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 - The phytohormone auxin plays a central role in shaping plant growth and development. With decades of genetic and biochemical studies, numerous core molecular components and their networks, underlying auxin biosynthesis, transport, and signaling, have been identified. Notably, protein phosphorylation, catalyzed by kinases and oppositely hydrolyzed by phosphatases, has been emerging to be a crucial type of post-translational modification, regulating physiological and developmental auxin output at all levels. In this review, we comprehensively discuss earlier and recent advances in our understanding of genetics, biochemistry, and cell biology of the kinases and phosphatases participating in auxin action. We provide insights into the mechanisms by which reversible protein phosphorylation defines developmental auxin responses, discuss current challenges, and provide our perspectives on future directions involving the integration of the control of protein phosphorylation into the molecular auxin network.
AU - Tan, Shutang
AU - Luschnig, Christian
AU - Friml, Jiří
ID - 8992
IS - 1
JF - Molecular Plant
SN - 16742052
TI - Pho-view of auxin: Reversible protein phosphorylation in auxin biosynthesis, transport and signaling
VL - 14
ER -
TY - JOUR
AB - Phenomenological relations such as Ohm’s or Fourier’s law have a venerable history in physics but are still scarce in biology. This situation restrains predictive theory. Here, we build on bacterial “growth laws,” which capture physiological feedback between translation and cell growth, to construct a minimal biophysical model for the combined action of ribosome-targeting antibiotics. Our model predicts drug interactions like antagonism or synergy solely from responses to individual drugs. We provide analytical results for limiting cases, which agree well with numerical results. We systematically refine the model by including direct physical interactions of different antibiotics on the ribosome. In a limiting case, our model provides a mechanistic underpinning for recent predictions of higher-order interactions that were derived using entropy maximization. We further refine the model to include the effects of antibiotics that mimic starvation and the presence of resistance genes. We describe the impact of a starvation-mimicking antibiotic on drug interactions analytically and verify it experimentally. Our extended model suggests a change in the type of drug interaction that depends on the strength of resistance, which challenges established rescaling paradigms. We experimentally show that the presence of unregulated resistance genes can lead to altered drug interaction, which agrees with the prediction of the model. While minimal, the model is readily adaptable and opens the door to predicting interactions of second and higher-order in a broad range of biological systems.
AU - Kavcic, Bor
AU - Tkačik, Gašper
AU - Bollenbach, Tobias
ID - 8997
IS - 1
JF - PLOS Computational Biology
KW - Modelling and Simulation
KW - Genetics
KW - Molecular Biology
KW - Antibiotics
KW - Drug interactions
SN - 1553-7358
TI - Minimal biophysical model of combined antibiotic action
VL - 17
ER -
TY - JOUR
AB - In many basic shear flows, such as pipe, Couette, and channel flow, turbulence does not
arise from an instability of the laminar state, and both dynamical states co-exist. With decreasing flow speed (i.e., decreasing Reynolds number) the fraction of fluid in laminar motion increases while turbulence recedes and eventually the entire flow relaminarizes. The first step towards understanding the nature of this transition is to determine if the phase change is of either first or second order. In the former case, the turbulent fraction would drop discontinuously to zero as the Reynolds number decreases while in the latter the process would be continuous. For Couette flow, the flow between two parallel plates, earlier studies suggest a discontinuous scenario. In the present study we realize a Couette flow between two concentric cylinders which allows studies to be carried out in large aspect ratios and for extensive observation times. The presented measurements show that the transition in this circular Couette geometry is continuous suggesting that former studies were limited by finite size effects. A further characterization of this transition, in particular its relation to the directed percolation universality class, requires even larger system sizes than presently available.
AU - Avila, Kerstin
AU - Hof, Björn
ID - 8999
IS - 1
JF - Entropy
TI - Second-order phase transition in counter-rotating taylor-couette flow experiment
VL - 23
ER -
TY - JOUR
AB - Studies on the experimental realization of two-dimensional anyons in terms of quasiparticles have been restricted, so far, to only anyons on the plane. It is known, however, that the geometry and topology of space can have significant effects on quantum statistics for particles moving on it. Here, we have undertaken the first step toward realizing the emerging fractional statistics for particles restricted to move on the sphere instead of on the plane. We show that such a model arises naturally in the context of quantum impurity problems. In particular, we demonstrate a setup in which the lowest-energy spectrum of two linear bosonic or fermionic molecules immersed in a quantum many-particle environment can coincide with the anyonic spectrum on the sphere. This paves the way toward the experimental realization of anyons on the sphere using molecular impurities. Furthermore, since a change in the alignment of the molecules corresponds to the exchange of the particles on the sphere, such a realization reveals a novel type of exclusion principle for molecular impurities, which could also be of use as a powerful technique to measure the statistics parameter. Finally, our approach opens up a simple numerical route to investigate the spectra of many anyons on the sphere. Accordingly, we present the spectrum of two anyons on the sphere in the presence of a Dirac monopole field.
