Related papers: Lehmer Transform and its Theoretical Properties
A method for computing the Hankel transform is proposed whereby the letter is reduced to a sum by representing the integrand as a smooth function times a Bessel function. The smooth function is replaced by its wavelet decomposition with a…
Besides natural language processing, transformers exhibit extraordinary performance in solving broader applications, including scientific computing and computer vision. Previous works try to explain this from the expressive power and…
We propose a mathematical theory for the refocusing properties observed in time-reversal experiments, where classical waves propagate through a medium, are recorded in time, then time-reversed and sent back into the medium. The salient…
The signature is an infinite graded sequence of statistics known to characterise a stream of data up to a negligible equivalence class. It is a transform which has previously been treated as a fixed feature transformation, on top of which a…
We propose and analyze estimators for statistical functionals of one or more distributions under nonparametric assumptions. Our estimators are based on the theory of influence functions, which appear in the semiparametric statistics…
Many flexible families of positive random variables exhibit non-closed forms of the density and distribution functions and this feature is considered unappealing for modelling purposes. However, such families are often characterized by a…
Transfer learning, also referred as knowledge transfer, aims at reusing knowledge from a source dataset to a similar target one. While many empirical studies illustrate the benefits of transfer learning, few theoretical results are…
The homogeneous transform has many practical applications outside the realm of mathematics, for instance to represent the proportions of several chemical substances. We aim here to present results about the transformation of measures, which…
Multivariate functional data present theoretical and practical complications which are not found in univariate functional data. One of these is a situation where the component functions of multivariate functional data are positive and are…
Nonlinear metasurfaces that dynamically manipulate the phase of a passing light beam are of interest for a wide range of applications. The controlled operation of such devices requires accurate measurements of the optical transmission phase…
The Transformer structures have been widely used in computer vision and have recently made an impact in the area of medical image registration. However, the use of Transformer in most registration networks is straightforward. These networks…
This work deals with the estimation of parameters of Mittag-Leffler (ML($\alpha, \sigma$)) distribution. We estimate the parameters of ML($\alpha, \sigma$) using empirical Laplace transform method. The simulation study indicates that the…
Shape-valued data are of interest in applied sciences, particularly in medical imaging. In this paper, inspired by a specific medical imaging example, we introduce a hypothesis testing method via the smooth Euler characteristic transform to…
We demonstrate that the Plancherel transform for Type-I groups provides one with a natural, unified perspective for the generalized continuous wavelet transform, on the one hand, and for a class of Wigner functions, on the other. The…
Latent class models are powerful statistical modeling tools widely used in psychological, behavioral, and social sciences. In the modern era of data science, researchers often have access to response data collected from large-scale surveys…
This paper proposes a simple and effective algorithm for incorporating lexical constraints in neural machine translation. Previous work either required re-training existing models with the lexical constraints or incorporating them during…
We propose a new class of generative diffusion models, called functional diffusion. In contrast to previous work, functional diffusion works on samples that are represented by functions with a continuous domain. Functional diffusion can be…
An index transform, involving the square of Whittaker's function is introduced and investigated. The corresponding inversion formula is established. Particular cases cover index transforms of the Lebedev type with products of the modified…
How can I decompose a nonstationary signal? What are the advantages of using the most recent methods available in the literature versus using classical methods like (short time) Fourier transform or wavelet transform? This paper tries to…
Meta-learning, or "learning to learn," is a subfield of machine learning where the goal is to develop models and algorithms that can learn from various tasks and improve their learning process over time. Unlike traditional machine learning…