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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.

Helin T.,University of Helsinki | Yudytskiy M.,Johann Radon Institute for Computational and Applied Mathematics RICAM
Inverse Problems | Year: 2013

The next generation ground-based telescopes rely heavily on adaptive optics for overcoming the limitation of atmospheric turbulence. In the future adaptive optics modalities, like multi-conjugate adaptive optics (MCAO), atmospheric tomography is the major mathematical and computational challenge. In this severely ill-posed problem, a fast and stable reconstruction algorithm is needed that can take into account many real-life phenomena of telescope imaging. We introduce a novel reconstruction method for the atmospheric tomography problem and demonstrate its performance and flexibility in the context of MCAO. Our method is based on using locality properties of compactly supported wavelets, both in the spatial and frequency domains. The reconstruction in the atmospheric tomography problem is obtained by solving the Bayesian MAP estimator with a conjugate-gradient-based algorithm. An accelerated algorithm with preconditioning is also introduced. Numerical performance is demonstrated on the official end-to-end simulation tool OCTOPUS of European Southern Observatory. © 2013 IOP Publishing Ltd.

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.

Fornasier M.,Johann Radon Institute for Computational and Applied Mathematics RICAM | Haskovec J.,Johann Radon Institute for Computational and Applied Mathematics RICAM | Toscani G.,University of Pavia
Physica D: Nonlinear Phenomena | Year: 2011

We introduce and discuss the possible dynamics of groups of indistinguishable agents, which are interacting according to their relative positions, with the aim of deriving hydrodynamic equations. These models are developed to mimic the collective motion of groups of species such as bird flocks, fish schools, herds of quadrupeds or bacteria colonies. Our starting model for these interactions is the Povzner equation [21], which describes a dilute gas in which binary collisions of elastic spheres depend on their relative positions. Following the Cucker and Smale model [9], we will consider binary interactions between agents that are dissipative collisions in which the coefficient of restitution depends on their relative distance. Under the assumption of weak dissipation, it is shown that the Povzner equation is modified through a correction in the form of a nonlinear friction type operator. Using this correction, we formally obtain from the Povzner equation in a direct way a fluid dynamic description of a system of agents with weak dissipative interactions, with a coefficient of restitution that depends on their relative distance. © 2010 Elsevier B.V. All rights reserved.

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.

Emans M.,Johann Radon Institute for Computational and Applied Mathematics RICAM | Emans M.,Industrial Mathematics Competence Center Gmb
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) | Year: 2012

We examine a modified implementation of the v-cycle multigrid scheme which takes into account the memory traffic, i.e. the movement of data between the memory and the processing units. It is known that the relatively slow data transfer is responsible for the poor parallel performance of multigrid algorithms on certain shared memory architectures e.g. those with a front-side bus memory controller. The modification is simple but it speeds up computations by up to 15%. © 2012 Springer-Verlag.

Phan D.,Johann Radon Institute for Computational and Applied Mathematics RICAM | Rodrigues S.S.,Johann Radon Institute for Computational and Applied Mathematics RICAM
2015 European Control Conference, ECC 2015 | Year: 2015

The approximate controllability by means of a few controls is proven for 2D Navier-Stokes system in an infinite channel under generalized Navier boundary conditions in the finite direction and the periodicity assumption in the infinite direction. The set of controls is given explicitly, and do not depend on the viscosity of the fluid. The case of 1D Burgers system in a bounded interval under Dirichlet boundary conditions, where the controls are supported in an arbitrary small nonempty open subset, is also discussed. © 2015 EUCA.

Langer U.,Johann Radon Institute for Computational and Applied Mathematics RICAM | Toulopoulos I.,Johann Radon Institute for Computational and Applied Mathematics RICAM
Computing and Visualization in Science | Year: 2016

In this work, we study the approximation properties of multipatch dG-IgA methods, that apply the multipatch Isogeometric Analysis discretization concept and the discontinuous Galerkin technique on the interfaces between the patches, for solving linear diffusion problems with diffusion coefficients that may be discontinuous across the patch interfaces. The computational domain is divided into non-overlapping subdomains, called patches in IgA, where B-splines, or NURBS approximations spaces are constructed. The solution of the problem is approximated in every subdomain without imposing any matching grid conditions and without any continuity requirements for the discrete solution across the interfaces. Numerical fluxes with interior penalty jump terms are applied in order to treat the discontinuities of the discrete solution on the interfaces. We provide a rigorous a priori discretization error analysis for diffusion problems in two- and three-dimensional domains, where solutions patchwise belong to (Formula presented.), with some (Formula presented.) and (Formula presented.). In any case, we show optimal convergence rates of the discretization with respect to the dG - norm. © 2016 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.

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.

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