相关论文: Covariant Multi-Scale Negative Coupling on Dynamic…

This paper establishes a rigorous mathematical framework for the Multi-Scale Negative Coupled System (MNCS), a dynamical model describing hierarchical state spaces with directed, sign-structured interactions. We address the stabilization of…

Complex dynamical systems frequently encounter a recurrent structural instability: the collapse of the spectral gap, driving the system toward a low-dimensional "Zero-Mode Attractor" (e.g., spectral pile-up or over-smoothing). Building upon…

A class of dissipative dynamical systems evolving on smooth constraint hypersurfaces endowed with degenerate induced bilinear forms is studied. The intrinsic evolution is generated by constraint--preserving vector fields on manifolds whose…

Bayesian inverse problems highly rely on efficient and effective inference methods for uncertainty quantification (UQ). Infinite-dimensional MCMC algorithms, directly defined on function spaces, are robust under refinement of physical…

We propose a microlocal-Riemannian framework for the three-dimensional incompressible Navier-Stokes equations on a smooth oriented Riemannian manifold (M,g). The dynamics is lifted to the unit cosphere bundle S*M via a normal-coordinate…

Large-scale neutrino observatories operate under unavoidable detector deadtime and signal pile-up, leading to systematic inefficiencies in conventional coincidence-based trigger systems. Such triggers typically rely on binary temporal…

Dimensionality reduction (DR) is characterized by two longstanding trade-offs. First, there is a global-local preservation tension: methods such as t-SNE and UMAP prioritize local neighborhood preservation, yet may distort global manifold…

Dynamical systems methods are used to investigate global behavior of the spatially flat Friedmann-Robertson-Walker cosmological model in gravitational theory with a non-minimally coupled scalar field and a constant potential function. We…

We establish an equivalence between infinitely many asymptotically stable periodic solutions and subsumed homoclinic connections for $N$-dimensional piecewise-linear continuous maps. These features arise as a codimension-three phenomenon.…

Nonlinear dimensionality reduction methods provide a valuable means to visualize and interpret high-dimensional data. However, many popular methods can fail dramatically, even on simple two-dimensional manifolds, due to problems such as…

Dimensionality reduction is a fundamental task that aims to simplify complex data by reducing its feature dimensionality while preserving essential patterns, with core applications in data analysis and visualisation. To preserve the…

The limiting slow dynamics of slow-fast, piecewise-linear, continuous systems of ODEs occurs on critical manifolds that are piecewise-linear. At points of non-differentiability, such manifolds are not normally hyperbolic and so the…

We present a dynamic subspace approach for efficiently approximating large-scale systems by learning time-continuous trajectories on the Grassmannian manifold. By parameterizing a low-dimensional basis as a geodesic path, the method allows…

In view of the possibility that the 3D Navier-Stokes equations (NSE) might not always have regular solutions, we introduce an abstract framework for studying the asymptotic behavior of multi-valued dissipative evolutionary systems with…

Anisotropic material properties, such as the thermal conductivities of engineering composites, exhibit variability due to inherent material heterogeneity and manufacturing-related uncertainties. Mathematically, these properties are modeled…

Motivated by quantum gravity and the CFT Distance Conjecture, we study infinite-distance limits in four-dimensional ${\cal N}=2$ superconformal field theories with higher-dimensional conformal manifolds and their AdS duals. We focus on…

For classical discrete systems under constant composition, canonical average provides equilibrium configuration from a set of many-body interactions, which typically acts as nonlinear map. The nonlinearity has recently been investigated in…

We develop a contraction-based framework to establish the existence and exponential stability of periodic solutions in planar nonsmooth dynamical systems governed by Filippov differential inclusions. The method integrates a time- and…

Continual learning systems operating in fixed-dimensional spaces face a fundamental geometric barrier: the flat manifold problem. When experience is represented as a linear trajectory in Euclidean space, the geodesic distance between…

We extend a recently introduced class of exactly solvable models for recurrent neural networks with competition between 1D nearest neighbour and infinite range information processing. We increase the potential for further frustration and…