Concept

Generalizations of the derivative

Publications associées (137)

Shift-Invariant Spaces from Rotation-Covariant Functions

Michaël Unser, Dimitri Nestor Alice Van De Ville, Thierry Blu

We consider shift-invariant multiresolution spaces generated by rotation-covariant functions ρ in

\mathbb{R}^{ 2 }

. To construct corresponding scaling and wavelet functions, ρ has to be localized with an appropriate multiplier, such that the localized ...

Elsevier2008

Self-Similarity: Part I—Splines and Operators

Michaël Unser, Thierry Blu

The central theme of this pair of papers (Parts I and II in this issue) is self-similarity, which is used as a bridge for connecting splines and fractals. The first part of the investigation is deterministic, and the context is that of L-splines; these are ...

IEEE2007

Image alignment with rotation manifolds built on sparse geometric expansions

Pascal Frossard, Effrosyni Kokiopoulou

In this paper we discuss the problem of alignment of patterns under arbitrary rotation. When a generic image pattern is geometrically transformed, it typically spans a (possibly nonlinear) manifold in a high dimensional space. When the pattern of interest ...

2007

Directed evolution of O6-alkylguanine-DNA alkyltransferase for applications in protein labeling

Kai Johnsson, Christian Heinis, Alexandre Juillerat, Christopher Chidley, Thomas Gronemeyer

The specific reaction of O6-alkylguanine-DNA alkyltransferase (AGT) with O6-benzylguanine (BG) derivatives allows for a specific labeling of AGT fusion proteins with chemically diverse compounds in living cells and in vitro. The efficiency of the labeling ...

Oxford University Press2006

Characterizing a heterogeneous aquifer by derivative analysis of pumping and recovery test data

David Andrew Barry

Evaluation of aquifer yields with the conventional time- drawdown method is based on the assumption of Theisian or infinite radial flow (IRF) of ground water to a well. However, long-term aquifer yields are controlled by heterogeneities and boundary condit ...

2006

Dealing with singularities in nonlinear unconstrained optimization

Michel Bierlaire, Michaël Clément Louis Ghislain Thémans

We propose new trust-region based optimization algorithms for solving unconstrained nonlinear problems whose second derivatives matrix is singular at a local solution. We give a theoretical characterization of the singularity in this context and we propose ...

2006

PID controller design with constraints on sensitivity functions using loop slope adjustment

Alireza Karimi, Roland Longchamp, Daniel Garcia

This paper presents a PID controller design method for stable minimum- phase systems. The approach is similar to the one proposed in the so-called modified Ziegler- Nichols method, where only one point on the frequency response of the plant is measured and ...

2006

Heterosubstituted or functionalized derivatives of 1- and 2-(trifluoromethyl)naphthalenes emanating from aryne adducts

Frédéric Bailly, Fabrice Cottet

More than two dozen new CF3-substituted naphthalene derivs. were prepd. in an expedient way by employing 3- and 4-(trifluoromethyl)benzyne as the key intermediates. 2- And 4-Chlorobenzotrifluoride were treated with butyllithium and the organometallic speci ...

2005

Time-lag in Derivative Convergence for Fixed Point Iterations

Daniel Kressner

In an earlier study it was proven and experimentally confirmed on a 2D Euler code that fixed point iterations can be differentiated to yield first and second order derivatives of implicit functions that are defined by state equations. It was also asserted ...

2005

Semi-Orthogonal Wavelets That Behave like Fractional Differentiators

Michaël Unser, Dimitri Nestor Alice Van De Ville, Thierry Blu

The approximate behavior of wavelets as differential operators is often considered as one of their most fundamental properties. In this paper, we investigate how we can further improve on the wavelet's behavior as differentiator. In particular, we propose ...

SPIE2005

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Shift-Invariant Spaces from Rotation-Covariant Functions

Michaël Unser, Dimitri Nestor Alice Van De Ville, Thierry Blu

We consider shift-invariant multiresolution spaces generated by rotation-covariant functions ρ in

\mathbb{R}^{ 2 }

. To construct corresponding scaling and wavelet functions, ρ has to be localized with an appropriate multiplier, such that the localized ...

Elsevier2008