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Concept

Wirtinger derivatives

Related publications (27)

Stability: a search for structure

Wouter Jongeneel

In this thesis we study stability from several viewpoints. After covering the practical importance, the rich history and the ever-growing list of manifestations of stability, we study the following. (i) (Statistical identification of stable dynamical syste ...

EPFL2024

IMPROVED REGULARITY OF SECOND DERIVATIVES FOR SUBHARMONIC FUNCTIONS

Xavier Fernandez-Real Girona, Riccardo Tione

In this note, we prove that if a subharmonic function Delta u >= 0 has pure second derivatives partial derivative(ii)u that are signed measures, then their negative part (partial derivative(ii)u)- belongs to L-1 (in particular, it is not singular). We then ...

American Mathematical Society (AMS)2023

Learning of Continuous and Piecewise-Linear Functions With Hessian Total-Variation Regularization

Michaël Unser, Shayan Aziznejad, Joaquim Gonçalves Garcia Barreto Campos

We develop a novel 2D functional learning framework that employs a sparsity-promoting regularization based on second-order derivatives. Motivated by the nature of the regularizer, we restrict the search space to the span of piecewise-linear box splines shi ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2022

Semiclassical methods in conformal field theories scrutinized by the epsilon-expansion

Gil Badel

Conformal Field Theories (CFTs) are crucial for our understanding of Quantum Field Theory (QFT). Because of their powerful symmetry properties, they play the role of signposts in the space of QFTs. Any method that gives us information about their structure ...

EPFL2022

A computational workflow for the expansion of heterologous biosynthetic pathways to natural product derivatives

Vassily Hatzimanikatis, Jasmin Maria Hafner

Plant natural products (PNPs) and their derivatives are important but underexplored sources of pharmaceutical molecules. To access this untapped potential, the reconstitution of heterologous PNP biosynthesis pathways in engineered microbes provides a valua ...

Nature Research2021

Local Non-Rigid Structure-from-Motion from Locally Diffeomorphic Mappings

Pascal Fua, Mathieu Salzmann, Shaifali Parashar

We propose a new formulation to the non-rigid structure-from-motion problem that only requires the deforming surface to meaning that its differential structure is preserved. This is a much weaker assumption than the traditional ones of isometry or conforma ...

2020

On the choice of metric in gradient-based theories of brain function

Wulfram Gerstner, Johanni Michael Brea, Jean-Pascal Théodor Pfister

The idea that the brain functions so as to minimize certain costs pervades theoretical neuroscience. Because a cost function by itself does not predict how the brain finds its minima, additional assumptions about the optimization method need to be made to ...

2020

Design, Synthesis and in vitro Controlled Release of New Adamantanodiarylketone Antimycobacterials

Stewart Cole, Anthony Vocat

In the present investigation, the synthesis, the biology and the development of matrix tablet formulations for the in vitro controlled release of new adamantane diarylketone antimycobacterial derivatives, is presented. In the skeleton of the new compounds, ...

WILEY-V C H VERLAG GMBH2019

An optimized self-sensing piezoelectric cantilever for micro-robotic applications

Yves Perriard, Louis Antoine Masson, Xinchang Liu

Quasi-static piezoelectric actuators are used in micro-robotics due to the small displacements they can achieve, and they have been proven to be suitable for Self-Sensing Actuation (SSA) applications. The morphology and material of an actuator, and therefo ...

2019

Noether Theorems and Quantum Anomalies

Tudor Ratiu

A quantum anomaly is the breaking of symmetry with respect to some transformations after the quantization of a classical Hamiltonian or Lagrangian system. It is shown that both the Noether theorems (including their infinite-dimensional versions) and the ex ...

Springer Verlag2017

Contributions to Modelling Extremes of Spatial Data

Linda Frossard

The increasing interest in using statistical extreme value theory to analyse environmental data is mainly driven by the large impact extreme events can have. A difficulty with spatial data is that most existing inference methods for asymptotically justifie ...

