Set-Based Analysis for Biological Modeling

Bounding the Range of a Sum of Multivariate Rational Functions

“…We noticed a similar situation for the minimum. Our algorithm finds in 0.015 ms in only one subdivision step (ℎ = 1) the lower bound 0.976190 attained at (6,4,12,6) for the minimum of 𝑓 . Since this bound is attained at a vertex index, the vertex condition in Theorem 2 holds, and we know that we already have found the minimum of 𝑓 .…”

Symbolic-Numeric Computation of the Bernstein Coefficients of a Polynomial from Those of One of Its Partial Derivatives and of the Product of Two Polynomials

“…Let p and q be bivariate polynomials of degree (4,2) and (3,2), respectively, with Bernstein matrices over u…”

Parameter synthesis of polynomial dynamical systems

“…Signal Temporal Logic (STL [55,56]) has been introduced for specifying properties of dense-time real-valued signals. It is particularly suitable for monitoring both industrial case studies (e.g., see [47,46,23]) and biological systems (e.g., see [25,67,20]). It has also been used in the study of parametric systems (e.g., see [7,43]) where parametric disturbance rejection properties are formalized in STL and then verified.…”