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Roche-Newton O.,Johann Radon Institute for Computational and Applied Mathematics RICAM
Leibniz International Proceedings in Informatics, LIPIcs | Year: 2015

In this note it is established that, for any finite set A of real numbers, there exist two elements a, b 2 A such that (equiton presented) In particular, it follows that |(A + A)(A + A)| ≈ |A|2/log |A| . The latter inequality had in fact already been established in an earlier work of the author and Rudnev [8], which built upon the recent developments of Guth and Katz [2] in their work on the Erdos distinct distance problem. Here, we do not use those relatively deep methods, and instead we need just a single application of the Szemerédi-Trotter Theorem. The result is also qualitatively stronger than the corresponding sum-product estimate from [8], since the set (a+A)(b+A) is defined by only two variables, rather than four. One can view this as a solution for the pinned distance problem, under an alternative notion of distance, in the special case when the point set is a direct product A × A. Another advantage of this more elementary approach is that these results can now be extended for the first time to the case when A-C.

Rodrigues S.S.,Johann Radon Institute for Computational and Applied Mathematics RICAM
ESAIM - Control, Optimisation and Calculus of Variations | Year: 2015

Controllability properties for the Navier-Stokes system are closely related to observability properties for the adjoint Oseen-Stokes system; boundary observability inequalities are derived, for that adjoint system, that will be appropriate to deal with suitable constrained controls, like finite-dimensional controls supported in a given subset of the boundary. As an illustration, new boundary controllability results for the Oseen-Stokes system are derived. Finally, some further plausible consequences of the derived inequalities, concerning the Navier-Stokes system, are discussed. © 2015 EDP Sciences, SMAI.

Fonseca J.P.,Institute of Molecular Biotechnology IMBA | Steffen P.A.,Institute of Molecular Biotechnology IMBA | Muller S.,Johann Radon Institute for Computational and Applied Mathematics RICAM | Lu J.,ETH Zurich | And 3 more authors.
Genes and Development | Year: 2012

Epigenetic memory mediated by Polycomb group (PcG) proteins must be maintained during cell division, but must also be flexible to allow cell fate transitions. Here we quantify dynamic chromatin-binding properties of PH::GFP and PC::GFP in living Drosophila in two cell types that undergo defined differentiation and mitosis events. Quantitative fluorescence recovery after photobleaching (FRAP) analysis demonstrates that PcG binding has a higher plasticity in stem cells than in more determined cells and identifies a fraction of PcG proteins that binds mitotic chromatin with up to 300-fold longer residence times than in interphase. Mathematical modeling examines which parameters best distinguish stem cells from differentiated cells. We identify phosphorylation of histone H3 at Ser 28 as a potential mechanism governing the extent and rate of mitotic PC dissociation in different lineages. We propose that regulation of the kinetic properties of PcG-chromatin binding is an essential factor in the choice between stability and flexibility in the establishment of cell identities. © 2012 by Cold Spring Harbor Laboratory Press.

Oelz D.,Johann Radon Institute for Computational and Applied Mathematics RICAM
Journal of Mathematical Biology | Year: 2014

A mathematical model in one dimension for a non-sarcomeric actomyosin bundle featuring anti-parallel flows of anti-parallel F-actin is introduced. The model is able to relate these flows to the effect of cross-linking and bundling proteins, to the forces due to myosin-II filaments and to external forces at the extreme tips of the bundle. The modeling is based on a coarse graining approach starting with a microscopic model which includes the description of chemical bonds as elastic springs and the force contribution of myosin filaments. In a second step we consider the asymptotic regime where the filament lengths are small compared to the overall bundle length and restrict to the lowest order contributions. There it becomes apparent that myosin filaments generate forces which are partly compensated by drag forces due to cross-linking proteins. The remaining local contractile forces are then propagated to the tips of the bundle by the viscosity effect of bundling proteins in the filament gel. The model is able to explain how a disordered bundle of comparatively short actin filaments interspersed with myosin filaments can effectively contract the two tips of the actomyosin bundle. It gives a quantitative description of these forces and of the anti-parallel flows of the two phases of anti-parallel F-actin. An asymptotic version of the model with infinite viscosity can be solved explicitly and yields an upper bound to the contractile force of the bundle. © 2013 Springer-Verlag Berlin Heidelberg.

Rodrigues S.S.,Johann Radon Institute for Computational and Applied Mathematics RICAM | Aguiar A.P.,University of Porto
IEEE Transactions on Automatic Control | Year: 2014

For a class of nonlinear systems, we investigate the problem of under what conditions there exists a coordinate transformation that yields a state affine linear system up to output injection with implicit outputs. In particular, we provide necessary and sufficient conditions for time-varying linearization up to multi-output injection. We highlight that if the conditions hold, as a consequence, it is possible in the new coordinates to construct an observer with linear error dynamics. We propose a methodology to find the coordinate transformation. Several examples illustrate the proposed procedure. © 1963-2012 IEEE.

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