Related papers: Applications of FIESTA
Within the framework of the renormalization group approach to the models of critical dynamics, we propose a method for a considerable reduction of the number of integrals needed to calculate the critical exponents. With this method we…
A partial fraction decomposition of the Fermi function resulting in a finite sum over simple poles is proposed. This allows for efficient calculations involving the Fermi function in various contexts of electronic structure or electron…
I formulate a general finite element method (FEM) for self-gravitating stellar systems. I split the configuration space to finite elements, and express the potential and density functions over each element in terms of their nodal values and…
New developments concerning the extension of the Feynman diagram analyzer DIANA are presented. We discuss new graphics facilities, different approaches to automation of momenta distribution and parallel processing facilities. Furthermore…
Motivated by potential applications to partial differential equations, we develop a theory of fine scales of decay rates for operator semigroups. The theory contains, unifies, and extends several notable results in the literature on decay…
We discuss the program EXP used to automate the successive application of asymptotic expansions to Feynman diagrams. We focus on the generation of the relevant subgraphs and the determination of the topologies for the remaining integrals.…
We formulate the statistics of the discrete multicomponent fragmentation event using a methodology borrowed from statistical mechanics. We generate the ensemble of all feasible distributions that can be formed when a single integer…
STEM XEDS spectrum images can be drastically denoised by application of the principal component analysis (PCA). This paper looks inside the PCA workflow step by step on an example of a complex semiconductor structure consisting of a number…
Non-differentiable and constrained optimization play a key role in machine learning, signal and image processing, communications, and beyond. For high-dimensional minimization problems involving large datasets or many unknowns, the…
The Feynman integral is one of the most accurate methods for calculating density operator dynamics in open quantum systems. However, the number of time steps that can realistically be used is always limited, therefore one often obtains an…
New types of relationships between Feynman integrals are presented. It is shown that Feynman integrals satisfy functional equations connecting integrals with different values of scalar invariants and masses. A method is proposed for…
This paper describes the many image decomposition models that allow to separate structures and textures or structures, textures, and noise. These models combined a total variation approach with different adapted functional spaces such as…
Scanning transmission electron microscopy (STEM) is an extremely versatile method for studying materials on the atomic scale. Many STEM experiments are supported or validated with electron scattering simulations. However, using the…
In this manuscript, which is to appear in the proceedings of the conference "MathemAmplitude 2019" in Padova, Italy, we provide an overview of the module intersection method for the the integration-by-parts (IBP) reduction of multi-loop…
The recently developed algorithm FIRE performs the reduction of Feynman integrals to master integrals. It is based on a number of strategies, such as applying the Laporta algorithm, the s-bases algorithm, region-bases and integrating…
In this paper, we introduce a new method for calculating fractional integrals and differentials. The method involves an equation that we have obtained from infinite applied integration by parts. The equation works for special class of…
The decomposition of multiport interferometers is a fundamental tool in quantum optics and computing. This note aims to serve as a concise reference for performing the decomposition according to the most common design approaches, offering a…
An algorithm for irreducible decomposition of representations of finite groups over fields of characteristic zero is described. The algorithm uses the fact that the decomposition induces a partition of the invariant inner product into a…
The program ftint is introduced which numerically evaluates dimensionally regulated integrals as they occur in the perturbative approach to the gradient-flow formalism in quantum field theory. It relies on sector decomposition in order to…
We present a new method for evaluating tensor integrals in the large-scale structure. Decomposing a $\Lambda$CDM-like universe into a finite sum of scaling universes using the FFTLog, we can recast loop integrals for biased tracers in the…