TY - CONF
AB - matching is compatible to two or more labeled point sets of size n with labels {1,…,n} if its straight-line drawing on each of these point sets is crossing-free. We study the maximum number of edges in a matching compatible to two or more labeled point sets in general position in the plane. We show that for any two labeled convex sets of n points there exists a compatible matching with ⌊2n−−√⌋ edges. More generally, for any ℓ labeled point sets we construct compatible matchings of size Ω(n1/ℓ) . As a corresponding upper bound, we use probabilistic arguments to show that for any ℓ given sets of n points there exists a labeling of each set such that the largest compatible matching has O(n2/(ℓ+1)) edges. Finally, we show that Θ(logn) copies of any set of n points are necessary and sufficient for the existence of a labeling such that any compatible matching consists only of a single edge.
AU - Aichholzer, Oswin
AU - Arroyo Guevara, Alan M
AU - Masárová, Zuzana
AU - Parada, Irene
AU - Perz, Daniel
AU - Pilz, Alexander
AU - Tkadlec, Josef
AU - Vogtenhuber, Birgit
ID - 9296
SN - 03029743
T2 - 15th International Conference on Algorithms and Computation
TI - On compatible matchings
VL - 12635
ER -
TY - JOUR
AB - Electrodepositing insulating lithium peroxide (Li2O2) is the key process during discharge of aprotic Li–O2 batteries and determines rate, capacity, and reversibility. Current understanding states that the partition between surface adsorbed and dissolved lithium superoxide governs whether Li2O2 grows as a conformal surface film or larger particles, leading to low or high capacities, respectively. However, better understanding governing factors for Li2O2 packing density and capacity requires structural sensitive in situ metrologies. Here, we establish in situ small- and wide-angle X-ray scattering (SAXS/WAXS) as a suitable method to record the Li2O2 phase evolution with atomic to submicrometer resolution during cycling a custom-built in situ Li–O2 cell. Combined with sophisticated data analysis, SAXS allows retrieving rich quantitative structural information from complex multiphase systems. Surprisingly, we find that features are absent that would point at a Li2O2 surface film formed via two consecutive electron transfers, even in poorly solvating electrolytes thought to be prototypical for surface growth. All scattering data can be modeled by stacks of thin Li2O2 platelets potentially forming large toroidal particles. Li2O2 solution growth is further justified by rotating ring-disk electrode measurements and electron microscopy. Higher discharge overpotentials lead to smaller Li2O2 particles, but there is no transition to an electronically passivating, conformal Li2O2 coating. Hence, mass transport of reactive species rather than electronic transport through a Li2O2 film limits the discharge capacity. Provided that species mobilities and carbon surface areas are high, this allows for high discharge capacities even in weakly solvating electrolytes. The currently accepted Li–O2 reaction mechanism ought to be reconsidered.
AU - Prehal, Christian
AU - Samojlov, Aleksej
AU - Nachtnebel, Manfred
AU - Lovicar, Ludek
AU - Kriechbaum, Manfred
AU - Amenitsch, Heinz
AU - Freunberger, Stefan Alexander
ID - 9301
IS - 14
JF - PNAS
KW - small-angle X-ray scattering
KW - oxygen reduction
KW - disproportionation
KW - Li-air battery
SN - 0027-8424
TI - In situ small-angle X-ray scattering reveals solution phase discharge of Li–O2 batteries with weakly solvating electrolytes
VL - 118
ER -
TY - JOUR
AB - We report the results of an experimental investigation into the decay of turbulence in plane Couette–Poiseuille flow using ‘quench’ experiments where the flow laminarises after a sudden reduction in Reynolds number Re. Specifically, we study the velocity field in the streamwise–spanwise plane. We show that the spanwise velocity containing rolls decays faster than the streamwise velocity, which displays elongated regions of higher or lower velocity called streaks. At final Reynolds numbers above 425, the decay of streaks displays two stages: first a slow decay when rolls are present and secondly a more rapid decay of streaks alone. The difference in behaviour results from the regeneration of streaks by rolls, called the lift-up effect. We define the turbulent fraction as the portion of the flow containing turbulence and this is estimated by thresholding the spanwise velocity component. It decreases linearly with time in the whole range of final Re. The corresponding decay slope increases linearly with final Re. The extrapolated value at which this decay slope vanishes is Reaz≈656±10, close to Reg≈670 at which turbulence is self-sustained. The decay of the energy computed from the spanwise velocity component is found to be exponential. The corresponding decay rate increases linearly with Re, with an extrapolated vanishing value at ReAz≈688±10. This value is also close to the value at which the turbulence is self-sustained, showing that valuable information on the transition can be obtained over a wide range of Re.
AU - Liu, T.
AU - Semin, B.
AU - Klotz, Lukasz
AU - Godoy-Diana, R.
AU - Wesfreid, J. E.
AU - Mullin, T.
