相关论文: Slow north-south dynamics on $\mathcal{PML}$

The rapid development of large language models (LLMs) has driven the demand for more efficient optimization techniques. Among these, the Lookahead family of optimizers employs a two-loop framework, maintaining fast and slow sets of model…

We show that nonrelativsitic scaling of the collisionless Vlasov-Maxwell system implies the existence of a formal invariant slow manifold in the infinite-dimensional Vlasov-Maxwell phase space. Vlasov-Maxwell dynamics restricted to the slow…

We prove that the size of the super summit set of a braid can grow exponentially with the canonical length of the braid, even for pseudo-Anosov braids.

For every atoroidal iwip automorphism $\phi$ of $F_N$ (i.e. the analogue of a pseudo-Anosov mapping class) it is shown that the algebraic lamination dual to the forward limit tree $T_+(\phi)$ is obtained as "diagonal closure" of the support…

Mirror descent plays a crucial role in constrained optimization and acceleration schemes, along with its corresponding low-resolution ordinary differential equations (ODEs) framework have been proposed. However, the low-resolution ODEs are…

This paper explores the connections between tempering (for Sequential Monte Carlo; SMC) and entropic mirror descent to sample from a target probability distribution whose unnormalized density is known. We establish that tempering SMC…

A wide class of matrix pencils connected with dissipative Hamiltonian descriptor systems is investigated. In particular, the following properties are shown: all eigenvalues are in the closed left half plane, the nonzero finite eigenvalues…

We show that the Liechti-Strenner's example for the closed nonorientable surface in \cite{LiechtiStrenner18} minimizes the dilatation within the class of pseudo-Anosov homeomorphisms with an orientable invariant foliation and all but the…

Inspired by one--dimensional light--particle systems, the dynamics of a non-Hamiltonian system with long--range forces is investigated. While the molecular dynamics does not reach an equilibrium state, it may be approximated in the…

Fundamental understanding of the light-matter interaction in the context of nano-particles is immensely bene- fited by the study of geometry dependent tunable Localized Surface Plasmon Resonance (LSPR) and has been demonstrated to have…

We consider deterministic fast-slow dynamical systems on $\mathbb{R}^m\times Y$ of the form \[ \begin{cases} x_{k+1}^{(n)} = x_k^{(n)} + n^{-1} a(x_k^{(n)}) + n^{-1/\alpha} b(x_k^{(n)}) v(y_k)\;,\quad y_{k+1} = f(y_k)\;, \end{cases} \]…

We use an explicitly isochoric two-temperature theory where the ion temperature is not assumed to be equal to the electron temperature, to analyze recent X-ray laser scattering data for Aluminum in the ultra-fast-matter (UFM) regime up to 6…

By means of extensive simulations, we investigate concentrated solutions of globular single-chain nanoparticles (SCNPs), an emergent class of synthetic soft nano-objects. By increasing the concentration, the SCNPs show a reentrant behaviour…

Combinatorial optimization algorithms which compute exact ground state configurations in disordered magnets are seen to exhibit critical slowing down at zero temperature phase transitions. Using arguments based on the physical picture of…

Gradient compression is of growing interests for solving constrained optimization problems including compressed sensing, noisy recovery and matrix completion under limited communication resources and storage costs. Convergence analysis of…

Since their introduction, Transformer architectures have dominated Natural Language Processing (NLP). However, recent research has highlighted an inherent anisotropy phenomenon in these models, presenting a significant challenge to their…

Online off-policy reinforcement learning (RL) is shaped by two coupled choices: the policy class and the update rule. Gaussian policies are fast and have tractable entropy, but struggle with multimodal action distributions. Generative…

Partial Observability -- where agents can only observe partial information about the true underlying state of the system -- is ubiquitous in real-world applications of Reinforcement Learning (RL). Theoretically, learning a near-optimal…

It has recently been proved that the popular nonlocal means (NLM) denoising algorithm does not optimally denoise images with sharp edges. Its weakness lies in the isotropic nature of the neighborhoods it uses to set its smoothing weights.…

Chaotic dynamics with sensitive dependence on initial conditions may result in exponential decay of correlation functions. We show that for one-dimensional interval maps the corresponding quantities, that is, Lyapunov exponents and…