TY - JOUR
AB - We study the problem of robust satisfiability of systems of nonlinear equations, namely, whether for a given continuous function f:K→ ℝn on a finite simplicial complex K and α > 0, it holds that each function g: K → ℝn such that ||g - f || ∞ < α, has a root in K. Via a reduction to the extension problem of maps into a sphere, we particularly show that this problem is decidable in polynomial time for every fixed n, assuming dimK ≤ 2n - 3. This is a substantial extension of previous computational applications of topological degree and related concepts in numerical and interval analysis. Via a reverse reduction, we prove that the problem is undecidable when dim K > 2n - 2, where the threshold comes from the stable range in homotopy theory. For the lucidity of our exposition, we focus on the setting when f is simplexwise linear. Such functions can approximate general continuous functions, and thus we get approximation schemes and undecidability of the robust satisfiability in other possible settings.
AU - Franek, Peter
AU - Krcál, Marek
ID - 1682
IS - 4
JF - Journal of the ACM
TI - Robust satisfiability of systems of equations
VL - 62
ER -
TY - JOUR
AB - Many species groups, including mammals and many insects, determine sex using heteromorphic sex chromosomes. Diptera flies, which include the model Drosophila melanogaster, generally have XY sex chromosomes and a conserved karyotype consisting of six chromosomal arms (five large rods and a small dot), but superficially similar karyotypes may conceal the true extent of sex chromosome variation. Here, we use whole-genome analysis in 37 fly species belonging to 22 different families of Diptera and uncover tremendous hidden diversity in sex chromosome karyotypes among flies. We identify over a dozen different sex chromosome configurations, and the small dot chromosome is repeatedly used as the sex chromosome, which presumably reflects the ancestral karyotype of higher Diptera. However, we identify species with undifferentiated sex chromosomes, others in which a different chromosome replaced the dot as a sex chromosome or in which up to three chromosomal elements became incorporated into the sex chromosomes, and others yet with female heterogamety (ZW sex chromosomes). Transcriptome analysis shows that dosage compensation has evolved multiple times in flies, consistently through up-regulation of the single X in males. However, X chromosomes generally show a deficiency of genes with male-biased expression, possibly reflecting sex-specific selective pressures. These species thus provide a rich resource to study sex chromosome biology in a comparative manner and show that similar selective forces have shaped the unique evolution of sex chromosomes in diverse fly taxa.
AU - Vicoso, Beatriz
AU - Bachtrog, Doris
ID - 1684
IS - 4
JF - PLoS Biology
TI - Numerous transitions of sex chromosomes in Diptera
VL - 13
ER -
TY - CONF
AB - Given a graph G cellularly embedded on a surface Σ of genus g, a cut graph is a subgraph of G such that cutting Σ along G yields a topological disk. We provide a fixed parameter tractable approximation scheme for the problem of computing the shortest cut graph, that is, for any ε > 0, we show how to compute a (1 + ε) approximation of the shortest cut graph in time f(ε, g)n3.
Our techniques first rely on the computation of a spanner for the problem using the technique of brick decompositions, to reduce the problem to the case of bounded tree-width. Then, to solve the bounded tree-width case, we introduce a variant of the surface-cut decomposition of Rué, Sau and Thilikos, which may be of independent interest.
AU - Cohen Addad, Vincent
AU - De Mesmay, Arnaud N
ID - 1685
TI - A fixed parameter tractable approximation scheme for the optimal cut graph of a surface
VL - 9294
ER -
TY - JOUR
AB - We show that the simplest building blocks of origami-based materials - rigid, degree-four vertices - are generically multistable. The existence of two distinct branches of folding motion emerging from the flat state suggests at least bistability, but we show how nonlinearities in the folding motions allow generic vertex geometries to have as many as five stable states. In special geometries with collinear folds and symmetry, more branches emerge leading to as many as six stable states. Tuning the fold energy parameters, we show how monostability is also possible. Finally, we show how to program the stability features of a single vertex into a periodic fold tessellation. The resulting metasheets provide a previously unanticipated functionality - tunable and switchable shape and size via multistability.
