Concept

Step function

Related publications (41)

Towards Trustworthy Deep Learning for Image Reconstruction

The remarkable ability of deep learning (DL) models to approximate high-dimensional functions from samples has sparked a revolution across numerous scientific and industrial domains that cannot be overemphasized. In sensitive applications, the good perform ...

EPFL2024

Stable parameterization of continuous and piecewise-linear functions

Michaël Unser, Alexis Marie Frederic Goujon, Joaquim Gonçalves Garcia Barreto Campos

Rectified-linear-unit (ReLU) neural networks, which play a prominent role in deep learning, generate continuous and piecewise-linear (CPWL) functions. While they provide a powerful parametric representation, the mapping between the parameter and function s ...

2023

PROBING INTRACELLULAR ELASTICITY WITH MINIMAL-HESSIAN REGISTRATION

Michaël Unser

We propose an image-based elastography method to measure the heterogeneous stiffness inside a cell and its nucleus. It uses a widely accessible setup consisting of plate compression imaged with fluorescence microscopy. Our framework recovers a spatial map ...

New York2023

The hunt for the Karman 'constant' revisited

Peter Monkewitz

The log law of the wall, joining the inner, near-wall mean velocity profile (MVP) in wall-bounded turbulent flows to the outer region, has been a permanent fixture of turbulence research for over hundred years, but there is still no general agreement on th ...

CAMBRIDGE UNIV PRESS2023

Polaron hopping through piecewise-linear functionals

Alfredo Pasquarello, Stefano Falletta

We use piecewise-linear functionals to study the polaron energy landscape and hopping rates in beta-Ga2O3, which we adopt as an example of an anisotropic material hosting multiple polaronic states. We illustrate various functionals for polaron localization ...

AMER PHYSICAL SOC2023

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

Hubbard U through polaronic defect states

Alfredo Pasquarello, Stefano Falletta

Since the preliminary work of Anisimov and co-workers, the Hubbard corrected DFT+U functional has been used for predicting properties of correlated materials by applying on-site effective Coulomb interactions to specific orbitals. However, the determinatio ...

NATURE PORTFOLIO2022

Addressing fairness in classification with a model-agnostic multi-objective algorithm

Boi Faltings, Claudiu-Cristian Musat, Diego Matteo Antognini

The goal of fairness in classification is to learn a classifier that does not discriminate against groups of individuals based on sensitive attributes, such as race and gender. One approach to designing fair algorithms is to use relaxations of fairness not ...

2021

A generalization of Kátai's orthogonality criterion with applications

Florian Karl Richter

We study properties of arithmetic sets coming from multiplicative number theory and obtain applications in the theory of uniform distribution and ergodic theory. Our main theorem is a generalization of Kátai's orthogonality cri ...

2019

Statistical and physical characterization of rainfall-driven overland flow morphologies

Mohsen Cheraghi

Environmental transport processes are highly coupled with the shape of landscapes. Modern catchment analysis with high-resolution data and huge computational powers demand more detailed within-cell metrics for surface evolution modeling. This dissertation ...

EPFL2019

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