Related papers: Intersection Numbers, Polynomial Division and Rela…
A scheme for systematically achieving accurate numerical evaluation of multi-loop Feynman diagrams is developed. This shows the feasibility of a project aimed to produce a complete calculation for two-loop predictions in the Standard Model.…
Two-loop vertex Feynman diagrams with infrared and collinear divergences are investigated by two independent methods. On the one hand, a method of calculating Feynman diagrams from their small momentum expansion extended to diagrams with…
Threshold graphs are recursive deterministic network models that have been proposed for describing certain economic and social interactions. One drawback of this graph family is that it has limited generative attachment rules. To mitigate…
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…
Applications of a method recently suggested by one of the authors (R.L.) are presented. This method is based on the use of dimensional recurrence relations and analytic properties of Feynman integrals as functions of the parameter of…
Spectral lines emitted by plasmas provide information about the thermodynamic conditions, the degree of randomness or the interactions prevailing in the medium. Collisions by plasma electrons penetrating the extent of bound-electron…
Through algebraic manipulations on Wro\'nskian matrices whose entries are reducible to Bessel moments, we present a new analytic proof of the quadratic relations conjectured by Broadhurst and Roberts, along with some generalizations. In the…
We study a Pfaffian of the system of differential equations annihilating Appell's hypergeometric series $F_4(a,b,c;x)$ by twisted cohomology groups associated with integrals representing solutions to this system. We simplify its connection…
This paper presents the first discrete-time distributed algorithm to track the tightest ellipsoids that outer approximates the global dynamic intersection of ellipsoids. Given an undirected network, we consider a setup where each node…
Intersection distribution and non-hitting index are concepts introduced recently by Li and Pott as a new way to view the behaviour of a collection of finite field polynomials. With both an algebraic interpretation via the intersection of a…
Negative dimensional integration is a step further dimensional regularization ideas. In this approach, based on the principle of analytic continuation, Feynman integrals are polynomial ones and for this reason very simple to handle,…
The analysis of observable phenomena (for instance, in biology or physics) allows the detection of dynamical behaviors and, conversely, starting from a desired behavior allows the design of objects exhibiting that behavior in engineering.…
We introduce a new method to evaluate algebraic integrals over the simplex numerically. This new approach employs techniques from tropical geometry and exceeds the capabilities of existing numerical methods by an order of magnitude. The…
Modern particle physics is increasingly becoming a precision science that relies on advanced theoretical predictions for the analysis and interpretation of experimental results. The planned physics program at the LHC and future colliders…
We describe a new algorithm to compute the geometric intersection number between two curves, given as edge vectors on an ideal triangulation. Most importantly, this algorithm runs in polynomial time in the bit-size of the two edge vectors.…
Persistence diagrams, combining geometry and topology for an effective shape description used in pattern recognition, have already proven to be an effective tool for shape representation with respect to a certainfiltering function.…
We present a new method for the numerical evaluation of loop integrals which is based on the Feynman Tree Theorem. The loop integrals are replaced by phase-space integration over fictitious extra on-shell particles. This integration can be…
We introduce an algorithm that samples a set of loop momenta distributed as a given Feynman integrand. The algorithm uses the tropical sampling method and can be applied to evaluate phase-space-type integrals efficiently. We provide an…
We present an approach over arbitrary fields to bound the degree of intersection of families of varieties in terms of how these concentrate on algebraic sets of smaller codimension. This provides in particular a substantial extension of the…
We use Feynman diagrams to prove a formula for the Jones polynomial of a link derived recently by N.~Reshetikhin. This formula presents the colored Jones polynomial as an integral over the coadjoint orbits corresponding to the…