Related papers: The Structure of Langevin's Memory Kernel From Lag…

The properties of molecules and materials containing light nuclei are affected by their quantum mechanical nature. Modelling these quantum nuclear effects accurately requires computationally demanding path integral techniques. Considerable…

Large time behaviour of heat semigroups (and more generally, of positive selfadjoint semigroups) is studied. Convergence of the semigroup to the ground state and of averaged logarithms of kernels to the ground state energy is shown in the…

We briefly summarize the kernel regression approach, as used recently in materials modelling, to fitting functions, particularly potential energy surfaces, and highlight how the linear algebra framework can be used to both predict and train…

The kernel of a pair of linear systems is studied in the framework of commutative ring theory with applications to behavioral perspective of linear systems

We consider a model where particles are described as localized concentrations of energy, with fixed rest mass and structure, which are not significantly affected by their self-induced gravitational field. We show that the volume average of…

As three particles are advected by a turbulent flow, they separate from each other and develop non trivial geometries, which effectively reflect the structure of the turbulence. We investigate here the geometry, in a statistical sense, of…

Kernel methods have great promise for learning rich statistical representations of large modern datasets. However, compared to neural networks, kernel methods have been perceived as lacking in scalability and flexibility. We introduce a…

In the training of over-parameterized model functions via gradient descent, sometimes the parameters do not change significantly and remain close to their initial values. This phenomenon is called lazy training, and motivates consideration…

In this paper we are concerned with the learnability of nonlocal interaction kernels for first order systems modeling certain social interactions, from observations of realizations of their dynamics. This paper is the first of a series on…

We consider a description of the stochastic oscillations of the general relativistic accretion disks around compact astrophysical objects based on the generalized Langevin equation, which accounts for the general retarded effects of the…

The long-time kinetics of the spherical model in an external magnetic field and below the equilibrium critical temperature is studied. The solution of the associated stochastic Langevin equation is reduced exactly to a single non-linear…

One important problem in constructing the reduced dynamics of molecular systems is the accurate modeling of the non-Markovian behavior arising from the dynamics of unresolved variables. The main complication emerges from the lack of scale…

Kernel random matrices have attracted a lot of interest in recent years, from both practical and theoretical standpoints. Most of the theoretical work so far has focused on the case were the data is sampled from a low-dimensional structure.…

We consider a cell-complex in an arbitrary Hausdorff space as a dynamical object that can be coupled to a field defined on the complex. The Langevin equation is then derived for this field. In other words, a noise-field is created resulting…

An exact description of the statistical motion of active particles in three dimension is presented in the framework of a generalized diffusion equation. Such a generalization contemplates a non-local, in time and space, connecting (memory)…

Important information on the structure of complex systems, consisting of more than one component, can be obtained by measuring to which extent the individual components exchange information among each other. Such knowledge is needed to…

When the density of the fluid surrounding suspended Brownian particles is appreciable, in addition to the forces appearing in the traditional Ornstein and Uhlenbeck theory of Brownian motion, additional forces emerge as the displaced fluid…

We introduce an example of thermodynamic uncertainty relation (TUR) for systems modeled by a one-dimensional generalised Langevin dynamics with memory, determining the motion of a micro-bead driven in a complex fluid. Contrary to TURs…

Study of Langevin dynamics and the fluctuation-dissipation relation (FDR) for a generic probe system (represented by a mass $M$), bilinearly coupled to a bath of harmonic oscillators, has been a standard paradigm for a microscopic theory of…

Modeling a high-dimensional Hamiltonian system in reduced dimensions with respect to coarse-grained (CG) variables can greatly reduce computational cost and enable efficient bottom-up prediction of main features of the system for many…