Related papers: On one approach to modeling numeral systems
A modeling formalism is proposed for the description and study of living and life-like systems. It provides an abstract conceptual model framework for real life and evolution of biological organisms. It is proposed, that this model…
We present a unified framework to construct well-posed formulations for large classes of linear operator equations including elliptic, parabolic and hyperbolic partial differential equations. This general approach incorporates known weak…
The advantages of mixed approach with using different kinds of programming techniques for symbolic manipulation are discussed. The main purpose of approach offered is merge the methods of object oriented programming that convenient for…
We propose an approximation of nonlinear renewal equations by means of ordinary differential equations. We consider the integrated state, which is absolutely continuous and satisfies a delay differential equation. By applying the…
Bayesian probabilistic numerical methods are a set of tools providing posterior distributions on the output of numerical methods. The use of these methods is usually motivated by the fact that they can represent our uncertainty due to…
We provide a protection system making use of encapsulation, messages communication, interface functions coming from an object oriented model described in previous works. Each user represents himself to the system by the mean of his "USER"…
Operator learning refers to the application of ideas from machine learning to approximate (typically nonlinear) operators mapping between Banach spaces of functions. Such operators often arise from physical models expressed in terms of…
Numerical stochastic integration is a powerful tool for the investigation of quantum dynamics in interacting many body systems. As with all numerical integration of differential equations, the initial conditions of the system being…
This article is devoted to applications of projection operators to simulate phenomenological properties of the molecular-genetic code system. Oblique projection operators are under consideration, which are connected with matrix…
We propose a new estimation methodology to address the presence of covariate measurement error by exploiting the availability of spatial data. The approach uses neighboring observations as repeated measurements, after suitably controlling…
This work revisits operator learning from a spectral perspective by introducing Polar Linear Algebra, a structured framework based on polar geometry that combines a linear radial component with a periodic angular component. Starting from…
Given a set of matrices, modeled as samples of a matrix-valued function, we suggest a method to approximate the underline function using a product approximation operator. This operator extends known approximation methods by exploiting the…
An observer-based Hamiltonian identification algorithm for quantum systems is proposed. For the 2-level case an exponential convergence result based on averaging arguments and some relevant transformations is provided. The convergence for…
Modelling of photonic devices traditionally involves solving the equations of light-matter interaction and light propagation, and it is restrained by their applicability. Here we demonstrate an alternative modelling methodology by creating…
This paper utilizes the recently proposed cubic observer to estimate the state of a class of nonlinear systems. The cubic observer is proposed as an alternative to linear observers for improved convergence rate and robustness. It is shown…
Neural operators have emerged as transformative tools for learning mappings between infinite-dimensional function spaces, offering useful applications in solving complex partial differential equations (PDEs). This paper presents a rigorous…
Diffusive representations of fractional differential and integral operators can provide a convenient means to construct efficient numerical algorithms for their approximate evaluation. In the current literature, many different variants of…
Examining the authenticity of images has become increasingly important as manipulation tools become more accessible and advanced. Recent work has shown that while CNN-based image manipulation detectors can successfully identify…
Modeling human operator's dynamic plays a very important role in the manual closed-loop control system, and it is an active research area for several decades. Based on the characteristics of human brain and behaviour, a new kind of…
In this article, numerical integration is formulated as evaluation of a matrix function of a matrix that is obtained as a projection of the multiplication operator on a finite-dimensional basis. The idea is to approximate the continuous…