Related papers: Analysis and X-ray tomography
These notes were compiled as lecture notes for a course developed and taught at the University of the Southern California. They should be accessible to a typical engineering graduate student with a strong background in Applied Mathematics.…
The application of machine learning to radiological images is an increasingly active research area that is expected to grow in the next five to ten years. Recent advances in machine learning have the potential to recognize and classify…
These are general notes on tensor calculus which can be used as a reference for an introductory course on tensor algebra and calculus. A basic knowledge of calculus and linear algebra with some commonly used mathematical terminology is…
The aim of this text is to provide a linguistically accessible, but comprehensive introduction into a variety of topics in dynamical systems and its applications. Whilst preliminary knowledge of dynamical systems is useful, it is not…
The aim of this paper is to provide a comprehensive review of statistical challenges in neuroimaging data analysis from neuroimaging techniques to large-scale neuroimaging studies to statistical learning methods. We briefly review eight…
The purpose of this text is to set up a few basic notions concerning quantum graphs, to indicate some areas addressed in the quantum graph research, and to provide some pointers to the literature. The pointers in many cases are secondary,…
The x-ray process is modelled using integer compositions as a two dimensional analogue of the object being x-rayed, where the examining rays are modelled by diagonal lines with equation $x-y=n$ for non negative integers $n$. This process is…
These informal notes discuss a few basic notions and examples, with emphasis on constructions that may be relevant for analysis on metric spaces.
Astronomy is by nature a visual science. The high quality imagery produced by the world's observatories can be a key to effectively engaging with the public and helping to inspire the next generation of scientists. Creating compelling…
X-ray spectroscopy is one of the most powerful tools to access structure and properties of matter in different states of aggregation as it allows to trace atomic and molecular energy levels in course of various physical and chemical…
X-ray imaging is the most popular medical imaging technology. While x-ray radiography is rather cost-effective, tissue structures are superimposed along the x-ray paths. On the other hand, computed tomography (CT) reconstructs internal…
These lecture notes, suitable for a two-semester introductory course or self-study, offer an elementary and self-contained exposition of the basic tools and concepts that are encountered in practical computations in perturbative thermal…
The role of X-ray observations for cosmological studies and conclusions is briefly explored. X-rays currently yield cosmologically interesting results on the abundances, evolution and gas content of clusters of galaxies, on the clustering…
This is a series of lecture notes explaining topos theory and its application in physics.
Based on a simple example, it is explained how the homological analysis may be applied for modeling of the electric circuits. The homological branch, mesh and nodal analyses are presented. Geometrical interpretations are given.
This article discusses the opportunities, applications and future directions of large-scale pre-trained models, i.e., foundation models, for analyzing medical images. Medical foundation models have immense potential in solving a wide range…
The aim of these notes is to demonstrate the potential for ideas in machine learning to impact on the fields of inverse problems and data assimilation. The perspective is one that is primarily aimed at researchers from inverse problems…
A key goal of radio and $\gamma-$ray observations of active galactic nuclei is to characterize their time variability in order to elucidate physical processes responsible for the radiation. I describe algorithms for relevant time series…
R is a language and environment for statistical computing and graphics, which provides a wide variety of statistical tools (modeling, statistical testing, time series analysis, classification problems, machine learning, ...), together with…
Introductory statistical inference texts and courses treat the point estimation, hypothesis testing, and interval estimation problems separately, with primary emphasis on large-sample approximations. Here I present an alternative approach…