Publications related to Generalizations of the derivative

Characterization of image spaces of Riemann-Liouville fractional integral operators on Sobolev spaces W-m,W-p (omega)

Fractional operators are widely used in mathematical models describing abnormal and nonlocal phenomena. Although there are extensive numerical methods for solving the corresponding model problems, theoretical analysis such as the regularity result, or the ...

SCIENCE PRESS2020

Computation of "Best" Interpolants in the Lp Sense

Michaël Unser, Pakshal Narendra Bohra

We study a variant of the interpolation problem where the continuously defined solution is regularized by minimizing the L p -norm of its second-order derivative. For this continuous-domain problem, we propose an exact discretization scheme that restricts ...

2020

COMPUTATION OF "BEST" INTERPOLANTS IN THE L-p SENSE

Michaël Unser, Pakshal Narendra Bohra

We study a variant of the interpolation problem where the continuously defined solution is regularized by minimizing the L-p-norm of its second-order derivative. For this continuous-domain problem, we propose an exact discretization scheme that restricts t ...

IEEE2020

Radiative Backpropagation: An Adjoint Method for Lightning-Fast Differentiable Rendering

Wenzel Alban Jakob, Sébastien Nicolas Speierer, Merlin Eléazar Nimier-David

Physically based differentiable rendering has recently evolved into a powerful tool for solving inverse problems involving light. Methods in this area perform a differentiable simulation of the physical process of light transport and scattering to estimate ...

ASSOC COMPUTING MACHINERY2020

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

Optimal Spline Generators for Derivative Sampling

Michaël Unser, Shayan Aziznejad, Alireza Naderi

The goal of derivative sampling is to reconstruct a signal from the samples of the function and of its first-order derivative. In this paper, we consider this problem over a shift-invariant reconstruction subspace generated by two compact-support functions ...

IEEE2019

To positivity and beyond, where Higgs-Dilaton inflation has never gone before

Inar Timiryasov, Mario Herrero Valea, Anna Tokareva

We study the consequences of (beyond) positivity of scattering amplitudes in the effective field theory description of the Higgs-Dilaton inflationary model. By requiring the EFT to be compatible with a unitary, causal, local and Lorentz invariant UV comple ...

IOP PUBLISHING LTD2019

Method and system for the creation of an h-spline based data structure, data storage, and data representation

Michaël Unser, Zsuzsanna Püspöki, Daniel Andreas Schmitter

A method for generating a data structure to digitally represent a geometrical object based on H-splines, the method being performed on a computer device having a data processor and memory, the method including the steps of creating a first data structure a ...

2019

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Generalizations of the derivative

A critically degenerate elliptic Dirichlet problem, spectral theory and bifurcation

Characterization of image spaces of Riemann-Liouville fractional integral operators on Sobolev spaces W-m,W-p (omega)

Computation of "Best" Interpolants in the Lp Sense

COMPUTATION OF "BEST" INTERPOLANTS IN THE L-p SENSE

Radiative Backpropagation: An Adjoint Method for Lightning-Fast Differentiable Rendering

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

Optimal Spline Generators for Derivative Sampling

On the Averaged Green’s Function of an Elliptic Equation with Random Coefficients

To positivity and beyond, where Higgs-Dilaton inflation has never gone before

Method and system for the creation of an h-spline based data structure, data storage, and data representation

Graph Chatbot

Chat with Graph Search

Radiative Backpropagation: An Adjoint Method for Lightning-Fast Differentiable Rendering

COMPUTATION OF "BEST" INTERPOLANTS IN THE L-p SENSE

Computation of "Best" Interpolants in the Lp Sense

Optimal Spline Generators for Derivative Sampling

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

Method and system for the creation of an h-spline based data structure, data storage, and data representation

To positivity and beyond, where Higgs-Dilaton inflation has never gone before

Characterization of image spaces of Riemann-Liouville fractional integral operators on Sobolev spaces W-m,W-p (omega)

On the Averaged Green’s Function of an Elliptic Equation with Random Coefficients