Related papers: Backward Iteration Algorithms for Julia sets of M\…
This paper is devoted to the study of nonautonomous multivalued semiflows and their associated pullback attractors. For this kind of dynamical systems we are able to characterize the upper and lower bounds of the attractor as complete…
Modern generative machine learning models demonstrate surprising ability to create realistic outputs far beyond their training data, such as photorealistic artwork, accurate protein structures, or conversational text. These successes…
Reconstructing jets, which provide vital insights into the properties and histories of subatomic particles produced in high-energy collisions, is a main problem in data analyses in collider physics. This intricate task deals with estimating…
Semi-algebraic priors are ubiquitous in signal processing and machine learning. Prevalent examples include a) linear models where the signal lies in a low-dimensional subspace; b) sparse models where the signal can be represented by only a…
A random-batch method for multi-species interacting particle systems is proposed, extending the method of S. Jin, L. Li, and J.-G. Liu [J. Comput. Phys. 400 (2020), 108877]. The idea of the algorithmus is to randomly divide, at each time…
In this article, we consider hyperbolic rational maps restricted on thier Julia sets and study about the recurrence rate of typical orbits in arbitrarily small neighbourhoods around them and their relationship to the Hausdorff dimension of…
We introduce a new family of temporal logics designed to finely balance the trade-off between expressivity and complexity. Their key feature is the possibility of defining operators of a new kind that we call transformation operators. Some…
Complex systems often contain feedback loops that can be described as cyclic causal models. Intervening in such systems may lead to counterintuitive effects, which cannot be inferred directly from the graph structure. After establishing a…
Non-Hermitian systems offer new platforms for unusual physical properties that can be flexibly manipulated by redistribution of the real and imaginary parts of refractive indices, whose presence breaks conventional wave propagation…
We show that under the definition of computability which is natural from the point of view of applications, there exist non-computable quadratic Julia sets.
Ulrich ideals in numerical semigroup rings of small multiplicity are studied. If the semigroups are three-generated but not symmetric, the semigroup rings are Golod, since the Betti numbers of the residue class fields of the semigroup rings…
We develop theory and software for rotation equivariant operators on scalar and vector fields, with diverse applications in simulation, optimization and machine learning. Rotation equivariance (covariance) means all fields in the system…
We present a general framework for classifying partially observed dynamical systems based on the idea of learning in the model space. In contrast to the existing approaches using model point estimates to represent individual data items, we…
Robust Markov decision processes (MDPs) allow to compute reliable solutions for dynamic decision problems whose evolution is modeled by rewards and partially-known transition probabilities. Unfortunately, accounting for uncertainty in the…
Stochastic matrices and positive maps in matrix algebras proved to be very important tools for analysing classical and quantum systems. In particular they represent a natural set of transformations for classical and quantum states,…
In this paper we propose a (non-linear) smoothing algorithm for group-affine observation systems, a recently introduced class of estimation problems on Lie groups that bear a particular structure. As most non-linear smoothing methods, the…
Theorems relating permutations with objects in other fields of mathematics are often stated in terms of avoided patterns. Examples include various classes of Schubert varieties from algebraic geometry (Billey and Abe 2013), commuting…
A very classical subject in Commutative Algebra is the Invariant Theory of finite groups. In our work on 3-dimensional topology (S. King, Ideal Turaev-Viro invariants. To appear in Top. Appl.), we found certain examples of group actions on…
Pull-tabbing is an evaluation technique for functional logic programs which computes all non-deterministic results in a single graph structure. Pull-tab steps are local graph transformations to move non-deterministic choices towards the…
Let $K$ be a complete non-archimedean field of characteristic $0$ equipped with a discrete valuation. We establish the rationality of the Artin-Mazur zeta function on the Julia set for any subhyperbolic rational map defined over $K$ with a…