TY - JOUR AB - he approximate graph coloring problem, whose complexity is unresolved in most cases, concerns finding a c-coloring of a graph that is promised to be k-colorable, where c≥k. This problem naturally generalizes to promise graph homomorphism problems and further to promise constraint satisfaction problems. The complexity of these problems has recently been studied through an algebraic approach. In this paper, we introduce two new techniques to analyze the complexity of promise CSPs: one is based on topology and the other on adjunction. We apply these techniques, together with the previously introduced algebraic approach, to obtain new unconditional NP-hardness results for a significant class of approximate graph coloring and promise graph homomorphism problems. AU - Krokhin, Andrei AU - Opršal, Jakub AU - Wrochna, Marcin AU - Živný, Stanislav ID - 12563 IS - 1 JF - SIAM Journal on Computing KW - General Mathematics KW - General Computer Science SN - 0097-5397 TI - Topology and adjunction in promise constraint satisfaction VL - 52 ER - TY - JOUR AB - We study active surface wetting using a minimal model of bacteria that takes into account the intrinsic motility diversity of living matter. A mixture of “fast” and “slow” self-propelled Brownian particles is considered in the presence of a wall. The evolution of the wetting layer thickness shows an overshoot before stationarity and its composition evolves in two stages, equilibrating after a slow elimination of excess particles. Nonmonotonic evolutions are shown to arise from delayed avalanches towards the dilute phase combined with the emergence of a transient particle front. AU - Rojas Vega, Mauricio Nicolas AU - De Castro, Pablo AU - Soto, Rodrigo ID - 12545 IS - 1 JF - Physical Review E SN - 2470-0045 TI - Wetting dynamics by mixtures of fast and slow self-propelled particles VL - 107 ER - TY - JOUR AB - Let k be a number field and X a smooth, geometrically integral quasi-projective variety over k. For any linear algebraic group G over k and any G-torsor g : Z → X, we observe that if the étale-Brauer obstruction is the only one for strong approximation off a finite set of places S for all twists of Z by elements in H^1(k, G), then the étale-Brauer obstruction is the only one for strong approximation off a finite set of places S for X. As an application, we show that any homogeneous space of the form G/H with G a connected linear algebraic group over k satisfies strong approximation off the infinite places with étale-Brauer obstruction, under some compactness assumptions when k is totally real. We also prove more refined strong approximation results for homogeneous spaces of the form G/H with G semisimple simply connected and H finite, using the theory of torsors and descent. AU - Balestrieri, Francesca ID - 12427 IS - 3 JF - Proceedings of the American Mathematical Society SN - 0002-9939 TI - Some remarks on strong approximation and applications to homogeneous spaces of linear algebraic groups VL - 151 ER - TY - JOUR AB - In this issue of Neuron, Espinosa-Medina et al.1 present the TEMPO (Temporal Encoding and Manipulation in a Predefined Order) system, which enables the marking and genetic manipulation of sequentially generated cell lineages in vertebrate species in vivo. AU - Villalba Requena, Ana AU - Hippenmeyer, Simon ID - 12542 IS - 3 JF - Neuron TI - Going back in time with TEMPO VL - 111 ER - TY - JOUR AB - Single-molecule localization microscopy (SMLM) greatly advances structural studies of diverse biological tissues. For example, presynaptic active zone (AZ) nanotopology is resolved in increasing detail. Immunofluorescence imaging of AZ proteins usually relies on epitope preservation using aldehyde-based immunocompetent fixation. Cryofixation techniques, such as high-pressure freezing (HPF) and freeze substitution (FS), are widely used for ultrastructural studies of presynaptic architecture in electron microscopy (EM). HPF/FS demonstrated nearer-to-native preservation of AZ ultrastructure, e.g., by facilitating single filamentous structures. Here, we present a protocol combining the advantages of HPF/FS and direct stochastic optical reconstruction microscopy (dSTORM) to quantify nanotopology of the AZ scaffold protein Bruchpilot (Brp) at neuromuscular junctions (NMJs) of Drosophila melanogaster. Using this standardized model, we tested for preservation of Brp clusters in different FS protocols compared to classical aldehyde fixation. In HPF/FS samples, presynaptic boutons were structurally well preserved with ~22% smaller Brp clusters that allowed quantification of subcluster topology. In summary, we established a standardized near-to-native preparation and immunohistochemistry protocol for SMLM analyses of AZ protein clusters in a defined model synapse. Our protocol could be adapted to study protein arrangements at single-molecule resolution in other intact tissue preparations. AU - Mrestani, Achmed AU - Lichter, Katharina AU - Sirén, Anna Leena AU - Heckmann, Manfred AU - Paul, Mila M. AU - Pauli, Martin ID - 12567 IS - 3 JF - International Journal of Molecular Sciences TI - Single-molecule localization microscopy of presynaptic active zones in Drosophila melanogaster after rapid cryofixation VL - 24 ER -