Related papers: An ergodic averaging method to differentiate covar…
In this paper we combine two existing approaches for approximating attractors. One of them approximates the attractors arbitrarily well by sublevel sets related to solutions of infinite dimensional linear programming problems. A downside…
Collective variables (CVs) are low-dimensional projections of high-dimensional system states. They are used to gain insights into complex emergent dynamical behaviors of processes on networks. The relation between CVs and network measures…
Main results and techniques of the fractional calculus of variations are surveyed. We consider variational problems containing Caputo derivatives and study them using both indirect and direct methods. In particular, we provide necessary…
Free energy biasing methods have proven to be powerful tools to accelerate the simulation of important conformational changes of molecules by modifying the sampling measure. However, most of these methods rely on the prior knowledge of…
This paper provides a comprehensive and detailed derivation of the backpropagation algorithm for graph convolutional neural networks using matrix calculus. The derivation is extended to include arbitrary element-wise activation functions…
The Lyapunov exponent spectrum and covariant Lyapunov vectors are studied for a quasi-one-dimensional system of hard disks as a function of density and system size. We characterize the system using the angle distributions between covariant…
The classical $\overline \partial$-method has been generalized recently [lnv], [lnv2] to be used in the presence of exceptional points. We apply this generalization to solve Dirac inverse scattering problem with weak assumptions on…
We construct critical trajectories in kinetic geometry, i.e. curves in $\mathbb{R}^{1+2n}$ that are: tangential to the vector fields $\partial_t+v\cdot \nabla_x$ and $\nabla_v$, connecting any two given points, respecting the underlying…
Variational autoencoder (VAE) is a very popular and well-investigated generative model in neural learning research. To leverage VAE in practical tasks dealing with a massive dataset of large dimensions, it is required to deal with the…
In chaotic dynamical systems such as the weather, prediction errors grow faster in some situations than in others. Real-time knowledge about the error growth could enable strategies to adjust the modelling and forecasting infrastructure…
We consider the convergence of kinetic Langevin dynamics to its ergodic invariant measure, which is Gibbs distribution. Instead of the standard setup where the friction coefficient is a constant scalar, we investigate position-dependent…
Studies have shown that autonomous vehicles (AVs) behave conservatively in a traffic environment composed of human drivers and do not adapt to local conditions and socio-cultural norms. It is known that socially aware AVs can be designed if…
Egorov's theorem for transversally elliptic operators, acting on sections of a vector bundle over a compact foliated manifold, is proved. This theorem relates the quantum evolution of transverse pseudodifferential operators determined by a…
This contribution proposes a new formulation to efficiently compute directional derivatives of order one to fourth. The formulation is based on automatic differentiation implemented with dual numbers. Directional derivatives are particular…
The aim of this paper is to shed more light on some recent ideas about Lyapunov exponents and clarify the formal structures behind these ideas. In particular, we show that the vector of (averaged) Lyapunov exponents of a smooth…
We present a unified derivation of covariant time derivatives, which transform as tensors under a time-dependent coordinate change. Such derivatives are essential for formulating physical laws in a frame-independent manner. Three specific…
We derive large deviations type (LDT) estimates for linear cocycles over an ergodic multifrequency torus translation. These models are called quasi-periodic cocycles. We make the following assumptions on the model: the translation vector…
Existing equivariant neural networks require prior knowledge of the symmetry group and discretization for continuous groups. We propose to work with Lie algebras (infinitesimal generators) instead of Lie groups. Our model, the Lie algebra…
Classifying time series data using neural networks is a challenging problem when the length of the data varies. Video object trajectories, which are key to many of the visual surveillance applications, are often found to be of varying…
A new multivariate density estimator for stationary sequences is obtained by Fourier inversion of the thresholded empirical characteristic function. This estimator does not depend on the choice of parameters related to the smoothness of the…