Related papers: Rigidity and Non-recurrence along Sequences
Recently, two stronger versions of dynamical properties have been introduced and investigated: strong topological transitivity, which is a stronger version of the topological transitivity property, and hypermixing, which is a stronger…
Dynamic Complexity is a phenomenon exhibited by a nonlinearly interacting system within which multitudes of different sizes of large scale coherent structures emerge, resulting in a globally nonlinear stochastic behavior vastly different…
It is widely accepted that the complex dynamics characteristic of recurrent neural circuits contributes in a fundamental manner to brain function. Progress has been slow in understanding and exploiting the computational power of recurrent…
In spite of a few attempts in understanding the dynamical robustness of complex networks, this extremely important subject of research is still in its dawn as compared to the other dynamical processes on networks. We hereby consider the…
The robust disturbance rejection controller has been the subject of intensive research due to its undeniable importance for automation. Modern control theory tends to use model-based approaches versus model-free approaches, especially when…
Considering the retina as a high dimensional, non autonomous, dynamical system, layered and structured, with non stationary and spatially inhomogeneous entries (visual scenes), we present several examples where dynamical systems-,…
Nearly linear recurrences are a generalisation of linear recurrences and are instances of linear time-invariant systems in control theory and linear constraint loops in program analysis. In this paper we formulate the Positivity Problem for…
Many mechanical structures, both engineered and biological, combine heavy rigid elements such as bones and beams with lightweight flexible ones such as cables and membranes. These are referred to as tensegrities, reflecting that cables can…
We study a three-dimensional fluid model describing rapidly rotating convection that takes place in tall columnar structures. The purpose of this model is to investigate the cyclonic and anticyclonic coherent structures. Global existence,…
We investigate the properties of chain recurrent, chain transitive, and chain mixing maps (generalizations of the well-known notions of non-wandering, topologically transitive, and topologically mixing maps). We describe the structure of…
The two-fold singularity has played a significant role in our understanding of uniqueness and stability in piecewise smooth dynamical systems. When a vector field is discontinuous at some hypersurface, it can become tangent to that surface…
This article consists in two independent parts. In the first one, we investigate the geometric properties of almost periodicity of model sets (or cut-and-project sets, defined under the weakest hypotheses); in particular we show that they…
Complex systems are characterized by specific time-dependent interactions among their many constituents. As a consequence they often manifest rich, non-trivial and unexpected behavior. Examples arise both in the physical and non-physical…
This paper focuses on rotational phenomena of rigid body kinematics. It discusses them in a group-theoretic approach as completely as possible, using methods and notations as intuitive as possible. With a review of current literature, this…
In this paper we address the characterization of the structure of condensed materials, periodic and non-periodic. Carrying out an extensive study of over 7000 different groundstate structures of a 2D lattice model of binary packing, we find…
In this paper, we show that there is a close relation between consistency in a constraint network and set intersection. A proof schema is provided as a generic way to obtain consistency properties from properties on set intersection. This…
Parabolic geometric flows have the property of smoothing for short time however, over long time, singularities are typically unavoidable, can be very nasty and may be impossible to classify. The idea of this paper is that, by bringing in…
We characterize structures such as monotonicity, convexity, and modality in smooth regression curves using persistent homology. Persistent homology is a key tool in topological data analysis that detects higher-dimensional topological…
The study of granular crystals, metamaterials that consist of closely packed arrays of particles that interact elastically, is a vibrant area of research that combines ideas from disciplines such as materials science, nonlinear dynamics,…
Deep learning systems achieve remarkable empirical performance, yet the stability of the training process itself remains poorly understood. Training unfolds as a high-dimensional dynamical system in which small perturbations to…