Related papers: Illuminating Fourier Series with Audacity
In this work, we study some novel applications of conformal inference techniques to the problem of providing machine learning procedures with more transparent, accurate, and practical performance guarantees. We provide a natural extension…
Implicit neural representations (INRs) have emerged as powerful tools for encoding signals, yet dominant MLP-based designs often suffer from slow convergence, overfitting to noise, and poor extrapolation. We introduce FUTON (Fourier Tensor…
This article explains and illustrates the design of a laboratory experience for blind students to measure the inertia of simple objects, in this case, that of a disc around its axis of symmetry. Our adaptation consisted in modifying the…
In this paper, we introduce the fractional Fourier series on the fractional torus and study some basic facts of fractional Fourier series, such as fractional convolution and fractional approximation. Meanwhile, fractional Fourier inversion…
These notes provide a quick introduction to the Coq system and show how it can be used to define logical concepts and functions and reason about them. It is designed as a tutorial, so that readers can quickly start their own experiments,…
In this paper, we first establish an evaluation formula to calculate Wiener integrals of functionals on Wiener space. We then apply our evaluation formula to carry out very easily calculating for the analytic Fourier-Feynman transform of…
We provide an algorithm for computing semi-Fourier sequences for expressions constructed from arithmetic operations, exponentiations and integrations. The semi-Fourier sequence is a relaxed version of Fourier sequence for polynomials…
We present an optimization framework for learning a fair classifier in the presence of noisy perturbations in the protected attributes. Compared to prior work, our framework can be employed with a very general class of linear and…
Explainable AI (XAI) for Speech Emotion Recognition (SER) is critical for building transparent, trustworthy models. Current saliency-based methods, adapted from vision, highlight spectrogram regions but fail to show whether these regions…
Quantum illumination uses quantum entanglement as a resource to enable higher-resolution detection of low-reflectivity targets than is possible with classical techniques. This revolutionary technology could transform modern radar. However,…
We demonstrate a method for general linear optical networks that allows one to factorize any SU($n$) matrix in terms of two SU($n-1)$ blocks coupled by an SU(2) entangling beam splitter. The process can be recursively continued in an…
The Ambartsumian equation is arising in astronomy and used in the theory of surface brightness in a milky way. In this paper, we introduce system of fractional order Ambartsumian equations and use the Picard iterative method to obtain the…
In this paper we show that the discrete Fourier transform can be performed by scattering a coherent particle or laser beam off a two-dimensional potential that has the shape of rings or peaks. After encoding the initial vector into the…
A novel original procedure of encryption/decryption based on the polyadic algebraic structures and on signal processing methods is proposed. First, we use signals with integer amplitudes to send information. Then we use polyadic techniques…
This paper introduces a novel approach to bolster algorithmic fairness in scenarios where sensitive information is only partially known. In particular, we propose to leverage instances with uncertain identity with regards to the sensitive…
Approaches to automated grouping in singular spectrum analysis are considered. A new method for the identification of periodic components is proposed. The possibilities of extensions to multivariate time series and images are discussed.
A scheme to a complex-valued acquisition of the Fourier transform imaging was proposed. The main idea is to project the real and the imaginary parts of a diffraction field to intensity distributions respectively. The whole procedure was…
Random illumination is proposed to enforce absolute uniqueness and resolve all types of ambiguity, trivial or nontrivial, from phase retrieval. Almost sure irreducibility is proved for any complex-valued object of a full rank support. While…
The convergence between astronomy and data sonification represents a significant advancement in the approach and analysis of cosmic information. By surpassing the visual exclusivity in data analysis in astronomy, innovative projects have…
We consider how some methods of uniform and nonuniform interpolation by translates of radial basis functions -- specifically the so-called general multiquadrics -- perform in the presence of certain types of noise. These techniques provide…