Publications related to Minimizing movements along a sequence of functionals and curves of maximal slope

Generating Calligraphic Trajectories with Model Predictive Control

We describe a methodology for the interactive definition of curves and motion paths using a stochastic formulation of optimal control. We demonstrate how the same optimization framework can be used in different ways to generate curves and traces that are g ...

2017

Medial axis transformation as a solid modeling representation method for computer aided design software

Paul Xirouchakis, Mihai-Bogdan Lazar, Ian Anthony Stroud, Florian Barras, Guillaume Goualard

A method for achieving a representation of an object within a data structure for a Computer Aided Design system employing a Medial Axis Transformation (MAT), the representation of the object comprising a set of adjacent bounded surface elements called MAT ...

2016

An Inner-Product Calculus for Periodic Functions and Curves

Michaël Unser, Daniel Andreas Schmitter, Anaïs Laure Marie-Thérèse Badoual

Our motivation is the design of efficient algorithms to process closed curves represented by basis functions or wavelets. To that end, we introduce an inner-product calculus to evaluate correlations and

L _{ 2 }

distances between such curves. In partic ...

2016

Variational minimization of orbital-density-dependent functionals

Nicola Marzari, Giovanni Borghi, Andrea Ferretti

Orbital-density-dependent functionals, such as the Perdew-Zunger or the Koopmans-compliant functionals, are used to remove unphysical self-interaction energies and to restoremissing piece-wise linearity in approximate formulations of density-functional the ...

Amer Physical Soc2015

How Structural and Physicochemical Determinants Shape Sequence Constraints in a Functional Enzyme

Matteo Dal Peraro, Luciano Andres Abriata

The need for interfacing structural biology and biophysics to molecular evolution is being increasingly recognized. One part of the big problem is to understand how physics and chemistry shape the sequence space available to functional proteins, while sati ...

Public Library Science2015

Cross-Intersecting Families of Vectors

János Pach, Gábor Tardos

Given a sequence of positive integers , let denote the family of all sequences of positive integers such that for all . Two families of sequences (or vectors), , are said to be -cross-intersecting if no matter how we select and , there are at least distinc ...

Springer Japan Kk2015

Constructing reparameterization invariant metrics on spaces of plane curves

Martins Bruveris, Martin Bauer

Metrics on shape spaces are used to describe deformations that take one shape to another, and to define a distance between shapes. We study a family of metrics on the space of curves, which includes several recently proposed metrics, for which the metrics ...

Elsevier2014

Approximation theorems in metric spaces and functionals strictly subordinated to convergent series

Some new results are presented concerning the search and approximation of solutions of equations in metric spaces using functionals strictly subordinated to a convergent series and functionals compatible with a convergent series. These classes of functiona ...

Elsevier2014

Sampling Curves with Finite Rate of Innovation

Thierry Blu, Hanjie Pan, Pier Luigi Dragotti

In this paper, we extend the theory of sampling signals with finite rate of innovation (FRI) to a specific class of two-dimensional curves, which are defined implicitly as the zeros of a mask function. Here the mask function has a parametric representation ...

Institute of Electrical and Electronics Engineers2014

Passing to the limit in maximal slope curves: from a regularized Perona–Malik equation to the total variation flow

Maria Colombo

We prove that solutions of a mildly regularized Perona–Malik equation converge, in a slow time scale, to solutions of the total variation flow. The convergence result is global-in-time, and holds true in any space dimension. The proof is based on the gener ...

2012

Minimizing movements along a sequence of functionals and curves of maximal slope

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Generating Calligraphic Trajectories with Model Predictive Control

Medial axis transformation as a solid modeling representation method for computer aided design software

An Inner-Product Calculus for Periodic Functions and Curves

Variational minimization of orbital-density-dependent functionals

How Structural and Physicochemical Determinants Shape Sequence Constraints in a Functional Enzyme

Cross-Intersecting Families of Vectors

Constructing reparameterization invariant metrics on spaces of plane curves

Approximation theorems in metric spaces and functionals strictly subordinated to convergent series

Sampling Curves with Finite Rate of Innovation

Passing to the limit in maximal slope curves: from a regularized Perona–Malik equation to the total variation flow

Generating Calligraphic Trajectories with Model Predictive Control

Variational minimization of orbital-density-dependent functionals

Cross-Intersecting Families of Vectors

Constructing reparameterization invariant metrics on spaces of plane curves

Approximation theorems in metric spaces and functionals strictly subordinated to convergent series

Medial axis transformation as a solid modeling representation method for computer aided design software

An Inner-Product Calculus for Periodic Functions and Curves

How Structural and Physicochemical Determinants Shape Sequence Constraints in a Functional Enzyme

Passing to the limit in maximal slope curves: from a regularized Perona–Malik equation to the total variation flow

Sampling Curves with Finite Rate of Innovation