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This paper is devoted to a discussion of the Discrete Fourier Transform (DFT) representation of a chaotic finite-duration sequence. This representation has the advantage that is itself a finite-duration sequence corresponding to samples…

In this paper, a new variant to fractional signal processing is proposed known as the Reduced Order Fractional Fourier Transform. Various properties satisfied by its transformation kernel is derived. The properties associated with the…

We present a theory which explains (in the quasistatic limit) the experimentally observed [R. Gordon, {\it et al}, Phys. Rev. Lett. {\bf 92}, 037401 (2004)] squared dependence of the depolarization ratio on the aspect ratio of the holes, as…

This summary of the doctoral thesis provides a comprehensive formulation of the Extended Discrete Fourier Transform (EDFT), derived directly from the Fourier integral and its orthogonality properties. The method is obtained by solving…

The passive electronically scanned array (PESA) is widely used due to its simple structure and low cost. {Its antenna weights have unit modulus and thus, only the weights phases can be controlled. PESA has limited degrees of freedom for…

In a recent experiment [McGehee et al., Phys. Rev. Lett. 111, 145303 (2013)], the expansion of non-interacting ultracold fermions was studied in a random speckle potential, and the observed density profiles were interpreted based on 3D…

This paper demonstrates the advantages of aperiodic arrays in multi-user multiple-input multiple-output systems for future mobile communication applications. We propose a novel aperiodic array synthesis method which account for the…

Many signals on Cartesian product graphs appear in the real world, such as digital images, sensor observation time series, and movie ratings on Netflix. These signals are "multi-dimensional" and have directional characteristics along each…

While deep learning has received a surge of interest in a variety of fields in recent years, major deep learning models barely use complex numbers. However, speech, signal and audio data are naturally complex-valued after Fourier Transform,…

The goal of this note is to prove a compact embedding result for spaces of forward rate curves. As a consequence of this result, we show that any forward rate evolution can be approximated by a sequence of finite dimensional processes in…

We introduce a set of useful expressions of Differential Privacy (DP) notions in terms of the Laplace transform of the privacy loss distribution. Its bare form expression appears in several related works on analyzing DP, either as an…

The Doppler effects for the reflected wave from a moving media are systemically analyzed in this paper. The theoretical formula for the Doppler shift in the left-handed material, which is described by Drude's dispersion model, is presented.…

This article handles in a short manner a few Laplace transform pairs and some extensions to the basic equations are developed. They can be applied to a wide variety of functions in order to find the Laplace transform or its inverse when…

The electron mass shift in a laser field has long remained an elusive concept. We show that the mass shift can exist in pulses but that it is neither unique nor universal: it can be reduced by pulse shaping. We show also that the detection…

Shape and geometric patterns are essential in defining stylistic identity. However, current 3D style transfer methods predominantly focus on transferring colors and textures, often overlooking geometric aspects. In this paper, we introduce…

This paper presents a brief overview of some recent advances in numerical radiative transfer, which may help the molecular astrophysics community to achieve new breakthroughs in the interpretation of spectro-(polarimetric) observations.

Transformers have dominated the field of natural language processing, and recently impacted the computer vision area. In the field of medical image analysis, Transformers have also been successfully applied to full-stack clinical…

The main objective of this paper is to extend Morse-Forman theory to vector-valued functions. This is mostly motivated by the need to develop new tools and methods to compute multiparameter persistence. To generalize the theory, in addition…

Multi-peaked features appear on the integrated pulse profiles of fast radio burst observed below 2.5 GHz and the instantaneous spectrum of many bursts observed between 4 and 8 GHz. The mechanism of pulse or spectrum shaping has attracted…

Discrete transforms, such as the discrete Fourier transform, are widely used in machine learning to improve model performance by extracting meaningful features. However, with numerous transforms available, selecting an appropriate one often…