Related papers: Invertibility of Multi-Energy X-ray Transform
Under general multivariate regular variation conditions, the extreme Value-at-Risk of a portfolio can be expressed as an integral of a known kernel with respect to a generally unknown spectral measure supported on the unit simplex. The…
We present a simple, robust and efficient method for varying the parameters in a many-body wave function to optimize the expectation value of the energy. The effectiveness of the method is demonstrated by optimizing the parameters in…
This PhD thesis studies the broken ray transform, a generalization of the geodesic X-ray transform where geodesics are replaced with broken rays that reflect on a part of the boundary. The fundamental question is whether this transform is…
Inferring the means in the multivariate normal model $X \sim N_n(\theta, I)$ with unknown mean vector $\theta=(\theta_1,...,\theta_n)' \in \mathbb{R}^n$ and observed data $X=(X_1,...,X_n)'\in {\mathbb R}^n$ is a challenging task, known as…
The John equation serves as the mathematical foundation of the X-ray transform, describing the intrinsic compatibility conditions that projection data must satisfy. In this paper, within three-dimensional (3D) Euclidean space, an innovative…
Analyzing global data on the EMC effect, which denotes differences in parton distribution functions in nuclei compared to unbound nucleons, reveals tensions. Precise measurements at Jefferson Lab, studying both x and A dependence, show…
We review the main aspects of multiple photoionization processes in atoms exposed to intense, short wavelength radiation. The main focus is the theoretical framework for the description of such processes as well as the conditions under…
We present a combined theoretical and experimental study of X-ray optical wave mixing. This class of nonlinear phenomena combines the strengths of spectroscopic techniques from the optical domain, with the high-resolution capabilities of…
The following electromagnetism (EM) inverse problem is addressed. It consists in estimating local radioelectric properties of materials recovering an object from the global EM scattering measurement, at various incidences and wave…
We introduce a framework that allows to employ (non-negative) measure-valued processes for energy market modeling, in particular for electricity and gas futures. Interpreting the process' spatial structure as time to maturity, we show how…
Quantitative Magnetic Resonance Imaging (qMRI) provides researchers insight into pathological and physiological alterations of living tissue, with the help of which researchers hope to predict (local) therapeutic efficacy early and…
Recent advances have demonstrated the possibility of solving the deconvolution problem without prior knowledge of the noise distribution. In this paper, we study the repeated measurements model, where information is derived from multiple…
The combination of Maxwell and X-ray Bloch equations forms an appropriate framework to describe ultrafast time-resolved X-ray experiments on attosecond time scale in crystalline solids. However, broadband experiments such as X-ray…
In this paper, we present a new explainability formalism designed to shed light on how each input variable of a test set impacts the predictions of machine learning models. Hence, we propose a group explainability formalism for trained…
We prove that any C^{1+} transformation, possibly with a (non-flat) critical or singular region, admits an invariant probability measure absolutely continuous with respect to any expanding measure whose Jacobian satisfies a mild distortion…
This paper studies prediction with multiple candidate models, where the goal is to combine their outputs. This task is especially challenging in heterogeneous settings, where different models may be better suited to different inputs. We…
In this paper, we demonstrate that the modified Emden type equation (MEE), $\ddot{x}+\alpha x\dot{x}+\beta x^3=0$, is integrable either explicitly or by quadrature for any value of $\alpha$ and $\beta$. We also prove that the MEE possesses…
There exist two popular energy-momentum tensors for an electromagnetic wave in a dielectric medium. The Abraham expression is robust to experimental verification but more mathematically demanding, while the Minkowski expression is the…
In this work we study the necessary and sufficient conditions for a positive random variable whose expectation under the Wiener measure is one, to be represented as the Radon-Nikodym derivative of the image of the Wiener measure under an…
Precision tests of the Standard Model and searches for beyond the Standard Model physics often require nuclear structure input. There has been a tremendous progress in the development of nuclear ab initio techniques capable of providing…