Related papers: Vector-Valued (Super) Weaving Frames
Let $a$, $b$ be two fixed non-zero constants. A measurable set $E\subset \mathbb{R}$ is called a Weyl-Heisenberg frame set for $(a, b)$ if the function $g=\chi_{E}$ generates a Weyl-Heisenberg frame for $L^2(\mathbb{R})$ under modulates by…
Given an orthonormal basis $ {\mathcal V}= \{v_j\} _{j\in N}$ in a separable Hilbert space $H$ and a set of unit vectors $ {\mathcal B}=\{w_j\}_{j\in N}$, we consider the sets $ {\mathcal B}_N$ obtained by replacing the vectors $v_1, ...,\,…
Frames in a Hilbert space that are generated by operator orbits are vastly studied because of the applications in dynamic sampling and signal recovery. We demonstrate in this paper a representation theory for frames generated by operator…
In data rich environments we may sometimes deal with time series that are probability density-function valued, such as observations of cross-sectional income distributions over time. To apply the methods of functional time series analysis…
Gaussian processes are machine learning models capable of learning unknown functions in a way that represents uncertainty, thereby facilitating construction of optimal decision-making systems. Motivated by a desire to deploy Gaussian…
This paper considers different facets of the interplay between reproducing kernel Hilbert spaces (RKHS) and stable analysis/synthesis processes: First, we analyze the structure of the reproducing kernel of a RKHS using frames and…
Frames are the foundation of the linear operators used in the decomposition and reconstruction of signals, such as the discrete Fourier transform, Gabor, wavelets, and curvelet transforms. The emergence of sparse representation models has…
Frames have been investigated frequently over the last few decades due to their valuable properties, which are desirable for various applications as well as interesting for theory. Some applications additionally require distributed…
Weighted and controlled frames have been introduced recently to improve the numerical efficiency of iterative algorithms for inverting the frame operator. In this paper we develop systematically these notions, including their mutual…
Due to their flexibility, frames of Hilbert spaces are attractive alternatives to bases in approximation schemes for problems where identifying a basis is not straightforward or even feasible. Computing a best approximation using frames,…
Metric space magnitude, an active field of research in algebraic topology, is a scalar quantity that summarizes the effective number of distinct points that live in a general metric space. The {\em weighting vector} is a closely-related…
In this paper we consider the problem of approximating vector-valued functions over a domain $\Omega$. For this purpose, we use matrix-valued reproducing kernels, which can be related to Reproducing kernel Hilbert spaces of vectorial…
We consider existence and uniqueness of symmetric approximation of frames by normalized tight frames and of symmetric orthogonalization of bases by orthonormal bases in Hilbert spaces H . More precisely, we determine whether a given frame…
We introduce the notion of Hypergraph Weighted Model (HWM) that generically associates a tensor network to a hypergraph and then computes a value by tensor contractions directed by its hyperedges. A series r defined on a hypergraph family…
Innovations like protein diffusion have enabled significant progress in de novo protein design, which is a vital topic in life science. These methods typically depend on protein structure encoders to model residue backbone frames, where…
Motivated by a host of recent applications requiring some amount of redundancy, frames are becoming a standard tool in the signal processing toolbox. In this paper, we study a specific class of frames, known as discrete Fourier transform…
In recent years, complex valued artificial neural networks have gained increasing interest as they allow neural networks to learn richer representations while potentially incorporating less parameters. Especially in the domain of computer…
We investigate the relevance of admissibility criteria based on Plancherel measure for the characterization of tight Weyl-Heisenberg frames with integer oversampling. For this purpose we observe that functions giving rise to such…
The cross sections for several $\gamma \gamma \to VV$ processes exhibit strong enhancements near threshold, where $V$ denotes a vector meson. The pattern of these enhancements is not well understood; for example, $\gamma \gamma \to \rho^0…
The Support Vector Machine (SVM) of Vapnik (1998) has become widely established as one of the leading approaches to pattern recognition and machine learning. It expresses predictions in terms of a linear combination of kernel functions…