Related papers: Detecting discrete integrability: the singularity …
Determining whether a dynamical system is integrable is generally a difficult task which is currently done on a case by case basis requiring large human input. Here we propose and test an automated method to search for the existence of…
Researchers develop models to explain the unknowns. These models typically involve parameters that capture tangible quantities, the estimation of which is desired. Parameter identifiability investigates the recoverability of the unknown…
Ever since entanglement was identified as a computational and cryptographic resource, effort has been made to find an efficient way to tell whether a given density matrix represents an unentangled, or separable, state. Essentially, this is…
Extending the investigations about the theory of duals, we analyze duals built up with the aid of discrete symmetry operators. We scrutinize algebraic and physical constraints (encompassing them in a theoretical scope) in order to verify…
Some basic features of confinement are reviewed, in particular the symmetry patterns of the dual dynamics. Open problems and possible directions of progress are discussed.
This paper is the first part of a two part paper which introduces the study of the Whitney Equisingularity of families of Symmetric determinantal singularities. This study reveals how to use the multiplicity of polar curves associated to a…
A systematic study of the discrete second order projective system is presented, complemented by the integrability analysis of the associated multilinear mapping. Moreover, we show how we can obtain third order integrable equations as the…
Dimensionality reduction is a crucial technique in data analysis, as it allows for the efficient visualization and understanding of high-dimensional datasets. The circular coordinate is one of the topological data analysis techniques…
Serializability is a well-understood correctness criterion that simplifies reasoning about the behavior of concurrent transactions by ensuring they are isolated from each other while they execute. However, enforcing serializable isolation…
A notion of a particular integrability is introduced when two operators commute on a subspace of the space where they act. Particular integrals for one-dimensional (quasi)-exactly-solvable Schroedinger operators and Calogero-Sutherland…
Differentiable conjugacies link dynamical systems that share properties such as the stability multipliers of corresponding orbits. It provides a stronger classification than topological conjugacy, which only requires qualitative similarity.…
In the classification of real singularities by Arnold et al. (1985), normal forms, as representatives of equivalence classes under right equivalence, are not always uniquely determined. We describe the complete structure of the equivalence…
The identification of anomalies in temporal data is a core component of numerous research areas such as intrusion detection, fault prevention, genomics and fraud detection. This article provides an experimental comparison of the novelty…
Speckle patterns are a powerful tool for high-precision metrology, as they allow remarkable performance in relatively simple setups. Nonetheless, researchers in this field follow rather distinct paths due to underappreciated general…
An alternative approach to detect very weak singularities on the characteristics of a tunnel diode is proposed in which the numerical differential filtering is applied directly to measured current versus voltage dependence instead of the…
In (Arnold, 1985), V.I. Arnold has obtained normal forms and has developed a classifier for, in particular, all isolated hypersurface singularities over the complex numbers up to modality 2. Building on a series of 105 theorems, this…
Chaos degree defined through two complexities in information dynamics is applied to some deterministic dynamical models. It is shown that this degree well describes the chaostic feature of the models.
The central purpose of this article is to establish new inverse and implicit function theorems for differentiable maps with isolated critical points. One of the key ingredients is a discovery of the fact that differentiable maps with…
An algorithm for resolution of singularities in characteristic zero is described. It is expressed in terms of multi-ideals, that essentially are defined as a finite sequence of pairs, each one consiting of a sheaf of ideals and a positive…
The principles behind the sharp, singular structures in a crumpled sheet are well understood. Here we discuss more general ways of exploiting such sharp structures to control the shape of a sheet by deforming or forcing it elsewhere. Often,…