Concept

Knot polynomial

Publications associées (26)

Computational Exploration of Multistable Elastic Knots

Mark Pauly, Michele Vidulis, Yingying Ren

We present an algorithmic approach to discover, study, and design multistable elastic knots. Elastic knots are physical realizations of closed curves embedded in 3-space. When endowed with the material thickness and bending resistance of a physical wire, t ...

2023

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

Exploring the inner workings of the clove hitch knot

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

We perform a combined experimental and computational investigation of the clove hitch knot. We develop a physical model for the clove hitch by tying an elastic rod onto a rigid cylinder. In the experiments, we characterize the mechanical performance, geome ...

ELSEVIER2022

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 ...

2019

Advanced Machine Learning Techniques for Self-Interference Cancellation in Full-Duplex Radios

Andreas Peter Burg, Andreas Toftegaard Kristensen

In-band full-duplex systems allow for more efficient use of temporal and spectral resources by transmitting and receiving information at the same time and on the same frequency. However, this creates a strong self-interference signal at the receiver, makin ...

IEEE2019

Polynomial models in finance

Damien Edouard Ackerer

This thesis presents new flexible dynamic stochastic models for the evolution of market prices and new methods for the valuation of derivatives. These models and methods build on the recently characterized class of polynomial jump-diffusion processes for w ...

EPFL2017

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

Formal Verification of Integer Multipliers by Combining Gröbner Basis with Logic Reduction

Mathias Soeken

Formal verification utilizing symbolic computer algebra has demonstrated the ability to formally verify large Galois field arithmetic circuits and basic architectures of integer arithmetic circuits. The technique models the circuit as Gröbner basis polynom ...

IEEE2016

Untangling the Mechanics and Topology in the Frictional Response of Long Overhand Elastic Knots

Pedro Miguel Nunes Pereira de Almeida Reis

We combine experiments and theory to study the mechanics of overhand knots in slender elastic rods under tension. The equilibrium shape of the knot is governed by an interplay between topology, friction, and bending. We use precision model experiments to q ...

American Physical Society2015

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