Related papers: Local Causal States and Discrete Coherent Structur…
We give a mathematical framework to describe the evolution of an open quantum systems subjected to finitely many interactions with classical apparatuses. The systems in question may be composed of distinct, spatially separated subsystems…
It is commonplace to encounter heterogeneous or nonstationary data, of which the underlying generating process changes across domains or over time. Such a distribution shift feature presents both challenges and opportunities for causal…
We formulate a nonlinear synergistic theory of coevolutionary systems, disentangling and explaining dynamic complexity in terms of fundamental processes for optimised data analysis and dynamic model design: Dynamic Source Analysis (DSA).…
Open dynamical systems are mathematical models of machines that take input, change their internal state, and produce output. For example, one may model anything from neurons to robots in this way. Several open dynamical systems can be…
As toy models for space-time on the Planck scale, we consider examples of fermion systems in discrete space-time which are composed of one or two particles defined on two up to nine space-time points. We study the self-organization of the…
We formulate a relation between quantum-mechanical coherent states and complex-differentiable structures on the classical phase space ${\cal C}$ of a finite number of degrees of freedom. Locally-defined coherent states parametrised by the…
Neurons are often connected, spatially and temporally, in phenomenal ways that promote wave propagation. Therefore, it is essential to analyze the emergent spatiotemporal patterns to understand the working mechanism of brain activity,…
The paper continues a series of publications devoted to the 3D nonlinear localized coherent structures on the surface of vertically falling liquid films. The work is primarily focussed on experimental investigations. We study: (i)…
The supercritical state is currently viewed as uniform on the pressure-temperature phase diagram. Supercritical fluids have the dynamic motions of a gas but are able to dissolve materials like a liquid. They have started to be deployed in…
The long-term behavior of a modulationally unstable conservative nonintegrable system is known to be characterized by the soliton turbulence self-organization process. We consider this problem in the presence of a long-range interaction in…
A phase-space formulation of non-stationary nonlinear dynamics including both Hamiltonian (e.g., quantum-cosmological) and dissipative (e.g., dissipative laser) systems reveals an unexpected affinity between seemly different branches of…
The meaning of statistical experiments with single microsystems in quantum mechanics is discussed and a general model in the framework of non-relativistic quantum field theory is proposed, to describe both coherent and incoherent…
Confined active nematics exhibit rich dynamical behavior, including spontaneous flows, periodic defect dynamics, and chaotic `active turbulence'. Here, we study these phenomena using the framework of Exact Coherent Structures, which has…
Dynamical systems theory provides powerful methods to extract effective macroscopic dynamics from complex systems with slow modes and fast modes. Here we derive and theoretically support a macroscopic, spatially discrete, model for a class…
Coherent sets are time-dependent regions in the physical space of nonautonomous flows that exhibit little mixing with their neighborhoods, robustly under small random perturbations of the flow. They thus characterize the global long-term…
We show that in the limit of strongly interacting environment a system initially prepared in a Decoherence Free Subspace (DFS) coherently evolves in time, adiabatically following the changes of the DFS. If the reservoir cyclicly evolves in…
The concept of spatial coherence is usually hard to be understood the first time that it is studied. We propose here a fully intuitive geometric description that does not contain mathematical difficulties and permits to understand how a…
Considering some important classes of generalized coherent states known in literature, we demonstrated that all of them can be created via conventional fashion, i.e. the "lowering operator eigen-state" and the "displacement operator"…
We propose a mechanism to describe how a physical quantity, which initially can take continuous values, is restricted within some discrete values after a measurement. As an example of the present theory, in which interplay between coherence…
Alignment interactions in active matter are typically modeled as relaxational dynamics toward local consensus. In unbounded systems, this makes alignment effectively decoupled from local density and therefore unable to sustain self-confined…