ID - 9297
JF - Journal of Fluid Mechanics
SN - 0022-1120
TI - Decay of streaks and rolls in plane Couette-Poiseuille flow
VL - 915
ER -
TY - JOUR
AB - Hill's Conjecture states that the crossing number cr(𝐾𝑛) of the complete graph 𝐾𝑛 in the plane (equivalently, the sphere) is 14⌊𝑛2⌋⌊𝑛−12⌋⌊𝑛−22⌋⌊𝑛−32⌋=𝑛4/64+𝑂(𝑛3) . Moon proved that the expected number of crossings in a spherical drawing in which the points are randomly distributed and joined by geodesics is precisely 𝑛4/64+𝑂(𝑛3) , thus matching asymptotically the conjectured value of cr(𝐾𝑛) . Let cr𝑃(𝐺) denote the crossing number of a graph 𝐺 in the projective plane. Recently, Elkies proved that the expected number of crossings in a naturally defined random projective plane drawing of 𝐾𝑛 is (𝑛4/8𝜋2)+𝑂(𝑛3) . In analogy with the relation of Moon's result to Hill's conjecture, Elkies asked if lim𝑛→∞ cr𝑃(𝐾𝑛)/𝑛4=1/8𝜋2 . We construct drawings of 𝐾𝑛 in the projective plane that disprove this.
AU - Arroyo Guevara, Alan M
AU - Mcquillan, Dan
AU - Richter, R. Bruce
AU - Salazar, Gelasio
AU - Sullivan, Matthew
ID - 9295
JF - Journal of Graph Theory
SN - 0364-9024
TI - Drawings of complete graphs in the projective plane
ER -
TY - JOUR
AB - We establish finite time extinction with probability one for weak solutions of the Cauchy–Dirichlet problem for the 1D stochastic porous medium equation with Stratonovich transport noise and compactly supported smooth initial datum. Heuristically, this is expected to hold because Brownian motion has average spread rate O(t12) whereas the support of solutions to the deterministic PME grows only with rate O(t1m+1). The rigorous proof relies on a contraction principle up to time-dependent shift for Wong–Zakai type approximations, the transformation to a deterministic PME with two copies of a Brownian path as the lateral boundary, and techniques from the theory of viscosity solutions.
AU - Hensel, Sebastian
ID - 9307
JF - Stochastics and Partial Differential Equations: Analysis and Computations
SN - 21940401
TI - Finite time extinction for the 1D stochastic porous medium equation with transport noise
ER -
TY - JOUR
AB - Several Ising-type magnetic van der Waals (vdW) materials exhibit stable magnetic ground states. Despite these clear experimental demonstrations, a complete theoretical and microscopic understanding of their magnetic anisotropy is still lacking. In particular, the validity limit of identifying their one-dimensional (1-D) Ising nature has remained uninvestigated in a quantitative way. Here we performed the complete mapping of magnetic anisotropy for a prototypical Ising vdW magnet FePS3 for the first time. Combining torque magnetometry measurements with their magnetostatic model analysis and the relativistic density functional total energy calculations, we successfully constructed the three-dimensional (3-D) mappings of the magnetic anisotropy in terms of magnetic torque and energy. The results not only quantitatively confirm that the easy axis is perpendicular to the ab plane, but also reveal the anisotropies within the ab, ac, and bc planes. Our approach can be applied to the detailed quantitative study of magnetism in vdW materials.
AU - Nauman, Muhammad
AU - Kiem, Do Hoon
AU - Lee, Sungmin
AU - Son, Suhan
AU - Park, J-G
AU - Kang, Woun
AU - Han, Myung Joon
AU - Jo, Youn Jung
ID - 9282
JF - 2D Materials
KW - Mechanical Engineering
KW - General Materials Science
KW - Mechanics of Materials
KW - General Chemistry
KW - Condensed Matter Physics
SN - 2053-1583
TI - Complete mapping of magnetic anisotropy for prototype Ising van der Waals FePS3
ER -
TY - JOUR
AB - Assemblies of actin and its regulators underlie the dynamic morphology of all eukaryotic cells. To understand how actin regulatory proteins work together to generate actin-rich structures such as filopodia, we analyzed the localization of diverse actin regulators within filopodia in Drosophila embryos and in a complementary in vitro system of filopodia-like structures (FLSs). We found that the composition of the regulatory protein complex where actin is incorporated (the filopodial tip complex) is remarkably heterogeneous both in vivo and in vitro. Our data reveal that different pairs of proteins correlate with each other and with actin bundle length, suggesting the presence of functional subcomplexes. This is consistent with a theoretical framework where three or more redundant subcomplexes join the tip complex stochastically, with any two being sufficient to drive filopodia formation. We provide an explanation for the observed heterogeneity and suggest that a mechanism based on multiple components allows stereotypical filopodial dynamics to arise from diverse upstream signaling pathways.
AU - Dobramysl, Ulrich
AU - Jarsch, Iris Katharina
AU - Inoue, Yoshiko
AU - Shimo, Hanae
AU - Richier, Benjamin
AU - Gadsby, Jonathan R.
