Publications related to Multivariable calculus

Resistances to change in urban travel behaviors

Marc-Edouard Baptiste Grégoire Schultheiss

The social discourse surrounding the climate emergency progressively infuses the society, transforming into both micro- and macro-social injunctions to change. Yet, society - grounded in a territorial, social, and cultural contingency - appears to resist t ...

EPFL2023

Stability of Image-Reconstruction Algorithms

Michaël Unser, Sebastian Jonas Neumayer, Pol del Aguila Pla

Robustness and stability of image-reconstruction algorithms have recently come under scrutiny. Their importance to medical imaging cannot be overstated. We review the known results for the topical variational regularization strategies ( ℓ2 and ℓ1 regulariz ...

2023

Revisiting the General Identifiability Problem

Negar Kiyavash, Ehsan Mokhtarian, Yaroslav Kivva, Seyed Jalal Etesami

We revisit the problem of general identifiability originally introduced in [Lee et al., 2019] for causal inference and note that it is necessary to add positivity assumption of observational distribution to the original definition of the problem. We show t ...

2022

Gradient-based optimisation of the conditional-value-at-risk using the multi-level Monte Carlo method

Fabio Nobile, Sundar Subramaniam Ganesh

In this work, we tackle the problem of minimising the Conditional-Value-at-Risk (CVaR) of output quantities of complex differential models with random input data, using gradient-based approaches in combination with the Multi-Level Monte Carlo (MLMC) method ...

2023

Accurate equilibrium-based interlaminar stress recovery for isogeometric laminated composite Kirchhoff plates

Pablo Antolin Sanchez, Alessandro Reali

Despite the accelerated deployment of laminated composites in a wide variety of markets due to their peculiar engineering features, the design of those materials is often restrained by the lack of cost-efficient modeling techniques. In fact, the existing s ...

ELSEVIER SCI LTD2021

Linear Lipschitz and C-1 extension operators through random projection

Federico Stra

We construct a regular random projection of a metric space onto a closed doubling subset and use it to linearly extend Lipschitz and C-1 functions. This way we prove more directly a result by Lee and Naor [5] and we generalize the C-l extension theorem by ...

ACADEMIC PRESS INC ELSEVIER SCIENCE2021

Integral Convexity And Parabolic Systems

Bernard Dacorogna

In this work we give optimal, i.e., necessary and sufficient, conditions for integrals of the calculus of variations to guarantee the existence of solutions-both weak and variational solutions-to the associated L-2-gradient flow. The initial values are mer ...

SIAM PUBLICATIONS2020

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 ...

2019

Regularity of solutions for a fourth-order elliptic system via Conservation law

Changyu Guo

In this paper, we obtain interior Holder continuity for solutions of the fourth-order elliptic system Delta(2)u = Delta(V center dot del u) + div(w del u) + W center dot del u formulated by Lamm and Riviere [Comm. Partial Differential Equations 33 (2008) 2 ...

2020

A Data-driven Approach to Robust Control of Multivariable Systems by Convex Optimization

Alireza Karimi, Christoph Manuel Kammer

The frequency-domain data of a multivariable system in different operating points is used to design a robust controller with respect to the measurement noise and multimodel uncertainty. The controller is fully parametrized in terms of matrix polynomial fun ...

2017

Decentralized and Distributed Transient Control for Microgrids

Alireza Karimi, Christoph Manuel Kammer

This paper treats the problem of primary and secondary control design in low-inertia power grids with mixed lines and a large amount of inverter-interfaced generation. A dynamic phasor model is developed that represents the electromagnetic and electromecha ...

Institute of Electrical and Electronics Engineers2019

Spectral based Discontinuous Galerkin Reduced Basis Element method for parametrized Stokes problems

Alfio Quarteroni, Paolo Pacciarini

In this work we extend to the Stokes problem the Discontinuous Galerkin Reduced Basis Element (DGRBE) method introduced in Antonietti et al. (2015). By this method we aim at reducing the computational cost for the approximation of a parametrized Stokes pro ...

Pergamon-Elsevier Science Ltd2016

Calculus of Variations for Differential Forms

Swarnendu Sil

In this thesis we study calculus of variations for differential forms. In the first part we develop the framework of direct methods of calculus of variations in the context of minimization problems for functionals of one or several differential forms of th ...

EPFL2016

On the use of ANOVA expansions in reduced basis methods for high-dimensional parametric partial differential equations

Jan Sickmann Hesthaven

We propose two different improvements of reduced basis (RB) methods to enable the efficient and accurate evaluation of an output functional based on the numerical solution of parametrized partial differential equations with a possibly high-dimensional para ...

Springer Verlag2016

The Essence of Dependent Object Types

Martin Odersky, Tiark Rompf, Nada Amin, Sandro Stucki, Karl Samuel Grütter

Focusing on path-dependent types, the paper develops foundations for Scala from first principles. Starting from a simple calculus D-

Springer International Publishing2016

Calculus of variations with differential forms

Bernard Dacorogna, Saugata Bandyopadhyay, Swarnendu Sil

We study integrals of the form integral(Omega) f (d omega), where 1

European Mathematical Soc2015

H∞ Controller Design for Spectral MIMO Models by Convex Optimization

Alireza Karimi, Roland Longchamp, Gorka Galdos Sanz de Galdeano

A new method for robust ﬁxed-order H∞ controller design by convex optimization for multivariable systems is investigated. Linear Time-Invariant Multi-Input Multi- Output (LTI-MIMO) systems represented by a set of complex values in the frequency domain are ...

Elsevier2010

Continuity Properties of Law-Invariant (Quasi-)Convex Risk Functions on L∞

Gregor Svindland

We study continuity properties of law-invariant (quasi-)convex functions f : L1(Ω,F, P) to ( ∞,∞] over a non-atomic probability space (Ω,F, P) .This is a supplementary note to [12] ...

Springer Verlag2010

An introduction to reduced basis method for parametrized PDEs

Gianluigi Rozza

We provide an introduction on reduced basis (RB) method for the solution of parameterized partial differential equations (PDEs). We introduce all the main ingredients to describe the methodology and the algorithms used to build the approximation spaces and ...

WorldScientific2009

PID Controller Design for Multivariable Systems Using Gershgorin Bands

Alireza Karimi, Roland Longchamp, Daniel Garcia

A method to design decentralized PID controllers for MIMO systems is presented in this paper. Each loop is designed separately, but the Gershgorin bands are considered to take interactions into account. The method uses different design parameters: The infi ...

2005