Related papers: Scaling up to Multivariate Rational Function Recon…
Any loop QCD amplitude at full colour is constructed from kinematic and gauge-group building blocks. In a unitarity-based on-shell framework, both objects can be reconstructed from their respective counterparts in tree-level amplitudes.…
In this thesis, major developments in the publicly available program SecDec are presented, extending the numerical evaluation of multi-loop multi-scale integrals from Euclidean to physical kinematics. The power of this new feature is shown…
Given pointwise samples of an unknown function belonging to a certain model set, one seeks in Optimal Recovery to recover this function in a way that minimizes the worst-case error of the recovery procedure. While it is often known that…
Methods for computing the integral of the Planck blackbody function over a finite spectral range, the so-called incomplete Planck integral, are necessary to perform multigroup radiative transfer calculations. We present a comparison, in…
We consider Bayesian optimization of an expensive-to-evaluate black-box objective function, where we also have access to cheaper approximations of the objective. In general, such approximations arise in applications such as reinforcement…
This paper proposes a multiobjective multitasking optimization evolutionary algorithm based on decomposition with dual neighborhood. In our proposed algorithm, each subproblem not only maintains a neighborhood based on the Euclidean…
We consider approximation or recovery of functions based on a finite number of function evaluations. This is a well-studied problem in optimal recovery, machine learning, and numerical analysis in general, but many fundamental insights were…
In this paper, applied strictly monotonic increasing scaled maps, a kind of well-conditioned linear barycentric rational interpolations are proposed to approximate functions of singularities at the origin, such as $x^\alpha$ for $\alpha \in…
Previously proposed procedure for improving the effective potential by using renormalization group equation (RGE) is generalized so as to be applicable to any system containing several different mass scales. If one knows L-loop effective…
Multibang regularization and combinatorial integral approximation decompositions are two actively researched techniques for integer optimal control. We consider a class of polyhedral functions that arise particularly as convex lower…
We develop algorithms for multivariate integration and approximation in the weighted half-period cosine space of smooth non-periodic functions. We use specially constructed tent-transformed rank-1 lattice points as cubature nodes for…
In this work we present some results that allow to improve the decoding radius in solving polynomial linear systems with errors in the scenario where errors are additive and randomly distributed over a finite field. The decoding radius…
The paper suggests a method of recovering missing values for sequences, including sequences with a multidimensional index, based on optimal approximation by processes featuring spectrum degeneracy. The problem is considered in the pathwise…
This work shows that for rational multivariate functions, the Kolmogorov Superposition Theorem (KST) involves several single-variable functions, which can be written down by inspection. In other words, no computation is required for…
We design nearly-linear time numerical algorithms for the problem of multivariate multipoint evaluation over the fields of rational, real and complex numbers. We consider both \emph{exact} and \emph{approximate} versions of the algorithm.…
This literature review will discuss the use of deep learning methods for image reconstruction using fMRI data. More specifically, the quality of image reconstruction will be determined by the choice in decoding and reconstruction…
The computation of higher order processes very often involves a large number of diagrams. In addition, it is in general not possible to solve the occurring integrals explicitly and expansions in small quantities have to be performed. This…
The optical resolution of a digital camera is one of its most crucial parameters with broad relevance for consumer electronics, surveillance systems, remote sensing, or medical imaging. However, resolution is physically limited by the…
A new scaling and recovering algorithm is proposed for simultaneously computing the matrix $\varphi$-functions that arise in exponential integrator methods for the numerical solution of certain first-order systems of ordinary differential…
The rational covariance extension problem (RCEP) is an important problem in systems and control occurring in such diverse fields as control, estimation, system identification, and signal and image processing, leading to many fundamental…