@article{5886, abstract = {Problems involving quantum impurities, in which one or a few particles are interacting with a macroscopic environment, represent a pervasive paradigm, spanning across atomic, molecular, and condensed-matter physics. In this paper we introduce new variational approaches to quantum impurities and apply them to the Fröhlich polaron–a quasiparticle formed out of an electron (or other point-like impurity) in a polar medium, and to the angulon–a quasiparticle formed out of a rotating molecule in a bosonic bath. We benchmark these approaches against established theories, evaluating their accuracy as a function of the impurity-bath coupling.}, author = {Li, Xiang and Bighin, Giacomo and Yakaboylu, Enderalp and Lemeshko, Mikhail}, issn = {00268976}, journal = {Molecular Physics}, publisher = {Taylor and Francis}, title = {{Variational approaches to quantum impurities: from the Fröhlich polaron to the angulon}}, doi = {10.1080/00268976.2019.1567852}, year = {2019}, } @inproceedings{6556, abstract = {Motivated by fixed-parameter tractable (FPT) problems in computational topology, we consider the treewidth tw(M) of a compact, connected 3-manifold M, defined to be the minimum treewidth of the face pairing graph of any triangulation T of M. In this setting the relationship between the topology of a 3-manifold and its treewidth is of particular interest. First, as a corollary of work of Jaco and Rubinstein, we prove that for any closed, orientable 3-manifold M the treewidth tw(M) is at most 4g(M)-2, where g(M) denotes Heegaard genus of M. In combination with our earlier work with Wagner, this yields that for non-Haken manifolds the Heegaard genus and the treewidth are within a constant factor. Second, we characterize all 3-manifolds of treewidth one: These are precisely the lens spaces and a single other Seifert fibered space. Furthermore, we show that all remaining orientable Seifert fibered spaces over the 2-sphere or a non-orientable surface have treewidth two. In particular, for every spherical 3-manifold we exhibit a triangulation of treewidth at most two. Our results further validate the parameter of treewidth (and other related parameters such as cutwidth or congestion) to be useful for topological computing, and also shed more light on the scope of existing FPT-algorithms in the field.}, author = {Huszár, Kristóf and Spreer, Jonathan}, booktitle = {35th International Symposium on Computational Geometry}, isbn = {978-3-95977-104-7}, issn = {1868-8969}, keywords = {computational 3-manifold topology, fixed-parameter tractability, layered triangulations, structural graph theory, treewidth, cutwidth, Heegaard genus}, location = {Portland, Oregon, United States}, pages = {44:1--44:20}, publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik}, title = {{3-manifold triangulations with small treewidth}}, doi = {10.4230/LIPIcs.SoCG.2019.44}, volume = {129}, year = {2019}, } @article{7093, abstract = {In graph theory, as well as in 3-manifold topology, there exist several width-type parameters to describe how "simple" or "thin" a given graph or 3-manifold is. These parameters, such as pathwidth or treewidth for graphs, or the concept of thin position for 3-manifolds, play an important role when studying algorithmic problems; in particular, there is a variety of problems in computational 3-manifold topology - some of them known to be computationally hard in general - that become solvable in polynomial time as soon as the dual graph of the input triangulation has bounded treewidth. In view of these algorithmic results, it is natural to ask whether every 3-manifold admits a triangulation of bounded treewidth. We show that this is not the case, i.e., that there exists an infinite family of closed 3-manifolds not admitting triangulations of bounded pathwidth or treewidth (the latter implies the former, but we present two separate proofs). We derive these results from work of Agol, of Scharlemann and Thompson, and of Scharlemann, Schultens and Saito by exhibiting explicit connections between the topology of a 3-manifold M on the one hand and width-type parameters of the dual graphs of triangulations of M on the other hand, answering a question that had been raised repeatedly by researchers in computational 3-manifold topology. In particular, we show that if a closed, orientable, irreducible, non-Haken 3-manifold M has a triangulation of treewidth (resp. pathwidth) k then the Heegaard genus of M is at most 18(k+1) (resp. 4(3k+1)).}, author = {Huszár, Kristóf and Spreer, Jonathan and Wagner, Uli}, issn = {1920-180X}, journal = {Journal of Computational Geometry}, number = {2}, pages = {70–98}, publisher = {Computational Geometry Laborartoy}, title = {{On the treewidth of triangulated 3-manifolds}}, doi = {10.20382/JOGC.V10I2A5}, volume = {10}, year = {2019}, } @article{7197, abstract = {During bacterial cell division, the tubulin-homolog FtsZ forms a ring-like structure at the center of the cell. This Z-ring not only organizes the division machinery, but treadmilling of FtsZ filaments was also found to play a key role in distributing proteins at the division site. What regulates the architecture, dynamics and stability of the Z-ring is currently unknown, but FtsZ-associated proteins are known to play an important role. Here, using an in vitro reconstitution approach, we studied how the well-conserved protein ZapA affects FtsZ treadmilling and filament organization into large-scale patterns. Using high-resolution fluorescence microscopy and quantitative image analysis, we found that ZapA cooperatively increases the spatial order of the filament network, but binds only transiently to FtsZ filaments and has no effect on filament length and treadmilling velocity. Together, our data provides a model for how FtsZ-associated proteins can increase the precision and stability of the bacterial cell division machinery in a switch-like manner.}, author = {Dos Santos Caldas, Paulo R and Lopez Pelegrin, Maria D and Pearce, Daniel J. G. and Budanur, Nazmi B and Brugués, Jan and Loose, Martin}, issn = {2041-1723}, journal = {Nature Communications}, publisher = {Springer Nature}, title = {{Cooperative ordering of treadmilling filaments in cytoskeletal networks of FtsZ and its crosslinker ZapA}}, doi = {10.1038/s41467-019-13702-4}, volume = {10}, year = {2019}, } @article{7210, abstract = {The rate of biological evolution depends on the fixation probability and on the fixation time of new mutants. Intensive research has focused on identifying population structures that augment the fixation probability of advantageous mutants. But these amplifiers of natural selection typically increase fixation time. Here we study population structures that achieve a tradeoff between fixation probability and time. First, we show that no amplifiers can have an asymptotically lower absorption time than the well-mixed population. Then we design population structures that substantially augment the fixation probability with just a minor increase in fixation time. Finally, we show that those structures enable higher effective rate of evolution than the well-mixed population provided that the rate of generating advantageous mutants is relatively low. Our work sheds light on how population structure affects the rate of evolution. Moreover, our structures could be useful for lab-based, medical, or industrial applications of evolutionary optimization.}, author = {Tkadlec, Josef and Pavlogiannis, Andreas and Chatterjee, Krishnendu and Nowak, Martin A.}, issn = {2399-3642}, journal = {Communications Biology}, publisher = {Springer Nature}, title = {{Population structure determines the tradeoff between fixation probability and fixation time}}, doi = {10.1038/s42003-019-0373-y}, volume = {2}, year = {2019}, }