Stanislav Harizanov

Bulgarian Academy of Sciences | BAS · Institute of Information and Communication Technologies

The development of current sexing methods largely depends on the use of adequate sources of data and adjustable classification techniques. Most sex estimation methods have been based on linear measurements, while the angles have been largely ignored, potentially leading to the loss of valuable information for sex discrimination. This study aims to...

Let us consider the equation 𝒜α u = f , 0 < α < 1, where 𝒜 is a selfadjoint positive definite operator corresponding to a second order elliptic boundary value problem in a bounded domain Ω ∈ Rd, d ∈ {1, 2, 3}. We assume that the non-local fractional diffusion operator 𝒜α is defined through the spectral decomposition of 𝒜. The current advances in nu...

In this paper we introduce a time-dependent SEIR-based model with vaccination. In the suggested model the host population is divided into seven compartments: susceptible, exposed, infectious, recovered, deceased, vaccinated susceptible individuals and individuals with vaccination-acquired immunity. The dynamics of the infection in these groups is m...

The numerical solution of spectral fractional diffusion problems in the form Aαu=f is studied, where A is a selfadjoint elliptic operator in a bounded domain Ω⊂Rd, and α∈(0,1]. The finite difference approximation of the problem leads to the system Aαu=f, where A is a sparse, symmetric and positive definite (SPD) matrix, and Aα is defined by its spe...

Multiphysics or multiscale problems naturally involve coupling at interfaces which are manifolds of lower dimensions. The block-diagonal preconditioning of the related saddle-point systems is among the most efficient approaches for numerically solving large-scale problems in this class. At the operator level, the interface blocks of the preconditio...

In this contribution, analysis of usefulness of selected parameters of a distributed information system, for early detection of anomalies in its operation, is considered. Use of statistical analysis, or machine learning (ML), can result in high computational complexity and requirement to transfer large amount of data from the monitored system’s ele...

Numerical methods for spectral space-fractional elliptic equations are studied. The boundary value problem is defined in a bounded domain of general geometry, Ω⊂Rd, d∈{1,2,3}. Assuming that the finite difference method (FDM) or the finite element method (FEM) is applied for discretization in space, the approximate solution is described by the syste...

The numerical solution of spectral fractional diffusion problems in the form ${\mathcal A}^\alpha u = f$ is studied, where $\mathcal A$ is a selfadjoint elliptic operator in a bounded domain $\Omega\subset {\mathbb R}^d$, and $\alpha \in (0,1]$. The finite difference approximation of the problem leads to the system ${\mathbb A}^\alpha {\mathbf u} =...

Objective The present study aims to propose a dense approach for computation of facial soft tissue thickness (FSTT) data. For this purpose, three-dimensional surface models of the skull and skin were generated from computed tomography (CT) data and all possible skull-to-face distances were calculated for each skull-skin pair. Material and methods...

In this paper we discuss the topic of correct setting for the equation \((-\varDelta )^s u=f\), with \(0<s <1\). The definition of the fractional Laplacian on the whole space \(\mathbb R^n\), \(n=1,2,3\) is understood through the Fourier transform, see, e.g., Karniadakis et al. (arXiv, 2018). The real challenge however represents the case when this...

Since the end of 2019, with the outbreak of the new virus COVID-19, the world changed entirely in many aspects, with the pandemia affecting the economies, healthcare systems and the global socium. As a result from this pandemic, scientists from many countries across the globe united in their efforts to study the virsus's behavior and are attempting...

In this article, we present an experimental performance study of a parallel implementation of two Poissonian image restoration algorithms. Hybrid parallelization, based on MPI and OpenMP standards, is investigated. The implementation is tested for high‐resolution radiographic images, on a supercomputer based on Intel Xeon processors, combined with...

Adasiewicz, RafalGanzha, MariaPaprzycki, MarcinIvanovic, MirianaBadica, CostinLirkov, IvanFidanova, StefkaHarizanov, StanislavRecently, there is a growing trend to improve the quality of life, while reducing energy consumption and emissions of CO2. Here, the use of sensors, controllers, and indoor positioning brings us closer to achieving this goal...

The survey is devoted to numerical solution of the equation $ {\mathcal A}^\alpha u=f $ , 0 < α <1, where $ {\mathcal A} $ is a symmetric positive definite operator corresponding to a second order elliptic boundary value problem in a bounded domain Ω in ℝ d . The fractional power $ {\mathcal A}^\alpha $ is a non-local operator and is defined though...

In this paper we discuss the topic of correct setting for the equation $(-\Delta )^s u=f$, with $0<s <1$. The definition of the fractional Laplacian on the whole space $\mathbb R^n$, $n=1,2,3$ is understood through the Fourier transform, see, e.g., Lischke et.al. (J. Comp. Phys., 2020). The real challenge however represents the case when this equat...

The survey is devoted to numerical solution of the fractional equation $A^\alpha u=f$, $0 < \alpha <1$, where $A$ is a symmetric positive definite operator corresponding to a second order elliptic boundary value problem in a bounded domain $\Omega$ in $\mathbb R^d$. The operator fractional power is a non-local operator and is defined through the sp...

