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Concept

Computer algebra system

Related publications (24)

Collective motion in a sheet of microswimmers

Viktor Skultéty

Self-propelled particles such as bacteria or algae swimming through a fluid are non-equilibrium systems where particle motility breaks microscopic detailed balance, often resulting in large-scale collective motion. Previous theoretical work has identified ...

Nature Portfolio2024

Model order reduction based on functional rational approximants for parametric PDEs with meromorphic structure

Davide Pradovera

Many engineering fields rely on frequency-domain dynamical systems for the mathematical modeling of physical (electrical/mechanical/etc.) structures. With the growing need for more accurate and reliable results, the computational burden incurred by frequen ...

EPFL2021

Efficient Parsing with Derivatives and Zippers

Romain Edelmann

Parsing is the process that enables a computer system to make sense of raw data. Parsing is common to almost all computer systems: It is involved every time sequential data is read and elaborated into structured data. The theory of parsing usually focuses ...

EPFL2021

An Optimizing Multi-platform Source-to-source Compiler Framework for the NEURON MODeling Language

Felix Schürmann, James Gonzalo King, Pramod Shivaji Kumbhar, Omar Awile, Jorge Blanco Alonso

Domain-specific languages (DSLs) play an increasingly important role in the generation of high performing software. They allow the user to exploit domain knowledge for the generation of more efficient code on target architectures. Here, we describe a new c ...

Springer2020

Exact DAG-Aware Rewriting

Mathias Soeken, Heinz Riener

We present a generic resynthesis framework for optimizing Boolean networks parameterized with a multi-level logic representation, a cut-computation algorithm, and a resynthesis algorithm. The framework allows us to realize powerful optimization algorithms ...

IEEE2020

SAT-Based Exact Synthesis: Encodings, Topology Families, and Parallelism

Giovanni De Micheli, Mathias Soeken, Winston Jason Haaswijk

Exact synthesis is a versatile logic synthesis technique with applications to logic optimization, technology mapping, synthesis for emerging technologies, and cryptography. In recent years, advances in SAT solving have lead to a heightened research effort ...

2020

Multi space reduced basis preconditioners for parametrized partial differential equations

Niccolò Dal Santo

The multiquery solution of parametric partial differential equations (PDEs), that is, PDEs depending on a vector of parameters, is computationally challenging and appears in several engineering contexts, such as PDE-constrained optimization, uncertainty qu ...

EPFL2018

A Discontinuous Galerkin Reduced Basis Element Method For Elliptic Problems

Alfio Quarteroni, Paolo Pacciarini

We propose and analyse a new discontinuous reduced basis element method for the approximation of parametrized elliptic PDEs in partitioned domains. The method is built upon an offline stage (parameter independent) and an online (parameter dependent) one. I ...

Edp Sciences S A2016

Deductive Synthesis and Repair

Etienne Kneuss

In this thesis, we explore techniques for the development of recursive functional programs over unbounded domains that are proved correct according to their high-level specifications. We present algorithms for automatically synthesizing executable code, st ...

EPFL2016

SeBip: a symbolic executor for BIP

Simon Bliudze, Qiang Wang

This paper presents SeBip, the first symbolic executor for component-based systems modelled in BIP (Be- haviour, Interaction and Priority). To tackle the path explosion problem, SeBip combines partial order reduction technique to reduce the number of inter ...

IEEE Computer Society2015

Deductive Program Repair, Computer Aided Verification

Viktor Kuncak, Etienne Kneuss

We present an approach to program repair and its application to programs with recursive functions over unbounded data types. Our approach formulates program repair in the framework of deductive synthesis that uses existing program structure as a hint to gu ...

2015

Calibration of optical tweezers with non-spherical probes via high-resolution detection of Brownian motion

László Forró, Richard Gaal, Sylvia Jeney, Flavio Maurizio Mor

Optical tweezers are commonly used and powerful tools to perform force measurements on the piconewton scale and to detect nanometer-scaled displacements. However, the precision of these instruments relies to a great extent on the accuracy of the calibratio ...

Elsevier Science Bv2015

An indefinite variant of LOBPCG for definite matrix pencils

Daniel Kressner, Meiyue Shao

In this paper, we propose a novel preconditioned solver for generalized Hermitian eigenvalue problems. More specifically, we address the case of a definite matrix pencil , that is, A, B are Hermitian and there is a shift such that is definite. Our new meth ...

Springer2014

Comparison between reduced basis and stochastic collocation methods for elliptic problems

Alfio Quarteroni, Gianluigi Rozza, Peng Chen

The stochastic collocation method has recently been applied to stochastic problems that can be transformed into parametric systems. Meanwhile, the reduced basis method, primarily developed for solving parametric systems, has been recently used to deal with ...

Springer Verlag2014

LINVIEW: Incremental View Maintenance for Complex Analytical Queries

Christoph Koch, Milos Nikolic, Mohamed Elsayed Mohamed Ahmed El Seidy

Many analytics tasks and machine learning problems can be naturally expressed by iterative linear algebra programs. In this paper, we study the incremental view maintenance problem for such complex analytical queries. We develop a framework, called LINVIEW ...

2014

A preconditioned low-rank CG method for parameter-dependent Lyapunov matrix equations

Daniel Kressner, Christine Tobler

This paper is concerned with the numerical solution of symmetric large-scale Lyapunov equations with low-rank right-hand sides and coefficient matrices depending on a parameter. Specifically, we consider the situation when the parameter dependence is suffi ...

Wiley-Blackwell2013

Algebraic algorithms for network information flow

Javad Ebrahimi Boroojeni

Ahlswede et al. in the seminal paper [1] have shown that in data transfer over networks, processing the data at the nodes can significantly improve the throughput. As proved by Li et al. in [2], even with a simple type of operation, namely linear operation ...

EPFL2013

Finite Dimensional Methods for Differential Flatness

Basile Graf

In Control System Theory, the study of continuous-time, finite dimensional, underdetermined systems of ordinary differential equations is an important topic. Classification of systems in different categories is a natural initial step to the analysis of a g ...

EPFL2013

State Machine Replication : from Analytical Evaluation to High-Performance Paxos

Nuno Filipe de Sousa Santos

Since their invention more than half a century ago, computers have gone from being just an handful of expensive machines each filling an entire room, to being an integral part of almost every aspect of modern life. Nowadays computers are everywhere: in our ...

EPFL2012

Fast and accurate computation of hyper-singular integrals in Galerkin surface integral equation formulations via the direct evaluation method

Juan Ramon Mosig, Athanasios Polymeridis

Hypersingular 4-D integrals, arising in the Galerkin discretization of surface integral equation formulations, are computed by means of the direct evaluation method. The proposed scheme extends the basic idea of the singularity cancellation methods, usuall ...

Institute of Electrical and Electronics Engineers2011