Related papers: Computability in Dynamical Systems
The exact computation of orbits of discrete dynamical systems on the interval is considered. Therefore, a multiple-precision floating point approach based on error analysis is chosen and a general algorithm is presented. The correctness of…
Traditional computers work with finite numbers. Situations where the usage of infinite or infinitesimal quantities is required are studied mainly theoretically. In this paper, a recently introduced computational methodology (that is not…
A universal Turing machine is a powerful concept - a single device can compute any function that is computable. A universal spin model, similarly, is a class of physical systems whose low energy behavior simulates that of any spin system.…
Cosmology is a well established research area in physics while dynamical systems are well established in mathematics. It turns out that dynamical system techniques are very well suited to study many aspects of cosmology. The aim of this…
The use of graphics processing units for scientific computations is an emerging strategy that can significantly speed up various different algorithms. In this review, we discuss advances made in the field of computational physics, focusing…
We present the first example of a poly-time computable Julia set with a recurrent critical point: we prove that the Julia set of the Feigenbaum map is computable in polynomial time.
We need much better understanding of information processing and computation as its primary form. Future progress of new computational devices capable of dealing with problems of big data, internet of things, semantic web, cognitive robotics…
We extend in a natural way the operation of Turing machines to infinite ordinal time, and investigate the resulting supertask theory of computability and decidability on the reals. The resulting computability theory leads to a notion of…
We examine a variety of numerical methods that arise when considering dynamical systems in the context of physics-based simulations of deformable objects. Such problems arise in various applications, including animation, robotics, control…
The basic notions of quantum mechanics are formulated in terms of separable infinite dimensional Hilbert space $\mathcal{H}$. In terms of the Hilbert lattice $\mathcal{L}$ of closed linear subspaces of $\mathcal{H}$ the notions of state and…
The aim of this paper is to present an elementary computable theory of random variables, based on the approach to probability via valuations. The theory is based on a type of lower-measurable sets, which are controlled limits of open sets,…
We consider shift spaces in which elements of the alphabet may overlap nontransitively. We define a notion of entropy for such spaces, give several techniques for computing lower bounds for it, and show that it is equal to a limit of…
The investigations reported in this paper center on the process of dynamic uncertainty assessment during interpretation tasks in real domain. In particular, we are interested here in the nature of the control structure of computer programs…
We study the pairwise entanglement present in a quantum computer that simulates a dynamically localized system. We show that the concurrence is exponentially sensitive to changes in the Hamiltonian of the simulated system. Moreover,…
Several philosophical issues in connection with computer simulations rely on the assumption that results of simulations are trustworthy. Examples of these include the debate on the experimental role of computer simulations \cite{Parker2009,…
In this paper we consider the computational complexity of uniformizing a domain with a given computable boundary. We give nontrivial upper and lower bounds in two settings: when the approximation of boundary is given either as a list of…
We derive computationally tractable methods to select a small subset of experiment settings from a large pool of given design points. The primary focus is on linear regression models, while the technique extends to generalized linear models…
We discuss what is special about the reproducibility of workflows in computer algebra. It is emphasized how the programming language Julia and the new computer algebra system OSCAR support such a reproducibility, and how users can benefit…
The TTE approach to Computable Analysis is the study of so-called representations (encodings for continuous objects such as reals, functions, and sets) with respect to the notions of computability they induce. A rich variety of such…
The basic idea of lifelike computing systems is the transfer of concepts in living systems to technical use that goes even beyond existing concepts of self-adaptation and self-organisation (SASO). As a result, these systems become even more…