AU - Waitukaitis, Scott R
AU - Menaut, Rémi
AU - Chen, Bryan
AU - Van Hecke, Martin
ID - 121
IS - 5
JF - APS Physics, Physical Review Letters
TI - Origami multistability: From single vertices to metasheets
VL - 114
ER -
TY - JOUR
AB - Motility is a basic feature of living microorganisms, and how it works is often determined by environmental cues. Recent efforts have focused on developing artificial systems that can mimic microorganisms, in particular their self-propulsion. We report on the design and characterization of synthetic self-propelled particles that migrate upstream, known as positive rheotaxis. This phenomenon results from a purely physical mechanism involving the interplay between the polarity of the particles and their alignment by a viscous torque. We show quantitative agreement between experimental data and a simple model of an overdamped Brownian pendulum. The model notably predicts the existence of a stagnation point in a diverging flow. We take advantage of this property to demonstrate that our active particles can sense and predictably organize in an imposed flow. Our colloidal system represents an important step toward the realization of biomimetic microsystems with the ability to sense and respond to environmental changes.
AU - Palacci, Jérémie A
AU - Sacanna, Stefano
AU - Abramian, Anaïs
AU - Barral, Jérémie
AU - Hanson, Kasey
AU - Grosberg, Alexander Y.
AU - Pine, David J.
AU - Chaikin, Paul M.
ID - 9057
IS - 4
JF - Science Advances
SN - 2375-2548
TI - Artificial rheotaxis
VL - 1
ER -
TY - JOUR
AB - The breaking of internal tides is believed to provide a large part of the power needed to mix the abyssal ocean and sustain the meridional overturning circulation. Both the fraction of internal tide energy that is dissipated locally and the resulting vertical mixing distribution are crucial for the ocean state, but remain poorly quantified. Here we present a first worldwide estimate of mixing due to internal tides generated at small‐scale abyssal hills. Our estimate is based on linear wave theory, a nonlinear parameterization for wave breaking and uses quasi‐global small‐scale abyssal hill bathymetry, stratification, and tidal data. We show that a large fraction of abyssal‐hill generated internal tide energy is locally dissipated over mid‐ocean ridges in the Southern Hemisphere. Significant dissipation occurs above ridge crests, and, upon rescaling by the local stratification, follows a monotonic exponential decay with height off the bottom, with a nonuniform decay scale. We however show that a substantial part of the dissipation occurs over the smoother flanks of mid‐ocean ridges, and exhibits a middepth maximum due to the interplay of wave amplitude with stratification. We link the three‐dimensional map of dissipation to abyssal hills characteristics, ocean stratification, and tidal forcing, and discuss its potential implementation in time‐evolving parameterizations for global climate models. Current tidal parameterizations only account for waves generated at large‐scale satellite‐resolved bathymetry. Our results suggest that the presence of small‐scale, mostly unresolved abyssal hills could significantly enhance the spatial inhomogeneity of tidal mixing, particularly above mid‐ocean ridges in the Southern Hemisphere.
AU - Lefauve, Adrien
AU - MULLER, Caroline J
AU - Melet, Angélique
ID - 9141
IS - 7
JF - Journal of Geophysical Research: Oceans
SN - 2169-9275
TI - A three-dimensional map of tidal dissipation over abyssal hills
VL - 120
ER -
TY - JOUR
AB - The actomyosin cytoskeleton is a primary force-generating mechanism in morphogenesis, thus a robust spatial control of cytoskeletal positioning is essential. In this report, we demonstrate that actomyosin contractility and planar cell polarity (PCP) interact in post-mitotic Ciona notochord cells to self-assemble and reposition actomyosin rings, which play an essential role for cell elongation. Intriguingly, rings always form at the cells′ anterior edge before migrating towards the center as contractility increases, reflecting a novel dynamical property of the cortex. Our drug and genetic manipulations uncover a tug-of-war between contractility, which localizes cortical flows toward the equator and PCP, which tries to reposition them. We develop a simple model of the physical forces underlying this tug-of-war, which quantitatively reproduces our results. We thus propose a quantitative framework for dissecting the relative contribution of contractility and PCP to the self-assembly and repositioning of cytoskeletal structures, which should be applicable to other morphogenetic events.
