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Fractional equations have become the model of choice in several applications where heterogeneities at the microstructure result in anomalous diffusive behavior at the macroscale. In this work we introduce a new fractional operator…
An improved QED Parton Shower algorithm to calculate photonic radiative corrections to QED processes at flavour factories is described. We consider the possibility of performing photon generation in order to take into account also the…
Feynman's prescription for a quantum simulator was to find a hamitonian for a system that could serve as a computer. P\'olya and Hilbert conjecture was to demonstrate Riemann's hypothesis through the spectral decomposition of hermitian…
Multi-term floating-point addition appears in vector dot-product computations, matrix multiplications, and other forms of floating-point data aggregation. A critical step in multi-term floating point addition is the alignment of fractions…
Quantum algorithms for diverse problems, including search and optimization problems, require the implementation of a reflection operator over a target state. Commonly, such reflections are approximately implemented using phase estimation.…
The numerical computation of the exponentiation of a real matrix has been intensively studied. The main objective of a good numerical method is to deal with round-off errors and computational cost. The situation is more complicated when…
Tensor network states and parton wave functions are two pivotal methods for studying quantum many-body systems. This work connects these two subjects as we demonstrate that a variety of parton wave functions, such as projected Fermi sea and…
We discuss the algorithm of the cutting rules of calculating the imaginary part of physical amplitude and the optical theorem. We ameliorate the conventional cutting rules to make it suitable for actual calculation and give the right…
An exponential interaction is constructed so that one-dimensional atoms and chains of atoms mimic the general behavior of their three-dimensional counterparts. Relative to the more commonly used soft-Coulomb interaction, the exponential…
The problem of efficiently coloring $3$-colorable graphs with few colors has received much attention on both the algorithmic and inapproximability fronts. We consider exponential time approximations, in which given a parameter $r$, we aim…
To understand quantum optics experiments, we must perform calculations that consider the principal sources of noise, such as losses, spectral impurity and partial distinguishability. In both discrete and continuous variable systems, these…
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…
High-quality simulated data is crucial for particle physics discoveries. Therefore, parton shower algorithms are a major building block of the data synthesis in event generator programs. However, the core algorithms used to generate parton…
In this paper, we consider the composition of two independent processes : one process corresponds to position and the other one to time. Such processes will be called iterated processes. We first propose an algorithm based on the Euler…
We introduce a generalization of the well known graph (vertex) coloring problem, which we call the problem of \emph{component coloring of graphs}. Given a graph, the problem is to color the vertices using minimum number of colors so that…
We investigate the simulation of events with gaps between jets with a veto on additional radiation in the gap in Herwig++. We discover that the currently-used random treatment of radiation in the parton shower is generating some unphysical…
It is shown how the pre-exponential factor of the Feynman propagator for a large class of potentials can be computed using contour integrals. This is of direct relevance in the context of tunnelling processes in quantum theories. The…
Presented here is a technique of propagating uncertainties through the parton shower by means of an alternate event weight. This technique provides a mechanism to systematically quantify the effect of variations of certain components of the…
The not necessarily unitary evolution operator of a finite dimensional quantum system is studied with the help of a projection operators technique. Applying this approach to the Schr\"odinger equation allows the derivation of an alternative…
This paper deals with the complexity of some natural graph problems when parametrized by {measures that are restrictions of} clique-width, such as modular-width and neighborhood diversity. The main contribution of this paper is to introduce…