Related papers: A Calculus for Modular Loop Acceleration

Efficient parallelization of algorithms on general-purpose GPUs is essential in many areas today. However, it is a non-trivial task for software engineers to utilize GPUs to improve the performance of high-level programs in general.…

Constrained Horn Clauses (CHCs) are often used in automated program verification. Thus, techniques for (dis-)proving satisfiability of CHCs are a very active field of research. On the other hand, acceleration techniques for computing…

One-loop functions with loop masses larger than external masses and momenta can always be expanded in terms of external masses and momenta. The precision requested for observables determines the number of the expansion terms retained in the…

A term calculus for the proofs in multiplicative-additive linear logic is introduced and motivated as a programming language for channel based concurrency. The term calculus is proved complete for a semantics in linearly distributive…

These course notes are about computing modular forms and some of their arithmetic properties. Their aim is to explain and prove the modular symbols algorithm in as elementary and as explicit terms as possible, and to enable the devoted…

Iterative methods are ubiquitous in large-scale scientific computing applications, and a number of approaches based on meta-learning have been recently proposed to accelerate them. However, a systematic study of these approaches and how…

We present a new approach to termination analysis of numerical computations in logic programs. Traditional approaches fail to analyse them due to non well-foundedness of the integers. We present a technique that allows overcoming these…

We present a simple and efficient acceleration technique for an arbitrary method for computing the Euclidean projection of a point onto a convex polytope, defined as the convex hull of a finite number of points, in the case when the number…

Accurately and efficiently estimating system performance under uncertainty is paramount in power system planning and operation. Monte Carlo simulation is often used for this purpose, but convergence may be slow, especially when detailed…

Incremental computation aims to compute more efficiently on changed input by reusing previously computed results. We give a high-level overview of works on incremental computation, and highlight the essence underlying all of them, which we…

A fully numerical method to calculate loop integrals, a numerical contour-integration method, is proposed. Loop integrals can be interpreted as a contour integral in a complex plane for an integrand with multi-poles in the plane. Stable and…

Two general methods for establishing the logarithmic behavior of recursively defined sequences of real numbers are presented. One is the interlacing method, and the other one is based on calculus. Both methods are used to prove logarithmic…

We report on the development of tools to calculate loop integrals and amplitudes beyond one loop. In particular, we review new features of the program SecDec which can be used for the numerical evaluation of parametric integrals like…

I present a few new and recent ideas of the multiloop calculations.

Future applications demand more performance, but technology advances have been faltering. A promising approach to further improve computer system performance under energy constraints is to employ hardware accelerators. Already today, mobile…

We propose a modular method for proving termination of general logic programs (i.e., logic programs with negation). It is based on the notion of acceptable programs, but it allows us to prove termination in a truly modular way. We consider…

Computing modular coincidences can show whether a given substitution system, which is supported on a point lattice in R^d, consists of model sets or not. We prove the computatibility of this problem and determine an upper bound for the…

In a previous paper a new approach has been introduced for computing, recursively and numerically, one-loop tensor integrals. Here we describe a few modifications of the original method that allow a more efficient numerical implementation…

In studying the complexity of iterative processes it is usually assumed that the arithmetic operations of addition, multiplication, and division can be performed in certain constant times. This assumption is invalid if the precision…

Acceleration in symbolic verification consists in computing the exact effect of some control-flow loops in order to speed up the iterative fix-point computation of reachable states. Even if no termination guarantee is provided in theory,…