Related papers: Creative Telescoping on Multiple Sums
The size and complexity of modern astronomical surveys has grown to the point where, in many cases, traditional human scheduling of observations are tedious at best and impractical at worst. Automated scheduling algorithms present an…
Astronomical instruments make intensity measurements; any precise astronomical experiment ought to involve modeling those measurements. People make catalogues, but because a catalogue requires hard decisions about calibration and detection,…
Reducing the conditions under which a given set satisfies the stipulations of the subset sum proposition to a set of linear relationships, the question of whether a set satisfies subset sum may be answered in a polynomial number of steps by…
Finding valid light paths that involve specular vertices in Monte Carlo rendering requires solving many non-linear, transcendental equations in high-dimensional space. Existing approaches heavily rely on Newton iterations in path space,…
A method is proposed to handle the sign problem in the simulation of systems having indefinite or complex-valued measures. In general, this new approach, which is based on renormalisation blocking, is shown to yield statistical errors…
The present paper deals with the discrete inverse problem of reconstructing binary matrices from their row and column sums under additional constraints on the number and pattern of entries in specified minors. While the classical…
In seeking out an algorithm to test out the capability of the IBM Quantum Experience quantum computer, we were given a review paper covering various algorithms for solving the subset-sum problem, including both classical and quantum…
Inverse rendering methods have achieved remarkable performance in reconstructing high-fidelity 3D objects with disentangled geometries, materials, and environmental light. However, they still face huge challenges in reflective surface…
In the convergence analysis of numerical methods for solving partial differential equations (such as finite element methods) one arrives at certain generalized eigenvalue problems, whose maximal eigenvalues need to be estimated as…
In this survey article we present difference field algorithms for symbolic summation. Special emphasize is put on new aspects in how the summation problems are rephrased in terms of difference fields, how the problems are solved there, and…
Monte Carlo rendering algorithms are widely used to produce photorealistic computer graphics images. However, these algorithms need to sample a substantial amount of rays per pixel to enable proper global illumination and thus require an…
The Abramov-Petkovsek reduction computes an additive decomposition of a hypergeometric term, which extends the functionality of the Gosper algorithm for indefinite hypergeometric summation. We modify the Abramov-Petkovsek reduction so as to…
The EM algorithm is a powerful tool for maximum likelihood estimation with missing data. In practice, the calculations required for the EM algorithm are often intractable. We review numerous methods to circumvent this intractability, all of…
In this paper, we consider lasso problems with zero-sum constraint, commonly required for the analysis of compositional data in high-dimensional spaces. A novel algorithm is proposed to solve these problems, combining a tailored active-set…
In Single Photon Emission Computed Tomography (SPECT), 3D images usually reconstructed by performing a set of bidimensional (2D) analytical or iterative reconstructions can also be reconstructed using an iterative reconstruction algorithm…
Machine-learning excels in many areas with well-defined goals. However, a clear goal is usually not available in art forms, such as photography. The success of a photograph is measured by its aesthetic value, a very subjective concept. This…
This paper sets up a methodology for approximately solving optimal investment problems using duality methods combined with Monte Carlo simulations. In particular, we show how to tackle high dimensional problems in incomplete markets, where…
In classical computation, a problem can be solved in multiple steps where calculated results of each step can be copied and used repeatedly. While in quantum computation, it is difficult to realize a similar multi-step computation process…
The subset sum problem is a typical NP-complete problem that is hard to solve efficiently in time due to the intrinsic superpolynomial-scaling property. Increasing the problem size results in a vast amount of time consuming in…
We discuss possible sources of systematic errors in the computation of critical exponents by renormalization-group methods, extrapolations from exact enumerations and Monte Carlo simulations. A careful Monte Carlo determination of the…