Concept

Multivariable calculus

Related publications (39)

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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 ...

2022

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

A Mechanized Theory of Quoted Code Patterns

The pattern matching on code from the new macro system of Scala 3 is modeled by a calculus called λ half-circle. We present a mechanized proof of soundness of the calculus in Coq and discuss encountered challenges. ...

2020

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

Formal foundations for GADTs in Scala

GADTs are a very useful language feature that allow encoding some invariants in types. GADT reasoning is currently implemented in Scala and Dotty, but it’s plagued with soundness issues. To get a better understanding of GADTs in Scala, we explore how they ...

2020

Isogeometric analysis with C1 hierarchical functions on planar two-patch geometries

Rafael Vazquez Hernandez

Adaptive isogeometric methods for the solution of partial diifferential equations rely on the construction of locally refinable spline spaces. A simple and efficient way to obtain these spaces is to apply the multi-level construction of hierarchical spline ...

2020