In this paper we explore a time-depended SEIR model, in which the dynamics of the infection in four groups from a selected target group (population), divided according to the infection, are modeled by a system of nonlinear ordinary differential equations. Several basic parameters are involved in the model: coefficients of infection rate, incubation...

Let us consider the non-local problem −Lαu=f, α∈(0,1), L is a second order self-adjoint elliptic operator in Ω⊂Rd with Neumann boundary conditions on ∂Ω. The problem is discretized by finite difference or finite element method, thus obtaining the linear system Aαu=f, A is sparse symmetric and positive semidefinite matrix. The proposed method is bas...

The handbook is intended to be used as a complementary part of the courses on “Numerical Methods for Sparse Linear Systems” and “Convex Analysis and its Applications to Image Processing” that are currently taught within the Master’s program “Computational Mathematics and Mathematical Modelling” in Sofia University “St. Kliment Ohridski”. The presen...

The International Workshop on Numerical Solution of Fractional Differential Equations and Applications (NSFDE&A’20) is organized by the Institute of Information and Communication Technologies, Bulgarian Academy of Sciences, in cooperation with the Bulgarian Section of SIAM and the Center of Excellence in Informatics and Information and Communicatio...

Here we study theoretically and compare experimentally with the methods developed in [1], [2] an efficient method for solving systems of algebraic equations A˜αu˜h=f˜h, 0<α<1, where A˜ is an N×N matrix coming from the discretization of a fractional diffusion operator. More specifically, we focus on matrices obtained from finite difference or finite...

In this paper we consider one particular mathematical problem of this large area of fractional powers of self-adjoined elliptic operators, defined either by Dunford-Taylor-like integrals or by the representation through the spectrum of the elliptic operator. Due to the mathematical modeling of various non-local phenomena using such operators recent...

We consider the numerical method for fractional diffusion problems which is based on an extension to a mixed boundary value problem for a local operator in a higher dimensional space. We observe that, when this problem is discretized using tensor product spaces as is commonly done, the solution can be very well approximated by low-rank tensors; we...

The paper is devoted to the numerical solution of algebraic systems of the type (Aα+qI)u=f, 0<α<1, q>0, u,f∈RN, where A is a symmetric and positive definite matrix. We assume that A is obtained by finite difference approximation of a second order diffusion problem in Ω⊂Rd, d=1,2 so that Aα+qI approximates the related fractional diffusion–reaction o...

The paper is devoted to the numerical solution of algebraic systems of the type \({\mathbb A}^\alpha \mathbf {u}=\mathbf {f}\), 0 < α < 1, where \({\mathbb A}\) is a symmetric and positive definite matrix. We assume that \({\mathbb A}\) is obtained from finite difference or finite element approximations of second order elliptic problems in \(\mathb...

Here we study theoretically and compare experimentally an efficient method for solving systems of algebraic equations, where the matrix comes from the discretization of a fractional diffusion operator. More specifically, we focus on matrices obtained from finite difference or finite element approximation of second order elliptic problems in $\mathb...

We consider the numerical method for fractional diffusion problems which is based on an extension to a mixed boundary value problem for a local operator in a higher dimensional space. We observe that, when this problem is discretized using tensor product spaces as is commonly done, the solution can be very well approximated by low-rank tensors. Thi...

This study is inspired by the rapidly growing interest in the numerical solution of factional diffusion problems, strongly motivated by their advanced applications. Several different techniques are proposed to localize the nonlocal fractional diffusion operator. First three of them are based on transformation of the original problem to local ellipt...

Foramen magnum (FM) has a well-protected position, which makes it of particular interest in forensic research. The aim of the study is to assess the sex differences in size and shape of FM, develop discriminant functions and logistic regression models based on the FM measurements, compare the accuracy results of the measurements obtained through di...

This study is motivated by the recent development in the fractional calculus and its applications. During last few years, several different techniques are proposed to localize the nonlocal fractional diffusion operator. They are based on transformation of the original problem to a local elliptic or pseudoparabolic problem, or to an integral represe...

We discuss, study, and compare experimentally three methods for solving the system of algebraic equations $\mathbb{A}^\alpha \bf{u}=\bf{f}$, $0< \alpha <1$, where $\mathbb{A}$ is a symmetric and positive definite matrix obtained from finite difference or finite element approximations of second order elliptic problems in $\mathbb{R}^d$, $d=1,2,3$. T...

Digital image processing is a vastly emerging and extremely active research field, that combines mathematical and computer science knowledge, and has applications in practically all our daily activities. This paper is devoted to denoising images, corrupted by Poisson noise. Several multi-constrained generalizations of a single-constrained convex op...

2D CT radiographic images are widely used in industrial as well as medical applications to examine different types of objects whenever non-destructive measurements of quality are necessary. To extract meaningful structural information for the scanned object from a low-dose input without increasing the radiation level of the scanner, we propose and...