EPFL2017

Benzothiophene, benzyloxybenzylidene and indoline derivatives useful for the treatment of tuberculosis

Stewart Cole, Jan Lars Rybniker

The present invention relates to benzothiophene, benzyloxybenzylidene and indoline-2-one derivatives and the use of said derivatives in the treatment and/or prevention of tuberculosis. ...

2016

2-homopiperazine-1-yl-4h-1,3-benzothiazine-4-one derivatives and process for the preparation of 2- (homo)piperazine 1,3-benzothiazine-4-one hydrochlorides

2-homopiperazine-1-yl-4H-l, 3 -bensothiazine-4-one derivatives of formula (I) are provided. They are useful in the treatment of bacterial infections, in particular tuberculosis, buruli ulcer and leprosy. A process for the preparation of 2- (homo)piperazine ...

2016

Generalized Poisson Summation Formula for Tempered Distributions

Michaël Unser, Quy Ha Nguyen

The Poisson summation formula (PSF), which relates the sampling of an analog signal with the periodization of its Fourier transform, plays a key role in the classical sampling theory. In its current forms, the formula is only applicable to a limited class ...

IEEE2015

Discontinuous Galerkin method for fractional convection-diffusion equations

Jan Sickmann Hesthaven

We propose a discontinuous Galerkin method for convection-subdiffusion equations with a fractional operator of order alpha [1,2] defined through the fractional Laplacian. The fractional operator of order alpha is expressed as a composite of first order der ...

Society for Industrial and Applied Mathematics2014

Bivariate Matrix Functions

Daniel Kressner

A definition of bivariate matrix functions is introduced and some theoretical as well as algorithmic aspects are analyzed. It is shown that our framework naturally extends the usual notion of (univariate) matrix functions and allows to unify existing resul ...

Element2014

Generalized Bombieri-Lagarias' Theorem And Generalized Li'S Criterion With Its Arithmetic Interpretation

Serguei Sekatski

We show that Li's criterion equivalent to the Riemann hypothesis, i.e., the statement that the sums k(n) = Sigma(rho)(1-(1-1/rho)(n)) over zeros of the Riemann xi-function and the derivatives lambda(n) equivalent to 1/(n-1)! d(n)/dz(n)(z(n-1) ln (xi(z)))ve ...

Springer Verlag2014

Enhanced Conversion of Carbohydrates to the Platform Chemical 5-Hydroxymethylfurfural Using Designer Ionic Liquids

Paul Joseph Dyson, Rosario Scopelliti, Gabor Laurenczy, Zhaofu Fei, Ning Yan, Sviatlana Siankevich

5-Hydroxymethylfurfural (HMF) is a key platform chemical that may be obtained from various cellulosic (biomass) derivatives. Previously, it has been shown that ionic liquids (ILs) facilitate the catalytic conversion of glucose into HMF. Herein, we demonstr ...

Wiley-V C H Verlag Gmbh2014

Synthesis and Reactivity of Mononuclear Iron Models of [Fe]-Hydrogenase that Contain an Acylmethylpyridinol Ligand

Xile Hu, Dafa Chen

[Fe]-hydrogenase has a single iron-containing active site that features an acylmethylpyridinol ligand. This unique ligand environment had yet to be reproduced in synthetic models; however the synthesis and reactivity of a new class of small molecule mimics ...

Wiley-V C H Verlag Gmbh2014

Hessian Schatten-Norm Regularization for Linear Inverse Problems

Michaël Unser, John Paul Ward, Stamatios Lefkimmiatis

We introduce a novel family of invariant, convex, and non-quadratic functionals that we employ to derive regularized solutions of ill-posed linear inverse imaging problems. The proposed regularizers involve the Schatten norms of the Hessian matrix, which a ...

Ieee-Inst Electrical Electronics Engineers Inc2013