5 citations · 10 across the 8 of their papers we have counts for
12 papers
Proving the existence of loops in robot trajectories
Simon Rohou, Peter Franek, Clement Aubry +1
This paper presents a reliable method to verify the existence of loops along the uncertain trajectory of a robot, based on proprioceptive measurements only, within a bounded-error…
Computing simplicial representatives of homotopy group elements
Marek Filakovsky, Peter Franek, Uli Wagner +1
A central problem of algebraic topology is to understand the homotopy groups of a topological space . For the computational version of the problem, it is well known tha…
Solving equations and optimization problems with uncertainty
Peter Franek, Marek Krčál, Hubert Wagner
We study the problem of detecting zeros of continuous functions that are known only up to an error bound, extending the earlier theoretical work with explicit algorithms and experi…
Persistence of Zero Sets
Peter Franek, Marek Krčál
We study robust properties of zero sets of continuous maps . Formally, we analyze the family of all zero sets of all contin…
On Computability and Triviality of Well Groups
Peter Franek, Marek Krcal
The concept of well group in a special but important case captures homological properties of the zero set of a continuous map on a compact space K that are invariant w…
Robust Satisfiability of Systems of Equations
Peter Franek, Marek Krcal
We study the problem of \emph{robust satisfiability} of systems of nonlinear equations, namely, whether for a given continuous function on a~finite simplicia…
Quasi-decidability of a Fragment of the First-order Theory of Real Numbers
Peter Franek, Stefan Ratschan, Piotr Zgliczynski
In this paper we consider a fragment of the first-order theory of the real numbers that includes systems of equations of continuous functions in bounded domains, and for which all…
Effective Topological Degree Computation Based on Interval Arithmetic
Peter Franek, Stefan Ratschan
We describe a new algorithm for calculating the topological degree deg (f, B, 0) where B \subseteq Rn is a product of closed real intervals and f : B \rightarrow Rn is a real-value…
Symmetries of Quasi-Values
Ales Antonin Kubena, Peter Franek
According to Shapley's game-theoretical result, there exists a unique game value of finite cooperative games that satisfies axioms on additivity, efficiency, null-player property a…
Hyperplane section of the complex Cayley plane as the homogeneous space
Peter Franek, Karel Pazourek, Vít Tuček
We prove that the exceptional complex Lie group has a transitive action on the hyperplane section of the complex Cayley plane . Our proof is direct and constru…
Generalized Dolbeault sequences in parabolic geometry
Peter Franek
In this paper, we show the existence of a sequence of invariant differential operators on a particular homogeneous model of a Cartan geometry. The first operator in this sequ…
Several Dirac Operator in parabolic geometry
Peter Franek
In this thesis, we show the existence of a sequence of differential operators starting with with the Dirac operator in k Clifford variables, , where $D_i=\sum_j e…