Related papers: On calculating response functions via their Lorent…
We point out, by exhibiting two examples and mentioning a third one, that it is sometimes useful to consider Lorentz transformations as generated from hyperplane or line reflections. One example concerns the construction of boosts linking…
The inversion of nabla Laplace transform, corresponding to a causal sequence, is considered. Two classical methods, i.e., residual calculation method and partial fraction method are developed to perform the inverse nabla Laplace transform.…
Inverse reinforcement learning (IRL) is the problem of inferring the reward function of an agent, given its policy or observed behavior. Analogous to RL, IRL is perceived both as a problem and as a class of methods. By categorically…
The paper considers the problem of performing a task defined on a model parameter that is only observed indirectly through noisy data in an ill-posed inverse problem. A key aspect is to formalize the steps of reconstruction and task as…
An analytical-numeric calculation method of extremely complicated integrals is presented. These integrals appear often in magnet soliton theory. The appropriate analytical continuation and a corresponding integration contour allow to reduce…
We prove that all functions obeying the Kramers-Kronig relations can be approximated as superpositions of Lorentzian functions, to any precision. As a result, the typical text-book analysis of dielectric dispersion response functions in…
The longitudinal structure function of the d(e,e'p) exclusive cross section is calculated with the Lorentz integral transform method. In this approach final state interaction is fully taken into account, but without using a final state wave…
In recent years, Radon type transforms that integrate functions over various sets of ellipses/ellipsoids have been considered in SAR, ultrasound reflection tomography, and radio tomography. In this paper, we consider the transform that…
The Mittag-Leffler function is computed via a quadrature approximation of a contour integral representation. We compare results for parabolic and hyperbolic contours, and give special attention to evaluation on the real line. The main point…
Due to the increasing use of machine learning in practice it becomes more and more important to be able to explain the prediction and behavior of machine learning models. An instance of explanations are counterfactual explanations which…
Inversion of Radon transforms is the mathematical foundation of many modern tomographic imaging modalities. In this paper we study a conical Radon transform, which is important for computed tomography taking Compton scattering into account.…
We consider estimation procedures which are recursive in the sense that each successive estimator is obtained from the previous one by a simple adjustment. We propose a wide class of recursive estimation procedures for the general…
Image reconstruction under multiple light scattering is crucial in a number of applications such as diffraction tomography. The reconstruction problem is often formulated as a nonconvex optimization, where a nonlinear measurement model is…
A program for molecular calculations with B functions is reported and its performance is analyzed. All the one- and two-center integrals, and the three-center nuclear attraction integrals are computed by direct procedures, using previously…
Fourier transforms of Lorentz invariant functions in Minkowski space, with support on both the timelike and the spacelike domains are performed by means of direct integration. The cases of 1+1 and 1+2 dimensions are worked out in detail,…
This work belongs to the framework of inverse problems with linear model. The resolution of this type of problem consists in minimizing (possibly under constraints) a function of discrepancy between the measurements and a physical model of…
A number of applications require the computation of the trace of a matrix that is implicitly available through a function. A common example of a function is the inverse of a large, sparse matrix, which is the focus of this paper. When the…
We consider the inverse problem of reconstructing an effective model for a prototypical diffusion process in strongly heterogeneous media based on coarse measurements. The approach is motivated by quasi-local numerical effective forward…
We introduce a technique for recovering a sufficiently smooth function from its ray transform over a wide class of curves in a general region of Euclidean space. The method is based on a complexification of the underlying vector fields…
Rapidly applying the effects of detector response to physics objects (e.g. electrons, muons, showers of particles) is essential in high energy physics. Currently available tools for the transformation from truth-level physics objects to…