Publications related to Calculus

SC-TPTP: An Extension of the TPTP Derivation Format for Sequent-Based Calculus

Motivated by the transfer of proofs between proof systems, and in particular from first order automated theorem provers (ATPs) to interactive theorem provers (ITPs), we specify an extension of the TPTP derivation text format to describe proofs in first-ord ...

2024

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

Type-Level Programming with Match Types

Martin Odersky, Olivier Eric Paul Blanvillain

Type-level programming is becoming more and more popular in the realm of functional programming. However, the combination of type-level programming and subtyping remains largely unexplored in practical programming languages. This paper presents match types ...

ASSOC COMPUTING MACHINERY2022

A Continuized View on Nesterov Acceleration

Nicolas Henri Bernard Flammarion, Raphaël Jean Berthier

We introduce the "continuized" Nesterov acceleration, a close variant of Nesterov acceleration whose variables are indexed by a continuous time parameter. The two variables continuously mix following a linear ordinary differential equation and take gradien ...

2021

On the stress tensor light-ray operator algebra

Grégoire Olivier Mathys, Matthew Thomas Walters, Alexandre Mathieu Frédéric Belin

We study correlation functions involving generalized ANEC operators of the form integral dx-x-n+2T--x -> in four dimensions. We compute two, three, and ...

Springer Nature2021

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

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 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

Exterior Convexity And Classical Calculus Of Variations

Saugata Bandyopadhyay, Swarnendu Sil

We study the relation between various notions of exterior convexity introduced in [S. Bandyopadhyay, B. Dacorogna and S. Sil, J. Eur. Math. Soc. 17 (2015) 1009-1039.] with the classical notions of rank one convexity, quasiconvexity and polyconvexity. To th ...

Edp Sciences S A2016

Implementing Higher-Kinded Types in Dotty

Martin Odersky, Guillaume André Fradji Martres, Dmytro Petrashko

dotty is a new, experimental Scala compiler based on DOT, the calculus of Dependent Object Types. Higher-kinded types are a natural extension of first-order lambda calculus, and have been a core construct of Haskell and Scala. As long as such types are jus ...

ACM2016

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

A Decision Procedure for Regular Membership and Length Constraints over Unbounded Strings

Andrew Joseph Reynolds

We prove that the quantifier-free fragment of the theory of character strings with regular language membership constraints and linear integer constraints over string lengths is decidable. We do that by describing a sound, complete and terminating tableaux ...

Springer-Verlag Berlin2015

Le "Fragmentum de inventionibus scientiarum" de Diego Palomino

Nouara Chekhar

The objective of this PhD thesis is the translation of, and the mathematical commentary on, a 16th-century Latin book. Its author, Diego Palomino is not well known. With a background in theology, he was a prior. In order to obtain his PhD at the University ...

EPFL2012

On equalities involving integrals of the logarithm of the Riemann zeta-function and equivalent to the Riemann hypothesis

Serguei Sekatski

By using the generalized Littlewood theorem about a contour integral involving the logarithm of an analytic function, we show how an infinite number of integral equalities involving integrals of the logarithm of the Riemann zeta-function and equivalent to ...

Springer US2012

Qualitative Spatial and Temporal Reasoning with Answer Set Programming

Jingshi Li

Representing and reasoning spatial and temporal information is a key research issue in Computer Science and Artificial Intelligence. In this paper, we introduce tools that produce three novel encodings which translate problems in qualitative spatial and te ...

2012

Challenges in Computational Electromagnetics : Analysis and Optimization of Planar Multilayered Structures

Ruzica Golubovic

To meet strict requirements of the information society technologies, antennas and circuit elements are becoming increasingly complex. Frequently, their electromagnetic (EM) properties cannot be anymore expressed in closed-form analytical expressions mainly ...

EPFL2011

Enhancement of e-learning in geomatics by the integration of dynamic mathematics' tools

Pierre-Yves Gilliéron, Arnaud Deshogues

The Swiss Federal Institute of Technology in Lausanne (EPFL) has introduced a Learning Management System (LMS) based on Moodle. This trend was a source of motivation for our teaching staff who have initiated a project called Exomatic for the enhancement of ...

ISPRS2010

Ordered Sets in the Calculus of Data Structures

Viktor Kuncak, Philippe Paul Henri Suter, Ruzica Piskac

Our goal is to identify families of relations that are useful for reasoning about software. We describe such families using decidable quantifier-free classes of logical constraints with a rich set of operations. A key challenge is to define such classes of ...

Springer2010

Competition of Wireless Providers for Atomic Users: Equilibrium and Social Optimality

Bixio Rimoldi, Vojislav Gajic

We study a problem where wireless service providers compete for heterogenous and atomic (non-infinitesimal) wireless users. The users differ in their utility functions as well as in the perceived quality of service of individual providers. We model the int ...

2009

Physical limits to broadening compensation in a linear slow light system

Luc Thévenaz

The dispersion experienced by a signal in a slow light system leads to a significant pulse broadening and sets a limit to the maximum delay actually achievable by the system. To overcome this limitation, a substantial research effort is currently being car ...

2009