Related papers: A Constructive Approach for Building Wavelet Bases…
We consider the efficient construction of polynomial lattice rules, which are special cases of so-called quasi-Monte Carlo (QMC) rules. These are of particular interest for the approximate computation of multivariate integrals where the…
We study the possibility for the implementation of linear wave structures on discrete grids with various dimensions. The systems of the first order differential equations for the set of virtual functions, describing the wave propagation,…
Medical image segmentation aims to identify anatomical structures at the voxel-level. Segmentation accuracy relies on distinguishing voxel differences. Compared to advancements achieved in studies of the inter-class variance, the…
The solution of a partial differential equation can be obtained by computing the inverse operator map between the input and the solution space. Towards this end, we introduce a \textit{multiwavelet-based neural operator learning scheme}…
In this manuscript, we extend the variational multiscale enrichment (VME) method to model the dynamic response of hyperelastic materials undergoing large deformations. This approach enables the simulation of wave propagation under…
The analysis of multivariate time series data is challenging due to the various frequencies of signal changes that can occur over both short and long terms. Furthermore, standard deep learning models are often unsuitable for such datasets,…
Electromagnetic wavelets are constructed using scalar wavelets as superpotentials, together with an appropriate polarization. It is shown that oblate spheroidal antennas, which are ideal for their production and reception, can be made by…
We study mutually unbiased bases (MUBs) in which all the bases are unextendible maximally entangled ones. We first present a necessary and sufficient condition of constructing a pair of MUBs in $C^2 \otimes C^4$. Based on this condition, an…
We reformulate the projected imaginary-time evolution of Full Configuration Interaction Quantum Monte Carlo in terms of a Lagrangian minimization. This naturally leads to the admission of polynomial complex wavefunction parameterizations,…
Integrating visual and linguistic information into a single multimodal representation is an unsolved problem with wide-reaching applications to both natural language processing and computer vision. In this paper, we present a simple method…
Even though convolutional neural networks have become the method of choice in many fields of computer vision, they still lack interpretability and are usually designed manually in a cumbersome trial-and-error process. This paper aims at…
Resolvents of set-valued operators play a central role in various branches of mathematics and in particular in the design and the analysis of splitting algorithms for solving monotone inclusions. We propose a generalization of this notion,…
The first part of the present article consists in a survey about the dynamical constructive method designed using dynamical theories and dynamical algebraic structures. Dynamical methods uncovers a hidden computational content for numerous…
Multivariate (MTV) porous materials exhibit unique structural complexities based on diverse spatial arrangements of multiple building block combinations. These materials possess potential synergistic functionalities that exceed the sum of…
In the present paper we introduce a Virtual Element Method (VEM) for the approximate solution of general linear second order elliptic problems in mixed form, allowing for variable coefficients. We derive a theoretical convergence analysis…
High-order wave-making theories are becoming available but are limited to certain ranges of waves and wavemaker types in their applicability. Alternatively, machine learning can be considered to find nonlinear functional relationships.…
Wavelet systems on the generalized Vilenkin groups are considered. An algorithmic method for the construction of orthogonal wavelet bases is presented. These bases consist of compactly supported test functions (i.e. functions whose Fourier…
The ability to design passive structures that perform different operations on different electromagnetic fields is key to many technologies, from beam-steering to optical computing. While many techniques have been developed to optimise…
In this paper we design and use two Deep Learning models to generate the ground and excited wavefunctions of different Hamiltonians suitable for the study the vibrations of molecular systems. The generated neural networks are trained with…
This paper addresses robust waveform design for multiple-input-multiple-output (MIMO) radar detection. A probabilistic model is proposed to describe the target uncertainty. Considering that waveform design based on maximizing the…