20 papers · ranked by Valyu relevance
Mehdi Ramezani, Morteza Nikaeen, Farnaz Farman, Seyed Mahmoud Ashrafi + 1 more
'Seyed Mahmoud Ashrafi' 'Alireza Bahrampour'] The problem of efficient multiplication of large numbers has been a long-standing challenge in classical computation and has been extensively studied for centuries. It appears that the existing classical algorithms are close to their theoretical limit and offer little room…
Haiye Huo
In this paper, we first introduce a new notion of canonical convolution operator, and show that it satisfies the commutative, associative, and distributive properties, which may be quite useful in signal processing. Moreover, it is proved that the generalized convolution theorem and generalized Young's inequality are…
Feng Ji, Wee Peng Tay, Antonio Ortega
In the 1930s-1940s, L. Pontryagin and other mathematicians (e.g., E. van Kampen and A. Weil) laid down the foundations of the theory of Pontryagin duality [1], [2]. The theory takes the point of view that the Fourier kernel e −i2πξ(·) defines a duality between R and itself. The entire Fourier theory can be built from…
Sarga Varghese, Manab Kundu
The windowed quadratic phase Fourier transform (WQPFT) combines the localization capabilities of windowed transforms with the phase modulation structure of the quadratic phase Fourier transform (QPFT). This paper investigates fundamental properties of the WQPFT, including linearity, shifting, modulation, conjugation…
Alexander Muacevic, John R Adler, Hassan Kesserwani
The mathematization of nature is an age-old concept. The Greeks sought harmony in the celestial spheres. The Arab geometers constructed a spherical geometry of the heavens. Later, Galileo Galilei arithmetized kinematics. As the centuries advanced, polymaths like the Dutchman Christiaan Huygens applied more advanced…
Dominique Gibert, Fernando Lopes, Vincent Courtillot, Jean-Baptiste Boulé
'Jean-Baptiste Boulé'] | 1 | The Fourier transform | 15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |…
Baltabek Kanguzhin, Niyaz Tokmagambetov
We introduce the concepts of the Fourier transform and convolution generated by an arbitrary restriction of the differentiation operator in the space L2(0, b). In contrast to the classical convolution, the introduced convolution explicitly depends on the boundary condition that defines the domain of the operator L. The…
Leon A. Luxemburg, Steven B. Damelin
In this paper we study the scale-space classification of signals via the maximal set of kernels. We use a geometric approach which arises naturally when we consider parameter variations in scale-space. We derive the Fourier transform formulas for quick and efficient computation of zero-crossings and the corresponding…
Authors not listed
Obtaining quantitative information about residence time behavior (i.e., the residence time distribution function) in realistic experimental systems is oftentimes experimentally challenging and numerically complex. The conventional way is to conduct very simple pulse or step tracer experiments or construct elaborate…
Adam W. Marcus, Daniel A. Spielman, Nikhil Srivastava
We study three convolutions of polynomials in the context of free probability theory. We prove that these convolutions can be written as the expected characteristic polynomials of sums and products of unitarily invariant random matrices. The symmetric additive and multiplicative convolutions were introduced by Walsh…
Natalie Baddour
It is well known that the Hankel transform possesses neither a shift-modulation nor a convolution-multiplication rule, both of which have found many uses when used with other integral transforms. In this paper, the generalized shift operator, as defined by Levitan, is applied to the Hankel transform. It is shown that…
Qi Wang, Jianghan Zhu, Can He, Shihang Wang + 4 more
'Terry Tao Ye' 'Andrea Murari'] Convolution plays a significant role in many scientific and technological computations, such as artificial intelligence and signal processing. Convolutional computations consist of many dot-product operations (multiplication-accumulation, or MAC), for which the Winograd algorithm is…
Amelia Carolina Sparavigna
In an article by Thibault et al., 2002, we can find measurements of Raman linewidths in the Q branch of carbon monoxide, for mixtures with Argon at different temperatures. A plot is available for the Q(5) line with a fitted Voigt function. Here we show that a q-Gaussian Tsallis function can be used for fitting this…
Zhimin Dai, Huacan Li, Qunfang Li
The purpose of this paper is to derive some Coifman type inequalities for the fractional convolution operator applied to differential forms. The Lipschitz norm and BMO norm estimates for this integral type operator acting on differential forms are also obtained.
Jonatan Contreras, Martine Ceberio, Vladik Kreinovich, Rafał Rak
One of the most effective image processing techniques is the use of convolutional neural networks that use convolutional layers. In each such layer, the value of the layer’s output signal at each point is a combination of the layer’s input signals corresponding to several neighboring points. To improve the accuracy…
Moussa Djioua
This study presents improvements to the Hodgkin-Huxley (HH) models of ionic conductance and action potential generation. Sodium and potassium conductances are expressed by a single analytical formula describing the impulse response of a convolution of exponential distributions within a short-memory integration space.…
M. L. Kringelbach, G. Deco
Brain dynamics can be described in three different convenient mathematical languages, namely connectome harmonics, turbulence and complex harmonics (CHARM). Here we demonstrate that these theoretical frameworks can be rigorously unified, under the functional calculus, as one self-adjoint operator and its single…
Amelia Carolina Sparavigna
Previous studies (Sparavigna, 2023) have demonstrated the Tsallis q-Gaussian functions suitable for the analysis of Raman spectra. These functions can be used for simulating the different lineshapes of Raman bands. Here we apply q-Gaussians to graphite Raman spectra from RRUFF and Raman Open Database.
Jacob Huth, Timothée Masquelier, Angelo Arleo
We developed Convis, a Python simulation toolbox for large scale neural populations which offers arbitrary receptive fields by 3D convolutions executed on a graphics card. The resulting software proves to be flexible and easily extensible in Python, while building on the PyTorch library [27], which was previously used…
Vasile V. Moca, Adriana Nagy-Dăbâcan, Harald Bârzan, Raul C. Mureşan
Time-frequency analysis is ubiquitous in many fields of science. Due to the Heisenberg-Gabor uncertainty principle, a single measurement cannot estimate precisely the localization of a finite oscillation in both time and frequency. Classical spectral estimators, like the short-time Fourier transform (STFT) or the…