Related papers: Nonhomogeneous Wavelet Systems in High Dimensions
By decomposing the image formation process into a sequential application of denoising autoencoders, diffusion models (DMs) achieve state-of-the-art synthesis results on image data and beyond. Additionally, their formulation allows for a…
Volumetric maps are widely used in robotics due to their desirable properties in applications such as path planning, exploration, and manipulation. Constant advances in mapping technologies are needed to keep up with the improvements in…
Disorder is more the rule than the exception in natural and synthetic materials. Nonetheless, wave propagation within inhomogeneously disordered materials has received scant attention. We combine microwave experiments and theory to find the…
Networks of interconnected agents are essential to study complex networked systems' state evolution, stability, resilience, and control. Nevertheless, the high dimensionality and nonlinear dynamics are vital factors preventing us from…
We introduce multi-frequency vector diffusion maps (MFVDM), a new framework for organizing and analyzing high dimensional datasets. The new method is a mathematical and algorithmic generalization of vector diffusion maps (VDM) and other…
In this article, we follow closely the approach in Hernandez and Weiss's seminal text in describing the construction of an orthonormal wavelet from a multi-resolution analysis. We assume the reader has a modest background in analysis and…
We show the relevance of a multifractal-type analysis for pointwise convergence and divergence properties of wavelet series: Depending on the sequence space which the wavelet coefficients sequence belongs to, we obtain deterministic upper…
Moire engineering in two-dimensional transition metal dichalcogenides enables access to correlated quantum phenomena. Realizing such effects demands simultaneous control over twist angle and material composition to modulate phonons,…
In this paper, we introduce a new (constructive) characterization of tight wavelet frames on non-flat domains in both continuum setting, i.e. on manifolds, and discrete setting, i.e. on graphs; discuss how fast tight wavelet frame…
Topological mechanical metamaterials have enabled new ways to control stress and deformation propagation. Exemplified by Maxwell lattices, they have been studied extensively using a linearized formalism. Herein, we study a two-dimensional…
We consider the design of an orthogonal symmetric/antisymmetric multiwavelet from its matrix product filter by matrix spectral factorization (MSF). As a test problem, we construct a simple matrix product filter with desirable properties,…
In analogy with steerable wavelets, we present a general construction of adaptable tight wavelet frames, with an emphasis on scaling operations. In particular, the derived wavelets can be "dilated" by a procedure comparable to the operation…
The danger of confusing long-range dependence with non-stationarity has been pointed out by many authors. Finding an answer to this difficult question is of importance to model time-series showing trend-like behavior, such as river run-off…
Variational Autoencoders (VAE) are probabilistic deep generative models underpinned by elegant theory, stable training processes, and meaningful manifold representations. However, they produce blurry images due to a lack of explicit…
For an arbitrary matrix dilation, any integer n and any integer/semi-integer c, we describe all masks that are symmetric with respect to the point c and have sum rule of order n. For each such mask, we give explicit formulas for wavelet…
Dimensionless numbers and scaling laws provide elegant insights into the characteristic properties of physical systems. Classical dimensional analysis and similitude theory fail to identify a set of unique dimensionless numbers for a…
Many network datasets exhibit connectivity with variance by resolution and large-scale organization that coexists with localized departures. When vertices have observed ordering or embedding, such as geography in spatial and village…
The spectra of random feature matrices provide essential information on the conditioning of the linear system used in random feature regression problems and are thus connected to the consistency and generalization of random feature models.…
Honeycomb-like microstructures have been shown to exhibit local elastic buckling under compression, with three possible geometric buckling modes, or pattern transformations. The individual pattern transformations, and consequently also…
An inspiration at the origin of wavelet analysis (when Grossmann, Morlet, Meyer and collaborators were interacting and exploring versions of multiscale representations) was provided by the analysis of holomorphic signals, for which the…