in this paper, we propose to extend the hierarchical bivariatehermite interpolant to the spherical case. let $t$ be an arbitraryspherical triangle of the unit sphere $s$ and  let $u$ be a functiondefined over the triangle $t$. for $kin mathbb{n}$, we consider ahermite spherical interpolant problem $h_k$ defined by some datascheme $mathcal{d}_k(u)$ and which admits a unique solution $p_k$in the ...

Feynman periods are integrals that do not depend on external kinematics. Their computation, which is necessary for many applications of quantum field theory, greatly facilitated by graphical functions or the equivalent conformal four-point integrals. We describe a set transformation rules act such and allow their recursive computation in arbitrary even dimensions. As concrete example we compute...

We propose a recursive method for the computation of cumulants self-exciting point processes Hawkes type, based on standard combinatorial tools such as Bell polynomials. This closed-form approach is easier to implement higher-order in comparison with existing methods differential equations, tree enumeration or martingale arguments. The results are corroborated by Monte Carlo simulations, and al...

In this paper the combinatorial problem of determining the number of minimal path sets of a consecutive-k-out-of-n: F system is considered. For the cases where k = 2, 3 the explicit formulae are given and for k ≥ 4 a recursive relation is obtained. Direct computation for determining the number of minimal path sets of a consecutive-k-out-of-n: F system for k ≥ 4 remains a difficult task. ...