Related papers: Cosine Series Representation
Spectral representations of the dilation and translation operators on $L^2({\mathbb R})$ are built through appropriate bases. Orthonormal wavelets and multiresolution analysis are then described in terms of rigid operator-valued functions…
This paper studies the combinatoric structure of the set of all representations, up to equivalence, of a finite-dimensional semisimple Lie algebra. This has intrinsic interest as a previously unsolved problem in representation theory, and…
Functional linear regression is one of the fundamental and well-studied methods in functional data analysis. In this work, we investigate the functional linear regression model within the context of reproducing kernel Hilbert space by…
In this work we propose a generalized additive functional regression model for partially observed functional data. Our approach accommodates functional predictors of varying dimensions without requiring imputation of missing observations.…
The aim of this paper is to extend the so called slice analysis to a general case in which the codomain is a real vector space of even dimension, i.e. is of the form $\mathbb{R}^{2n}$. We define a cone $\mathcal{W}_\mathcal{C}^d$ in…
On the one hand the Fermi-Dirac and Bose-Einstein functions have been extended in such a way that they are closely related to the Riemann and other zeta functions. On the other hand the Fourier transform representation of the gamma and…
Applications of functional data with large numbers of predictors have grown precipitously in recent years, driven, in part, by rapid advances in genotyping technologies. Given the large numbers of genetic mutations encountered in genetic…
We consider the decomposition of bounded linear operators on Hilbert spaces in terms of functions forming frames. Similar to the singular-value decomposition, the resulting frame decompositions encode information on the structure and…
Functional linear discriminant analysis (FLDA) is a powerful tool that extends LDA-mediated multiclass classification and dimension reduction to univariate time-series functions. However, in the age of large multivariate and incomplete…
In a previous paper [1] it was discussed the viability of functional analysis using as a basis a couple of generic functions, and hence vectorial decomposition. Here we complete the paradigm exploiting one of the analysis methodologies…
Neural operators extend data-driven models to map between infinite-dimensional functional spaces. These models have successfully solved continuous dynamical systems represented by differential equations, viz weather forecasting, fluid flow,…
In many applications, linear models fit the data poorly. This article studies an appealing alternative, the generalized regression model. This model only assumes that there exists an unknown monotonically increasing link function connecting…
We introduce a method that allows the evaluation of general expressions for the spectral functions of the one-dimensional Hubbard model for all values of the on-site electronic repulsion U. The spectral weights are expressed in terms of…
A fundamental challenge in neuroscience is to decode mental states from brain activity. While functional magnetic resonance imaging (fMRI) offers a non-invasive approach to capture brain-wide neural dynamics with high spatial precision,…
Modern imaging techniques for probing brain function, including functional Magnetic Resonance Imaging, intrinsic and extrinsic contrast optical imaging, and magnetoencephalography, generate large data sets with complex content. In this…
A number of fundamental quantities in statistical signal processing and information theory can be expressed as integral functions of two probability density functions. Such quantities are called density functionals as they map density…
In this brief review, we report some new development in the functional determinant approach (FDA), an exact numerical method, in the studies of a heavy quantum impurity immersed in Fermi gases and manipulated with radio-frequency pulses.…
This is a tutorial introduction to the functional analysis mathematics needed in many physical problems, such as in waves in continuous media. Functional analysis takes us beyond finite matrices, allowing us to work with infinite sets of…
Data analyses are often constructed in an imperative manner, where commands representing actions taken on the data are issued sequentially. The publication of these commands, along with the data, is essential to the reproducibility of the…
The imaginary-time Green's function is a building block of various numerical methods for correlated electron systems. Recently, it was shown that a model-independent compact orthogonal representation of the Green's function can be…