Related papers: Discrete-time multi-scale systems
Multiparameter persistent homology has been largely neglected as an input to machine learning algorithms. We consider the use of lattice-based convolutional neural network layers as a tool for the analysis of features arising from…
We introduce a new method for speeding up the inference of deep neural networks. It is somewhat inspired by the reduced-order modeling techniques for dynamical systems.The cornerstone of the proposed method is the maximum volume algorithm.…
This paper addresses the problem of identifying a linear time-varying (LTV) system characterized by a (possibly infinite) discrete set of delays and Doppler shifts. We prove that stable identifiability is possible if the upper uniform…
The search for highly coherent degrees of freedom in noisy solid-state environments is a major challenge in condensed matter. In disordered dipolar systems, such as magnetically doped insulators, compact clusters of two-level systems (TLS)…
Despite the appeal of deep neural networks that largely replace the traditional handmade filters, they still suffer from isolated cases that cannot be properly handled only by the training of convolutional filters. Abnormal factors,…
Time-decaying perturbations of nonlinear oscillatory systems in the plane are considered. It is assumed that the unperturbed systems are non-isochronous and the perturbations oscillate with an asymptotically constant frequency. Resonance…
Score-based models generate samples by mapping noise to data (and vice versa) via a high-dimensional diffusion process. We question whether it is necessary to run this entire process at high dimensionality and incur all the inconveniences…
We study diffusion in systems of classical particles whose dynamics conserves the total center of mass. This conservation law leads to several interesting consequences. In finite systems, it allows for equilibrium distributions that are…
We propose a robust spectrum sensing framework based on deep learning. The received signals at the secondary user's receiver are filtered, sampled and then directly fed into a convolutional neural network. Although this deep sensing is…
Scientific datasets often arise from multiple independent mechanisms such as spatial, categorical or structural effects, whose combined influence obscures their individual contributions. We introduce DIVIDE, a framework that disentangles…
We consider the feedback design for stabilizing a rigid body system by making and breaking multiple contacts with the environment without prespecifying the timing or the number of occurrence of the contacts. We model such a system as a…
We informally review the construction of spacetime geometries with multifractal and, more generally, multiscale properties. Based on fractional calculus, these continuous spacetimes have their dimension changing with the scale; they display…
Wave equations containing spatial derivatives which are higher than second order arise naturally in the context of condensed matter systems. The solutions of such equations contain more than two modes and consequently, the range of possible…
Mathematical models of biological populations commonly use discrete structure classes to capture trait variation among individuals (e.g. age, size, phenotype, intracellular state). Upscaling these discrete models into continuum descriptions…
This work deals with planar dynamical systems with and without noise. In the first part, we seek to gain a refined understanding of such systems by studying their differential-geometric transformation properties under an arbitrary smooth…
It is shown that any convolution operator in the time domain can be represented exactly as a multiplication operator in the time-scale (wavelet) domain. The Mellin transform gives a one-to-one correspondence between frequency filters…
In this paper, we address the full discretization of Friedrichs' systems with a two-field structure, such as Maxwell's equations or the acoustic wave equation in div-grad form, cf. [14]. We focus on a discontinuous Galerkin space…
We study circular shells in a (2+1)-dimensional background within the framework of Einstein-Born-Infeld theory. For shells around black holes we analyze the mechanical stability under perturbations preserving the symmetry. Shells around…
The motivation of this paper is to recognize a geometric shape from a noisy sample in the form of a point cloud. Inspired by the HDBSCAN clustering algorithm, we introduce the core dissimilarity, from which we construct the core…
We consider a two-dimensional model of double-diffusive convection and its time discretisation using a second-order scheme which treat the nonlinear term explicitly (backward differentiation formula with a one-leg method). Uniform bounds on…