AU - Brooks, Morris
AU - Lemeshko, Mikhail
AU - Lundholm, D.
AU - Yakaboylu, Enderalp
ID - 9005
IS - 1
JF - Physical Review Letters
SN - 00319007
TI - Molecular impurities as a realization of anyons on the two-sphere
VL - 126
ER -
TY - JOUR
AB - We study dynamics and thermodynamics of ion transport in narrow, water-filled channels, considered as effective 1D Coulomb systems. The long range nature of the inter-ion interactions comes about due to the dielectric constants mismatch between the water and the surrounding medium, confining the electric filed to stay mostly within the water-filled channel. Statistical mechanics of such Coulomb systems is dominated by entropic effects which may be accurately accounted for by mapping onto an effective quantum mechanics. In presence of multivalent ions the corresponding quantum mechanics appears to be non-Hermitian. In this review we discuss a framework for semiclassical calculations for the effective non-Hermitian Hamiltonians. Non-Hermiticity elevates WKB action integrals from the real line to closed cycles on a complex Riemann surfaces where direct calculations are not attainable. We circumvent this issue by applying tools from algebraic topology, such as the Picard-Fuchs equation. We discuss how its solutions relate to the thermodynamics and correlation functions of multivalent solutions within narrow, water-filled channels.
AU - Gulden, Tobias
AU - Kamenev, Alex
ID - 9020
IS - 1
JF - Entropy
TI - Dynamics of ion channels via non-hermitian quantum mechanics
VL - 23
ER -
TY - GEN
AB - We determine an asymptotic formula for the number of integral points of bounded height on a blow-up of $\mathbb{P}^3$ outside certain planes using universal torsors.
AU - Wilsch, Florian Alexander
ID - 9034
T2 - arXiv
TI - Integral points of bounded height on a log Fano threefold
ER -
TY - JOUR
AB - We develop a geometric version of the circle method and use it to compute the compactly supported cohomology of the space of rational curves through a point on a smooth affine hypersurface of sufficiently low degree.
AU - Browning, Timothy D
AU - Sawin, Will
ID - 177
IS - 3
JF - Annals of Mathematics
TI - A geometric version of the circle method
VL - 191
ER -
TY - JOUR
AB - An asymptotic formula is established for the number of rational points of bounded anticanonical height which lie on a certain Zariski dense subset of the biprojective hypersurface x1y21+⋯+x4y24=0 in ℙ3×ℙ3. This confirms the modified Manin conjecture for this variety, in which the removal of a thin set of rational points is allowed.
AU - Browning, Timothy D
AU - Heath Brown, Roger
ID - 179
IS - 16
JF - Duke Mathematical Journal
TI - Density of rational points on a quadric bundle in ℙ3×ℙ3
VL - 169
ER -
TY - JOUR
AB - We introduce dynamically warping grids for adaptive liquid simulation. Our primary contributions are a strategy for dynamically deforming regular grids over the course of a simulation and a method for efficiently utilizing these deforming grids for liquid simulation. Prior work has shown that unstructured grids are very effective for adaptive fluid simulations. However, unstructured grids often lead to complicated implementations and a poor cache hit rate due to inconsistent memory access. Regular grids, on the other hand, provide a fast, fixed memory access pattern and straightforward implementation. Our method combines the advantages of both: we leverage the simplicity of regular grids while still achieving practical and controllable spatial adaptivity. We demonstrate that our method enables adaptive simulations that are fast, flexible, and robust to null-space issues. At the same time, our method is simple to implement and takes advantage of existing highly-tuned algorithms.
AU - Hikaru, Ibayashi
AU - Wojtan, Christopher J
AU - Thuerey, Nils
AU - Igarashi, Takeo
AU - Ando, Ryoichi
ID - 5681
IS - 6
JF - IEEE Transactions on Visualization and Computer Graphics
SN - 10772626
TI - Simulating liquids on dynamically warping grids
VL - 26
ER -