TY - JOUR
AB - When can a polyomino piece of paper be folded into a unit cube? Prior work studied tree-like polyominoes, but polyominoes with holes remain an intriguing open problem. We present sufficient conditions for a polyomino with one or several holes to fold into a cube, and conditions under which cube folding is impossible. In particular, we show that all but five special “basic” holes guarantee foldability.
AU - Aichholzer, Oswin
AU - Akitaya, Hugo A.
AU - Cheung, Kenneth C.
AU - Demaine, Erik D.
AU - Demaine, Martin L.
AU - Fekete, Sándor P.
AU - Kleist, Linda
AU - Kostitsyna, Irina
AU - Löffler, Maarten
AU - Masárová, Zuzana
AU - Mundilova, Klara
AU - Schmidt, Christiane
ID - 8317
JF - Computational Geometry: Theory and Applications
SN - 09257721
TI - Folding polyominoes with holes into a cube
VL - 93
ER -
TY - JOUR
AB - It is well known that special Kubo-Ando operator means admit divergence center interpretations, moreover, they are also mean squared error estimators for certain metrics on positive definite operators. In this paper we give a divergence center interpretation for every symmetric Kubo-Ando mean. This characterization of the symmetric means naturally leads to a definition of weighted and multivariate versions of a large class of symmetric Kubo-Ando means. We study elementary properties of these weighted multivariate means, and note in particular that in the special case of the geometric mean we recover the weighted A#H-mean introduced by Kim, Lawson, and Lim.
AU - Pitrik, József
AU - Virosztek, Daniel
ID - 8373
JF - Linear Algebra and its Applications
KW - Kubo-Ando mean
KW - weighted multivariate mean
KW - barycenter
SN - 0024-3795
TI - A divergence center interpretation of general symmetric Kubo-Ando means, and related weighted multivariate operator means
VL - 609
ER -
TY - JOUR
AB - Cell and tissue polarization is fundamental for plant growth and morphogenesis. The polar, cellular localization of Arabidopsis PIN‐FORMED (PIN) proteins is crucial for their function in directional auxin transport. The clustering of PIN polar cargoes within the plasma membrane has been proposed to be important for the maintenance of their polar distribution. However, the more detailed features of PIN clusters and the cellular requirements of cargo clustering remain unclear.
Here, we characterized PIN clusters in detail by means of multiple advanced microscopy and quantification methods, such as 3D quantitative imaging or freeze‐fracture replica labeling. The size and aggregation types of PIN clusters were determined by electron microscopy at the nanometer level at different polar domains and at different developmental stages, revealing a strong preference for clustering at the polar domains.
Pharmacological and genetic studies revealed that PIN clusters depend on phosphoinositol pathways, cytoskeletal structures and specific cell‐wall components as well as connections between the cell wall and the plasma membrane.
This study identifies the role of different cellular processes and structures in polar cargo clustering and provides initial mechanistic insight into the maintenance of polarity in plants and other systems.
AU - Li, Hongjiang
AU - von Wangenheim, Daniel
AU - Zhang, Xixi
AU - Tan, Shutang
AU - Darwish-Miranda, Nasser
AU - Naramoto, Satoshi
AU - Wabnik, Krzysztof T
AU - de Rycke, Riet
AU - Kaufmann, Walter
AU - Gütl, Daniel J
AU - Tejos, Ricardo
AU - Grones, Peter
AU - Ke, Meiyu
AU - Chen, Xu
AU - Dettmer, Jan
AU - Friml, Jiří
ID - 8582
IS - 1
JF - New Phytologist
SN - 0028646X
TI - Cellular requirements for PIN polar cargo clustering in Arabidopsis thaliana
VL - 229
ER -
TY - JOUR
AB - To adapt to the diverse array of biotic and abiotic cues, plants have evolved sophisticated mechanisms to sense changes in environmental conditions and modulate their growth. Growth-promoting hormones and defence signalling fine tune plant development antagonistically. During host-pathogen interactions, this defence-growth trade-off is mediated by the counteractive effects of the defence hormone salicylic acid (SA) and the growth hormone auxin. Here we revealed an underlying mechanism of SA regulating auxin signalling by constraining the plasma membrane dynamics of PIN2 auxin efflux transporter in Arabidopsis thaliana roots. The lateral diffusion of PIN2 proteins is constrained by SA signalling, during which PIN2 proteins are condensed into hyperclusters depending on REM1.2-mediated nanodomain compartmentalisation. Furthermore, membrane nanodomain compartmentalisation by SA or Remorin (REM) assembly significantly suppressed clathrin-mediated endocytosis. Consequently, SA-induced heterogeneous surface condensation disrupted asymmetric auxin distribution and the resultant gravitropic response. Our results demonstrated a defence-growth trade-off mechanism by which SA signalling crosstalked with auxin transport by concentrating membrane-resident PIN2 into heterogeneous compartments.
