Related papers: Discrete Vector-Valued Nonuniform Gabor Frames
A diffusion taking value in probability measures on a graph with a vertex set $V$, $\sum_{i\in V}x_i\delta_i$, is studied. The masses on each vertices satisfy the stochastic differential equation of the form $dx_i=\sum_{j\in…
Recently, the theory concerning piecewise smooth vector fields (PSVFs for short) have been undergoing important improvements. In fact, many results obtained do not have an analogous for smooth vector fields. For example, the chaoticity of…
The widespread use of Deep Neural Networks (DNNs) has recently resulted in their application to challenging scientific visualization tasks. While advanced DNNs demonstrate impressive generalization abilities, understanding factors like…
Modeling sequential data has become more and more important in practice. Some applications are autonomous driving, virtual sensors and weather forecasting. To model such systems so called recurrent models are used. In this article we…
A Python package for the calculation of spectrograms with optimized time and frequency resolution for application in the analysis of numerical simulations on ultrashort pulse propagation is presented. Gabor's uncertainty principle prevents…
This paper proposes robust estimators of the variogram, a statistical tool that is commonly used in geostatistics to capture the spatial dependence structure of data. The new estimators are based on the highly robust minimum covariance…
Dynamic Camera Clusters (DCCs) are multi-camera systems where one or more cameras are mounted on actuated mechanisms such as a gimbal. Existing methods for DCC calibration rely on joint angle measurements to resolve the time-varying…
In this paper, authors focus effort on improving the conventional discrete velocity method (DVM) into a multiscale scheme in finite volume framework for gas flow in all flow regimes. Unlike the typical multiscale kinetic methods unified…
Reasoning about complex visual scenes involves perception of entities and their relations. Scene graphs provide a natural representation for reasoning tasks, by assigning labels to both entities (nodes) and relations (edges). Unfortunately,…
In the field of graph signal processing (GSP), directed graphs present a particular challenge for the "standard approaches" of GSP to due to their asymmetric nature. The presence of negative- or complex-weight directed edges, a graphical…
Flexible slender structures such as rods, ribbons, plates, and shells exhibit extreme nonlinear responses bending, twisting, buckling, wrinkling, and self contact, that defy conventional simulation frameworks. Discrete Differential Geometry…
We develop spectral theorems for nonautonomous linear difference systems, considering different types of $\mu$-dichotomies, both uniform and nonuniform. In the nonuniform case, intriguing scenarios emerge -- that have been employed but…
In this paper a large class of universal windows for Gabor frames (Weyl-Heisenberg frames) is constructed. These windows have the fundamental property that every overcritical rectangular lattice generates a Gabor frame. Likewise, every…
Audio signal processing frequently requires time-frequency representations and in many applications, a non-linear spacing of frequency-bands is preferable. This paper introduces a framework for efficient implementation of invertible signal…
In social settings, individuals interact through webs of relationships. Each individual is a node in a complex network (or graph) of interdependencies and generates data, lots of data. We label the data by its source, or formally stated, we…
Directed acyclic graphs (DAGs) are commonly used to model causal relationships among random variables. In general, learning the DAG structure is both computationally and statistically challenging. Moreover, without additional information,…
The architectures of deep neural networks (DNN) rely heavily on the underlying grid structure of variables, for instance, the lattice of pixels in an image. For general high dimensional data with variables not associated with a grid, the…
Vibrational sum- and difference-frequency generation (SFG and DFG) spectroscopy probes the nonlinear response of interfaces at mid-infrared (MIR) wavelengths while detecting upconverted signals in the visible. Recent work has moved from…
We study an intriguing question in frame theory we call "Weaving Frames" that is partially motivated by preprocessing of Gabor frames. Two frames $\{\varphi_i\}_{i\in I}$ and $\{\psi_i \}_{i\in I}$ for a Hilbert space ${\mathbb H}$ are…
Dynamic graph signal processing provides a principled framework for analyzing time-varying data defined on irregular graph domains. However, existing joint time-vertex transforms such as the joint time-vertex fractional Fourier transform…