Related papers: An overview of Marchenko methods
A detailed case study of $\gamma$-hadron segregation for a ground based atmospheric Cherenkov telescope is presented. We have evaluated and compared various supervised machine learning methods such as the Random Forest method, Artificial…
In the context of Bayesian inversion for scientific and engineering modeling, Markov chain Monte Carlo sampling strategies are the benchmark due to their flexibility and robustness in dealing with arbitrary posterior probability density…
We present changes of variables that transform new integrable hierarchies found by Szablikowski and B{\l}aszak using the $R$-matrix deformation technique [J. Math. Phys. 47 (2006), paper 043505, nlin.SI/0501044] into known Harry-Dym-type…
Bayesian models have become very popular over the last years in several fields such as signal processing, statistics, and machine learning. Bayesian inference requires the approximation of complicated integrals involving posterior…
State-of-the-art weather forecasts usually rely on ensemble prediction systems, accounting for the different sources of uncertainty. As ensembles are typically uncalibrated, they should get statistically postprocessed. Several multivariate…
The uniqueness question of the multivariate moment problem is studied by different methods: Hilbert space operators, complex function theory, polynomial approximation, disintegration, integral geometry. Most of the known results in the…
A deformation of special relativistic kinematics (possible signal of a theory of quantum gravity at low energies) leads to a modification of the notion of spacetime. At the classical level, this modification is required when one considers a…
In my thesis I study mesoscopic corrections on diffuse transport. I first describe the diffuse transport of light, using the scalar approximation and the radiative transfer approach. Next, I focus on the correlations in transmission, I…
We present a brief overview of the different domain and space decomposition techniques that enter in developing and analyzing solvers for discontinuous Galerkin methods. Emphasis is given to the novel and distinct features that arise when…
Dynamic mode decomposition (DMD) and its variants have emerged as popular methods for the post-processing of fluid dynamics' simulations in order to visualize dominant coherent structures and to reduce the practical degrees of freedom to a…
Inference for spatial generalized linear mixed models (SGLMMs) for high-dimensional non-Gaussian spatial data is computationally intensive. The computational challenge is due to the high-dimensional random effects and because Markov chain…
We present a manifestly covariant formulation of the gradient descent method, ensuring consistency across arbitrary coordinate systems and general curved trainable spaces. The optimization dynamics is defined using a covariant force vector…
This paper presents two new approaches to decomposing and solving large Markov decision problems (MDPs), a partial decoupling method and a complete decoupling method. In these approaches, a large, stochastic decision problem is divided into…
We consider the multi-channel inverse scattering problem in one-dimension in the presence of thresholds and bound states for a potential of finite support. Utilizing the Levin representation, we derive the general Marchenko integral…
The formalism for describing a metric and the corresponding scalar in terms of multipole moments has recently been developed for scalar-tensor theories. We take advantage of this formalism in order to obtain expressions for the observables…
In this paper we propose to evaluate and compare Markov chain Monte Carlo (MCMC) methods to estimate the parameters in a generalized extreme value model. We employed the Bayesian approach using traditional Metropolis-Hastings methods,…
Semi-Markov processes are a generalization of Markov processes since the exponential distribution of time intervals is replaced with an arbitrary distribution. This paper provides an integro-differential form of the Kolmogorov's backward…
An iterative method is derived for image reconstruction. Among other attributes, this method allows constraints unrelated to the radiation measurements to be incorporated into the reconstructed image. A comparison is made with the widely…
We present a novel method to estimate the stability of the Marchenko equation for finite data-sets. We show that we can derive a recursion relationship for the Fourier expansion coefficients of the kernel which is solved by the Marchenko…
We provide a pedagogical introduction to the two main variants of real-space quantum Monte Carlo methods for electronic-structure calculations: variational Monte Carlo (VMC) and diffusion Monte Carlo (DMC). Assuming no prior knowledge on…