multilocus evolutionary model of a mutation‐limited population adapting under strong selection, we investigate the effects of the frequency of environmental fluctuations on adaptation. Our results rely on an “adaptive‐walk” approximation and use mathematical methods from evolutionary computation theory to investigate the interplay between fluctuation frequency, the similarity of environments, and the number of loci contributing to adaptation. First, we assume a linear additive fitness function, but later generalize our results to include several types of epistasis. We show that frequent environmental changes prevent populations from reaching a fitness peak, but they may also prevent the large fitness loss that occurs after a single environmental change. Thus, the population can survive, although not thrive, in a wide range of conditions. Furthermore, we show that in a frequently changing environment, the similarity of threats that a population faces affects the level of adaptation that it is able to achieve. We check and supplement our analytical results with simulations. AU - Trubenova, Barbora AU - Krejca, Martin AU - Lehre, Per Kristian AU - Kötzing, Timo ID - 6637 IS - 7 JF - Evolution TI - Surfing on the seascape: Adaptation in a changing environment VL - 73 ER - TY - JOUR AB - In this paper we prove several new results around Gromov's waist theorem. We give a simple proof of Vaaler's theorem on sections of the unit cube using the Borsuk-Ulam-Crofton technique, consider waists of real and complex projective spaces, flat tori, convex bodies in Euclidean space; and establish waist-type results in terms of the Hausdorff measure. AU - Akopyan, Arseniy AU - Hubard, Alfredo AU - Karasev, Roman ID - 6634 IS - 2 JF - Topological Methods in Nonlinear Analysis TI - Lower and upper bounds for the waists of different spaces VL - 53 ER - TY - JOUR AB - The crossing number of a graph G is the least number of crossings over all possible drawings of G. We present a structural characterization of graphs with crossing number one. AU - Silva, André AU - Arroyo Guevara, Alan M AU - Richter, Bruce AU - Lee, Orlando ID - 6638 IS - 11 JF - Discrete Mathematics SN - 0012-365X TI - Graphs with at most one crossing VL - 342 ER - TY - JOUR AB - The spatiotemporal organization of cell divisions constitutes an integral part in the development of multicellular organisms, and mis-regulation of cell divisions can lead to severe developmental defects. Cell divisions have an important morphogenetic function in development by regulating growth and shape acquisition of developing tissues, and, conversely, tissue morphogenesis is known to affect both the rate and orientation of cell divisions. Moreover, cell divisions are associated with an extensive reorganization of the cytoskeleton and adhesion apparatus in the dividing cells that in turn can affect large-scale tissue rheological properties. Thus, the interplay between cell divisions and tissue morphogenesis plays a key role in embryo and tissue morphogenesis. AU - Godard, Benoit G AU - Heisenberg, Carl-Philipp J ID - 6631 JF - Current Opinion in Cell Biology SN - 0955-0674 TI - Cell division and tissue mechanics VL - 60 ER - TY - JOUR AB - Commercially available full-color 3D printing allows for detailed control of material deposition in a volume, but an exact reproduction of a target surface appearance is hampered by the strong subsurface scattering that causes nontrivial volumetric cross-talk at the print surface. Previous work showed how an iterative optimization scheme based on accumulating absorptive materials at the surface can be used to find a volumetric distribution of print materials that closely approximates a given target appearance. In this work, we first revisit the assumption that pushing the absorptive materials to the surface results in minimal volumetric cross-talk. We design a full-fledged optimization on a small domain for this task and confirm this previously reported heuristic. Then, we extend the above approach that is critically limited to color reproduction on planar surfaces, to arbitrary 3D shapes. Our method enables high-fidelity color texture reproduction on 3D prints by effectively compensating for internal light scattering within arbitrarily shaped objects. In addition, we propose a content-aware gamut mapping that significantly improves color reproduction for the pathological case of thin geometric features. Using a wide range of sample objects with complex textures and geometries, we demonstrate color reproduction whose fidelity is superior to state-of-the-art drivers for color 3D printers. AU - Sumin, Denis AU - Weyrich, Tim AU - Rittig, Tobias AU - Babaei, Vahid AU - Nindel, Thomas AU - Wilkie, Alexander AU - Didyk, Piotr AU - Bickel, Bernd AU - Křivánek, Jaroslav AU - Myszkowski, Karol ID - 6660 IS - 4 JF - ACM Transactions on Graphics SN - 0730-0301 TI - Geometry-aware scattering compensation for 3D printing VL - 38 ER -