Related papers: A Lax Functorial Definition of Open Dynamics
A clear definition of system dynamics modeling can provide shared understanding and clarify the impact of the field. We introduce a set of characteristics that define quantitative system dynamics, selected to capture core philosophy,…
No abstract given. Contents: I. Definition and Introduction II. Schelling Model III. Opinion Dynamics IV. Languages, Hierarchies and Football V. Future Directions
We propose a notion of operator monotonicity for functions of several variables, which extends the well known notion of operator monotonicity for functions of only one variable. The notion is chosen such that a fundamental relationship…
UML activity diagrams have become an established notation to model control and data ow on various levels of abstraction, ranging from fine-grained descriptions of algorithms to high-level workflow models in business applications. A formal…
We analyze a class of dynamics of open quantum systems which is governed by the dynamical map mutually commuting at different times. Such evolution may be effectively described via spectral analysis of the corresponding time dependent…
The paper proposes a general notion of interaction between attributes, which can be applied to many fields in decision making and data analysis. It generalizes the notion of interaction defined for criteria modelled by capacities, by…
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…
The study of local function in topological spaces is remarkable. Various branches have been developed through this study. In this paper, we further consider the local function and exploring the various properties of the same by considering…
It is explained how the time evolution of the operadic variables may be introduced. As an example, an operadic Lax representation of the harmonic oscillator is considered.
This paper discusses several methods for describing the dynamics of open quantum systems, where the environment of the open system is infinite-dimensional. These are purifications, phase space forms, master equation and liouville equation…
The scope of the paper is a theoretical analysis of the dynamical system, the model of which was reduced to Weierstrasse function. A fractal structure of the trajectory was proved and the entropy of the system information designated.
A discrete--dynamics model, which is specified solely in terms of the system's equilibrium structure, is defined for the density correlators of a simple fluid. This model yields results for the evolution of glassy dynamics which are…
The Lagrangian relativistic direct interaction theory in the various forms of dynamics is formulated and its connections with the Fokker-type action theory and with the constrained Hamiltonian mechanics are established. The motion of…
This paper is a contribution to the theoretical foundations of strategies. We first present a general definition of abstract strategies which is extensional in the sense that a strategy is defined explicitly as a set of derivations of an…
This paper studies nonstationary open dynamical systems from the statistical viewpoint. By open, we mean that trajectories may escape through holes in the phase space. By nonstationary, we mean that the dynamical model itself (as well as…
Notion of an open system of second order is introduced. Characteristic function for such an open system is obtained. Model representations of a quadratic non-self-adjoint operator pencil are found.
We dwell on how a definition of a theoretical concept of an operating system, suitable to be incorporated in a mathematical theory of operating systems, could look like. This is considered a valuable preparation for the development of a…
We regard explanations as a blending of the input sample and the model's output and offer a few definitions that capture various desired properties of the function that generates these explanations. We study the links between these…
Most of the real world is governed by complex and chaotic dynamical systems. All of these dynamical systems pose a challenge in modelling them using neural networks. Currently, reservoir computing, which is a subset of recurrent neural…
We treat here the interrelation between formal languages and those dynamical systems that can be described by cellular automata (CA). There is a well-known injective map which identifies any CA-invariant subshift with a central formal…