TY - JOUR AB - The fact that the complete graph K5 does not embed in the plane has been generalized in two independent directions. On the one hand, the solution of the classical Heawood problem for graphs on surfaces established that the complete graph Kn embeds in a closed surface M (other than the Klein bottle) if and only if (n−3)(n−4) ≤ 6b1(M), where b1(M) is the first Z2-Betti number of M. On the other hand, van Kampen and Flores proved that the k-skeleton of the n-dimensional simplex (the higher-dimensional analogue of Kn+1) embeds in R2k if and only if n ≤ 2k + 1. Two decades ago, Kühnel conjectured that the k-skeleton of the n-simplex embeds in a compact, (k − 1)-connected 2k-manifold with kth Z2-Betti number bk only if the following generalized Heawood inequality holds: (k+1 n−k−1) ≤ (k+1 2k+1)bk. This is a common generalization of the case of graphs on surfaces as well as the van Kampen–Flores theorem. In the spirit of Kühnel’s conjecture, we prove that if the k-skeleton of the n-simplex embeds in a compact 2k-manifold with kth Z2-Betti number bk, then n ≤ 2bk(k 2k+2)+2k+4. This bound is weaker than the generalized Heawood inequality, but does not require the assumption that M is (k−1)-connected. Our results generalize to maps without q-covered points, in the spirit of Tverberg’s theorem, for q a prime power. Our proof uses a result of Volovikov about maps that satisfy a certain homological triviality condition. AU - Goaoc, Xavier AU - Mabillard, Isaac AU - Paták, Pavel AU - Patakova, Zuzana AU - Tancer, Martin AU - Wagner, Uli ID - 610 IS - 2 JF - Israel Journal of Mathematics TI - On generalized Heawood inequalities for manifolds: A van Kampen–Flores type nonembeddability result VL - 222 ER - TY - JOUR AB - Small RNAs (sRNAs) regulate genes in plants and animals. Here, we show that population-wide differences in color patterns in snapdragon flowers are caused by an inverted duplication that generates sRNAs. The complexity and size of the transcripts indicate that the duplication represents an intermediate on the pathway to microRNA evolution. The sRNAs repress a pigment biosynthesis gene, creating a yellow highlight at the site of pollinator entry. The inverted duplication exhibits steep clines in allele frequency in a natural hybrid zone, showing that the allele is under selection. Thus, regulatory interactions of evolutionarily recent sRNAs can be acted upon by selection and contribute to the evolution of phenotypic diversity. AU - Bradley, Desmond AU - Xu, Ping AU - Mohorianu, Irina AU - Whibley, Annabel AU - Field, David AU - Tavares, Hugo AU - Couchman, Matthew AU - Copsey, Lucy AU - Carpenter, Rosemary AU - Li, Miaomiao AU - Li, Qun AU - Xue, Yongbiao AU - Dalmay, Tamas AU - Coen, Enrico ID - 611 IS - 6365 JF - Science SN - 00368075 TI - Evolution of flower color pattern through selection on regulatory small RNAs VL - 358 ER - TY - JOUR AB - Bacteria in groups vary individually, and interact with other bacteria and the environment to produce population-level patterns of gene expression. Investigating such behavior in detail requires measuring and controlling populations at the single-cell level alongside precisely specified interactions and environmental characteristics. Here we present an automated, programmable platform that combines image-based gene expression and growth measurements with on-line optogenetic expression control for hundreds of individual Escherichia coli cells over days, in a dynamically adjustable environment. This integrated platform broadly enables experiments that bridge individual and population behaviors. We demonstrate: (i) population structuring by independent closed-loop control of gene expression in many individual cells, (ii) cell-cell variation control during antibiotic perturbation, (iii) hybrid bio-digital circuits in single cells, and freely specifiable digital communication between individual bacteria. These examples showcase the potential for real-time integration of theoretical models with measurement and control of many individual cells to investigate and engineer microbial population behavior. AU - Chait, Remy P AU - Ruess, Jakob AU - Bergmiller, Tobias AU - Tkacik, Gasper AU - Guet, Calin C ID - 613 IS - 1 JF - Nature Communications SN - 20411723 TI - Shaping bacterial population behavior through computer interfaced control of individual cells VL - 8 ER - TY - JOUR AB - We show that the Dyson Brownian Motion exhibits local universality after a very short time assuming that local rigidity and level repulsion of the eigenvalues hold. These conditions are verified, hence bulk spectral universality is proven, for a large class of Wigner-like matrices, including deformed Wigner ensembles and ensembles with non-stochastic variance matrices whose limiting densities differ from Wigner's semicircle law. AU - Erdös, László AU - Schnelli, Kevin ID - 615 IS - 4 JF - Annales de l'institut Henri Poincare (B) Probability and Statistics SN - 02460203 TI - Universality for random matrix flows with time dependent density VL - 53 ER - TY - CHAP AB - Genetic factors might be largely responsible for the development of autism spectrum disorder (ASD) that alone or in combination with specific environmental risk factors trigger the pathology. Multiple mutations identified in ASD patients that impair synaptic function in the central nervous system are well studied in animal models. How these mutations might interact with other risk factors is not fully understood though. Additionally, how systems outside of the brain are altered in the context of ASD is an emerging area of research. Extracerebral influences on the physiology could begin in utero and contribute to changes in the brain and in the development of other body systems and further lead to epigenetic changes. Therefore, multiple recent studies have aimed at elucidating the role of gene-environment interactions in ASD. Here we provide an overview on the extracerebral systems that might play an important associative role in ASD and review evidence regarding the potential roles of inflammation, trace metals, metabolism, genetic susceptibility, enteric nervous system function and the microbiota of the gastrointestinal (GI) tract on the development of endophenotypes in animal models of ASD. By influencing environmental conditions, it might be possible to reduce or limit the severity of ASD pathology. AU - Hill Yardin, Elisa AU - Mckeown, Sonja AU - Novarino, Gaia AU - Grabrucker, Andreas ED - Schmeisser, Michael ED - Boekers, Tobias ID - 623 SN - 03015556 T2 - Translational Anatomy and Cell Biology of Autism Spectrum Disorder TI - Extracerebral dysfunction in animal models of autism spectrum disorder VL - 224 ER -