AU - Sehring, Ivonne
AU - Recho, Pierre
AU - Denker, Elsa
AU - Kourakis, Matthew
AU - Mathiesen, Birthe
AU - Hannezo, Edouard B
AU - Dong, Bo
AU - Jiang, Di
ID - 928
JF - eLife
TI - Assembly and positioning of actomyosin rings by contractility and planar cell polarity
VL - 4
ER -
TY - JOUR
AB - Although collective cell motion plays an important role, for example during wound healing, embryogenesis, or cancer progression, the fundamental rules governing this motion are still not well understood, in particular at high cell density. We study here the motion of human bronchial epithelial cells within a monolayer, over long times. We observe that, as the monolayer ages, the cells slow down monotonously, while the velocity correlation length first increases as the cells slow down but eventually decreases at the slowest motions. By comparing experiments, analytic model, and detailed particle-based simulations, we shed light on this biological amorphous solidification process, demonstrating that the observed dynamics can be explained as a consequence of the combined maturation and strengthening of cell-cell and cell-substrate adhesions. Surprisingly, the increase of cell surface density due to proliferation is only secondary in this process. This analysis is confirmed with two other cell types. The very general relations between the mean cell velocity and velocity correlation lengths, which apply for aggregates of self-propelled particles, as well as motile cells, can possibly be used to discriminate between various parameter changes in vivo, from noninvasive microscopy data.
AU - García, Simón
AU - Hannezo, Edouard B
AU - Elgeti, Jens
AU - Joanny, Jean
AU - Silberzan, Pascal
AU - Gov, Nir
ID - 933
IS - 50
JF - PNAS
TI - Physics of active jamming during collective cellular motion in a monolayer
VL - 112
ER -
TY - JOUR
AB - The tunability of topological surface states and controllable opening of the Dirac gap are of fundamental and practical interest in the field of topological materials. In the newly discovered topological crystalline insulators (TCIs), theory predicts that the Dirac node is protected by a crystalline symmetry and that the surface state electrons can acquire a mass if this symmetry is broken. Recent studies have detected signatures of a spontaneously generated Dirac gap in TCIs; however, the mechanism of mass formation remains elusive. In this work, we present scanning tunnelling microscopy (STM) measurements of the TCI Pb 1â'x Sn x Se for a wide range of alloy compositions spanning the topological and non-topological regimes. The STM topographies reveal a symmetry-breaking distortion on the surface, which imparts mass to the otherwise massless Dirac electrons-a mechanism analogous to the long sought-after Higgs mechanism in particle physics. Interestingly, the measured Dirac gap decreases on approaching the trivial phase, whereas the magnitude of the distortion remains nearly constant. Our data and calculations reveal that the penetration depth of Dirac surface states controls the magnitude of the Dirac mass. At the limit of the critical composition, the penetration depth is predicted to go to infinity, resulting in zero mass, consistent with our measurements. Finally, we discover the existence of surface states in the non-topological regime, which have the characteristics of gapped, double-branched Dirac fermions and could be exploited in realizing superconductivity in these materials.
AU - Zeljkovic, Ilija
AU - Okada, Yoshinori
AU - Maksym Serbyn
AU - Sankar, Raman
AU - Walkup, Daniel
AU - Zhou, Wenwen
AU - Liu, Junwei
AU - Chang, Guoqing
AU - Wang, Yungjui
AU - Hasan, Md Z
AU - Chou, Fangcheng
AU - Lin, Hsin
AU - Bansil, Arun
AU - Fu, Liang
AU - Madhavan, Vidya
ID - 981
IS - 3
JF - Nature Materials
TI - Dirac mass generation from crystal symmetry breaking on the surfaces of topological crystalline insulators
VL - 14
ER -
TY - JOUR
AB - We propose a new approach to probing ergodicity and its breakdown in one-dimensional quantum manybody systems based on their response to a local perturbation. We study the distribution of matrix elements of a local operator between the system's eigenstates, finding a qualitatively different behavior in the manybody localized (MBL) and ergodic phases. To characterize how strongly a local perturbation modifies the eigenstates, we introduce the parameter g(L) = (In (Vnm/δ)) which represents the disorder-averaged ratio of a typical matrix element of a local operator V to energy level spacing δ this parameter is reminiscent of the Thouless conductance in the single-particle localization. We show that the parameter g(L) decreases with system size L in the MBL phase and grows in the ergodic phase. We surmise that the delocalization transition occurs when g(L) is independent of system size, g(L)=gc ~ 1. We illustrate our approach by studying the many-body localization transition and resolving the many-body mobility edge in a disordered one-dimensional XXZ spin-1=2 chain using exact diagonalization and time-evolving block-decimation methods. Our criterion for the MBL transition gives insights into microscopic details of transition. Its direct physical consequences, in particular, logarithmically slow transport at the transition and extensive entanglement entropy of the eigenstates, are consistent with recent renormalization-group predictions.
AU - Maksym Serbyn
AU - Papić, Zlatko
AU - Abanin, Dmitry A
ID - 982
IS - 4
JF - Physical Review X
TI - Criterion for many-body localization-delocalization phase transition
VL - 5
ER -