9 citations · 18 across the 14 of their papers we have counts for
15 papers
Algorithm for globally identifiable reparametrizations of ODEs
Sebastian Falkensteiner, Alexey Ovchinnikov, J. Rafael Sendra
Structural global parameter identifiability indicates whether one can determine a parameter's value in an ODE model from given inputs and outputs. If a given model has parameters f…
The fundamental theorem of tropical differential algebra for formal Puiseux series
Sebastian Falkensteiner, Stefano Mereta
The fundamental theorem of tropical differential algebra has been established for formal power series solutions of systems of algebraic differential equations. It has been shown th…
Tropical initial degeneration for systems of algebraic differential equations
Lara Bossinger, Sebastian Falkensteiner, Cristhian Garay-López +1
We study the notion of degeneration for affine schemes associated to systems of algebraic differential equations with coefficients in the fraction field of a multivariate formal po…
Rational Solutions of Parametric First-Order Algebraic Differential Equations
Sebastian Falkensteiner, Rafael Sendra
In this paper, we give an algorithm for finding general rational solutions of a given first-order ODE with parametric coefficients that occur rationally. We present an analysis, co…
Infinite matroids in tropical differential algebra
F. Aroca, L. Bossinger, S. Falkensteiner +3
We consider a finite-dimensional vector space over an arbitrary field and an arbitrary set . We show that the set consisting of the minimal…
On real and observable rational realizations of input-output equations
Sebastian Falkensteiner, Dmitrii Pavlov, Rafael Sendra
Given a single (differential-algebraic) input-output equation, we present a method for finding different representations of the associated system in the form of rational realizatio…
Rationality and Parametrizations of Algebraic Curves under Specializations
Sebastian Falkensteiner, Rafael Sendra
Rational algebraic curves have been intensively studied in the last decades, both from the theoretical and applied point of view. In applications (e.g. level curves, linear homotop…
Transforming Radical Differential Equations to Algebraic Differential Equations
Sebastian Falkensteiner, Rafael Sendra
In this paper we present an algorithmic procedure that transforms, if possible, a given system of ordinary or partial differential equations with radical dependencies in the unknow…
Algebraic and Puiseux series solutions of systems of autonomous algebraic ODEs of dimension one in several variables
Jose Cano, Sebastian Falkensteiner, Daniel Robertz +1
In this paper we study systems of autonomous algebraic ODEs in several differential indeterminates. We develop a notion of algebraic dimension of such systems by considering them a…
Puiseux Series and Algebraic Solutions of First Order Autonomous AODEs -- A MAPLE Package
Francois Boulier, Jose Cano, Sebastian Falkensteiner +1
There exist several methods for computing exact solutions of algebraic differential equations. Most of the methods, however, do not ensure existence and uniqueness of the solutions…
The Fundamental Theorem of Tropical Partial Differential Algebraic Geometry
Sebastian Falkensteiner, Cristhian Garay-López, Mercedes Haiech +3
Tropical Differential Algebraic Geometry considers difficult or even intractable problems in Differential Equations and tries to extract information on their solutions from a restr…
Algebraic, rational and Puiseux series solutions of systems of autonomous algebraic ODEs of dimension one
Jose Cano, Sebastian Falkensteiner, J. Rafael Sendra
In this paper, we study the algebraic, rational and formal Puiseux series solutions of certain type of systems of autonomous ordinary differential equations. More precisely, we dea…
Existence and convergence of Puiseux series solutions for autonomous first order differential equations
Jose Cano, Sebastian Falkensteiner, J. Rafael Sendra
Given an autonomous first order algebraic ordinary differential equation F(y,y')=0, we prove that every formal Puiseux series solution, expanded around any finite point or at infin…
On Existence and Uniqueness of Formal Power Series Solutions of Algebraic Ordinary Differential Equations
Sebastian Falkensteiner, Yi Zhang, Thieu N. Vo
Given an algebraic ordinary differential equation (AODE), we propose a computational method to determine when a truncated power series can be extended to a formal power series solu…
Solving First Order Autonomous Algebraic Ordinary Differential Equations by Places
Sebastian Falkensteiner, J. Rafael Sendra
Given a first-order autonomous algebraic ordinary differential equation, we present a method for computing formal power series solutions by means of places. We provide an algorithm…