Background: The aim of the study is to measure the facial soft tissue thicknesses (STTs) in Bulgarians, to evaluate the relation of the STTs to the nutritional status, sex and bilateral asymmetry, and to examine the correlations between the separate STTs as well as between the STTs and body weight, height, and body mass index (BMI). In the present...

This study is motivated by the recent development in the fractional calculus and its applications. During last few years, several different techniques are proposed to localize the nonlocal fractional diffusion operator. They are based on transformation of the original problem to a local elliptic or pseudoparabolic problem, or to an integral represe...

Digital radiography is a powerful technique with a wide variety of applications. Using state of the art mathematical models and algorithms one can extract important information about the structure and the characteristics of the scanned object even from its low quality radiographic images, resulting e.g. from low-dose or short exposure time scanning...

2D CT radiographic images are widely used in industrial as well as medical applications to examine different types of objects whenever contactless measurements of quality are necessary. To extract meaningful structural information for the scanned object from a low-dose input without increasing the radiation level of the scanner, we propose and expe...

Volume constrained image segmentation aims at improving the quality of image reconstruction via incorporating physical information for the underline object of interest into the mathematical modeling of the segmentation problem. In this paper, we develop a general framework for 3D 2-phase image segmentation, based on constrained minimization of a no...

In multiple areas of image processing, such as Computed Tomography, in which data acquisition is based on counting particles that hit a detector surface, Poisson noise occurs. Using variance-stabilizing transformations , the Poisson noise can be approximated by a Gaussian one, for which classical denoising filters can be used. This paper presents a...

In this paper we consider efficient algorithms for solving the algebraic equation ${\mathcal A}^\alpha {\bf u}={\bf f}$, $0< \alpha <1$, where ${\mathcal A}$ is a symmetric and positive definite matrix obtained form finite difference or finite element approximations of second order elliptic problems in ${\mathbb R}^d$, $d=1,2,3$. The method is base...

In this paper we propose an iterative steepest-descent-type algorithm that is observed to converge towards the exact solution of the 0 discrete optimization problem, related to graph-Laplacian based image segmentation. Such an algorithm allows for significant additional improvements on the segmentation quality once the minimizer of the associated r...

Digital radiography is a powerful technique with a wide variety of applications in medicine and Non Destructive Testing. Using state of the art mathematical models and algorithms one can extract important information about the structure and the characteristics of the scanned object even from its low quality radiographic images, resulting e.g. from...

This paper deals with the restoration of images corrupted by a non-invertible or ill-conditioned linear transform and Poisson noise. The paper is experimental and can be seen as a continuation of “as reported by Harizanov et al. (Epigraphical Projection for Solving Least Squares Anscombe Transformed Constrained Optimization Problems 2013)”. The con...

In this paper we perform a 2-class segmentation of a gray-scale 3D image under the restriction that the number of voxels within the phases are a priori fixed. Two parallel algorithms, based on the graph 2-Laplacian model [1] are proposed, implemented, and numerically tested.

We propose a graph theoretical algorithm for image segmentation which preserves both the volume and the connectivity of the solid (non-void) phase of the image. The approach uses three stages. Each step optimizes the approximation error between the image intensity vector and piece-wise constant (indicator) vector characterizing the segmentation of...

Elastic structures with material or geometrical discontinuities often appear among engineering applications. The appropriate usage of space discretization functions is essential for deriving mathematical models with sufficient accuracy. In the current work, a beam with stoppers is considered as an example of elastic structure with discontinuities....

Normal multi-scale transform [4] is a nonlinear multi-scale transform for representing geometric objects that has been recently investigated [1, 7, 10]. The restrictive role of the exact order of polynomial reproduction $P_e$ of the approximating subdivision operator $S$ in the analysis of the $S$ normal multi-scale transform, established in [7, Th...

This papers deals with the restoration of images corrupted by a non-invertible or ill-conditioned linear transform and Poisson noise. Poisson data typically occur in imaging processes where the images are obtained by counting particles, e.g., photons, that hit the image support. By using the Anscombe transform, the Poisson noise can be approximated...

In this paper we introduce a family of globally well-posed and convergent normal multi-scale transforms with high-order detail decay rate for smooth curves, based on adaptivity. For one of the members in the family, we propose a concrete algorithm what the adaptive criteria should be, and provide numerical evidence for the implementation. We compar...

Extending upon the work of Cohen, Dyn, and Matei (Appl. Comput. Harmon. Anal. 15:89–116, 2003) and of Amat and Liandrat (Appl. Comput. Harmon. Anal. 18:198–206, 2005), we present a new general sufficient condition for the Lipschitz stability of nonlinear subdivision schemes and multiscale transforms in the univariate case. It covers the special cas...

Extending upon Daubechies et al. (Constr. Approx. 20:399–463, 2004) and Runborg (Multiscale Methods in Science and Engineering, pp. 205–224, 2005), we provide the theoretical analysis of normal multi-scale transforms for curves with general linear predictor S, and a more flexible choice of normal directions. The main parameters influencing the asym...

Stability of nonlinear subdivision and multiresolution has recently been addressed in [1]. Here we give applications to convexity/monotonicity preserving schemes introduced in [2], [3]. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)