Related papers: Discrete-time multi-scale systems
We consider $k$-dimensional discrete-time systems of the form $x_{n+1}=F(x_n,\ldots,x_{n-k+1})$ in which the map $F$ is continuous and monotonic in each one of its arguments. We define a partial order on $\mathbb{R}^{2k}_+$, compatible with…
We apply the consistent discretization scheme to general relativity particularized to the Gowdy space-times. This is the first time the framework has been applied in detail in a non-linear generally-covariant gravitational situation with…
Denoising diffusion models (DDMs) have recently attracted increasing attention by showing impressive synthesis quality. DDMs are built on a diffusion process that pushes data to the noise distribution and the models learn to denoise. In…
We present a general setting where wavelet filters and multiresolution decompositions can be defined, beyond the classical $\mathbf L^2(\mathbb R,dx)$ setting. This is done in a framework of {\em iterated function system} (IFS) measures;…
Deep learning has dramatically improved the performance of speech recognition systems through learning hierarchies of features optimized for the task at hand. However, true end-to-end learning, where features are learned directly from…
Assuming only a smooth and slow change of spacetime dimensionality at large scales, we find, in a background- and model-independent way, the general profile of the Hausdorff and the spectral dimension of multiscale geometries such as those…
We describe an efficient algorithm for computing the matrix vector products that appear in the numerical resolution of boundary integral equations in 2 space dimension. This work is an extension of the so-called Sparse Cardinal Sine…
This paper investigates the stability properties of a nonlinear fractional differential equation with two discrete delays and a delay-dependent coefficient. Such equations arise in various biological and control systems where temporal…
In this paper we introduce and study the algebraic generalization of non commutative convolutional neural networks. We leverage the theory of algebraic signal processing to model convolutional non commutative architectures, and we derive…
We propose an extension of the discretization approaches for multilayer shallow water models, aimed at making them more flexible and efficient for realistic applications to coastal flows. A novel discretization approach is proposed, in…
A framework for exponential time discretization of the multilayer rotating shallow water equations is developed in combination with a mimetic discretization in space. The method is based on a combination of existing exponential time…
The simulation of the time-dependent evolution of the resonant tunneling diode is done by a multiscale algorithm exploiting the existence of resonant states. After revisiting and improving the algorithm developed in [N. Ben Abdallah, O.…
This work provides a rigorous functional-analytic justification for a time-domain Foldy-Lax framework that describes multiple acoustic scattering by a cluster of dispersive resonators (modeling gas-filled bubbles), explicitly incorporating…
In this paper, we extend the structure-preserving interpolatory model reduction framework, originally developed for linear systems, to structured bilinear control systems. Specifically, we give explicit construction formulae for the model…
This work addresses the problem of analyzing multi-channel time series data %. In this paper, we by proposing an unsupervised fusion framework based on %the recently proposed convolutional transform learning. Each channel is processed by a…
The total generalized variation extends the total variation by incorporating higher-order smoothness. Thus, it can also suffer from similar discretization issues related to isotropy. Inspired by the success of novel discretization schemes…
In this work, we leverage the 2-contraction theory, which extends the capabilities of classical contraction theory, to develop a global stability framework. Coupled with powerful geometric tools such as the Poincare index theory, the…
The study of resonances (and well-posedness) for complex systems under time-periodic loading is of broad interest in application. The work of Galdi et al.~(2014) connects asymptotic stability of solutions to an unforced Cauchy problem to…
The $2n$ dimensional manifold with two mutually commutative operators of differentiation is introduced. Nontrivial multidimensional integrable systems connected with arbitrary graded (semisimple) algebras are constructed. The general…
Group convolutional neural networks are a useful tool for utilizing symmetries known to be in a signal; however, they require that the signal is defined on the group itself. Existing approaches either work directly with group signals, or…