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Concept

Series expansion

Related publications (25)

The time-domain Cartesian multipole expansion of electromagnetic fields

Farhad Rachidi-Haeri, Marcos Rubinstein, Nicolas Mora Parra, Elias Per Joachim Le Boudec, Emanuela Radici

Time-domain solutions of Maxwell’s equations in homogeneous and isotropic media are paramount to studying transient or broadband phenomena. However, analytical solutions are generally unavailable for practical applications, while numerical solutions are co ...

Nature Publishing Group2024

Differential Entropy of the Conditional Expectation Under Additive Gaussian Noise

Michael Christoph Gastpar, Alper Köse, Ahmet Arda Atalik

The conditional mean is a fundamental and important quantity whose applications include the theories of estimation and rate-distortion. It is also notoriously difficult to work with. This paper establishes novel bounds on the differential entropy of the co ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2022

Differential Entropy of the Conditional Expectation under Gaussian Noise

Michael Christoph Gastpar, Alper Köse, Ahmet Arda Atalik

This paper considers an additive Gaussian noise channel with arbitrarily distributed finite variance input signals. It studies the differential entropy of the minimum mean-square error (MMSE) estimator and provides a new lower bound which connects the diff ...

IEEE2021

Robust Differentiable SVD

Pascal Fua, Mathieu Salzmann, Wei Wang, Yinlin Hu, Zheng Dang

Eigendecomposition of symmetric matrices is at the heart of many computer vision algorithms. However, the derivatives of the eigenvectors tend to be numerically unstable, whether using the SVD to compute them analytically or using the Power Iteration (PI) ...

2021

ON WAVEFRONT ABERRATIONS IN ASYMMETRIC AND MULTIPLE APERTURE OPTICAL SYSTEMS

Alessandro Grosso

The present work deals with monochromatic wavefront aberrations in optical systems without symmetries. The treatment begins with a class of systems characterized by misaligned spherical surfaces whose behavior is analyzed using the wavefront aberration exp ...

EPFL2021

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

Bold Signal Deconvolution Under Uncertain HÆModynamics: A Semi-Blind Approach

Dimitri Nestor Alice Van De Ville, Fikret Isik Karahanoglu, Younes Farouj

The investigation of spontaneous and evoked neuronal activity from functional Magnetic Resonance Imaging (fMRI) data has come to play a significant role in deepening our understanding of brain function. As this research trend continues, activity detection ...

IEEE2019

Maximum-likelihood estimation of kinetic parameters via the extent-based incremental approach

Dominique Bonvin, Julien Léo Billeter, Diogo Filipe Mateus Rodrigues

For lumped homogeneous reaction systems, this paper presents a kinetic model identification scheme that provides maximum-likelihood parameter estimates and guarantees convergence to global optimality. The use of the extent-based incremental approach allows ...

PERGAMON-ELSEVIER SCIENCE LTD2019

An Analytical Model for Beam Flexure Modules Based on Timoshenko Beam Theory

Simon Nessim Henein, Mohammad Hussein Kahrobaiyan, Mohamed Gamal Abdelrahman Ahmed Zanaty

Short beams are the key building blocks in many compliant mechanisms. Hence, deriving a simple yet accurate model of their elastokinematics is an important issue. Since the Euler-Bernoulli beam theory fails to accurately model these beams, we use the Timos ...

2017

A Modulated-Gradient Parametrization for the Large-Eddy Simulation of the Atmospheric Boundary Layer Using the Weather Research and Forecasting Model

Fernando Porté Agel, Sina Khani

The performance of the modulated-gradient subgrid-scale (SGS) model is investigated using large-eddy simulation (LES) of the neutral atmospheric boundary layer within the weather research and forecasting model. Since the model includes a finite-difference ...

Springer2017

Semiclassics, Goldstone bosons and CFT data

Riccardo Rattazzi, Alexander Monin, David Pirtskhalava, Fiona Katharina Seibold

Hellerman et al. (arXiv:1505.01537) have shown that in a generic CFT the spectrum of operators carrying a large U(1) charge can be analyzed semiclassically in an expansion in inverse powers of the charge. The key is the operator state correspondence by whi ...

Springer Nature2017

Polynomial models in finance

Damien Edouard Ackerer

This thesis presents new flexible dynamic stochastic models for the evolution of market prices and new methods for the valuation of derivatives. These models and methods build on the recently characterized class of polynomial jump-diffusion processes for w ...

EPFL2017

Global Identification of Kinetic Parameters via the Extent-based Incremental Approach

Dominique Bonvin, Julien Léo Billeter, Diogo Filipe Mateus Rodrigues

The identification of reaction kinetics represents the main challenge in building models for reaction systems. The identification task can be performed via either simultaneous model identification (SMI) or incremental model identification (IMI), the latter ...

2017

Radial expansion for spinning conformal blocks

João Miguel Augusto Penedones Fernandes

This paper develops a method to compute any bosonic conformal block as a series expansion in the optimal radial coordinate introduced by Hogervorst and Rychkov. The method reduces to the known result when the external operators are all the same scalar oper ...

Springer Nature2016

A posteriori error estimation for partial differential equations with random input data

Diane Sylvie Guignard

This thesis is devoted to the derivation of error estimates for partial differential equations with random input data, with a focus on a posteriori error estimates which are the basis for adaptive strategies. Such procedures aim at obtaining an approximati ...

EPFL2016

The Bethe Free Energy Allows to Compute the Conditional Entropy of Graphical Code Instances: A Proof From the Polymer Expansion

Nicolas Macris, Marc Vuffray

The main objective of this paper is to explore the precise relationship between the Bethe free energy (or entropy) and the Shannon conditional entropy of graphical error correcting codes. The main result shows that the Bethe free energy associated with a l ...

Ieee-Inst Electrical Electronics Engineers Inc2016

Aggressively Truncated Taylor Series Method For Accurate Computation Of Exponentials Of Essentially Nonnegative Matrices

Meiyue Shao

Small relative perturbations to the entries of an essentially nonnegative matrix introduce small relative errors to entries of its exponential. It is thus desirable to compute the exponential with high componentwise relative accuracy. Taylor series approxi ...

Siam Publications2014

Perturbation analysis for the Darcy problem with log-normal permeability

Fabio Nobile, Francesca Bonizzoni

We study the single-phase flow in a saturated, bounded heterogeneous porous medium. We model the permeability as a log-normal random field. We perform a perturbation analysis, expanding the solution in Taylor series. The series is directly computable in th ...

2014

On the Development of a Dynamic Non-linear Closure for Large-Eddy Simulation of the Atmospheric Boundary Layer

Fernando Porté Agel, Hao Lu

A dynamic procedure is developed to compute the model coefficients in the recently introduced modulated gradient models for both momentum and scalar fluxes. The magnitudes of the subgrid-scale (SGS) stress and the SGS flux are estimated using the local equ ...

Springer2014

Proof of a conjecture by Gazeau et al. using the Gould-Hopper polynomials

Olivier Lévêque

We provide here some probabilistic interpretations of the generalized binomial distributions proposed by Gazeau et al. ["Generating functions for generalized binomial distributions," J. Math. Phys. 53, 103304 (2012)]. In the second part, we prove the "stro ...

Amer Inst Physics2013