TY - JOUR
AB - This short note aims to study quantum Hellinger distances investigated recently by Bhatia et al. (Lett Math Phys 109:1777–1804, 2019) with a particular emphasis on barycenters. We introduce the family of generalized quantum Hellinger divergences that are of the form ϕ(A,B)=Tr((1−c)A+cB−AσB), where σ is an arbitrary Kubo–Ando mean, and c∈(0,1) is the weight of σ. We note that these divergences belong to the family of maximal quantum f-divergences, and hence are jointly convex, and satisfy the data processing inequality. We derive a characterization of the barycenter of finitely many positive definite operators for these generalized quantum Hellinger divergences. We note that the characterization of the barycenter as the weighted multivariate 1/2-power mean, that was claimed in Bhatia et al. (2019), is true in the case of commuting operators, but it is not correct in the general case.
AU - Pitrik, Jozsef
AU - Virosztek, Daniel
ID - 7618
IS - 8
JF - Letters in Mathematical Physics
SN - 0377-9017
TI - Quantum Hellinger distances revisited
VL - 110
ER -
TY - JOUR
AB - Cell polarity is a fundamental feature of all multicellular organisms. In plants, prominent cell polarity markers are PIN auxin transporters crucial for plant development. To identify novel components involved in cell polarity establishment and maintenance, we carried out a forward genetic screening with PIN2:PIN1-HA;pin2 Arabidopsis plants, which ectopically express predominantly basally localized PIN1 in the root epidermal cells leading to agravitropic root growth. From the screen, we identified the regulator of PIN polarity 12 (repp12) mutation, which restored gravitropic root growth and caused PIN1-HA polarity switch from basal to apical side of root epidermal cells. Complementation experiments established the repp12 causative mutation as an amino acid substitution in Aminophospholipid ATPase3 (ALA3), a phospholipid flippase with predicted function in vesicle formation. ala3 T-DNA mutants show defects in many auxin-regulated processes, in asymmetric auxin distribution and in PIN trafficking. Analysis of quintuple and sextuple mutants confirmed a crucial role of ALA proteins in regulating plant development and in PIN trafficking and polarity. Genetic and physical interaction studies revealed that ALA3 functions together with GNOM and BIG3 ARF GEFs. Taken together, our results identified ALA3 flippase as an important interactor and regulator of ARF GEF functioning in PIN polarity, trafficking and auxin-mediated development.
AU - Zhang, Xixi
AU - Adamowski, Maciek
AU - Marhavá, Petra
AU - Tan, Shutang
AU - Zhang, Yuzhou
AU - Rodriguez Solovey, Lesia
AU - Zwiewka, Marta
AU - Pukyšová, Vendula
AU - Sánchez, Adrià Sans
AU - Raxwal, Vivek Kumar
AU - Hardtke, Christian S.
AU - Nodzynski, Tomasz
AU - Friml, Jiří
ID - 7619
IS - 5
JF - The Plant Cell
SN - 1040-4651
TI - Arabidopsis flippases cooperate with ARF GTPase exchange factors to regulate the trafficking and polarity of PIN auxin transporters
VL - 32
ER -
TY - JOUR
AB - The International Young Physicists' Tournament (IYPT) continued in 2018 in Beijing, China and 2019 in Warsaw, Poland with its 31st and 32nd editions. The IYPT is a modern scientific competition for teams of high school students, also known as the Physics World Cup. It involves long-term theoretical and experimental work focused on solving 17 publicly announced open-ended problems in teams of five. On top of that, teams have to present their solutions in front of other teams and a scientific jury, and get opposed and reviewed by their peers. Here we present a brief information about the competition with a specific focus on one of the IYPT 2018 tasks, the 'Ring Oiler'. This seemingly simple mechanical problem appeared to be of such a complexity that even the dozens of participating teams and jurying scientists were not able to solve all of its subtleties.
AU - Plesch, Martin
AU - Plesník, Samuel
AU - Ruzickova, Natalia
ID - 7622
IS - 3
JF - European Journal of Physics
SN - 01430807
TI - The IYPT and the 'Ring Oiler' problem
VL - 41
ER -
TY - JOUR
AB - A two-dimensional mathematical model for cells migrating without adhesion capabilities is presented and analyzed. Cells are represented by their cortex, which is modeled as an elastic curve, subject to an internal pressure force. Net polymerization or depolymerization in the cortex is modeled via local addition or removal of material, driving a cortical flow. The model takes the form of a fully nonlinear degenerate parabolic system. An existence analysis is carried out by adapting ideas from the theory of gradient flows. Numerical simulations show that these simple rules can account for the behavior observed in experiments, suggesting a possible mechanical mechanism for adhesion-independent motility.
AU - Jankowiak, Gaspard
AU - Peurichard, Diane
AU - Reversat, Anne
AU - Schmeiser, Christian
AU - Sixt, Michael K
ID - 7623
JF - Mathematical Models and Methods in Applied Sciences
SN - 02182025
TI - Modeling adhesion-independent cell migration
ER -
TY - THES
AB - This thesis is based on three main topics: In the first part, we study convergence of discrete gradient flow structures associated with regular finite-volume discretisations of Fokker-Planck equations. We show evolutionary I convergence of the discrete gradient flows to the L2-Wasserstein gradient flow corresponding to the solution of a Fokker-Planck
equation in arbitrary dimension d >= 1. Along the argument, we prove Mosco- and I-convergence results for discrete energy functionals, which are of independent interest for convergence of equivalent gradient flow structures in Hilbert spaces.
The second part investigates L2-Wasserstein flows on metric graph. The starting point is a Benamou-Brenier formula for the L2-Wasserstein distance, which is proved via a regularisation scheme for solutions of the continuity equation, adapted to the peculiar geometric structure of metric graphs. Based on those results, we show that the L2-Wasserstein space over a metric graph admits a gradient flow which may be identified as a solution of a Fokker-Planck equation.
In the third part, we focus again on the discrete gradient flows, already encountered in the first part. We propose a variational structure which extends the gradient flow structure to Markov chains violating the detailed-balance conditions. Using this structure, we characterise contraction estimates for the discrete heat flow in terms of convexity of
corresponding path-dependent energy functionals. In addition, we use this approach to derive several functional inequalities for said functionals.
AU - Forkert, Dominik L
ID - 7629
SN - 2663-337X
TI - Gradient flows in spaces of probability measures for finite-volume schemes, metric graphs and non-reversible Markov chains
ER -