@article{8697, abstract = {In the computation of the material properties of random alloys, the method of 'special quasirandom structures' attempts to approximate the properties of the alloy on a finite volume with higher accuracy by replicating certain statistics of the random atomic lattice in the finite volume as accurately as possible. In the present work, we provide a rigorous justification for a variant of this method in the framework of the Thomas–Fermi–von Weizsäcker (TFW) model. Our approach is based on a recent analysis of a related variance reduction method in stochastic homogenization of linear elliptic PDEs and the locality properties of the TFW model. Concerning the latter, we extend an exponential locality result by Nazar and Ortner to include point charges, a result that may be of independent interest.}, author = {Fischer, Julian L and Kniely, Michael}, issn = {13616544}, journal = {Nonlinearity}, number = {11}, pages = {5733--5772}, publisher = {IOP Publishing}, title = {{Variance reduction for effective energies of random lattices in the Thomas-Fermi-von Weizsäcker model}}, doi = {10.1088/1361-6544/ab9728}, volume = {33}, year = {2020}, } @article{8680, abstract = {Animal development entails the organization of specific cell types in space and time, and spatial patterns must form in a robust manner. In the zebrafish spinal cord, neural progenitors form stereotypic patterns despite noisy morphogen signaling and large-scale cellular rearrangements during morphogenesis and growth. By directly measuring adhesion forces and preferences for three types of endogenous neural progenitors, we provide evidence for the differential adhesion model in which differences in intercellular adhesion mediate cell sorting. Cell type–specific combinatorial expression of different classes of cadherins (N-cadherin, cadherin 11, and protocadherin 19) results in homotypic preference ex vivo and patterning robustness in vivo. Furthermore, the differential adhesion code is regulated by the sonic hedgehog morphogen gradient. We propose that robust patterning during tissue morphogenesis results from interplay between adhesion-based self-organization and morphogen-directed patterning.}, author = {Tsai, Tony Y.-C. and Sikora, Mateusz K and Xia, Peng and Colak-Champollion, Tugba and Knaut, Holger and Heisenberg, Carl-Philipp J and Megason, Sean G.}, issn = {1095-9203}, journal = {Science}, keywords = {Multidisciplinary}, number = {6512}, pages = {113--116}, publisher = {American Association for the Advancement of Science}, title = {{An adhesion code ensures robust pattern formation during tissue morphogenesis}}, doi = {10.1126/science.aba6637}, volume = {370}, year = {2020}, } @article{8707, abstract = {Dynamic changes in the three-dimensional (3D) organization of chromatin are associated with central biological processes, such as transcription, replication and development. Therefore, the comprehensive identification and quantification of these changes is fundamental to understanding of evolutionary and regulatory mechanisms. Here, we present Comparison of Hi-C Experiments using Structural Similarity (CHESS), an algorithm for the comparison of chromatin contact maps and automatic differential feature extraction. We demonstrate the robustness of CHESS to experimental variability and showcase its biological applications on (1) interspecies comparisons of syntenic regions in human and mouse models; (2) intraspecies identification of conformational changes in Zelda-depleted Drosophila embryos; (3) patient-specific aberrant chromatin conformation in a diffuse large B-cell lymphoma sample; and (4) the systematic identification of chromatin contact differences in high-resolution Capture-C data. In summary, CHESS is a computationally efficient method for the comparison and classification of changes in chromatin contact data.}, author = { Galan, Silvia and Machnik, Nick N and Kruse, Kai and Díaz, Noelia and Marti-Renom, Marc A and Vaquerizas, Juan M}, issn = {15461718}, journal = {Nature Genetics}, pages = {1247--1255}, publisher = {Springer Nature}, title = {{CHESS enables quantitative comparison of chromatin contact data and automatic feature extraction}}, doi = {10.1038/s41588-020-00712-y}, volume = {52}, year = {2020}, } @article{8679, abstract = {A central goal of artificial intelligence in high-stakes decision-making applications is to design a single algorithm that simultaneously expresses generalizability by learning coherent representations of their world and interpretable explanations of its dynamics. Here, we combine brain-inspired neural computation principles and scalable deep learning architectures to design compact neural controllers for task-specific compartments of a full-stack autonomous vehicle control system. We discover that a single algorithm with 19 control neurons, connecting 32 encapsulated input features to outputs by 253 synapses, learns to map high-dimensional inputs into steering commands. This system shows superior generalizability, interpretability and robustness compared with orders-of-magnitude larger black-box learning systems. The obtained neural agents enable high-fidelity autonomy for task-specific parts of a complex autonomous system.}, author = {Lechner, Mathias and Hasani, Ramin and Amini, Alexander and Henzinger, Thomas A and Rus, Daniela and Grosu, Radu}, issn = {2522-5839}, journal = {Nature Machine Intelligence}, pages = {642--652}, publisher = {Springer Nature}, title = {{Neural circuit policies enabling auditable autonomy}}, doi = {10.1038/s42256-020-00237-3}, volume = {2}, year = {2020}, } @article{8670, abstract = {The α–z Rényi relative entropies are a two-parameter family of Rényi relative entropies that are quantum generalizations of the classical α-Rényi relative entropies. In the work [Adv. Math. 365, 107053 (2020)], we decided the full range of (α, z) for which the data processing inequality (DPI) is valid. In this paper, we give algebraic conditions for the equality in DPI. For the full range of parameters (α, z), we give necessary conditions and sufficient conditions. For most parameters, we give equivalent conditions. This generalizes and strengthens the results of Leditzky et al. [Lett. Math. Phys. 107, 61–80 (2017)].}, author = {Zhang, Haonan}, issn = {00222488}, journal = {Journal of Mathematical Physics}, number = {10}, publisher = {AIP Publishing}, title = {{Equality conditions of data processing inequality for α-z Rényi relative entropies}}, doi = {10.1063/5.0022787}, volume = {61}, year = {2020}, }