相关论文: A partially linearized spin-mapping approach for n…

Adapted from biological sequence alignment, trace alignment is a process mining technique used to visualize and analyze workflow data. Any analysis done with this method, however, is affected by the alignment quality. The best existing…

The fully nonlinear governing equations for spin 1/2 quantum plasmas are presented. Starting from the Pauli equation, the relevant plasma equations are derived, and it is shown that nontrivial quantum spin couplings arise, enabling studies…

Time-varying linear state-space models are powerful tools for obtaining mathematically interpretable representations of neural signals. For example, switching and decomposed models describe complex systems using latent variables that evolve…

The process of transforming observed data into predictive mathematical models of the physical world has always been paramount in science and engineering. Although data is currently being collected at an ever-increasing pace, devising…

Path Integral Molecular Dynamics (PIMD) is a well established simulation technique to compute exact equilibrium properties for a quantum system using classical trajectories in an extended phase space. Standard PIMD simulations are…

Reduced-order models have long been used to understand the behavior of nonlinear partial differential equations (PDEs). Naturally, reduced-order modeling techniques come at the price of computational accuracy for a decrease in computation…

This work investigates a dynamical system functioning as a nonsmooth adaptation of the continuous Newton method, aimed at minimizing the sum of a primal lower-regular and a locally Lipschitz function, both potentially nonsmooth. The…

To fully understand, analyze, and determine the behavior of dynamical systems, it is crucial to identify their intrinsic modal coordinates. In nonlinear dynamical systems, this task is challenging as the modal transformation based on the…

Optimizing Deep Learning-based Simultaneous Localization and Mapping (DL-SLAM) algorithms is essential for efficient implementation on resource-constrained embedded platforms, enabling real-time on-board computation in autonomous mobile…

We show how the dynamically nonlocal formulation of classical nuclear motion in the presence of quantal electronic transitions presented many years ago by Pechukas can be localized in time using time dependent perturbation theory to give an…

A general, variational approach to derive low-order reduced systems for nonlinear systems subject to an autonomous forcing, is introduced. The approach is based on the concept of optimal parameterizing manifold (PM) that substitutes the…

This paper establishes a robust link between quantum dynamics and classical ones by deriving probabilistic representation for both continuous time and discrete time quantum walks. We first adapt Molchanov formula, originally employed in the…

The dynamic mode decomposition (DMD) has become a leading tool for data-driven modeling of dynamical systems, providing a regression framework for fitting linear dynamical models to time-series measurement data. We present a simple…

With the fast development of various positioning techniques such as Global Position System (GPS), mobile devices and remote sensing, spatio-temporal data has become increasingly available nowadays. Mining valuable knowledge from…

This paper studies a \textit{partial functional partially linear single-index model} that consists of a functional linear component as well as a linear single-index component. This model generalizes many well-known existing models and is…

This work presents an extended framework for learning-based bipedal locomotion that incorporates a heuristic step-planning strategy guided by desired torso velocity tracking. The framework enables precise interaction between a humanoid…

We study the problem of modeling a non-linear dynamical system when given a time series by deriving equations directly from the data. Despite the fact that time series data are given as input, models for dynamics and estimation algorithms…

Many real-world data sets, especially in biology, are produced by complex nonlinear dynamical systems. In this paper, we focus on brain calcium imaging (CaI) of different organisms (zebrafish and rat), aiming to build a model of joint…

The validity of the adiabatic approach to spin-Peierls transitions is assessed. An alternative approach is developed which maps the initial magneto-elastic problem to an effective magnetic problem only. Thus the equivalence of…

Legged robot locomotion on a dynamic rigid surface (i.e., a rigid surface moving in the inertial frame) involves complex full-order dynamics that is high-dimensional, nonlinear, and time-varying. Towards deriving an analytically tractable…