Related papers: Canonical differential equations and intersection …
Applications of decision diagrams in quantum circuit analysis have been an active research area. Our work introduces FeynmanDD, a new method utilizing standard and multi-terminal decision diagrams for quantum circuit simulation and…
Recently, fractional differential equations have been investigated via the famous variational iteration method. However, all the previous works avoid the term of fractional derivative and handle them as a restricted variation. In order to…
In this paper, we study systematically scalar one-loop two-, three-, and four-point Feynman integrals with complex internal masses. Our analytic results presented in this report are valid for both real and complex internal masses. The…
Interferences in multi-path systems for single and multiple particles are theoretically analyzed. A holistic method is presented, which allows to construct the unitary transition matrix describing interferometers for any port number d and…
Given a factorable function f, we propose a procedure that constructs a concave underestimator of f that is tight at a given point. These underestimators can be used to generate intersection cuts. A peculiarity of these underestimators is…
The Kalman canonical form for quantum linear systems was derived in \cite{ZGPG18}. The purpose of this paper is to present an alternative derivation by means of a Gramian matrix approach. Controllability and observability Gramian matrices…
For regular linear time-invariant DAEs the corresponding matrix pencil is regular and the computation of a standard canonical form is well-understood. Although the investigation of linear DAEs with time-varying coefficients is more complex,…
We review the method of the differential equations for the evaluation of multi-loop Feynman integrals. In particular, we focus on the series expansion approach for solving the system of differential equation and we discuss how to perform…
The article deals with the subject of solving the problem of canonical-map synthesis for Hamiltonian systems. For this purpose, the controlling-function method has been developed that allows appropriate changes of the variables in terms of…
The computation of Feynman integrals is often the bottleneck of multi-loop calculations. We propose and implement a new method to efficiently evaluate such integrals in the physical region through the numerical integration of a suitable set…
We find that all Feynman integrals (FIs), having any number of loops, can be completely determined once linear relations between FIs are provided. Therefore, FIs computation is conceptually changed to a linear algebraic problem. Examples up…
Bayesian calibration is widely used for inverse analysis and uncertainty analysis for complex systems in the presence of both computer models and observation data. In the present work, we focus on large-scale fluid-structure interaction…
Line integration of generalized functions is studied. Second order partial differential equations with piecewise continuous and generalized variable coefficients over Cayley-Dickson algebras are investigated. Formulas for integrations of…
We apply a recently suggested new strategy to solve differential equations for Feynman integrals. We develop this method further by analyzing asymptotic expansions of the integrals. We argue that this allows the systematic application of…
In the present work, an attempted was made to develop a numerical algorithm by the use of new orthogonal hybrid functions formed from hybrid of piecewise constant orthogonal sample-and-hold functions and piecewise linear orthogonal…
A practical version of the polynomial canonical formalism is developed for normal mesoscopic systems consisting of N independent electrons. Drastic simplification of calculations is attained by means of proper ordering excited states of the…
High-dimensional fractional reaction-diffusion equations have numerous applications in the fields of biology, chemistry, and physics, and exhibit a range of rich phenomena. While classical algorithms have an exponential complexity in the…
We consider a new splitting based on the Sherman-Morrison-Woodbury formula, which is particularly effective with iterative methods for the numerical solution of large linear systems. These systems involve matrices that are perturbations of…
Canonical correlation analysis is a classic well-known multivariate statistical method focusing on the relationships between two sets of variables. The visualisation of those relationships can be achieved by means of a biplot of the…
In this talk, we discuss how to generalize ideas developed for Banana integrals to two two-loop non-planar triangle Feynman integrals involving elliptic curves, which have non-trivial sub-sectors and whose Picard-Fuchs operators share less…