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We give a quantum algorithm for solving a shifted multiplicative character problem over Z/nZ and finite fields. We show that the algorithm can be interpreted as a matrix factorization or as solving a deconvolution problem and give…
Egyptian hieroglyphs, the ancient Egyptian writing system, are composed entirely of drawings. Translating these glyphs into English poses various challenges, including the fact that a single glyph can have multiple meanings. Deep learning…
Word segmentation plays a pivotal role in improving any Arabic NLP application. Therefore, a lot of research has been spent in improving its accuracy. Off-the-shelf tools, however, are: i) complicated to use and ii) domain/dialect…
The classical Hausdorff-Young inequalities for the Fourier transform acting between appropriate $L_p$ spaces are cornerstones of Fourier analysis. Here we extend it to weighted spaces of Besov or Sobolev type where the weight has the form…
We propose a new method for (global) Hurst exponent determination based on wavelets. Using this method, we analyze synthetic data with predefined Hurst exponents, fracture surfaces and data from economy. The results are compared with those…
Handwritten recognition (HWR) is the ability of a computer to receive and interpret intelligible handwritten input from source such as paper documents, photographs, touch-screens and other devices. In this paper we will using three (3)…
Machine-learning models have demonstrated a great ability to learn complex patterns and make predictions. In high-dimensional nonlinear problems of fluid dynamics, data representation often greatly affects the performance and…
In this work, we propose an algorithm for a filter based on the Fast Fourier Transform (FFT), which, due to its characteristics, allows for an efficient computational implementation, ease of use, and minimizes amplitude variation in the…
By the important applications of Gabor transform in time-frequency analysis and signal analysis, in this paper, we consider the Gabor quaternion Fourier transform (GQFT), and we prove of it a version Benedicks-type uncertainty principle for…
Inspired by recent work on compression with and for young humans, the success of transform-based approaches to information processing, and the rise of powerful language-based AI, we propose \emph{textual transform coding}. It shares some of…
Real life signals are in general non--stationary and non--linear. The development of methods able to extract their hidden features in a fast and reliable way is of high importance in many research fields. In this work we tackle the problem…
In this manuscript, we introduce the quadratic--phase Fourier--Bessel transform and develop its foundational properties, including continuity, the Riemann--Lebesgue lemma, reversibility, and Parseval's identity. We define the associated…
Data augmentation in feature space is effective to increase data diversity. Previous methods assume that different classes have the same covariance in their feature distributions. Thus, feature transform between different classes is…
Many algorithms in numerical analysis are affine equivariant: they are immune to changes of affine coordinates. This is because those algorithms are defined using affine invariant constructions. There is, however, a crucial ingredient…
Transformers have significantly advanced the field of natural language processing, but comprehending their internal mechanisms remains a challenge. In this paper, we introduce a novel geometric perspective that elucidates the inner…
In particle physics, the fundamental forces are subject to symmetries called gauge invariance. It is a redundancy in the mathematical description of any physical system. In this article I will demonstrate that the transformer architecture…
In spite of advances in object recognition technology, Handwritten Bangla Character Recognition (HBCR) remains largely unsolved due to the presence of many ambiguous handwritten characters and excessively cursive Bangla handwritings. Even…
This paper explores the use of a learned classifier for post-OCR text correction. Experiments with the Arabic language show that this approach, which integrates a weighted confusion matrix and a shallow language model, improves the vast…
Both of Wavelet and Fast Fourier Transform are strong signal processing tools in the field of Data Analysis. In this paper fast fourier transform (FFT) and Wavelet Transform are employed to observe some important features of Solar image…
Finding a computationally efficient algorithm for the inverse continuous wavelet transform is a fundamental topic in applications. In this paper, we show the convergence of the inverse wavelet transform.