Egac

Tognazzi, Stefano; Tribastone, Mirco; Tschaikowski, Max; Vandin, Andrea

doi:10.1145/3071178.3071265

Cited by 8 publications

(2 citation statements)

References 26 publications

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“…Our own line of research [21,56,18,20,65,19,17,38] consists of a computer-science perspective to the abstraction problem, borrowing ideas from the concurrency theory community. We recast the ODE reduction problem to that of finding an appropriate equivalence relation over ODE variables, akin to classical models of computation based on labelled transition systems.…”

Section: Introductionmentioning

confidence: 99%

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Language-based Abstractions for Dynamical Systems

Vandin

2017

Electron. Proc. Theor. Comput. Sci.

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Ordinary differential equations (ODEs) are the primary means to modelling dynamical systems in many natural and engineering sciences. The number of equations required to describe a system with high heterogeneity limits our capability of effectively performing analyses. This has motivated a large body of research, across many disciplines, into abstraction techniques that provide smaller ODE systems while preserving the original dynamics in some appropriate sense. In this paper we give an overview of a recently proposed computer-science perspective to this problem, where ODE reduction is recast to finding an appropriate equivalence relation over ODE variables, akin to classical models of computation based on labelled transition systems.

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Section: Introductionmentioning

confidence: 99%

“…This paper briefly reviews our framework for ODE reduction. A more detailed tutorial-like presentation unifying the two approaches can be found in [65], while [18,56] address the more general problem of computing all differential equivalences of a model.…”

Section: Introductionmentioning

confidence: 99%

Language-based Abstractions for Dynamical Systems

Vandin

2017

Electron. Proc. Theor. Comput. Sci.

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Approximate Constrained Lumping of Polynomial Differential Equations

Leguizamon-Robayo,

Jiménez-Pastor,

Tribastone

et al. 2023

Lecture Notes in Computer Science

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Gaining insights from realistic dynamical models of biochemical systems can be challenging given their large number of state variables. Model reduction techniques can mitigate this by decreasing complexity by mapping the model onto a lower-dimensional state space. Exact constrained lumping identifies reductions as linear combinations of the original state variables in systems of nonlinear ordinary differential equations, preserving specific user-defined output variables without error. However, exact reductions can be too stringent in practice, as model parameters are often uncertain or imprecise-a particularly relevant problem for biochemical systems. We propose approximate constrained lumping. It allows for a relaxation of exactness within a given tolerance parameter ε, while still working in polynomial time. We prove that the accuracy, i.e., the difference between the output variables in the original and reduced model, is in the order of ε. Furthermore, we provide a heuristic algorithm to find the smallest ε for a given maximum allowable size of the lumped system. Our method is applied to several models from the literature, resulting in coarser aggregations than exact lumping while still capturing the dynamics of the original system accurately.

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Forward and Backward Constrained Bisimulations for Quantum Circuits

Jiménez-Pastor,

Larsen,

Tribastone

et al. 2024

Lecture Notes in Computer Science

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Efficient methods for the simulation of quantum circuits on classic computers are crucial for their analysis due to the exponential growth of the problem size with the number of qubits. Here we study lumping methods based on bisimulation, an established class of techniques that has been proven successful for (classic) stochastic and deterministic systems such as Markov chains and ordinary differential equations. Forward constrained bisimulation yields a lower-dimensional model which exactly preserves quantum measurements projected on a linear subspace of interest. Backward constrained bisimulation gives a reduction that is valid on a subspace containing the circuit input, from which the circuit result can be fully recovered. We provide an algorithm to compute the constraint bisimulations yielding coarsest reductions in both cases, using a duality result relating the two notions. As applications, we provide theoretical bounds on the size of the reduced state space for well-known quantum algorithms for search, optimization, and factorization. Using a prototype implementation, we report significant reductions on a set of benchmarks. Furthermore, we show that constraint bisimulation complements state-of-the-art methods for the simulation of quantum circuits based on decision diagrams.

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Egac

Cited by 8 publications

References 26 publications

Language-based Abstractions for Dynamical Systems

Language-based Abstractions for Dynamical Systems

Approximate Constrained Lumping of Polynomial Differential Equations

Forward and Backward Constrained Bisimulations for Quantum Circuits

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