Related papers: Geophysical tomography in engineering geology: an …
Probability representation entropy (tomographic entropy) of arbitrary quantum state is introduced. Using the properties of spin tomogram to be standard probability distribution function the tomographic entropy notion is discussed. Relation…
We introduce diffusion geometry as a new framework for geometric and topological data analysis. Diffusion geometry uses the Bakry-Emery $\Gamma$-calculus of Markov diffusion operators to define objects from Riemannian geometry on a wide…
We present an algorithm for focusing inversion of electrical resistivity tomography (ERT) data. ERT is a typical example of ill-posed problem. Regularization is the most common way to face this kind of problems; it basically consists in…
Partial symplectic conditional and joint probability representations of quantum mechanics are considered. The correspondence rules for most interesting physical operators are found and the expressions of the dual symbols of operators are…
We provide a geometric interpretation to Bayesian inference that allows us to introduce a natural measure of the level of agreement between priors, likelihoods, and posteriors. The starting point for the construction of our geometry is the…
We develop a computational framework that leverages the features of sophisticated software tools and numerics to tackle some of the pressing issues in the realm of earth sciences. The algorithms to handle the physics of multiphase flow,…
A tomographic method is described to quantify the three-dimensional power-spectrum of the ionospheric electron-density fluctuations based on radio-interferometric observations by a two-dimensional planar array. The method is valid to…
Atomic electron tomography (AET) enables the determination of 3D atomic structures by acquiring a sequence of 2D tomographic projection measurements of a particle and then computationally solving for its underlying 3D representation.…
Some inequalities for probability vector are discussed. The probability representation of quantum mechanics where the states are mapped onto probability vectors (either finite or infinite dimensional) called the state tomograms is used.…
Understanding the orientation of geological structures is crucial for analyzing the complexity of the Earths' subsurface. For instance, information about geological structure orientation can be incorporated into local anisotropic…
The proton radiography diagnostic is widely used in laser-plasma experiments to make magnetic field measurements. Recent developments in analysis have enabled quantitative reconstruction of path-integrated magnetic field values, but making…
The study of homological invariants such as Tor, Ext and local cohomology modules constitutes an important direction in commutative algebra. Explicit descriptions of these invariants are notoriously difficult to find and often involve…
We elaborate on the notion of generalized tomograms, both in the classical and quantum domains. We construct a scheme of star-products of thick tomographic symbols and obtain in explicit form the kernels of classical and quantum generalized…
Seismic inversion is essential for geophysical exploration and geological assessment, but it is inherently subject to significant uncertainty. This uncertainty stems primarily from the limited information provided by observed seismic data,…
A possibility of describing two-level atom states in terms of positive probability distributions (analog to the symplectic tomography scheme) is considered. As a result the basis of the irreducible representation of a rotation group can be…
The symplectic tomograms of 2D Hermite--Gauss beams are found and expressed in terms of the Hermite polynomials squared. It is shown that measurements of optical-field intensities may be used to determine the tomograms of…
Using a new Bayesian method for solving inverse quantum problems, potentials of quantum systems are reconstructed from coordinate measurements in non-stationary states. The approach is based on two basic inputs: 1. a likelihood model,…
We develop a computational framework to quantify uncertainty in shear elastography imaging of anomalies in tissues. We adopt a Bayesian inference formulation. Given the observed data, a forward model and their uncertainties, we find the…
Maximum-likelihood methods are applied to the problem of absorption tomography. The reconstruction is done with the help of an iterative algorithm. We show how the statistics of the illuminating beam can be incorporated into the…
Topological data analysis refers to approaches for systematically and reliably computing abstract ``shapes'' of complex data sets. There are various applications of topological data analysis in life and data sciences, with growing interest…