相关论文: Symmetry of forward and reverse path populations

The dynamics of one dimensional iterative maps in the regime of fully developed chaos is studied in detail. Motivated by the observation of dynamical structures around the unstable fixed point we introduce the geometrical concept of a…

Rectified flow (Liu et al., 2022; Liu, 2022; Wu et al., 2023) is a method for defining a transport map between two distributions, and enjoys popularity in machine learning, although theoretical results supporting the validity of these…

For a paradigmatic case, the standard map, we discuss how the statistical description of the approach to equilibrium is related to the sensitivity to the initial conditions of the system. Using a numerical analysis we present an anomalous…

We present difference schemes for stochastic transport equations with low-regularity velocity fields. We establish $L^2$ stability and convergence of the difference approximations under conditions that are less strict than those required…

In this paper we consider a diffusion process obtained as a small random perturbation of a dynamical system attracted to a stable equilibrium point. The drift and the diffusive perturbation are assumed to evolve slowly in time. We describe…

We show that partial dynamical symmetries (PDS) can occur at critical-points of quantum phase transitions, in which case, underlying competing symmetries are conserved exactly by a subset of states, and mix strongly in other states. Several…

Predicting human behavior is a difficult and crucial task required for motion planning. It is challenging in large part due to the highly uncertain and multi-modal set of possible outcomes in real-world domains such as autonomous driving.…

In this letter, by regarding finite-time stability as an inverse problem, we reveal the essence of finite-time stability and fixed-time stability. Some necessary and sufficient conditions are given. As application, we give a new approach…

Transitive consistency is an intrinsic property for collections of linear invertible transformations between Euclidean coordinate frames. In practice, when the transformations are estimated from data, this property is lacking. This work…

We discuss the conditions under which identical particles may yet be distinguishable and the relationship between particle permutation and exchange. We show that we can always define permutation-symmetric state vectors. When the particles…

In this paper, we consider the travel time tomography problem for conformal metrics on a bounded domain, which seeks to determine the conformal factor of the metric from the lengths of geodesics joining boundary points. We establish forward…

We discuss the time-continuous path integration in the coherent states basis in a way that is free from inconsistencies. Employing this notion we reproduce known and exact results working directly in the continuum. Such a formalism can set…

This work interprets and generalizes consensus-type algorithms as switching dynamics leading to symmetrization of some vector variables with respect to the actions of a finite group. We show how the symmetrization framework we develop…

An asymmetry exists between time and space in the sense that physical systems inevitably evolve over time whereas there is no corresponding ubiquitous translation over space. The asymmetry, which is presumed to be elemental, is represented…

We study the dynamics of an ensemble of globally coupled chaotic logistic maps under the action of a learning algorithm aimed at driving the system from incoherent collective evolution to a state of spontaneous full synchronization.…

The probability distribution of the proper delay times during scattering on a chaotic system is derived in the framework of the random matrix approach and the supersymmetry method. The result obtained is valid for an arbitrary number of…

Understanding collective properties of driven particle systems is significant for naturally occurring aggregates and because the knowledge gained can be used as building blocks for the design of artificial ones. We model self propelling…

Evolution of coherent states is considered for a particle confined to a cylinder moving in a harmonic oscillator potential. Because of the discontinuous changes as time goes by of the phase representing the position of a particle on a…

We study the coupled dynamics of two populations of random replicators by means of statistical mechanics methods, and focus on the effects of relative population size, strategy correlations and heterogeneities in the respective co-operation…

Collective human movement is a hallmark of complex systems, exhibiting emergent order across diverse settings, from pedestrian flows to biological collectives. In high-speed scenarios, alignment interactions ensure efficient flow and…