Publications related to Special functions

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

Optimal denoising of rotationally invariant rectangular matrices

Florent Gérard Krzakala, Lenka Zdeborová, Emanuele Troiani, Vittorio Erba

In this manuscript we consider denoising of large rectangular matrices: given a noisy observation of a signal matrix, what is the best way of recovering the signal matrix itself? For Gaussian noise and rotationally-invariant signal priors, we completely ch ...

2022

A Majority Lemma for Randomised Query Complexity

Mika Tapani Göös, Gilbert Théodore Maystre

We show that computing the majority of n copies of a boolean function g has randomised query complexity R(Maj∘gⁿ) = Θ(n⋅R ̅_{1/n}(g)). In fact, we show that to obtain a similar result for any composed function f∘gⁿ, it suffices to prove a sufficiently stro ...

Schloss Dagstuhl - Leibniz-Zentrum für Informatik2021

Polynomial Evaluation on Superscalar Architecture, Applied to the Elementary Function e(x)

Felix Schürmann, Francesco Cremonesi, Timothée Ewart

The evaluation of small degree polynomials is critical for the computation of elementary functions. It has been extensively studied and is well documented. In this article, we evaluate existing methods for polynomial evaluation on superscalar architecture. ...

2020

Random field solutions to linear SPDEs driven by symmetric pure jump Levy space-time white noises

Robert Dalang, Thomas Marie Jean-Baptiste Humeau

We study the notions of mild solution and generalized solution to a linear stochastic partial differential equation driven by a pure jump symmetric Levy white noise, with symmetric alpha-stable Levy white noise as an important special case. We identify con ...

UNIV WASHINGTON, DEPT MATHEMATICS2019

Asian option pricing with orthogonal polynomials

Sander Félix M Willems

In this paper we derive a series expansion for the price of a continuously sampled arithmetic Asian option in the Black-Scholes setting. The expansion is based on polynomials that are orthogonal with respect to the log-normal distribution. All terms in the ...

ROUTLEDGE JOURNALS, TAYLOR & FRANCIS LTD2019

Lorenz Type Behaviors Associated To Fractal-Non-Fractal Transition In The Dynamics Of The Complex Systems

Maria-Alexandra Paun

In the framework of Fractal Theory of Motion for the Scale Relativity Theory with arbitrary and constant fractal dimensions, dynamics in complex systems associated to the fractal-non-fractal transition are analyzed. Working with the assumption that these d ...

UNIV POLITEHNICA BUCHAREST, SCI BULL2019

Engineering Stem Cell Self-organization to Build Better Organoids

Matthias Lütolf, Jonathan Brassard

Organoids form through self-organization processes in which initially homogeneous populations of stem cells spontaneously break symmetry and undergo in-vivo-like pattern formation and morphogenesis, though the processes controlling this are poorly characte ...

CELL PRESS2019

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Special functions

Stable parameterization of continuous and piecewise-linear functions

WeChat as an unavoidable research tool for fieldwork, and its problems

Optimal denoising of rotationally invariant rectangular matrices

A Majority Lemma for Randomised Query Complexity

Polynomial Evaluation on Superscalar Architecture, Applied to the Elementary Function e(x)

Random field solutions to linear SPDEs driven by symmetric pure jump Levy space-time white noises

Asian option pricing with orthogonal polynomials

The Complexity of Splitting Necklaces and Bisecting Ham Sandwiches

Lorenz Type Behaviors Associated To Fractal-Non-Fractal Transition In The Dynamics Of The Complex Systems

Engineering Stem Cell Self-organization to Build Better Organoids

Graph Chatbot

Chat with Graph Search

Optimal denoising of rotationally invariant rectangular matrices

Lorenz Type Behaviors Associated To Fractal-Non-Fractal Transition In The Dynamics Of The Complex Systems

Polynomial Evaluation on Superscalar Architecture, Applied to the Elementary Function e(x)

Random field solutions to linear SPDEs driven by symmetric pure jump Levy space-time white noises

A Majority Lemma for Randomised Query Complexity

WeChat as an unavoidable research tool for fieldwork, and its problems

Engineering Stem Cell Self-organization to Build Better Organoids

The Complexity of Splitting Necklaces and Bisecting Ham Sandwiches

Asian option pricing with orthogonal polynomials

Stable parameterization of continuous and piecewise-linear functions