AU - Mason, Julia
AU - Szałapak, Alicja
AU - Ioannou, Pantelis Savvas
AU - Correia, Guilherme Pereira
AU - Walrant, Astrid
AU - Butler, Richard
AU - Hannezo, Edouard B
AU - Simons, Benjamin D.
AU - Gallop, Jennifer L.
ID - 9306
IS - 4
JF - The Journal of Cell Biology
TI - Stochastic combinations of actin regulatory proteins are sufficient to drive filopodia formation
VL - 220
ER -
TY - JOUR
AB - Partially observable Markov decision processes (POMDPs) are standard models for dynamic systems with probabilistic and nondeterministic behaviour in uncertain environments. We prove that in POMDPs with long-run average objective, the decision maker has approximately optimal strategies with finite memory. This implies notably that approximating the long-run value is recursively enumerable, as well as a weak continuity property of the value with respect to the transition function.
AU - Chatterjee, Krishnendu
AU - Saona Urmeneta, Raimundo J
AU - Ziliotto, Bruno
ID - 9311
JF - Mathematics of Operations Research
KW - Management Science and Operations Research
KW - General Mathematics
KW - Computer Science Applications
SN - 0364-765X
TI - Finite-memory strategies in POMDPs with long-run average objectives
ER -
TY - JOUR
AB - The leaf is a crucial organ evolved with remarkable morphological diversity to maximize plant photosynthesis. The leaf shape is a key trait that affects photosynthesis, flowering rates, disease resistance, and yield. Although many genes regulating leaf development have been identified in the past years, the precise regulatory architecture underlying the generation of diverse leaf shapes remains to be elucidated. We used cotton as a reference model to probe the genetic framework underlying divergent leaf forms. Comparative transcriptome analysis revealed that the GhARF16‐1 and GhKNOX2‐1 genes might be potential regulators of leaf shape. We functionally characterized the auxin‐responsive factor ARF16‐1 acting upstream of GhKNOX2‐1 to determine leaf morphology in cotton. The transcription of GhARF16‐1 was significantly higher in lobed‐leaved cotton than in smooth‐leaved cotton. Furthermore, the overexpression of GhARF16‐1 led to the upregulation of GhKNOX2‐1 and resulted in more and deeper serrations in cotton leaves, similar to the leaf shape of cotton plants overexpressing GhKNOX2‐1. We found that GhARF16‐1 specifically bound to the promoter of GhKNOX2‐1 to induce its expression. The heterologous expression of GhARF16‐1 and GhKNOX2‐1 in Arabidopsis led to lobed and curly leaves, and a genetic analysis revealed that GhKNOX2‐1 is epistatic to GhARF16‐1 in Arabidopsis, suggesting that the GhARF16‐1 and GhKNOX2‐1 interaction paradigm also functions to regulate leaf shape in Arabidopsis. To our knowledge, our results uncover a novel mechanism by which auxin, through the key component ARF16‐1 and its downstream‐activated gene KNOX2‐1, determines leaf morphology in eudicots.
AU - He, P
AU - Zhang, Yuzhou
AU - Li, H
AU - Fu, X
AU - Shang, H
AU - Zou, C
AU - Friml, Jiří
AU - Xiao, G
ID - 8606
IS - 3
JF - Plant Biotechnology Journal
SN - 1467-7644
TI - GhARF16-1 modulates leaf development by transcriptionally regulating the GhKNOX2-1 gene in cotton
VL - 19
ER -
TY - JOUR
AB - Collective cell migration offers a rich field of study for non-equilibrium physics and cellular biology, revealing phenomena such as glassy dynamics, pattern formation and active turbulence. However, how mechanical and chemical signalling are integrated at the cellular level to give rise to such collective behaviours remains unclear. We address this by focusing on the highly conserved phenomenon of spatiotemporal waves of density and extracellular signal-regulated kinase (ERK) activation, which appear both in vitro and in vivo during collective cell migration and wound healing. First, we propose a biophysical theory, backed by mechanical and optogenetic perturbation experiments, showing that patterns can be quantitatively explained by a mechanochemical coupling between active cellular tensions and the mechanosensitive ERK pathway. Next, we demonstrate how this biophysical mechanism can robustly induce long-ranged order and migration in a desired orientation, and we determine the theoretically optimal wavelength and period for inducing maximal migration towards free edges, which fits well with experimentally observed dynamics. We thereby provide a bridge between the biophysical origin of spatiotemporal instabilities and the design principles of robust and efficient long-ranged migration.
AU - Boocock, Daniel R
AU - Hino, Naoya
AU - Ruzickova, Natalia
AU - Hirashima, Tsuyoshi
AU - Hannezo, Edouard B
ID - 8602
JF - Nature Physics
SN - 17452473
TI - Theory of mechanochemical patterning and optimal migration in cell monolayers
VL - 17
ER -