AU - Ke, M
AU - Ma, Z
AU - Wang, D
AU - Sun, Y
AU - Wen, C
AU - Huang, D
AU - Chen, Z
AU - Yang, L
AU - Tan, Shutang
AU - Li, R
AU - Friml, Jiří
AU - Miao, Y
AU - Chen, X
ID - 8608
IS - 2
JF - New Phytologist
SN - 0028-646x
TI - Salicylic acid regulates PIN2 auxin transporter hyper-clustering and root gravitropic growth via Remorin-dependent lipid nanodomain organization in Arabidopsis thaliana
VL - 229
ER -
TY - JOUR
AB - This paper continues the discussion started in [CK19] concerning Arnold's legacy on classical KAM theory and (some of) its modern developments. We prove a detailed and explicit `global' Arnold's KAM Theorem, which yields, in particular, the Whitney conjugacy of a non{degenerate, real{analytic, nearly-integrable Hamiltonian system to an integrable system on a closed, nowhere dense, positive measure subset of the phase space. Detailed measure estimates on the Kolmogorov's set are provided in the case the phase space is: (A) a uniform neighbourhood of an arbitrary (bounded) set times the d-torus and (B) a domain with C2 boundary times the d-torus. All constants are explicitly given.
AU - Chierchia, Luigi
AU - Koudjinan, Edmond
ID - 8689
IS - 1
JF - Regular and Chaotic Dynamics
KW - Nearly{integrable Hamiltonian systems
KW - perturbation theory
KW - KAM Theory
KW - Arnold's scheme
KW - Kolmogorov's set
KW - primary invariant tori
KW - Lagrangian tori
KW - measure estimates
KW - small divisors
KW - integrability on nowhere dense sets
KW - Diophantine frequencies.
SN - 1560-3547
TI - V.I. Arnold's ''Global'' KAM theorem and geometric measure estimates
VL - 26
ER -
TY - JOUR
AB - We develop a version of Ekedahl’s geometric sieve for integral quadratic forms of rank at least five. As one ranges over the zeros of such quadratic forms, we use the sieve to compute the density of coprime values of polynomials, and furthermore, to address a question about local solubility in families of varieties parameterised by the zeros.
AU - Browning, Timothy D
AU - Heath-Brown, Roger
ID - 8742
IS - 1
JF - Forum Mathematicum
SN - 09337741
TI - The geometric sieve for quadrics
VL - 33
ER -
TY - JOUR
AB - Traditional scientific conferences and seminar events have been hugely disrupted by the COVID-19 pandemic, paving the way for virtual forms of scientific communication to take hold and be put to the test.
AU - Bozelos, Panagiotis
AU - Vogels, Tim P
ID - 8757
IS - 1
JF - Nature Reviews Neuroscience
SN - 1471003X
TI - Talking science, online
VL - 22
ER -
TY - JOUR
AB - Let g be a complex semisimple Lie algebra. We give a classification of contravariant forms on the nondegenerate Whittaker g-modules Y(χ,η) introduced by Kostant. We prove that the set of all contravariant forms on Y(χ,η) forms a vector space whose dimension is given by the cardinality of the Weyl group of g. We also describe a procedure for parabolically inducing contravariant forms. As a corollary, we deduce the existence of the Shapovalov form on a Verma module, and provide a formula for the dimension of the space of contravariant forms on the degenerate Whittaker modules M(χ,η) introduced by McDowell.
AU - Brown, Adam
AU - Romanov, Anna
ID - 8773
IS - 1
JF - Proceedings of the American Mathematical Society
KW - Applied Mathematics
KW - General Mathematics
SN - 0002-9939
TI - Contravariant forms on Whittaker modules
VL - 149
ER -
TY - JOUR
AB - We study optimal election sequences for repeatedly selecting a (very) small group of leaders among a set of participants (players) with publicly known unique ids. In every time slot, every player has to select exactly one player that it considers to be the current leader, oblivious to the selection of the other players, but with the overarching goal of maximizing a given parameterized global (“social”) payoff function in the limit. We consider a quite generic model, where the local payoff achieved by a given player depends, weighted by some arbitrary but fixed real parameter, on the number of different leaders chosen in a round, the number of players that choose the given player as the leader, and whether the chosen leader has changed w.r.t. the previous round or not. The social payoff can be the maximum, average or minimum local payoff of the players. Possible applications include quite diverse examples such as rotating coordinator-based distributed algorithms and long-haul formation flying of social birds. Depending on the weights and the particular social payoff, optimal sequences can be very different, from simple round-robin where all players chose the same leader alternatingly every time slot to very exotic patterns, where a small group of leaders (at most 2) is elected in every time slot. Moreover, we study the question if and when a single player would not benefit w.r.t. its local payoff when deviating from the given optimal sequence, i.e., when our optimal sequences are Nash equilibria in the restricted strategy space of oblivious strategies. As this is the case for many parameterizations of our model, our results reveal that no punishment is needed to make it rational for the players to optimize the social payoff.
AU - Zeiner, Martin
AU - Schmid, Ulrich
AU - Chatterjee, Krishnendu
ID - 8793
IS - 1
JF - Discrete Applied Mathematics
SN - 0166218X
TI - Optimal strategies for selecting coordinators
VL - 289
ER -
TY - JOUR
AB - Area-dependent quantum field theory is a modification of two-dimensional topological quantum field theory, where one equips each connected component of a bordism with a positive real number—interpreted as area—which behaves additively under glueing. As opposed to topological theories, in area-dependent theories the state spaces can be infinite-dimensional. We introduce the notion of regularised Frobenius algebras in Hilbert spaces and show that area-dependent theories are in one-to-one correspondence to commutative regularised Frobenius algebras. We also provide a state sum construction for area-dependent theories. Our main example is two-dimensional Yang–Mills theory with compact gauge group, which we treat in detail.
AU - Runkel, Ingo
AU - Szegedy, Lorant
ID - 8816
IS - 1
JF - Communications in Mathematical Physics
SN - 00103616
TI - Area-dependent quantum field theory
VL - 381
ER -