相关论文: Functional Dynamics II : Syntactic Structure

We investigate the use of iterated function system (IFS) models for data analysis. An IFS is a discrete dynamical system in which each time step corresponds to the application of one of a finite collection of maps. The maps, which represent…

Many real-world scientific processes are governed by complex nonlinear dynamic systems that can be represented by differential equations. Recently, there has been increased interest in learning, or discovering, the forms of the equations…

Kinetic theory describes a dilute monatomic gas using a distribution function $f(q,p,t)$, the expected phase-space density of particles. The distribution function evolves according to the collisionless Boltzmann equation in the high Knudsen…

Two different types of agency are discussed based on dynamically coherent and incoherent couplings with an environment respectively. I propose that until a private syntax (syntactic autonomy) is discovered by dynamically coherent agents,…

We consider a dynamical systems formulation for models with an exponential scalar field and matter with a linear equation of state in a spatially flat and isotropic spacetime. In contrast to earlier work, which only considered linear…

A dynamic logic ${\mathbf B}$ can be assigned to every automaton ${\mathcal A}$ without regard if ${\mathcal A}$ is deterministic or nondeterministic. This logic enables us to formulate observations on ${\mathcal A}$ in the form of composed…

The interrelation of dynamic processes active on separated time-scales in glasses and viscous liquids is investigated using a model displaying two time-scale bifurcations both between fast and secondary relaxation and between secondary and…

We propose a new class of generative diffusion models, called functional diffusion. In contrast to previous work, functional diffusion works on samples that are represented by functions with a continuous domain. Functional diffusion can be…

Dynamical systems theory has long provided a foundation for understanding evolving phenomena across scientific domains. Yet, the application of this theory to complex real-world systems remains challenging due to issues in mathematical…

A wide range of techniques exist for extracting the dominant flow dynamics and features about steady, or periodic base flows. However, there have been limited efforts in extracting the dominant dynamics about unsteady, aperiodic base flow.…

The data generated by long-delayed dynamical systems can be organized in patterns by means of the so-called spatio-temporal representation, uncovering the role of multiple time-scales as independent degrees of freedom. However, their…

Force-based models describe pedestrian dynamics in analogy to classical mechanics by a system of second order ordinary differential equations. By investigating the linear stability of two main classes of forces, parameter regions with…

In this note we describe the theory of functional asynchronous networks and one of the main results, the Modularization of Dynamics Theorem, which for a large class of functional asynchronous networks gives a factorization of dynamics in…

We establish several delay-independent criteria for the existence and stability of positive periodic solutions of n-dimensional nonautonomous functional differential equation by several fixed point theorems. Examples from positive and…

The distinction between a theory's kinematics and its dynamics, that is, between the space of physical states it posits and its law of evolution, is central to the conceptual framework of many physicists. A change to the kinematics of a…

A procedure to characterize chaotic dynamical systems with concepts of complex networks is pursued, in which a dynamical system is mapped onto a network. The nodes represent the regions of space visited by the system, while edges represent…

Linear finite dynamical systems play an important role, for example, in coding theory and simulations. Methods for analyzing such systems are often restricted to cases in which the system is defined over a field %and usually strive to…

The recent discovery of universal principles underlying many complex networks occurring across a wide range of length scales in the biological world has spurred physicists in trying to understand such features using techniques from…

Motivated by modern observational studies, we introduce a class of functional models that expands nested and crossed designs. These models account for the natural inheritance of correlation structure from sampling design in studies where…

We uncover a geometric organization of the differential equations for the wavefunction coefficients of conformally coupled scalars in power-law cosmologies. To do this, we introduce a basis of functions inspired by a decomposition of the…