@article{12287, abstract = {We present criteria for establishing a triangulation of a manifold. Given a manifold M, a simplicial complex A, and a map H from the underlying space of A to M, our criteria are presented in local coordinate charts for M, and ensure that H is a homeomorphism. These criteria do not require a differentiable structure, or even an explicit metric on M. No Delaunay property of A is assumed. The result provides a triangulation guarantee for algorithms that construct a simplicial complex by working in local coordinate patches. Because the criteria are easily verified in such a setting, they are expected to be of general use.}, author = {Boissonnat, Jean-Daniel and Dyer, Ramsay and Ghosh, Arijit and Wintraecken, Mathijs}, issn = {1432-0444}, journal = {Discrete & Computational Geometry}, keywords = {Computational Theory and Mathematics, Discrete Mathematics and Combinatorics, Geometry and Topology, Theoretical Computer Science}, pages = {156--191}, publisher = {Springer Nature}, title = {{Local criteria for triangulating general manifolds}}, doi = {10.1007/s00454-022-00431-7}, volume = {69}, year = {2023}, } @article{12165, abstract = {It may come as a surprise that a phenomenon as ubiquitous and prominent as the transition from laminar to turbulent flow has resisted combined efforts by physicists, engineers and mathematicians, and remained unresolved for almost one and a half centuries. In recent years, various studies have proposed analogies to directed percolation, a well-known universality class in statistical mechanics, which describes a non-equilibrium phase transition from a fluctuating active phase into an absorbing state. It is this unlikely relation between the multiscale, high-dimensional dynamics that signify the transition process in virtually all flows of practical relevance, and the arguably most basic non-equilibrium phase transition, that so far has mainly been the subject of model studies, which I review in this Perspective.}, author = {Hof, Björn}, issn = {2522-5820}, journal = {Nature Reviews Physics}, keywords = {General Physics and Astronomy}, pages = {62--72}, publisher = {Springer Nature}, title = {{Directed percolation and the transition to turbulence}}, doi = {10.1038/s42254-022-00539-y}, volume = {5}, year = {2023}, } @article{12421, abstract = {The actin cytoskeleton plays a key role in cell migration and cellular morphodynamics in most eukaryotes. The ability of the actin cytoskeleton to assemble and disassemble in a spatiotemporally controlled manner allows it to form higher-order structures, which can generate forces required for a cell to explore and navigate through its environment. It is regulated not only via a complex synergistic and competitive interplay between actin-binding proteins (ABP), but also by filament biochemistry and filament geometry. The lack of structural insights into how geometry and ABPs regulate the actin cytoskeleton limits our understanding of the molecular mechanisms that define actin cytoskeleton remodeling and, in turn, impact emerging cell migration characteristics. With the advent of cryo-electron microscopy (cryo-EM) and advanced computational methods, it is now possible to define these molecular mechanisms involving actin and its interactors at both atomic and ultra-structural levels in vitro and in cellulo. In this review, we will provide an overview of the available cryo-EM methods, applicable to further our understanding of the actin cytoskeleton, specifically in the context of cell migration. We will discuss how these methods have been employed to elucidate ABP- and geometry-defined regulatory mechanisms in initiating, maintaining, and disassembling cellular actin networks in migratory protrusions.}, author = {Fäßler, Florian and Javoor, Manjunath and Schur, Florian KM}, issn = {1470-8752}, journal = {Biochemical Society Transactions}, keywords = {Biochemistry}, number = {1}, pages = {87--99}, publisher = {Portland Press}, title = {{Deciphering the molecular mechanisms of actin cytoskeleton regulation in cell migration using cryo-EM}}, doi = {10.1042/bst20220221}, volume = {51}, year = {2023}, } @article{12105, abstract = {Data-driven dimensionality reduction methods such as proper orthogonal decomposition and dynamic mode decomposition have proven to be useful for exploring complex phenomena within fluid dynamics and beyond. A well-known challenge for these techniques is posed by the continuous symmetries, e.g. translations and rotations, of the system under consideration, as drifts in the data dominate the modal expansions without providing an insight into the dynamics of the problem. In the present study, we address this issue for fluid flows in rectangular channels by formulating a continuous symmetry reduction method that eliminates the translations in the streamwise and spanwise directions simultaneously. We demonstrate our method by computing the symmetry-reduced dynamic mode decomposition (SRDMD) of sliding windows of data obtained from the transitional plane-Couette and turbulent plane-Poiseuille flow simulations. In the former setting, SRDMD captures the dynamics in the vicinity of the invariant solutions with translation symmetries, i.e. travelling waves and relative periodic orbits, whereas in the latter, our calculations reveal episodes of turbulent time evolution that can be approximated by a low-dimensional linear expansion.}, author = {Marensi, Elena and Yalniz, Gökhan and Hof, Björn and Budanur, Nazmi B}, issn = {1469-7645}, journal = {Journal of Fluid Mechanics}, publisher = {Cambridge University Press}, title = {{Symmetry-reduced dynamic mode decomposition of near-wall turbulence}}, doi = {10.1017/jfm.2022.1001}, volume = {954}, year = {2023}, } @article{12514, abstract = {The concept of a “speciation continuum” has gained popularity in recent decades. It emphasizes speciation as a continuous process that may be studied by comparing contemporary population pairs that show differing levels of divergence. In their recent perspective article in Evolution, Stankowski and Ravinet provided a valuable service by formally defining the speciation continuum as a continuum of reproductive isolation, based on opinions gathered from a survey of speciation researchers. While we agree that the speciation continuum has been a useful concept to advance the understanding of the speciation process, some intrinsic limitations exist. Here, we advocate for a multivariate extension, the speciation hypercube, first proposed by Dieckmann et al. in 2004, but rarely used since. We extend the idea of the speciation cube and suggest it has strong conceptual and practical advantages over a one-dimensional model. We illustrate how the speciation hypercube can be used to visualize and compare different speciation trajectories, providing new insights into the processes and mechanisms of speciation. A key strength of the speciation hypercube is that it provides a unifying framework for speciation research, as it allows questions from apparently disparate subfields to be addressed in a single conceptual model.}, author = {Bolnick, Daniel I. and Hund, Amanda K. and Nosil, Patrik and Peng, Foen and Ravinet, Mark and Stankowski, Sean and Subramanian, Swapna and Wolf, Jochen B.W. and Yukilevich, Roman}, issn = {1558-5646}, journal = {Evolution: International journal of organic evolution}, number = {1}, pages = {318--328}, publisher = {Oxford University Press}, title = {{A multivariate view of the speciation continuum}}, doi = {10.1093/evolut/qpac004}, volume = {77}, year = {2023}, }