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Topologie géométrique

Publications associées (22)

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Optical-resolution photoacoustic microscopy by use of a multimode fiber

Demetri Psaltis, Christophe Moser, Salma Farahi, Emmanuel André Henri Bossy

We demonstrate Optical-Resolution Photoacoustic Microscopy (OR-PAM), where the optical field is focused and scanned using Digital Phase Conjugation through a multimode fiber. The focus is scanned across the field of view using digital means, and the acoust ...

American Institute of Physics2013

Long knots and maps between operads

Kathryn Hess Bellwald

We identify the space of tangentially straightened long knots in R^m, for m greater than or equal to 4, as the double loops on the space of derived operad maps from the associative operad into a version of the little m-disk operad. This verifies a conjectu ...

Geometry & Topology Publications2012

Fourier Approximation Of Symmetric Ideal Knots

Henryk Gerlach, Mathias Carlen

Enforcing a specific symmetry group on a curve, knotted or not, is not trivial using standard interpolations such as polygons or splines. For a prescribed symmetry group we present a symmetrization process based on a Fourier description of a knot. The pres ...

2012

Tightening of DNA knots by supercoiling facilitates their unknotting by type II DNA topoisomerases

Giovanni Dietler, Andrzej Stasiak, Guillaume Witz

Using numerical simulations, we compare properties of knotted DNA molecules that are either torsionally relaxed or supercoiled. We observe that DNA supercoiling tightens knotted portions of DNA molecules and accentuates the difference in curvature between ...

2011

Computation and visualization of ideal knot shapes

Mathias Carlen

We investigate numerical simulations and visualizations of the problem of tying a knot in a piece of rope. The goal is to use the least possible rope of a fixed, prescribed radius to tie a particular knot, e.g. a trefoil, a figure eight, and so on. The rop ...

EPFL2010

DNA Topology : A Biophysical Study of DNA Rings, Knots, and Catenanes by Means of Atomic Force Microscopy and Numerical Simulations

Guillaume Witz

This thesis explores different aspects of DNA topology through experimental and numerical techniques. Topology is a vast mathematical field, that deals with the spatial properties of objects undergoing continuous deformations, but here it is restricted to ...

EPFL2010

Modélisation mécanique de fils pour la simulation chirurgicale

Lindo Robert Duratti

Minimally Invasive Surgery (MIS) represents one of the major progresses in surgery in the last decade. In general, it is based on the application of small body-cuts through which instruments are inserted into the patient's body allowing the surgeon to carr ...

EPFL2008

Scaling properties of DNA knots studied by atomic force microscopy

Erika Ercolini

The main subject of the present thesis is the experimental study of the scaling properties of DNA knots of different complexities by tapping mode atomic force microscopy (AFM) in air. Homo- or heterogeneous mixture of DNA knot types were deposited onto mic ...

EPFL2008

Fractal dimension and localization of DNA knots

Giovanni Dietler, Paolo De Los Rios, Guillaume Witz, Erika Ercolini

The scaling properties of DNA knots of different complexities were studied by atomic force microscope. Following two different protocols DNA knots are adsorbed onto a mica surface in regimes of (i) strong binding, that induces a kinetic trapping of the thr ...

American Physical Society2007

Simulations of electrophoretic collisions of DNA knots with gel obstacles

Giovanni Dietler, Paolo De Los Rios, Cédric Weber, Andrzej Stasiak

Gel electrophoresis can be used to separate nicked circular DNA molecules of equal length but forming different knot types. At low electric fields, complex knots drift faster than simpler knots. However, at high electric field the opposite is the case and ...

Institute of Physics2006

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DNA Topology : A Biophysical Study of DNA Rings, Knots, and Catenanes by Means of Atomic Force Microscopy and Numerical Simulations

Guillaume Witz

EPFL2010