[HTML][HTML] Within-host mathematical modeling on crucial inflammatory mediators and drug interventions in COVID-19 identifies combination therapy to be most effective …
The unprecedented Covid-19 pandemic has resulted in more than 14.75 million infections
and 6, 10, 839 deaths in 212 countries. Appropriate interventions can decrease the rate of …
and 6, 10, 839 deaths in 212 countries. Appropriate interventions can decrease the rate of …
Formalization of real analysis: A survey of proof assistants and libraries
In the recent years, numerous proof systems have improved enough to be used for formally
verifying non-trivial mathematical results. They, however, have different purposes and it is …
verifying non-trivial mathematical results. They, however, have different purposes and it is …
Verified reachability analysis of continuous systems
F Immler - Tools and Algorithms for the Construction and Analysis …, 2015 - Springer
Ordinary differential equations (ODEs) are often used to model the dynamics of (often safety-
critical) continuous systems. This work presents the formal verification of an algorithm for …
critical) continuous systems. This work presents the formal verification of an algorithm for …
A verified ODE solver and the Lorenz attractor
F Immler - Journal of automated reasoning, 2018 - Springer
A rigorous numerical algorithm, formally verified with Isabelle/HOL, is used to certify the
computations that Tucker used to prove chaos for the Lorenz attractor. The verification is …
computations that Tucker used to prove chaos for the Lorenz attractor. The verification is …
The flow of ODEs: Formalization of variational equation and Poincaré map
F Immler, C Traut - Journal of Automated Reasoning, 2019 - Springer
Formal analysis of ordinary differential equations (ODEs) and dynamical systems requires a
solid formalization of the underlying theory. The formalization needs to be at the correct level …
solid formalization of the underlying theory. The formalization needs to be at the correct level …
A Coq formal proof of the Lax-Milgram theorem
S Boldo, F Clément, F Faissole, V Martin… - Proceedings of the 6th …, 2017 - dl.acm.org
The Finite Element Method is a widely-used method to solve numerical problems coming for
instance from physics or biology. To obtain the highest confidence on the correction of …
instance from physics or biology. To obtain the highest confidence on the correction of …
Formally verified computation of enclosures of solutions of ordinary differential equations
F Immler - NASA Formal Methods: 6th International Symposium …, 2014 - Springer
Ordinary differential equations (ODEs) are ubiquitous when modeling continuous dynamics.
Classical numerical methods compute approximations of the solution, however without any …
Classical numerical methods compute approximations of the solution, however without any …
A Coq Formalization of Taylor Models and Power Series for Solving Ordinary Differential Equations
In exact real computation real numbers are manipulated exactly without round-off errors,
making it well-suited for high precision verified computation. In recent work we propose an …
making it well-suited for high precision verified computation. In recent work we propose an …
The flow of ODEs
F Immler, C Traut - … Theorem Proving: 7th International Conference, ITP …, 2016 - Springer
Formal analysis of ordinary differential equations (ODEs) and dynamical systems requires a
solid formalization of the underlying theory. The formalization needs to be at the correct level …
solid formalization of the underlying theory. The formalization needs to be at the correct level …
A Coq formalization of Lebesgue integration of nonnegative functions
S Boldo, F Clément, F Faissole, V Martin… - Journal of Automated …, 2022 - Springer
Integration, just as much as differentiation, is a fundamental calculus tool that is widely used
in many scientific domains. Formalizing the mathematical concept of integration and the …
in many scientific domains. Formalizing the mathematical concept of integration and the …