相关论文: Symbolic Dynamics and Markov Partitions
Discovering governing equations of complex network dynamics is a fundamental challenge in contemporary science with rich data, which can uncover the mysterious patterns and mechanisms of the formation and evolution of complex phenomena in…
Symbolic computation, powered by modern computer algebra systems, has important applications in mathematical reasoning through exact deep computations. The efficiency of symbolic computation is largely constrained by such deep computations…
We show that the dynamics of a quantum system can be represented by the dynamics of an underlying classical systems obeying the Hamilton equations of motion. This is achieved by transforming the phase space of dimension $2n$ into a Hilbert…
The semiring of discrete dynamical systems is a simple algebraic model for modularity in deterministic systems. The objects of the semiring are finite transformations (viewed as directed graphs and regarded up to isomorphism), the sum of…
In recent years, machine learning methods have been widely used to study physical systems that are challenging to solve with governing equations. Physicists and engineers are framing the data-driven paradigm as an alternative approach to…
Machine learning techniques not only offer efficient tools for modelling dynamical systems from data, but can also be employed as frontline investigative instruments for the underlying physics. Nontrivial information about the original…
The brain is often called a computer and likened to a Turing machine, in part because the mind can manipulate discrete symbols such as numbers. But the brain is a dynamical system, more like a Watt governor than a Turing machine. Can a…
We present kinematic simulations of a galactic dynamo model based on the large scale differential rotation and the small scale helical fluctuations due to supernova explosions. We report for the first time direct numerical simulations of…
We consider an autonomous differential system in $\mathbb{R}^n$ with a periodic orbit and we give a new method for computing the characteristic multipliers associated to it. Our method works when the periodic orbit is given by the…
Physical systems that dissipate, mix and develop turbulence also irreversibly transport statistical density. In statistical physics, laws for these processes have a mathematical form and tractability that depends on whether the description…
Markov Population Models are a widespread formalism used to model the dynamics of complex systems, with applications in Systems Biology and many other fields. The associated Markov stochastic process in continuous time is often analyzed by…
We survey an area of recent development, relating dynamics to theoretical computer science. We discuss the theoretical limits of simulation and computation of interesting quantities in dynamical systems. We will focus on central objects of…
We discuss general concept of Markov statistical dynamics in the continuum. For a class of spatial birth-and-death models, we develop a perturbative technique for the construction of statistical dynamics. Particular examples of such systems…
This work establishes a robust mathematical foundation for compositional System Dynamics modeling, leveraging category theory to formalize and enhance the representation, analysis, and composition of system models. Here, System Dynamics…
For minimal $\mathbb{Z}^{2}$-topological dynamical systems, we introduce a cube structure and a variation of the regionally proximal relation for $\mathbb{Z}^2$ actions, which allow us to characterize product systems and their factors. We…
We describe a neural-based method for generating exact or approximate solutions to differential equations in the form of mathematical expressions. Unlike other neural methods, our system returns symbolic expressions that can be interpreted…
Incorporating a priori physics knowledge into machine learning leads to more robust and interpretable algorithms. In this work, we combine deep learning techniques and classic numerical methods for differential equations to address two…
Many complex systems are representable as macroscopic set of elements which interact by simple rules. The complex macroscopically relevant phenomena are then the result of the generic emergence of a space-time multi-scale dynamics. Critical…
These notes develop aspects of perturbation theory of matrices related to so-called diagonalisation schemes. Primary focus is on constructive tools to derive asymptotic expansions for small/large parameters of eigenvalues and…
This note discusses dynamical systems-systems that evolve through time. We start with two contemporary examples illustrating the qualitative and the quantitative behavior of dynamical systems. These are two broad categories, usually called…