Related papers: Reconstruction of rational functions made simple
This paper studies linear reconstruction of partially observed functional data which are recorded on a discrete grid. We propose a novel estimation approach based on approximate factor models with increasing rank taking into account…
We present a detailed description of the recent idea for a direct decomposition of Feynman integrals onto a basis of master integrals by projections, as well as a direct derivation of the differential equations satisfied by the master…
Compression is an important task for many practical applications of light fields. Although previous work has proposed numerous methods for efficient light field compression, the effect of view selection on this task is not well exploited.…
Flux reconstruction provides a framework for solving partial differential equations in which functions are discontinuously approximated within elements. Typically, this is done by using polynomials. Here, the use of radial basis functions…
In functional linear regression, the parameters estimation involves solving a non necessarily well-posed problem and it has points of contact with a range of methodologies, including statistical smoothing, deconvolution and projection on…
We present a method to accelerate the numerical evaluation of spatial integrals of Feynman diagrams when expressed on the real frequency axis. This can be realized through use of a renormalized perturbation expansion with a constant but…
We develop a method to reconstruct, from measured displacements of an underlying elastic substrate, the spatially dependent forces that cells or tissues impart on it. Given newly available high-resolution images of substrate displacements,…
A light field records numerous light rays from a real-world scene. However, capturing a dense light field by existing devices is a time-consuming process. Besides, reconstructing a large amount of light rays equivalent to multiple light…
Recently we have reported a new method of rational approximation of the sinc function obtained by sampling and the Fourier transforms. However, this method requires a trigonometric multiplier that originates from shifting property of the…
We introduce a new method for the reconstruction of a function from linear measurements by means of oblique projections. The space spanned by the measurement vectors may be different from the subspace in which the function is reconstructed.…
In this paper we explore methods to exploit symmetries for ensuring sample efficiency in reinforcement learning (RL), this problem deserves ever increasing attention with the recent advances in the use of deep networks for complex RL tasks…
I present an algorithm for the reconstruction of multivariate rational functions from black-box probes. The arguably most important application in high-energy physics is the calculation of multi-loop and multi-leg amplitudes, where rational…
With Fourier sensing, it is commonly the case that the field-of-view (FOV), the area of space to be imaged, is known prior to reconstruction. To date, reconstruction algorithms have focused on FOVs with simple geometries: a rectangle or a…
Nonnegative Matrix Factorization (NMF) models are widely used to recover linearly mixed nonnegative data. When the data is made of samplings of continuous signals, the factors in NMF can be constrained to be samples of nonnegative rational…
We study phaseless sampling in spline spaces generated by B-splines with arbitrary knots. For real spline spaces, we give a necessary and sufficient condition for a sequence of sampling points to admit a local phase retrieval of any…
A rational function $f(x)$ is rationally summable if there exists a rational function $g(x)$ such that $f(x)=g(x+1)-g(x)$. Detecting whether a given rational function is summable is an important and basic computational subproblem that…
From a sufficiently large point sample lying on a compact Riemannian submanifold of Euclidean space, one can construct a simplicial complex which is homotopy-equivalent to that manifold with high confidence. We describe a corresponding…
We propose a method to reconstruct sparse signals degraded by a nonlinear distortion and acquired at a limited sampling rate. Our method formulates the reconstruction problem as a nonconvex minimization of the sum of a data fitting term and…
This work introduces efficient symbolic algorithms for quantitative reactive synthesis. We consider resource-constrained robotic manipulators that need to interact with a human to achieve a complex task expressed in linear temporal logic.…
A method for automatic computation of parameter derivatives of numerically computed light scattering signals is demonstrated. The finite-element based method is validated in a numerical convergence study, and it is applied to investigate…