Related papers: Multiresolution analysis of electronic structure: …
This survey provides a comprehensive overview of recent advances in multimodal alignment and fusion within the field of machine learning, driven by the increasing availability and diversity of data modalities such as text, images, audio,…
The paper presents a versatile library of analytic and quasi-analytic complex-valued wavelet packets (WPs) which originate from discrete splines of arbitrary orders. The real parts of the quasi-analytic WPs are the regular spline-based…
Multi-layered structures are widely used in the construction of metamaterial devices to realize various cutting-edge waveguide applications. This paper makes several contributions to the mathematical analysis of subwavelength resonances in…
Recent advances in material technology and in micro- and nano-electronics have profoundly changed the design of intracranial electrophysiology electrodes. It is now possible to manufacture electrodes that record cortical activity at a…
In this paper, we introduce a new scheme for the efficient numerical treatment of the electronic Schr\"odinger equation for molecules. It is based on the combination of a many-body expansion, which corresponds to the so-called bond order…
Self-consistent computations of the potential profile in complex semiconductor heterostructures can be successfully applied for comprehensive simulation of the gain and the absorption spectra, for the analysis of the capture, escape,…
In this paper, we develop new fast and efficient algorithms for designing single/multiple unimodular waveforms/codes with good auto- and cross-correlation or weighted correlation properties, which are highly desired in radar and…
The surface of a molecule determines much of its chemical and physical property, and is of great interest and importance. In this Letter, we introduce the concept of molecular multiresolution surfaces as a new paradigm of multiscale…
In the present paper, the models of structural analysis and evaluation of efficiency indicators (reliability, fault tolerance, viability, and flexibility) of a multi core processor with variable structure, equipped with multi functional…
The simultaneous treatment of static and dynamical correlations in strongly-correlated electron systems is a critical challenge. In particular, finding a universal scheme for identifying a single-particle orbital basis that minimizes the…
We present a novel approach, which is based on multiple-valued logic (MVL), to the verification and analysis of digital hardware designs, which extends the common ternary or quaternary approaches for simulations. The simulations which are…
We give an overview of recent advances in analysis of equations of electrodynamics with the aid of biquaternionic technique. We discuss both models with constant and variable coefficients, integral representations of solutions, a numerical…
Wavelet families arise by scaling and translations of a prototype function, called the {\em {mother wavelet}}. The construction of wavelet bases for cardinal spline spaces is generally carried out within the multi-resolution analysis…
While there have been many developments in computational probes of both strongly-correlated molecular systems and machine-learning accelerated molecular dynamics, there remains a significant gap in capabilities in simulating accurate…
The nuclear many-body problem for medium-mass systems is commonly addressed using wave-function expansion methods that build upon a second-quantized representation of many-body operators with respect to a chosen computational basis. While…
In this paper, we present a finite element method (FEM) framework enhanced by an operator-adapted wavelet decomposition algorithm designed for the efficient analysis of multiscale electromagnetic problems. Usual adaptive FEM approaches,…
Free electrons provide a powerful tool to probe material properties at atomic-scale spatial resolution. Recent advances in ultrafast electron microscopy enable the manipulation of free electron wavefunctions using laser pulses. It would be…
This paper analyzes the structure of the set of nodal solutions of a class of one-dimensional superlinear indefinite boundary values problems with an indefinite weight functions in front of the spectral parameter. Quite astonishingly, the…
The goal of this paper is to sketch a broader outline of the mathematical structures present in the Nonlinear Maxwell Theory in continuation of work presented in my previous articles. In particular, I display new types of both dynamic and…
We discuss the possibility of introducing a multi-resolution in a Hilbert space which is not necessarily a space of functions. We investigate which of the classical properties can be translated to this more general framework and the way in…