Concept

Alexander polynomial

Related publications (18)

HYPERBOLA METHOD ON TORIC VARIETIES

We develop a very general version of the hyperbola method which extends the known method by Blomer and Brudern for products of projective spaces to complete smooth split toric varieties. We use it to count Campana points of bounded log-anticanonical height ...

Ecole Polytechnique2024

Mechanics of Physical Knots: From Filaments in Contact to Surgical Suturing

Paul Johanns

In this thesis, we study the mechanics of tight physical knots. Knots are omnipresent in surgery, climbing, and sailing, with disastrous consequences when the filament or the rope fails to perform its function. Even if the importance of mechanical analysis ...

EPFL2023

The shapes of physical trefoil knots

Pedro Miguel Nunes Pereira de Almeida Reis, John Maddocks, Tomohiko Sano, Paul Johanns, Changyeob Baek, Paul Grandgeorge

We perform a compare-and-contrast investigation between the equilibrium shapes of physical and ideal trefoil knots, both in closed and open configurations. Ideal knots are purely geometric abstractions for the tightest configuration tied in a perfectly fle ...

2021

Design and Implementation of a Neural Network Based Predistorter for Enhanced Mobile Broadband

Alexios Konstantinos Balatsoukas Stimming

Digital predistortion is the process of using digital signal processing to correct nonlinearities caused by the analog RF front-end of a wireless transmitter. These nonlinearities contribute to adjacent channel leakage, degrade the error vector magnitude o ...

IEEE2019

A Generalized Index for Static Voltage Stability of Unbalanced Polyphase Power Systems including Thévenin Equivalents and Polynomial Models

Mario Paolone, Andreas Martin Kettner

This paper proposes a Voltage Stability Index (VSI) suitable for unbalanced polyphase power systems. To this end, the grid is represented by a polyphase multiport network model (i.e., hybrid parameters), and the aggregate behavior of the devices in each no ...

IEEE Institute of Electrical and Electronics Engineers2019

Controller design and value function approximation for nonlinear dynamical systems

Colin Neil Jones, Milan Korda

This work considers the infinite-time discounted optimal control problem for continuous time input-affine polynomial dynamical systems subject to polynomial state and box input constraints. We propose a sequence of sum-of-squares (SOS) approximations of th ...

Pergamon-Elsevier Science Ltd2016

Homoclinic Points And Floer Homology

A new relation between homoclinic points and Lagrangian Floer homology is presented: in dimension two, we construct a Floer homology generated by primary homoclinic points. We compute two examples and prove an invariance theorem. Moreover, we establish a l ...

Int Press Boston, Inc2013

Sedimentation of macroscopic rigid knots and its relation to gel electrophoretic mobility of DNA knots

Giovanni Dietler, Cédric Weber, Andrzej Stasiak, Mathias Carlen

We address the general question of the extent to which the hydrodynamic behaviour of microscopic freely fluctuating objects can be reproduced by macrosopic rigid objects. In particular, we compare the sedimentation speeds of knotted DNA molecules undergoin ...

Nature Publishing Group2013

Transport, Flux And Growth Of Homoclinic Floer Homology

We point out an interesting relation between transport in Hamiltonian dynamics and Floer homology. We generalize homoclinic Floer homology from R-2 and closed surfaces to two-dimensional cylinders. The relative symplectic action of two homoclinic points is ...

Amer Inst Mathematical Sciences2012

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

Ideal knots and other packing problems of tubes

Henryk Gerlach

This thesis concerns optimal packing problems of tubes, or thick curves, where thickness is defined as follows. Three points on a closed space curve define a circle. Taking the infimum over all radii of pairwise-distinct point triples defines the thickness ...

EPFL2010

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

Reasoning algebraically about P-solvable loops

Laura Ildiko Kovacs

We present a method for generating polynomial invariants for a subfamily of imperative loops operating on numbers, called the P-solvable loops. The method uses algorithmic combinatorics and algebraic techniques. The approach is shown to be complete for som ...

Springer-Verlag New York, Ms Ingrid Cunningham, 175 Fifth Ave, New York, Ny 10010 Usa2008

Aligator: A mathematica package for invariant generation

Laura Ildiko Kovacs

We describe the new software package Aligator for automatically inferring polynomial loop invariants, The package combines algorithms from symbolic summation and polynomial algebra with computational logic, and is applicable to the rich class of P-solvable ...

Springer-Verlag New York, Ms Ingrid Cunningham, 175 Fifth Ave, New York, Ny 10010 Usa2008

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

Rate-Distortion Optimized Tree-Structured Compression Algorithms for Piecewise Polynomial Images

Martin Vetterli, Pier Luigi Dragotti, Minh Do, Rahul Shukla

This paper presents novel coding algorithms based on tree-structured segmentation, which achieve the correct asymp- totic rate-distortion (R-D) behavior for a simple class of signals, known as piecewise polynomials, by using an R-D based prune and join sch ...

2005

Symmetry breaking in mechanical systems

The first part of this thesis studies the problem of symmetry breaking in the context of simple mechanical systems with compact symmetry Lie group G. In this part we shall assume that the principal stratum of the G-action on the configuration space Q of a ...

EPFL2005